TU IOST | Entrance paper

BIT Entrance Exam 2080 Questions with Answers

147 questions, 2 hours. Correct option marked, with our explanation and the chapter to revise.

Mathematics

Q1Mathematical logic

In the followings, the statement is

agive me a book
b$x-2=10$
cRara lake is in Pokhara
d$y>0$

Answer (c): A statement is a sentence that is definitely true or false. Commands and open sentences with a variable are not statements, but 'Rara lake is in Pokhara' is a declarative sentence with a truth value (false).

Revise: Algebra (Class 11 notes)

Q2Sets

If $S={x: x\in\mathbb{R} \text{ and } x^{2}+4=0}$ then the set $S$ is

asingleton set
b$x-2=10$
c${-2i, 2i}$
d $\emptyset$

Answer (d): $x^2+4=0$ gives $x=\pm 2i$, which are not real numbers, so no real $x$ satisfies it and $S=\emptyset$.

Revise: Algebra (Class 11 notes)

Q3Sets

The set is a collection of

along rivers of Nepal
blongest rivers of Nepal
ctall plants in a garden
dnice books

Answer (b): A set needs a well-defined collection. 'Long', 'tall' and 'nice' are vague, while 'longest rivers of Nepal' is precisely defined.

Revise: Algebra (Class 11 notes)

Q4Intervals

$S={x: x\ge -2, x\in\mathbb{R}}$ is represented by

a$[-2,\infty)$
b$(-2,\infty)$
c$(\infty,-2]$
d$[-2,\infty]$

Answer (a): $x\ge -2$ includes $-2$ (closed bracket) and has no upper bound, and infinity is always written with an open bracket.

Revise: Algebra (Class 11 notes)

Q5Absolute value inequalities

$|x-5|\le 3$ has values of $x=$

a$(2,8)$
b$[2,8]$
c${-2,8}$
d${2,8}$

Answer (b): $|x-5|\le 3$ means $-3\le x-5\le 3$, so $2\le x\le 8$, i.e. $[2,8]$.

Revise: Algebra (Class 11 notes)

Q6Ordered pairs

The ordered pair $(a,b)$ for $(2a-1,-3)=(1,b+3)$ is

a$(1,-6)$
b$[1,-6]$
c${1,-6}$
d$[1,6]$

Answer (a): Equal ordered pairs have equal components: $2a-1=1$ gives $a=1$, and $b+3=-3$ gives $b=-6$.

Revise: Algebra (Class 11 notes)

Q7Functions

If a function $f:\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=2x+5$ then the pre-image of $7$ in $\mathbb{R}$ is

a $3$
bno pre-image
c $1$
d $-2$

Answer (c): Solve $2x+5=7$: $x=1$.

Revise: Algebra (Class 11 notes)

Q8Domain of a function

The domain of the function $f:\mathbb{R}\to\mathbb{R}$ defined by $f(x)=\sqrt{1-x^{2}}$ is

a$[0,1]$
b${1,-1}$
c$[0,\infty)$
d$[-1,1]$

Answer (d): We need $1-x^2\ge 0$, so $x^2\le 1$, giving $-1\le x\le 1$.

Revise: Algebra (Class 11 notes)

Q9Exponential functions

The base of an exponential function $y=a^{x}$ passing through $(2,4)$ is

a $4$
b $2$
c $8$
d $1$

Answer (b): $a^2=4$ and the base must be positive, so $a=2$.

Revise: Algebra (Class 11 notes)

Q10Logarithms

$3^{2\log_3 x}=$

a $2x$
b $x$
c$x^{2}$
d$x/2$

Answer (c): $3^{2\log_3 x}=3^{\log_3 x^2}=x^2$ using $a^{\log_a m}=m$.

Revise: Algebra (Class 11 notes)

Q11Even and odd functions

The function $f(x)=x^{2}-2$ is

aan even function
ban odd number
cnot a function
dneither odd nor even

Answer (a): $f(-x)=(-x)^2-2=x^2-2=f(x)$, so it is even.

Revise: Algebra (Class 11 notes)

Q12Number system

A number which can be expressed in the form $p/q$, $q\ne 0$; $p,q$ are integers, is called

aa rational number
ban integer number
can irrational number
da prime number

Answer (a): This is exactly the definition of a rational number.

Revise: Algebra (Class 11 notes)

Q13Geometric series

The sum of an infinite geometric sequence $a, ak, ak^{2},\dots$ exists if

a$k>1$
b$k>-1$
c$-1\le k\le 1$
d$-1<k<1$

Answer (d): An infinite G.P. has a finite sum only when the common ratio satisfies $|k|<1$.

Revise: Algebra (Class 11 notes)

Q14Arithmetic progression

If $2k+1$, $3k+2$ and $5k+1$ are in A.P., then $k=$

a $2$
b $6$
c $-8$
d $0$

Answer (a): In an A.P. the middle term is the average: $2(3k+2)=(2k+1)+(5k+1)$, so $6k+4=7k+2$ and $k=2$.

Revise: Algebra (Class 11 notes)

Q15Types of matrices

The matrix $\begin{pmatrix}0&1\-1&0\end{pmatrix}$ is

asymmetric
bskew-symmetric
cunit
dnone

Answer (b): Its transpose is $\begin{pmatrix}0&-1\1&0\end{pmatrix}=-A$, so it is skew-symmetric.

Revise: Algebra (Class 11 notes)

Q16Inverse of a matrix

If $A=\begin{pmatrix}-5&3\2&-1\end{pmatrix}$ then $A^{-1}=$

a$\begin{pmatrix}5&3\-2&-1\end{pmatrix}$
b$\begin{pmatrix}-5&-3\-2&1\end{pmatrix}$
c$\begin{pmatrix}5&3\2&1\end{pmatrix}$
d$\begin{pmatrix}1&3\-2&-5\end{pmatrix}$

Answer (d): $|A|=5-6=-1$, so $A^{-1}=-\begin{pmatrix}-1&-3\-2&-5\end{pmatrix}=\begin{pmatrix}1&3\2&5\end{pmatrix}$. Option d is this matrix with a sign misprint in the second row, so it is the intended answer.

Revise: Algebra (Class 11 notes)

Q17Determinants

If $A=\begin{vmatrix}2a+1&1\3a&2\end{vmatrix}=0$, then $a=$

a $0$
b $2$
c $-2$
d $1$

Answer (c): $2(2a+1)-3a=a+2=0$, so $a=-2$.

Revise: Algebra (Class 11 notes)

Q18Types of matrices

A square matrix

A

is said to be singular if

a$|A|>0$
b$|A|<0$
c$|A|\ne 0$
d$|A|=0$

Answer (d): A singular matrix has zero determinant and no inverse.

Revise: Algebra (Class 11 notes)

Q19Quadratic equations

If the roots of the equation $px^{2}+qx+r=0$ are equal in magnitude but opposite in sign, then

a$p=0$
b$q=0$
c$r=0$
d$p=q$

Answer (b): Sum of roots $=-q/p=0$, so $q=0$.

Revise: Algebra (Class 11 notes)

Q20Quadratic equations

If the discriminant of the equation $x^{2}+kx+4=0$ is zero then $k=$

a $\pm 4$
b $-4$
c $4$
d $0$

Answer (a): $k^2-4(1)(4)=0$ gives $k^2=16$, so $k=\pm 4$.

Revise: Algebra (Class 11 notes)

Q21Complex numbers

If $i$ is the imaginary unit, then $\dfrac{1-i}{1+i}=$

a $1$
b $-i$
c $i$
d $-1$

Answer (b): $\frac{(1-i)^2}{(1+i)(1-i)}=\frac{1-2i+i^2}{2}=\frac{-2i}{2}=-i$.

Revise: Algebra (Class 11 notes)

Q22Complex numbers

The square roots of a complex number $5+12i$ is

a$\pm(3+2i)$
b$\pm(2+3i)$
c$\pm(3-2i)$
d$\pm(2-3i)$

Answer (a): $(3+2i)^2=9+12i+4i^2=5+12i$, so the roots are $\pm(3+2i)$.

Revise: Algebra (Class 11 notes)

Q23Inverse trigonometric functions

$\sin(\cos^{-1}x)=$

a$\sqrt{1+x^{2}}$
b$\sin\theta$
c$\sqrt{1-x^{2}}$
d$x\sqrt{1-x^{2}}$

Answer (c): Let $\theta=\cos^{-1}x$, so $\cos\theta=x$ and $\sin\theta=\sqrt{1-x^2}$.

Revise: Trigonometry (Class 11 notes)

Q24Trigonometric equations

The general solution of $4\sin^{2}x=1$, for $n\in Z$ is

a$x=n\pi\pm\frac{\pi}{6}$
b$x=n\pi\pm\frac{\pi}{4}$
c$x=n\pi\pm\frac{\pi}{3}$
d$x=2n\pi\pm\frac{\pi}{6}$

Answer (a): $\sin^2x=\frac14=\sin^2\frac{\pi}{6}$, and $\sin^2x=\sin^2\alpha$ gives $x=n\pi\pm\alpha$.

Revise: Trigonometry (Class 11 notes)

Q25Straight line

The slope of the line $px+qy+c=0$ is

a $p$
b $q$
c$p/q$
d$-p/q$

Answer (d): $y=-\frac{p}{q}x-\frac{c}{q}$, so the slope is $-p/q$.

Revise: Analytic geometry (Class 11 notes)

Q26Distance from a point to a line

If the length of the perpendicular from the point $(k,2)$ to $3x-4y+6=0$ is $2$, then $k=$

a $8$
b $6$
c $4$
d $5$

Answer (c): $\frac{|3k-8+6|}{5}=2$ so $|3k-2|=10$, giving $k=4$ (the other root $-8/3$ is not listed).

Revise: Analytic geometry (Class 11 notes)

Q27Pair of lines

The homogeneous equation is

a$ax^{2}+bxy+c=0$
b$ax^{2}+xy+by^{2}=0$
c$ax^{2}+bxy+by^{2}+c=0$
d$x^{2}+by^{2}+y^{3}=0$

Answer (b): A homogeneous equation has all terms of the same degree; only (b) has every term of degree 2.

Revise: Analytic geometry (Class 11 notes)

Q28Pair of lines

The two lines represented by $kx^{2}+xy-y^{2}=0$ are perpendicular to each other if $k=$

a $1$
b $-1$
c $0$
d$k\ne 0$

Answer (a): Perpendicular lines need coefficient of $x^2$ plus coefficient of $y^2$ equal to zero: $k-1=0$.

Revise: Analytic geometry (Class 11 notes)

Q293D coordinates

The distance of the point $(1,2,3)$ from origin is

a $1$
b $3$
c$\sqrt{14}$
d $2$

Answer (c): $d=\sqrt{1+4+9}=\sqrt{14}$.

Revise: Analytic geometry (Class 11 notes)

Q303D lines

The direction ratios of the line $AB$ joining the points $A(4,5,0)$ and $B(2,3,4)$ are

a$-2,2,-4$
b$2,2,-4$
c$2,2,4$
d$-2,-2,-4$

Answer (b): $B-A=(-2,-2,4)$, and $(2,2,-4)$ is its negative, which is also a valid set of direction ratios.

Revise: Analytic geometry (Class 11 notes)

Q31Vectors

The direction of the vector $a\mathbf{i}+b\mathbf{j}$ is

a$\tan^{-1}\left(-\frac{a}{b}\right)$
b$\tan^{-1}\left(\frac{b}{a}\right)$
c$\tan^{-1}\left(-\frac{b}{a}\right)$
dnone

Answer (b): The angle with the x-axis satisfies $\tan\theta=\frac{b}{a}$.

Revise: Vectors (Class 11 notes)

Q32Vectors

The unit vector along $x\mathbf{i}-y\mathbf{j}$ is

a$\frac{x\mathbf{i}-y\mathbf{j}}{\sqrt{x^{2}-y^{2}}}$
b$\frac{x\mathbf{i}-y\mathbf{j}}{\sqrt{x^{2}y^{2}}}$
c$\frac{x\mathbf{i}-y\mathbf{j}}{x^{2}+y^{2}}$
d$\frac{x\mathbf{i}-y\mathbf{j}}{\sqrt{x^{2}+y^{2}}}$

Answer (d): Unit vector $=\vec v/|\vec v|$ with $|\vec v|=\sqrt{x^2+y^2}$.

Revise: Vectors (Class 11 notes)

Q33Standard deviation

The standard deviation of $3,6,9,12,15$ is

a$3\sqrt{2}$
b $12$
c$2\sqrt{3}$
d $2$

Answer (a): Mean $=9$; squared deviations $36+9+0+9+36=90$; variance $=90/5=18$; SD $=\sqrt{18}=3\sqrt2$.

Revise: Statistics and Probability (Class 11 notes)

Q34Probability

The probability of getting an ace of club or a king of spade from a pack of 52 cards is

a $1/26$
b $1/13$
c $1/52$
d $1/2$

Answer (a): Two favourable cards out of 52: $2/52=1/26$.

Revise: Statistics and Probability (Class 11 notes)

Q35Limits

If $\lim_{x\to a}\frac{x^{4}-a^{4}}{x-a}=256$, then $a=$

a $5$
b $3$
c $4$
d $6$

Answer (c): The limit is $4a^3=256$, so $a^3=64$ and $a=4$.

Revise: Calculus (Class 11 notes)

Q36Limits

$\lim_{x\to 0}\frac{\tan 3x}{x}=$

a $3$
b $0/0$
c $0$
d $x$

Answer (a): $\frac{\tan3x}{3x}\to1$, so the limit is $3\cdot1=3$.

Revise: Calculus (Class 11 notes)

Q37Continuity

A function $f(x)=2x+1$ is continuous at $x=1$, if

a$\lim_{x\to0}f(x)=3$
b$\lim_{x\to1}f(x)$ exists
c$\lim_{x\to0}f(x)=f(1)$
dnone

Answer (c): Continuity at $x=1$ needs the limit to equal $f(1)$. Option c is printed with $x\to0$, a misprint for $x\to1$; option b alone is not sufficient.

Revise: Calculus (Class 11 notes)

Q38Differentiation

If $y=e^{\sin x^{2}}$, then $\frac{dy}{dx}=$

a$e^{\sin x^{2}}$
b$2xy\cos x^{2}$
c$2xe^{\sin x^{2}}$
d$y\cos x^{2}$

Answer (b): Chain rule: $\frac{dy}{dx}=e^{\sin x^2}\cos x^2\cdot2x=2xy\cos x^2$.

Revise: Calculus (Class 11 notes)

Q39Differentiation

If $y=x^{3}-x^{2}$, then for $\frac{dy}{dx}=0$, $x=$

a$0,-2/3$
b$0,3/2$
c$0,3$
d$0,2/3$

Answer (d): $\frac{dy}{dx}=3x^2-2x=x(3x-2)=0$ gives $x=0,\frac23$.

Revise: Calculus (Class 11 notes)

Q40Increasing and decreasing functions

The function $f(x)=2x+5$ on $R$ is

adecreasing
bstationary
cincreasing
dnone

Answer (c): $f'(x)=2>0$ everywhere, so it is increasing.

Revise: Calculus (Class 11 notes)

Q41Integration

$\int\frac{dx}{ax+b}=$

a$\frac1a\log|ax+b|+c$
b$a\log|ax+b|+c$
c$|\log(ax+b)|+c$
d$\log|ax+b|+c$

Answer (a): Substitute $u=ax+b$, $du=a,dx$, giving $\frac1a\log|ax+b|+c$.

Revise: Calculus (Class 11 notes)

Q42Integration

$\int\frac{dx}{2\cos^{2}x\sin^{2}x}=$

a$2\cot2x+c$
b$-2\cot2x+c$
c$\cot2x+c$
d$-\cot2x+c$

Answer (d): $2\sin x\cos x=\sin2x$ so the integrand is $\frac{2}{\sin^22x}=2\csc^22x$, and $\int2\csc^22x,dx=-\cot2x+c$.

Revise: Calculus (Class 11 notes)

Q43Definite integrals

$\int_1^3\frac{\sin(\ln t)}{t}dt=$

a$\cos(\ln3)$
b$-\cos(\ln3)$
c$1-\cos(\ln3)$
d$1-\sin(\ln3)$

Answer (c): Put $u=\ln t$: $\int_0^{\ln3}\sin u,du=1-\cos(\ln3)$.

Revise: Calculus (Class 11 notes)

Q44Area under a curve

The area under the curve $y=x^{2}$ bounded by the x axis and the ordinates $x=1$ and $x=4$ is

a $21$
b $64/3$
c $64$
d $7$

Answer (a): $\int_1^4x^2dx=\frac{4^3-1^3}{3}=\frac{63}{3}=21$.

Revise: Calculus (Class 11 notes)

Q45Newton-Raphson method

The general formula for Newton-Raphson method is

a$x_{n+1}=x_n-\frac{f'(x_n)}{f(x_n)}$
b$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$
c$x_{n+1}=x_n+\frac{f'(x_n)}{f(x_n)}$
d$x_{n+1}=x_{n+1}-\frac{f'(x_n)}{f(x_n)}$

Answer (b): Newton-Raphson: next estimate is the current one minus function value over derivative.

Revise: Computational methods (Class 11 notes)

Q46Numerical integration

The approximate value of $\int_0^2x^{2}dx$ using midpoint rule with one interval is

a $4$
b $8$
c $2$
d $0$

Answer (c): Midpoint $=1$, so the estimate is $f(1)\cdot(2-0)=1\cdot2=2$.

Revise: Computational methods (Class 11 notes)

Q47Equilibrium of forces

If three equal forces $P$, $Q$ and $R$ are acting at a point of rigid body are in equilibrium, then the angle between any two forces is

a$120^\circ$
b$30^\circ$
c$60^\circ$
dnone

Answer (a): Three equal forces balance only if they form an equilateral triangle of forces, so each pair makes $120^\circ$.

Revise: Mechanics (Class 11 notes)

Q48Resolution of forces

A force equal to $4N$ acting vertically upwards is resolved into forces, one being horizontal and equal to $3N$. The magnitude of the other remaining force is

a $7N$
b $1N$
c $2N$
d $5N$

Answer (d): The other force must cancel the horizontal $3N$ and supply the vertical $4N$: $\sqrt{3^2+4^2}=5N$.

Revise: Mechanics (Class 11 notes)

Q49Linear motion

If the acceleration of a particle, starting from rest is $5,m/sec^{2}$, then the velocity at the end of 3 seconds is

a$8,m/sec^{2}$
b$15,m/sec^{2}$
c$5,m/sec^{2}$
dnone

Answer (b): $v=u+at=0+5\times3=15$ m/s. The option's unit is printed as m/sec^2, a misprint.

Revise: Mechanics (Class 11 notes)

Q50Motion under gravity

A stone is thrown vertically upwards with a velocity of $30$ m/sec from the top of a tower and hits the ground after $10$ secs, then the height of the tower is

a$100,m$
b$300,m$
c$200,m$
d$50,m$

Answer (c): Take $g=10$: displacement $s=ut-\frac12gt^2=300-500=-200$ m, so the tower is $200$ m high.

Revise: Mechanics (Class 11 notes)

English

Q51Synonyms

Choose the word or group of words which is most nearly same in meaning as the word "woeful".

adeplorable
bpunishable
cculpable
dshaky

Answer (a): Woeful means very bad or causing sorrow, which is 'deplorable'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q52Synonyms

Choose the word or group of words which is most nearly same in meaning as the word "rotund".

around
bplump
ccircular
dhealthy

Answer (b): Rotund describes a person who is round and fat, so 'plump'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q53Synonyms

Choose the word or group of words which is most nearly same in meaning as the word "facetious".

asweet
bhandsome
cflippant
dcharming

Answer (c): Facetious means treating serious matters with inappropriate humour, i.e. 'flippant'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q54Synonyms

Choose the word or group of words which is most nearly same in meaning as the word "coagulate".

asweeten
bsharpen
cmix up
dcongeal

Answer (d): To coagulate is to thicken or clot, same as 'congeal'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q55Antonyms

Choose the word or group of words which is most opposite to the meaning of the word "grotesque".

aproportionate
bsymmetrical
cugly
dcongruous

Answer (a): Grotesque means distorted and misshapen; the best opposite among the options is 'proportionate' (well-shaped). 'Symmetrical' is a weaker contrast.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q56Antonyms

Choose the word or group of words which is most opposite to the meaning of the word "erase".

adrop
bdelete
cengrave
ddefend

Answer (c): Erase means to rub out; to engrave is to cut in permanently, its opposite.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q57Antonyms

Choose the word or group of words which is most opposite to the meaning of the word "tranquil".

apeaceful
bagitated
cangry
ddull

Answer (b): Tranquil means calm, so 'agitated' is the opposite.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q58Antonyms

Choose the word or group of words which is most opposite to the meaning of the word "spurious".

agenuine
bduplicate
cvalid
dreliable

Answer (a): Spurious means fake, the opposite of 'genuine'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q59One-word substitution

Give a single word to this expression: "fossils and other forms of early life"

apaleontology
bpomology
cphilology
dteleology

Answer (a): Paleontology is the study of fossils and ancient life. Pomology is fruit study.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q60One-word substitution

Give a single word to this expression: "the study of life and habits of birds"

aornithology
bembryology
cgeology
dbiology

Answer (a): Ornithology is the scientific study of birds.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q61One-word substitution

Give a single word to this expression: "the subject that studies God and religion"

aaxiology
btheology
cmetaphysics
depistemology

Answer (b): Theology is the study of God and religious belief.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q62One-word substitution

Give a single word to this expression: "a person who is commanding, haughty and arrogant"

aeccentric
bimperious
cgarrulous
damiable

Answer (b): Imperious means domineering and arrogantly commanding.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q63Phrasal verbs

Pick up the correct phrasal verb for the expression "the two friends....this afternoon".

afall on
bfall in
cfall out
dfall upon

Answer (c): 'Fall out' means to quarrel, which fits two friends and 'this afternoon' (past: fell out).

Revise: Grammar and Usage (Class 11 notes)

Q64Phrasal verbs

Pick up the correct phrasal verb for the expression "It is not easy to....rebellion".

aput on
bput out
cput down
dput up

Answer (c): 'Put down' a rebellion means to suppress it.

Revise: Grammar and Usage (Class 11 notes)

Q65Phrasal verbs

Pick up the correct phrasal verb for the expression "Tom just ... and lets me do all the work.".

asit out
bsit in
csit on
dsit back

Answer (d): 'Sit back' means to relax and take no part, which suits letting someone else do the work.

Revise: Grammar and Usage (Class 11 notes)

Q66Phrasal verbs

Pick up the correct phrasal verb for the expression "everything will ... all right in the end".

awork up
bwork off
cwork on
dwork out

Answer (d): 'Work out' means to turn out well.

Revise: Grammar and Usage (Class 11 notes)

Q67Idioms

Choose the appropriate meaning to the idiomatic expression "a flash in the pan".

aa short lived success or enthusiasm
bsudden fortune
csuccessful life start
dnew day in life

Answer (a): The idiom describes something that starts promisingly but quickly fails, a short-lived success.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q68Idioms

Choose the appropriate meaning to the idiomatic expression "up and about".

arich once again
brecovered and in good health
cliked by everybody
dpurpose behind an action

Answer (b): 'Up and about' means out of bed and active again after illness.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q69Idioms

Choose the appropriate meaning to the idiomatic expression "the thrills and spills".

acritical mind set
bsuccessful person
csuccess and failures
dnew attempts

Answer (c): The phrase refers to the excitement (thrills) and mishaps (spills) of an activity, i.e. successes and failures; this is the closest option.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q70Idioms

Choose the appropriate meaning to the idiomatic expression "be out like a light".

afit and fine
bfeel great success
chappy and healthy
dfall quickly into a deep sleep

Answer (d): To be 'out like a light' is to fall asleep very fast.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q71Idioms

Choose the appropriate meaning to the idiomatic expression "mind over matter".

aovercome physical weakness by means of will power
bvery conscious person
cidealist person
dignore materiality

Answer (a): It means willpower can overcome physical limits or difficulties.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q72Prepositions

Choose the appropriate preposition/s to fill up the blank spaces "she was fined....parking her car... a no parking area."

afor, at
bfor, in
cby, with
don, in

Answer (b): One is fined 'for' an offence, and the car is parked 'in' an area.

Revise: Grammar and Usage (Class 11 notes)

Q73Prepositions

Choose the appropriate preposition/s to fill up the blank spaces "a patient died... cancer whereas other sick person died... the loss of blood."

afor, from
bby, by
cof, from
dof, by

Answer (c): Die 'of' a disease and die 'from' an injury or loss of blood.

Revise: Grammar and Usage (Class 11 notes)

Q75Prepositions

Choose the appropriate preposition/s to fill up the blank spaces "one must guard family members...any danger and live ...honest labour."

aagainst, by
bfor, by
cby, by
dfor, from

Answer (a): Guard 'against' danger and live 'by' honest labour.

Revise: Grammar and Usage (Class 11 notes)

Q76Prepositions

Choose the appropriate preposition/s to fill up the blank spaces "I am in dire need ...money ...the treatment of my sick wife."

aof, of
bof, for
cfor, for
dby, from

Answer (b): 'Need of money' and money 'for' the treatment.

Revise: Grammar and Usage (Class 11 notes)

Q77Word stress

The word "plutonium" gets its prime stress on :

a1st syllable
b3rd syllable
c2nd syllable
d4th syllable

Answer (c): Plu-TO-ni-um: words ending in -ium put stress on the syllable before the ending.

Q78Word stress

The word "cyber squatting" gets its prime stress on :

a4th syllable
b2nd syllable
c3rd syllable
d1st syllable

Answer (d): As a compound noun, the stress falls on the first element: CY-ber squatting.

Q79Word stress

The word "retractable" gets its prime stress on :

a1st syllable
b2nd syllable
c3rd syllable
d4th syllable

Answer (b): re-TRAC-ta-ble: stress falls on the root syllable after the prefix.

Q80Synonyms

Give similar meaning word to "bankruptcy".

ainsolvency
bcorrupt
cpoverty
deconomical

Answer (a): Bankruptcy is the legal state of being unable to pay debts, i.e. insolvency.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q81Idioms

Give a right meaning to the idiom "a baptism of fire".

astart a new work
ba difficult introduction to a new job or activity
cvery successful beginning
dremarkable initiation

Answer (b): The idiom means a harsh first experience of something new.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q82Idioms

Give a right meaning to the idiom "face the music".

aready for further action
bbold and decisive
clikes to dance
daccept the criticism or punishment for one's own work

Answer (d): To 'face the music' is to accept the consequences of what you did.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q83Conjunctions

Choose a correct conjunction for "he got the job... he had no suitable qualification".

aalthough
beven
cif
din spite of

Answer (a): 'Although' introduces a contrast with a full clause; 'in spite of' needs a noun phrase.

Revise: Grammar and Usage (Class 11 notes)

Q84Conjunctions

Choose a correct conjunction for "he broke the window...he was angry....soon realized the mistake".

ahowever, though
bbecause, but
cin spite of, even
dwhen, despite of

Answer (b): 'Because he was angry' gives the reason, and 'but' contrasts with realising the mistake.

Revise: Grammar and Usage (Class 11 notes)

Q85Conjunctions

Choose a correct conjunction for "Kanu is illiterate ..... he can read ...write a single word".

aeither, or
bif, even if
cneither, nor
dfor, but

Answer (c): The sense is that he can neither read nor write a word; 'neither...nor' is the matching correlative pair.

Revise: Grammar and Usage (Class 11 notes)

Q86Passive voice

The suitcase was left outside and was.... away by someone.

atakes
btaking
ctook
dtaken

Answer (d): Passive voice needs 'was' plus the past participle: 'taken'.

Revise: Grammar and Usage (Class 11 notes)

Q87Possessive adjectives

On ...trip to Pokhara we visited several wonderful natural sites.

aour
btheir
cwhose
dits

Answer (a): The subject is 'we', so the possessive is 'our'.

Revise: Grammar and Usage (Class 11 notes)

Q88Prepositions

The dog was killed by a lorry which went ....it.

aunder
bover
cthrough
dbelow

Answer (b): A vehicle running over an animal is 'went over it'.

Revise: Grammar and Usage (Class 11 notes)

Q89Adverbs of degree

The statue was ...heavy that a crane was brought to lift it.

atoo
bmuch
cso
dvery

Answer (c): 'So ... that' expresses result.

Revise: Grammar and Usage (Class 11 notes)

Q90Collocations

I put on warm clothes so that I might not....cold.

acatch
baffect
ctake
dattack

Answer (a): The collocation is 'catch cold'.

Revise: Grammar and Usage (Class 11 notes)

Q91One-word substitution

A short journey for pleasure is called......

ajaunt
bstroll
citinerary
djunta

Answer (a): A jaunt is a short pleasure trip.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q92One-word substitution

The state of not getting married is....

abachelor
bspinster
ccelibacy
dunmarried

Answer (c): The abstract noun for the state of remaining unmarried is 'celibacy'; the others are persons or adjectives.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q93One-word substitution

Gradual recovery from an illness is.....

aamnesia
bhysteria
cconvalescence
dsuperannuating

Answer (c): Convalescence is the period of recovery after illness.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q94Prepositions

It is much easier to run...debt than to get out of it.

adown
bout
cfor
dinto

Answer (d): The idiom is 'run into debt'.

Revise: Grammar and Usage (Class 11 notes)

Q95Collocations

Walking in the morning, I heard the.....of thunder.

acrackling
brippling
cclanking
drumbling

Answer (d): Thunder is described as 'rumbling'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q96Prefixes

Which of the following is not used as a prefix in forming a word.

atyro -
banti-
cpost-
dpre-

Answer (a): Anti-, post- and pre- are common prefixes; 'tyro-' is not.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q97Prefixes

The word "hearted" takes the prefix:

aup
bdown
cover
dunder

Answer (b): 'Downhearted' is the existing word.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q98Sentence types

John, who is wearing a white shirt, is my best friend. This is a ....sentence.

asimple
bcompound
ccomplex
dcomplex-compound

Answer (c): It has one main clause and one dependent relative clause, so it is complex.

Revise: Grammar and Usage (Class 11 notes)

Q99Intonation

The sentence "I saw a blackbird" has a ...tone.

afalling
brising
cfall-rise
dnone

Answer (a): A plain statement is normally said with a falling tone.

Q100One-word substitution

Belief in the existence of one God but without any religious dogma

aPantheism
bdeism
ctheism
dhenotheism

Answer (b): Deism is belief in one God based on reason, without organised religious doctrine.

Revise: Vocabulary and Word Formation (Class 11 notes)

Computer

Q101Computer buses

Which bus is bidirectional?

aData bus
bsystem bus
cAddress bus
dAll of the above

Answer (a): The data bus carries data both to and from the CPU, while the address bus is one-way (CPU to memory).

Revise: Computer System (Class 11 notes)

Q102Memory

Which of the following is also known as flash memory?

aROM
bPROM
cEPROM
dEEPROM

Answer (d): Flash memory is a type of electrically erasable programmable ROM (EEPROM).

Revise: Computer System (Class 11 notes)

Q103Computer architecture

Which of the following is based on separate storage and signal pathway?

aVon-Neumann
bCISC
cHarvard
dQueue

Answer (c): Harvard architecture uses separate memories and buses for instructions and data.

Revise: Computer System (Class 11 notes)

Q104Binary arithmetic

$1000-100$ binary subtraction is equivalent to......

a900
b010
c100
d001

Answer (c): $1000_2=8$ and $100_2=4$, so the difference is $4=100_2$.

Revise: Number System and Boolean Logic (Class 11 notes)

Q105Types of software

Backberry is ..... software.

aSystem
bApplication
cUtility
dControl

Answer (a): BlackBerry (as an OS) is system software.

Revise: Computer Software and Operating System (Class 11 notes)

Q106Programming languages

Which of the following is high level procedural language?

aC++
bJava
cPython
dFortran

Answer (d): Fortran is a classic high-level procedural language, whereas C++ and Java are object-oriented.

Revise: Programming Concepts and Logic (Class 11 notes)

Q107Operators

Which of the following is logical operator

Answer (c): && is the logical AND; & is bitwise, = is assignment and == is relational.

Revise: Programming Concepts and Logic (Class 11 notes)

Q108Network types

Which of the following has smallest coverage?

aWAN
bLAN
cPAN
dMAN

Answer (c): A PAN covers only a few metres around a person.

Revise: Concept of Network and Data Communication (Class 12 notes)

Q109Transmission modes

Which among the following is full duplex transmission?

aWalkie-Talkie
bBluetooth
cKeyboard
dNone of the above

Answer (b): Bluetooth links can send and receive at the same time (full duplex); a walkie-talkie is half duplex and a keyboard is simplex.

Revise: Concept of Network and Data Communication (Class 12 notes)

Q110Networking

MAC stands for.....

aMedium Act Control
bMedia Act Control
cMedium Access Control
dMedia Access Control

Answer (d): MAC means Media Access Control.

Revise: Concept of Network and Data Communication (Class 12 notes)

Q111Cyber security

Which of the following is a component of cyber security?

aAI
bInternet of Things
cData warehouse
dRSA

Answer (d): RSA is a cryptographic algorithm, used for encryption in cyber security.

Revise: Information Security and Cyber Law (Class 11 notes)

Q112Hackers

Which among the following is not ethical hacker?

aBlack hat hacker
bGray hat hacker
cBiased hat hacker
dWhite hat hacker

Answer (a): Black hat hackers break in illegally, unlike ethical (white hat) hackers.

Revise: Information Security and Cyber Law (Class 11 notes)

Q113Types of computers

Which of the following is often used for automatic computation?

aHybrid
bAnalog
cDigital
dAll of the above

Answer (c): Digital computers perform automatic computation on discrete data.

Revise: Computer System (Class 11 notes)

Q114Memory hierarchy

Which of the following is the slowest memory?

aHard disk
bRAM
cCache
dRegister

Answer (a): Secondary storage such as a hard disk is much slower than RAM, cache and registers.

Revise: Computer System (Class 11 notes)

Q115CPU

The CPU is given instructions and data through programs. The CPU then fetches the program and data from the memory and performs ............. as per the given instructions and stores the result back to memory.

aLogical Operation
bArithmetic Operation
cArithmetic and Logic operations
dNone of the above

Answer (c): The ALU of the CPU performs both arithmetic and logic operations.

Revise: Computer System (Class 11 notes)

Q116Application packages

Which key on the keyboard can be used to view slide show?

aF1
bF2
cF5
dF10

Answer (c): F5 starts a slide show from the beginning in presentation software.

Revise: Application Package (Class 11 notes)

Q117Units of memory

1 PB (pentabyte) is equivalent to

a1024 KB
b1024 MB
c1024 GB
d1000 TB

Answer (d): In SI usage 1 PB (petabyte) is $10^{15}$ bytes, which is 1000 TB; the other options are far too small.

Revise: Computer System (Class 11 notes)

Q118Character codes

ASCII used ...... bits to represent characters.

a8 Bits
b7 bits
c6 bits
d5 bits

Answer (b): Standard ASCII is a 7-bit code (128 characters).

Revise: Number System and Boolean Logic (Class 11 notes)

Q119Character codes

The code for the character "a" belongs to....... ASCII code.

Answer (b): Lowercase 'a' has ASCII code 97 (A is 65).

Revise: Number System and Boolean Logic (Class 11 notes)

Q120Number conversion

Which of the following Binary numbers is equivalent to the decimal number 24?

a110111
b111111
c11000
d11001

Answer (c): $24=16+8=11000_2$.

Revise: Number System and Boolean Logic (Class 11 notes)

Q121Number systems

The octal number system is called base-8 system as it has total eight digits

a1 to 8
b0 to 7
c2 to 9
dNone of the above

Answer (b): Octal digits run from 0 to 7.

Revise: Number System and Boolean Logic (Class 11 notes)

Q122Operating system

What else is a command interpreter called?

aprompt
bkernel
cshell
dcommand

Answer (c): The shell interprets the commands typed by the user.

Revise: Computer Software and Operating System (Class 11 notes)

Q123Booting

What is the meaning of the Booting in the operating system?

aRestarting computer
bInstall the program
cTo scan
dTo turn off

Answer (a): Booting is starting the computer and loading the OS; of the choices, restarting is the closest.

Revise: Computer Software and Operating System (Class 11 notes)

Q124Booting

What is bootstrapping called?

aCold boot
bCold hot boot
cCold hot strap
dHot boot

Answer (a): Bootstrapping starts the computer from a powered-off state, which is a cold boot.

Revise: Computer Software and Operating System (Class 11 notes)

Q125Types of OS

Which of the following is an example of a Real Time Operating System?

aMAC
bMS-DOS
cWindows 10
dProcess Control

Answer (d): Process control systems are classic real-time systems; the others are general-purpose OSs.

Revise: Computer Software and Operating System (Class 11 notes)

Q127Programming

What will be the output of the following code snippet? #include <stdio.h> int main() { int a = 3, b = 5; int t = a; a = b; b = t; printf("%d %d", a, b); return 0; }

Answer (d): The values are swapped using $t$: $a$ becomes 5 and $b$ becomes 3, so it prints '5 3' (shown as 53).

Revise: Programming Concepts and Logic (Class 11 notes)

Q128Web technology

Which of the following can read and render HTML web pages?

aServer
bHead Tak
cWeb Browser
dEmpty

Answer (c): A web browser parses and displays HTML.

Revise: Web Technology I (Class 11 notes)

Q129Network protocols

Simple network management protocol uses which of the following port number

a161
b162
c163
d164

Answer (a): SNMP agents listen on UDP port 161 (traps use 162).

Revise: Concept of Network and Data Communication (Class 12 notes)

Q130HTML

Which of the following attributes defines the relationship between the current document and URL?

aURL
bREV
cREL
dUVL

Answer (c): The rel attribute specifies the relationship between the current document and the linked resource.

Revise: Web Technology I (Class 11 notes)

Q131HTML

How many sizes of headers are available in HTML by default?

Answer (d): HTML provides h1 to h6, six heading levels.

Revise: Web Technology I (Class 11 notes)

Q132Multimedia

Multimedia is also used for ....... communications and presentations.

aCorporate
bCompany
cCommunal
dCommercial

Answer (a): The standard phrase is 'corporate communications and presentations'.

Revise: Multimedia (Class 11 notes)

Q133Multimedia

A heavy video in a WBT may not load because of poor

aSignal
bKBPS
cPresentation
dBandwidth

Answer (d): Poor bandwidth limits how fast heavy media can load.

Revise: Multimedia (Class 11 notes)

Q134Cyber crimes

In which of the following, a person is constantly followed/chased by another person or group of several peoples?

aPhishing
bBulling
cStalking
dIdentity theft

Answer (c): Stalking is persistent following or harassment of a person.

Revise: Information Security and Cyber Law (Class 11 notes)

Q135Cyber ethics

Which of the following refers to exploring the appropriate, ethical behaviors related to the online environment and digital media platform?

aCyber Law
bCyber Ethics
cCyber Security
dCyber Safety

Answer (b): Cyber ethics concerns ethical behaviour online.

Revise: Information Security and Cyber Law (Class 11 notes)

Q136Malware

Code Red is a type of ........

aAn Antivirus Program
bA photo editing software
cA computer virus
dA video editing software

Answer (c): Code Red was a well-known computer worm/virus.

Revise: Information Security and Cyber Law (Class 11 notes)

Q137Firewall

Which of the following statements is correct about the firewall?

aIt is a device installed at the boundary of a company to prevent unauthorized physical access.
bIt is a device installed at the boundary of incorporation to protect it against unauthorized access.
cIt is a kind of wall built to prevent files from damaging the corporate.
dNone of the above.

Answer (b): A firewall sits at a network boundary and guards against unauthorised access; (a) wrongly says physical.

Revise: Information Security and Cyber Law (Class 11 notes)

Q138Malware

Which of the following is a type of independent malicious program that never requires any host program?

aTrojan Horse
bWorm
cTrap Door
dVirus

Answer (b): A worm is self-replicating and standalone; viruses need a host file.

Revise: Information Security and Cyber Law (Class 11 notes)

Q139Logic gates

How many AND gates are required to realize $Y=CD+EF+G$?

Answer (d): Two AND gates (for $CD$ and $EF$); $G$ goes straight to the OR gate.

Revise: Number System and Boolean Logic (Class 11 notes)

Q140Logic gates

How many two-input AND gates and two input OR gates are required to realize $Y=BD+CE+AB$?

a3, 2
b4, 2
c1, 1
d2, 3

Answer (a): Three product terms need 3 AND gates, and combining three terms with two-input ORs needs 2.

Revise: Number System and Boolean Logic (Class 11 notes)

Q141HTML

What is the color code of blue color in html?

a#ff0000
b#00ff00
c#0000ff
dFf00ff#

Answer (c): Hex colour is #RRGGBB, so pure blue is #0000ff.

Revise: Web Technology I (Class 11 notes)

Q142HTML

Which of the following tag is not valid in HTML5?

a<<l> tag
b<s> tag
c<p>
d<e>

Answer (d): <s>, <p> are valid HTML5 tags; <e> does not exist (so does <l>, which is garbled in the scan).

Revise: Web Technology I (Class 11 notes)

Q143Cyber crimes

A hacker contacts your phone or e-mail and attempts to acquire your password is called

aspamming
bspoofing
cphishing
dhamming

Answer (c): Phishing tricks users into giving up credentials.

Revise: Information Security and Cyber Law (Class 11 notes)

Q145Boolean algebra

Which of the following is absorption law in Boolean algebra?

a$(A')'=A$
b$A+(A\cdot B)=A$
c$(A+B)+C=A+(B+C)$
d$(A+B)'=A'\cdot B'$

Answer (b): Absorption law states $A+AB=A$.

Revise: Number System and Boolean Logic (Class 11 notes)

Q146Boolean algebra

Which one is an example of identity law?

a$a+0=0+a=a$
b$1+a=a+1=1$
c$ab=ba$
d$a+(b+c)=(a+b)+c$

Answer (a): Identity law: adding 0 leaves a unchanged. (b) is the null law, (c) commutative, (d) associative.

Revise: Number System and Boolean Logic (Class 11 notes)

Q147IP addressing

Which of the following is the correct IPv4 address?

a124.201.3.1.52
b01.200.128.123
c300.142.210.64
d128.64.0.0

Answer (d): An IPv4 address has four octets each 0 to 255; (a) has five, (c) has 300, and (b) has a leading zero.

Revise: Concept of Network and Data Communication (Class 12 notes)

Q148Cyber security

Which of the following is defined as an attempt to steal, spy, damage or destroy computer systems, networks, or their associated information?

aCyber attack
bComputer security
cCryptography
dDigital hacking

Answer (a): That is the definition of a cyber attack.

Revise: Information Security and Cyber Law (Class 11 notes)

Q149History of hacking

Where did the term "hacker" originate?

aMIT
bNew York University
cHarvard University
dBell's Lab

Answer (a): The term came from MIT's model railroad club in the 1960s.

Revise: Information Security and Cyber Law (Class 11 notes)

Q150Open source software

Which of the following is an open source software?

aUnix
bLinux
cWindows
dMS word

Answer (b): Linux is free and open source; Unix, Windows and MS Word are proprietary.

Revise: Computer Software and Operating System (Class 11 notes)

Timed test 2079 →

BIT entrance

Papers

By subject

Mathematics

Q1Mathematical logic

In the followings, the statement is

agive me a book
b $x-2=10$ $x-2=10$
cRara lake is in Pokhara
d $y>0$ $y>0$

Revise: Algebra (Class 11 notes)

Q2Sets

S=\{x: x\in\mathbb{R} \text{ and } x^{2}+4=0\}

then the set

S

isIf $S={x: x\in\mathbb{R} \text{ and } x^{2}+4=0}$ then the set $S$ is

asingleton set
b $x-2=10$ $x-2=10$
c $\{-2i, 2i\}$ ${-2i, 2i}$
d $\emptyset$

Answer (d): $x^2+4=0$ gives $x=\pm 2i$ , which are not real numbers, so no real $x$ satisfies it and $S=\emptyset$ .$x^2+4=0$ gives $x=\pm 2i$, which are not real numbers, so no real $x$ satisfies it and $S=\emptyset$.

Revise: Algebra (Class 11 notes)

Q3Sets

The set is a collection of

along rivers of Nepal
blongest rivers of Nepal
ctall plants in a garden
dnice books

Answer (b): A set needs a well-defined collection. 'Long', 'tall' and 'nice' are vague, while 'longest rivers of Nepal' is precisely defined.

Revise: Algebra (Class 11 notes)

Q4Intervals

S=\{x: x\ge -2, x\in\mathbb{R}\}

is represented by$S={x: x\ge -2, x\in\mathbb{R}}$ is represented by

a $[-2,\infty)$ $[-2,\infty)$
b $(-2,\infty)$ $(-2,\infty)$
c $(\infty,-2]$ $(\infty,-2]$
d $[-2,\infty]$ $[-2,\infty]$

Answer (a): $x\ge -2$ includes $-2$ (closed bracket) and has no upper bound, and infinity is always written with an open bracket.$x\ge -2$ includes $-2$ (closed bracket) and has no upper bound, and infinity is always written with an open bracket.

Revise: Algebra (Class 11 notes)

Q5Absolute value inequalities

|x-5|\le 3

has values of

x=

$|x-5|\le 3$ has values of $x=$

a $(2,8)$ $(2,8)$
b $[2,8]$ $[2,8]$
c $\{-2,8\}$ ${-2,8}$
d $\{2,8\}$ ${2,8}$

Answer (b): $|x-5|\le 3$ means $-3\le x-5\le 3$ , so $2\le x\le 8$ , i.e. $[2,8]$ .$|x-5|\le 3$ means $-3\le x-5\le 3$, so $2\le x\le 8$, i.e. $[2,8]$.

Revise: Algebra (Class 11 notes)

Q6Ordered pairs

The ordered pair

(a,b)

for

(2a-1,-3)=(1,b+3)

isThe ordered pair $(a,b)$ for $(2a-1,-3)=(1,b+3)$ is

a $(1,-6)$ $(1,-6)$
b $[1,-6]$ $[1,-6]$
c $\{1,-6\}$ ${1,-6}$
d $[1,6]$ $[1,6]$

Answer (a): Equal ordered pairs have equal components: $2a-1=1$ gives $a=1$ , and $b+3=-3$ gives $b=-6$ .Equal ordered pairs have equal components: $2a-1=1$ gives $a=1$, and $b+3=-3$ gives $b=-6$.

Revise: Algebra (Class 11 notes)

Q7Functions

If a function

f:\mathbb{R}\to\mathbb{R}

be defined by

f(x)=2x+5

then the pre-image of

7

\mathbb{R}

isIf a function $f:\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=2x+5$ then the pre-image of $7$ in $\mathbb{R}$ is

a $3$
bno pre-image
c $1$
d $-2$

Answer (c): Solve $2x+5=7$ : $x=1$ .Solve $2x+5=7$: $x=1$.

Revise: Algebra (Class 11 notes)

Q8Domain of a function

The domain of the function

f:\mathbb{R}\to\mathbb{R}

defined by

f(x)=\sqrt{1-x^{2}}

isThe domain of the function $f:\mathbb{R}\to\mathbb{R}$ defined by $f(x)=\sqrt{1-x^{2}}$ is

a $[0,1]$ $[0,1]$
b $\{1,-1\}$ ${1,-1}$
c $[0,\infty)$ $[0,\infty)$
d $[-1,1]$ $[-1,1]$

Answer (d): We need $1-x^2\ge 0$ , so $x^2\le 1$ , giving $-1\le x\le 1$ .We need $1-x^2\ge 0$, so $x^2\le 1$, giving $-1\le x\le 1$.

Revise: Algebra (Class 11 notes)

Q9Exponential functions

The base of an exponential function

y=a^{x}

passing through

(2,4)

isThe base of an exponential function $y=a^{x}$ passing through $(2,4)$ is

a $4$
b $2$
c $8$
d $1$

Answer (b): $a^2=4$ and the base must be positive, so $a=2$ .$a^2=4$ and the base must be positive, so $a=2$.

Revise: Algebra (Class 11 notes)

Q10Logarithms

3^{2\log_3 x}=

$3^{2\log_3 x}=$

a $2x$
b $x$
c $x^{2}$ $x^{2}$
d $x/2$ $x/2$

Answer (c): $3^{2\log_3 x}=3^{\log_3 x^2}=x^2$ using $a^{\log_a m}=m$ .$3^{2\log_3 x}=3^{\log_3 x^2}=x^2$ using $a^{\log_a m}=m$.

Revise: Algebra (Class 11 notes)

Q11Even and odd functions

The function

f(x)=x^{2}-2

isThe function $f(x)=x^{2}-2$ is

aan even function
ban odd number
cnot a function
dneither odd nor even

Answer (a): $f(-x)=(-x)^2-2=x^2-2=f(x)$ , so it is even.$f(-x)=(-x)^2-2=x^2-2=f(x)$, so it is even.

Revise: Algebra (Class 11 notes)

Q12Number system

A number which can be expressed in the form

p/q

q\ne 0

;

p,q

are integers, is calledA number which can be expressed in the form $p/q$, $q\ne 0$; $p,q$ are integers, is called

aa rational number
ban integer number
can irrational number
da prime number

Answer (a): This is exactly the definition of a rational number.

Revise: Algebra (Class 11 notes)

Q13Geometric series

The sum of an infinite geometric sequence

a, ak, ak^{2},\dots

exists ifThe sum of an infinite geometric sequence $a, ak, ak^{2},\dots$ exists if

a $k>1$ $k>1$
b $k>-1$ $k>-1$
c $-1\le k\le 1$ $-1\le k\le 1$
d $-1<k<1$ $-1<k<1$

Answer (d): An infinite G.P. has a finite sum only when the common ratio satisfies $|k|<1$ .An infinite G.P. has a finite sum only when the common ratio satisfies $|k|<1$.

Revise: Algebra (Class 11 notes)

Q14Arithmetic progression

2k+1

3k+2

and

5k+1

are in A.P., then

k=

If $2k+1$, $3k+2$ and $5k+1$ are in A.P., then $k=$

a $2$
b $6$
c $-8$
d $0$

Answer (a): In an A.P. the middle term is the average: $2(3k+2)=(2k+1)+(5k+1)$ , so $6k+4=7k+2$ and $k=2$ .In an A.P. the middle term is the average: $2(3k+2)=(2k+1)+(5k+1)$, so $6k+4=7k+2$ and $k=2$.

Revise: Algebra (Class 11 notes)

Q15Types of matrices

The matrix

\begin{pmatrix}0&1\\-1&0\end{pmatrix}

isThe matrix $\begin{pmatrix}0&1\-1&0\end{pmatrix}$ is

asymmetric
bskew-symmetric
cunit
dnone

Answer (b): Its transpose is $\begin{pmatrix}0&-1\\1&0\end{pmatrix}=-A$ , so it is skew-symmetric.Its transpose is $\begin{pmatrix}0&-1\1&0\end{pmatrix}=-A$, so it is skew-symmetric.

Revise: Algebra (Class 11 notes)

Q16Inverse of a matrix

A=\begin{pmatrix}-5&3\\2&-1\end{pmatrix}

then

A^{-1}=

If $A=\begin{pmatrix}-5&3\2&-1\end{pmatrix}$ then $A^{-1}=$

a $\begin{pmatrix}5&3\\-2&-1\end{pmatrix}$ $\begin{pmatrix}5&3\-2&-1\end{pmatrix}$
b $\begin{pmatrix}-5&-3\\-2&1\end{pmatrix}$ $\begin{pmatrix}-5&-3\-2&1\end{pmatrix}$
c $\begin{pmatrix}5&3\\2&1\end{pmatrix}$ $\begin{pmatrix}5&3\2&1\end{pmatrix}$
d $\begin{pmatrix}1&3\\-2&-5\end{pmatrix}$ $\begin{pmatrix}1&3\-2&-5\end{pmatrix}$

Answer (d): $|A|=5-6=-1$ , so $A^{-1}=-\begin{pmatrix}-1&-3\\-2&-5\end{pmatrix}=\begin{pmatrix}1&3\\2&5\end{pmatrix}$ . Option d is this matrix with a sign misprint in the second row, so it is the intended answer.$|A|=5-6=-1$, so $A^{-1}=-\begin{pmatrix}-1&-3\-2&-5\end{pmatrix}=\begin{pmatrix}1&3\2&5\end{pmatrix}$. Option d is this matrix with a sign misprint in the second row, so it is the intended answer.

Revise: Algebra (Class 11 notes)

Q17Determinants

A=\begin{vmatrix}2a+1&1\\3a&2\end{vmatrix}=0

, then

a=

If $A=\begin{vmatrix}2a+1&1\3a&2\end{vmatrix}=0$, then $a=$

a $0$
b $2$
c $-2$
d $1$

Answer (c): $2(2a+1)-3a=a+2=0$ , so $a=-2$ .$2(2a+1)-3a=a+2=0$, so $a=-2$.

Revise: Algebra (Class 11 notes)

Q18Types of matrices

A square matrix

A

is said to be singular if

a $|A|>0$ $|A|>0$
b $|A|<0$ $|A|<0$
c $|A|\ne 0$ $|A|\ne 0$
d $|A|=0$ $|A|=0$

Answer (d): A singular matrix has zero determinant and no inverse.

Revise: Algebra (Class 11 notes)

Q19Quadratic equations

If the roots of the equation

px^{2}+qx+r=0

are equal in magnitude but opposite in sign, thenIf the roots of the equation $px^{2}+qx+r=0$ are equal in magnitude but opposite in sign, then

a $p=0$ $p=0$
b $q=0$ $q=0$
c $r=0$ $r=0$
d $p=q$ $p=q$

Answer (b): Sum of roots $=-q/p=0$ , so $q=0$ .Sum of roots $=-q/p=0$, so $q=0$.

Revise: Algebra (Class 11 notes)

Q20Quadratic equations

If the discriminant of the equation

x^{2}+kx+4=0

is zero then

k=

If the discriminant of the equation $x^{2}+kx+4=0$ is zero then $k=$

a $\pm 4$
b $-4$
c $4$
d $0$

Answer (a): $k^2-4(1)(4)=0$ gives $k^2=16$ , so $k=\pm 4$ .$k^2-4(1)(4)=0$ gives $k^2=16$, so $k=\pm 4$.

Revise: Algebra (Class 11 notes)

Q21Complex numbers

i

is the imaginary unit, then

\dfrac{1-i}{1+i}=

If $i$ is the imaginary unit, then $\dfrac{1-i}{1+i}=$

a $1$
b $-i$
c $i$
d $-1$

Answer (b): $\frac{(1-i)^2}{(1+i)(1-i)}=\frac{1-2i+i^2}{2}=\frac{-2i}{2}=-i$ .$\frac{(1-i)^2}{(1+i)(1-i)}=\frac{1-2i+i^2}{2}=\frac{-2i}{2}=-i$.

Revise: Algebra (Class 11 notes)

Q22Complex numbers

The square roots of a complex number

5+12i

isThe square roots of a complex number $5+12i$ is

a $\pm(3+2i)$ $\pm(3+2i)$
b $\pm(2+3i)$ $\pm(2+3i)$
c $\pm(3-2i)$ $\pm(3-2i)$
d $\pm(2-3i)$ $\pm(2-3i)$

Answer (a): $(3+2i)^2=9+12i+4i^2=5+12i$ , so the roots are $\pm(3+2i)$ .$(3+2i)^2=9+12i+4i^2=5+12i$, so the roots are $\pm(3+2i)$.

Revise: Algebra (Class 11 notes)

Q23Inverse trigonometric functions

\sin(\cos^{-1}x)=

$\sin(\cos^{-1}x)=$

a $\sqrt{1+x^{2}}$ $\sqrt{1+x^{2}}$
b $\sin\theta$ $\sin\theta$
c $\sqrt{1-x^{2}}$ $\sqrt{1-x^{2}}$
d $x\sqrt{1-x^{2}}$ $x\sqrt{1-x^{2}}$

Answer (c): Let $\theta=\cos^{-1}x$ , so $\cos\theta=x$ and $\sin\theta=\sqrt{1-x^2}$ .Let $\theta=\cos^{-1}x$, so $\cos\theta=x$ and $\sin\theta=\sqrt{1-x^2}$.

Revise: Trigonometry (Class 11 notes)

Q24Trigonometric equations

The general solution of

4\sin^{2}x=1

, for

n\in Z

isThe general solution of $4\sin^{2}x=1$, for $n\in Z$ is

a $x=n\pi\pm\frac{\pi}{6}$ $x=n\pi\pm\frac{\pi}{6}$
b $x=n\pi\pm\frac{\pi}{4}$ $x=n\pi\pm\frac{\pi}{4}$
c $x=n\pi\pm\frac{\pi}{3}$ $x=n\pi\pm\frac{\pi}{3}$
d $x=2n\pi\pm\frac{\pi}{6}$ $x=2n\pi\pm\frac{\pi}{6}$

Answer (a): $\sin^2x=\frac14=\sin^2\frac{\pi}{6}$ , and $\sin^2x=\sin^2\alpha$ gives $x=n\pi\pm\alpha$ .$\sin^2x=\frac14=\sin^2\frac{\pi}{6}$, and $\sin^2x=\sin^2\alpha$ gives $x=n\pi\pm\alpha$.

Revise: Trigonometry (Class 11 notes)

Q25Straight line

The slope of the line

px+qy+c=0

isThe slope of the line $px+qy+c=0$ is

a $p$
b $q$
c $p/q$ $p/q$
d $-p/q$ $-p/q$

Answer (d): $y=-\frac{p}{q}x-\frac{c}{q}$ , so the slope is $-p/q$ .$y=-\frac{p}{q}x-\frac{c}{q}$, so the slope is $-p/q$.

Revise: Analytic geometry (Class 11 notes)

Q26Distance from a point to a line

If the length of the perpendicular from the point

(k,2)

3x-4y+6=0

2

, then

k=

If the length of the perpendicular from the point $(k,2)$ to $3x-4y+6=0$ is $2$, then $k=$

a $8$
b $6$
c $4$
d $5$

Answer (c): $\frac{|3k-8+6|}{5}=2$ so $|3k-2|=10$ , giving $k=4$ (the other root $-8/3$ is not listed).$\frac{|3k-8+6|}{5}=2$ so $|3k-2|=10$, giving $k=4$ (the other root $-8/3$ is not listed).

Revise: Analytic geometry (Class 11 notes)

Q27Pair of lines

The homogeneous equation is

a $ax^{2}+bxy+c=0$ $ax^{2}+bxy+c=0$
b $ax^{2}+xy+by^{2}=0$ $ax^{2}+xy+by^{2}=0$
c $ax^{2}+bxy+by^{2}+c=0$ $ax^{2}+bxy+by^{2}+c=0$
d $x^{2}+by^{2}+y^{3}=0$ $x^{2}+by^{2}+y^{3}=0$

Answer (b): A homogeneous equation has all terms of the same degree; only (b) has every term of degree 2.

Revise: Analytic geometry (Class 11 notes)

Q28Pair of lines

The two lines represented by

kx^{2}+xy-y^{2}=0

are perpendicular to each other if

k=

The two lines represented by $kx^{2}+xy-y^{2}=0$ are perpendicular to each other if $k=$

a $1$
b $-1$
c $0$
d $k\ne 0$ $k\ne 0$

Answer (a): Perpendicular lines need coefficient of $x^2$ plus coefficient of $y^2$ equal to zero: $k-1=0$ .Perpendicular lines need coefficient of $x^2$ plus coefficient of $y^2$ equal to zero: $k-1=0$.

Revise: Analytic geometry (Class 11 notes)

Q293D coordinates

The distance of the point

(1,2,3)

from origin isThe distance of the point $(1,2,3)$ from origin is

a $1$
b $3$
c $\sqrt{14}$ $\sqrt{14}$
d $2$

Answer (c): $d=\sqrt{1+4+9}=\sqrt{14}$ .$d=\sqrt{1+4+9}=\sqrt{14}$.

Revise: Analytic geometry (Class 11 notes)

Q303D lines

The direction ratios of the line

AB

joining the points

A(4,5,0)

and

B(2,3,4)

areThe direction ratios of the line $AB$ joining the points $A(4,5,0)$ and $B(2,3,4)$ are

a $-2,2,-4$ $-2,2,-4$
b $2,2,-4$ $2,2,-4$
c $2,2,4$ $2,2,4$
d $-2,-2,-4$ $-2,-2,-4$

Answer (b): $B-A=(-2,-2,4)$ , and $(2,2,-4)$ is its negative, which is also a valid set of direction ratios.$B-A=(-2,-2,4)$, and $(2,2,-4)$ is its negative, which is also a valid set of direction ratios.

Revise: Analytic geometry (Class 11 notes)

Q31Vectors

The direction of the vector

a\mathbf{i}+b\mathbf{j}

isThe direction of the vector $a\mathbf{i}+b\mathbf{j}$ is

a $\tan^{-1}\left(-\frac{a}{b}\right)$ $\tan^{-1}\left(-\frac{a}{b}\right)$
b $\tan^{-1}\left(\frac{b}{a}\right)$ $\tan^{-1}\left(\frac{b}{a}\right)$
c $\tan^{-1}\left(-\frac{b}{a}\right)$ $\tan^{-1}\left(-\frac{b}{a}\right)$
dnone

Answer (b): The angle with the x-axis satisfies $\tan\theta=\frac{b}{a}$ .The angle with the x-axis satisfies $\tan\theta=\frac{b}{a}$.

Revise: Vectors (Class 11 notes)

Q32Vectors

The unit vector along

x\mathbf{i}-y\mathbf{j}

isThe unit vector along $x\mathbf{i}-y\mathbf{j}$ is

a $\frac{x\mathbf{i}-y\mathbf{j}}{\sqrt{x^{2}-y^{2}}}$ $\frac{x\mathbf{i}-y\mathbf{j}}{\sqrt{x^{2}-y^{2}}}$
b $\frac{x\mathbf{i}-y\mathbf{j}}{\sqrt{x^{2}y^{2}}}$ $\frac{x\mathbf{i}-y\mathbf{j}}{\sqrt{x^{2}y^{2}}}$
c $\frac{x\mathbf{i}-y\mathbf{j}}{x^{2}+y^{2}}$ $\frac{x\mathbf{i}-y\mathbf{j}}{x^{2}+y^{2}}$
d $\frac{x\mathbf{i}-y\mathbf{j}}{\sqrt{x^{2}+y^{2}}}$ $\frac{x\mathbf{i}-y\mathbf{j}}{\sqrt{x^{2}+y^{2}}}$

Answer (d): Unit vector $=\vec v/|\vec v|$ with $|\vec v|=\sqrt{x^2+y^2}$ .Unit vector $=\vec v/|\vec v|$ with $|\vec v|=\sqrt{x^2+y^2}$.

Revise: Vectors (Class 11 notes)

Q33Standard deviation

The standard deviation of

3,6,9,12,15

isThe standard deviation of $3,6,9,12,15$ is

a $3\sqrt{2}$ $3\sqrt{2}$
b $12$
c $2\sqrt{3}$ $2\sqrt{3}$
d $2$

Answer (a): Mean $=9$ ; squared deviations $36+9+0+9+36=90$ ; variance $=90/5=18$ ; SD $=\sqrt{18}=3\sqrt2$ .Mean $=9$; squared deviations $36+9+0+9+36=90$; variance $=90/5=18$; SD $=\sqrt{18}=3\sqrt2$.

Revise: Statistics and Probability (Class 11 notes)

Q34Probability

The probability of getting an ace of club or a king of spade from a pack of 52 cards is

a $1/26$
b $1/13$
c $1/52$
d $1/2$

Answer (a): Two favourable cards out of 52: $2/52=1/26$ .Two favourable cards out of 52: $2/52=1/26$.

Revise: Statistics and Probability (Class 11 notes)

Q35Limits

\lim_{x\to a}\frac{x^{4}-a^{4}}{x-a}=256

, then

a=

If $\lim_{x\to a}\frac{x^{4}-a^{4}}{x-a}=256$, then $a=$

a $5$
b $3$
c $4$
d $6$

Answer (c): The limit is $4a^3=256$ , so $a^3=64$ and $a=4$ .The limit is $4a^3=256$, so $a^3=64$ and $a=4$.

Revise: Calculus (Class 11 notes)

Q36Limits

\lim_{x\to 0}\frac{\tan 3x}{x}=

$\lim_{x\to 0}\frac{\tan 3x}{x}=$

a $3$
b $0/0$
c $0$
d $x$

Answer (a): $\frac{\tan3x}{3x}\to1$ , so the limit is $3\cdot1=3$ .$\frac{\tan3x}{3x}\to1$, so the limit is $3\cdot1=3$.

Revise: Calculus (Class 11 notes)

Q37Continuity

A function

f(x)=2x+1

is continuous at

x=1

, ifA function $f(x)=2x+1$ is continuous at $x=1$, if

a $\lim_{x\to0}f(x)=3$ $\lim_{x\to0}f(x)=3$
b $\lim_{x\to1}f(x)$ exists$\lim_{x\to1}f(x)$ exists
c $\lim_{x\to0}f(x)=f(1)$ $\lim_{x\to0}f(x)=f(1)$
dnone

Answer (c): Continuity at $x=1$ needs the limit to equal $f(1)$ . Option c is printed with $x\to0$ , a misprint for $x\to1$ ; option b alone is not sufficient.Continuity at $x=1$ needs the limit to equal $f(1)$. Option c is printed with $x\to0$, a misprint for $x\to1$; option b alone is not sufficient.

Revise: Calculus (Class 11 notes)

Q38Differentiation

y=e^{\sin x^{2}}

, then

\frac{dy}{dx}=

If $y=e^{\sin x^{2}}$, then $\frac{dy}{dx}=$

a $e^{\sin x^{2}}$ $e^{\sin x^{2}}$
b $2xy\cos x^{2}$ $2xy\cos x^{2}$
c $2xe^{\sin x^{2}}$ $2xe^{\sin x^{2}}$
d $y\cos x^{2}$ $y\cos x^{2}$

Answer (b): Chain rule: $\frac{dy}{dx}=e^{\sin x^2}\cos x^2\cdot2x=2xy\cos x^2$ .Chain rule: $\frac{dy}{dx}=e^{\sin x^2}\cos x^2\cdot2x=2xy\cos x^2$.

Revise: Calculus (Class 11 notes)

Q39Differentiation

y=x^{3}-x^{2}

, then for

\frac{dy}{dx}=0

x=

If $y=x^{3}-x^{2}$, then for $\frac{dy}{dx}=0$, $x=$

a $0,-2/3$ $0,-2/3$
b $0,3/2$ $0,3/2$
c $0,3$ $0,3$
d $0,2/3$ $0,2/3$

Answer (d): $\frac{dy}{dx}=3x^2-2x=x(3x-2)=0$ gives $x=0,\frac23$ .$\frac{dy}{dx}=3x^2-2x=x(3x-2)=0$ gives $x=0,\frac23$.

Revise: Calculus (Class 11 notes)

Q40Increasing and decreasing functions

The function

f(x)=2x+5

R

isThe function $f(x)=2x+5$ on $R$ is

adecreasing
bstationary
cincreasing
dnone

Answer (c): $f'(x)=2>0$ everywhere, so it is increasing.$f'(x)=2>0$ everywhere, so it is increasing.

Revise: Calculus (Class 11 notes)

Q41Integration

\int\frac{dx}{ax+b}=

$\int\frac{dx}{ax+b}=$

a $\frac1a\log|ax+b|+c$ $\frac1a\log|ax+b|+c$
b $a\log|ax+b|+c$ $a\log|ax+b|+c$
c $|\log(ax+b)|+c$ $|\log(ax+b)|+c$
d $\log|ax+b|+c$ $\log|ax+b|+c$

Answer (a): Substitute $u=ax+b$ , $du=a\,dx$ , giving $\frac1a\log|ax+b|+c$ .Substitute $u=ax+b$, $du=a,dx$, giving $\frac1a\log|ax+b|+c$.

Revise: Calculus (Class 11 notes)

Q42Integration

\int\frac{dx}{2\cos^{2}x\sin^{2}x}=

$\int\frac{dx}{2\cos^{2}x\sin^{2}x}=$

a $2\cot2x+c$ $2\cot2x+c$
b $-2\cot2x+c$ $-2\cot2x+c$
c $\cot2x+c$ $\cot2x+c$
d $-\cot2x+c$ $-\cot2x+c$

Answer (d): $2\sin x\cos x=\sin2x$ so the integrand is $\frac{2}{\sin^22x}=2\csc^22x$ , and $\int2\csc^22x\,dx=-\cot2x+c$ .$2\sin x\cos x=\sin2x$ so the integrand is $\frac{2}{\sin^22x}=2\csc^22x$, and $\int2\csc^22x,dx=-\cot2x+c$.

Revise: Calculus (Class 11 notes)

Q43Definite integrals

\int_1^3\frac{\sin(\ln t)}{t}dt=

$\int_1^3\frac{\sin(\ln t)}{t}dt=$

a $\cos(\ln3)$ $\cos(\ln3)$
b $-\cos(\ln3)$ $-\cos(\ln3)$
c $1-\cos(\ln3)$ $1-\cos(\ln3)$
d $1-\sin(\ln3)$ $1-\sin(\ln3)$

Answer (c): Put $u=\ln t$ : $\int_0^{\ln3}\sin u\,du=1-\cos(\ln3)$ .Put $u=\ln t$: $\int_0^{\ln3}\sin u,du=1-\cos(\ln3)$.

Revise: Calculus (Class 11 notes)

Q44Area under a curve

The area under the curve

y=x^{2}

bounded by the x axis and the ordinates

x=1

and

x=4

isThe area under the curve $y=x^{2}$ bounded by the x axis and the ordinates $x=1$ and $x=4$ is

a $21$
b $64/3$
c $64$
d $7$

Answer (a): $\int_1^4x^2dx=\frac{4^3-1^3}{3}=\frac{63}{3}=21$ .$\int_1^4x^2dx=\frac{4^3-1^3}{3}=\frac{63}{3}=21$.

Revise: Calculus (Class 11 notes)

Q45Newton-Raphson method

The general formula for Newton-Raphson method is

a $x_{n+1}=x_n-\frac{f'(x_n)}{f(x_n)}$ $x_{n+1}=x_n-\frac{f'(x_n)}{f(x_n)}$
b $x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$ $x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$
c $x_{n+1}=x_n+\frac{f'(x_n)}{f(x_n)}$ $x_{n+1}=x_n+\frac{f'(x_n)}{f(x_n)}$
d $x_{n+1}=x_{n+1}-\frac{f'(x_n)}{f(x_n)}$ $x_{n+1}=x_{n+1}-\frac{f'(x_n)}{f(x_n)}$

Answer (b): Newton-Raphson: next estimate is the current one minus function value over derivative.

Revise: Computational methods (Class 11 notes)

Q46Numerical integration

The approximate value of

\int_0^2x^{2}dx

using midpoint rule with one interval isThe approximate value of $\int_0^2x^{2}dx$ using midpoint rule with one interval is

a $4$
b $8$
c $2$
d $0$

Answer (c): Midpoint $=1$ , so the estimate is $f(1)\cdot(2-0)=1\cdot2=2$ .Midpoint $=1$, so the estimate is $f(1)\cdot(2-0)=1\cdot2=2$.

Revise: Computational methods (Class 11 notes)

Q47Equilibrium of forces

If three equal forces

P

Q

and

R

are acting at a point of rigid body are in equilibrium, then the angle between any two forces isIf three equal forces $P$, $Q$ and $R$ are acting at a point of rigid body are in equilibrium, then the angle between any two forces is

a $120^\circ$ $120^\circ$
b $30^\circ$ $30^\circ$
c $60^\circ$ $60^\circ$
dnone

Answer (a): Three equal forces balance only if they form an equilateral triangle of forces, so each pair makes $120^\circ$ .Three equal forces balance only if they form an equilateral triangle of forces, so each pair makes $120^\circ$.

Revise: Mechanics (Class 11 notes)

Q48Resolution of forces

A force equal to

4N

acting vertically upwards is resolved into forces, one being horizontal and equal to

3N

. The magnitude of the other remaining force isA force equal to $4N$ acting vertically upwards is resolved into forces, one being horizontal and equal to $3N$. The magnitude of the other remaining force is

a $7N$
b $1N$
c $2N$
d $5N$

Answer (d): The other force must cancel the horizontal $3N$ and supply the vertical $4N$ : $\sqrt{3^2+4^2}=5N$ .The other force must cancel the horizontal $3N$ and supply the vertical $4N$: $\sqrt{3^2+4^2}=5N$.

Revise: Mechanics (Class 11 notes)

Q49Linear motion

If the acceleration of a particle, starting from rest is

5\,m/sec^{2}

, then the velocity at the end of 3 seconds isIf the acceleration of a particle, starting from rest is $5,m/sec^{2}$, then the velocity at the end of 3 seconds is

a $8\,m/sec^{2}$ $8,m/sec^{2}$
b $15\,m/sec^{2}$ $15,m/sec^{2}$
c $5\,m/sec^{2}$ $5,m/sec^{2}$
dnone

Answer (b): $v=u+at=0+5\times3=15$ m/s. The option's unit is printed as m/sec^2, a misprint.$v=u+at=0+5\times3=15$ m/s. The option's unit is printed as m/sec^2, a misprint.

Revise: Mechanics (Class 11 notes)

Q50Motion under gravity

A stone is thrown vertically upwards with a velocity of

30

m/sec from the top of a tower and hits the ground after

10

secs, then the height of the tower isA stone is thrown vertically upwards with a velocity of $30$ m/sec from the top of a tower and hits the ground after $10$ secs, then the height of the tower is

a $100\,m$ $100,m$
b $300\,m$ $300,m$
c $200\,m$ $200,m$
d $50\,m$ $50,m$

Answer (c): Take $g=10$ : displacement $s=ut-\frac12gt^2=300-500=-200$ m, so the tower is $200$ m high.Take $g=10$: displacement $s=ut-\frac12gt^2=300-500=-200$ m, so the tower is $200$ m high.

Revise: Mechanics (Class 11 notes)

English

Q51Synonyms

Choose the word or group of words which is most nearly same in meaning as the word "woeful".

adeplorable
bpunishable
cculpable
dshaky

Answer (a): Woeful means very bad or causing sorrow, which is 'deplorable'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q52Synonyms

Choose the word or group of words which is most nearly same in meaning as the word "rotund".

around
bplump
ccircular
dhealthy

Answer (b): Rotund describes a person who is round and fat, so 'plump'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q53Synonyms

Choose the word or group of words which is most nearly same in meaning as the word "facetious".

asweet
bhandsome
cflippant
dcharming

Answer (c): Facetious means treating serious matters with inappropriate humour, i.e. 'flippant'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q54Synonyms

Choose the word or group of words which is most nearly same in meaning as the word "coagulate".

asweeten
bsharpen
cmix up
dcongeal

Answer (d): To coagulate is to thicken or clot, same as 'congeal'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q55Antonyms

Choose the word or group of words which is most opposite to the meaning of the word "grotesque".

aproportionate
bsymmetrical
cugly
dcongruous

Answer (a): Grotesque means distorted and misshapen; the best opposite among the options is 'proportionate' (well-shaped). 'Symmetrical' is a weaker contrast.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q56Antonyms

Choose the word or group of words which is most opposite to the meaning of the word "erase".

adrop
bdelete
cengrave
ddefend

Answer (c): Erase means to rub out; to engrave is to cut in permanently, its opposite.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q57Antonyms

Choose the word or group of words which is most opposite to the meaning of the word "tranquil".

apeaceful
bagitated
cangry
ddull

Answer (b): Tranquil means calm, so 'agitated' is the opposite.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q58Antonyms

Choose the word or group of words which is most opposite to the meaning of the word "spurious".

agenuine
bduplicate
cvalid
dreliable

Answer (a): Spurious means fake, the opposite of 'genuine'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q59One-word substitution

Give a single word to this expression: "fossils and other forms of early life"

apaleontology
bpomology
cphilology
dteleology

Answer (a): Paleontology is the study of fossils and ancient life. Pomology is fruit study.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q60One-word substitution

Give a single word to this expression: "the study of life and habits of birds"

aornithology
bembryology
cgeology
dbiology

Answer (a): Ornithology is the scientific study of birds.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q61One-word substitution

Give a single word to this expression: "the subject that studies God and religion"

aaxiology
btheology
cmetaphysics
depistemology

Answer (b): Theology is the study of God and religious belief.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q62One-word substitution

Give a single word to this expression: "a person who is commanding, haughty and arrogant"

aeccentric
bimperious
cgarrulous
damiable

Answer (b): Imperious means domineering and arrogantly commanding.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q63Phrasal verbs

Pick up the correct phrasal verb for the expression "the two friends....this afternoon".

afall on
bfall in
cfall out
dfall upon

Answer (c): 'Fall out' means to quarrel, which fits two friends and 'this afternoon' (past: fell out).

Revise: Grammar and Usage (Class 11 notes)

Q64Phrasal verbs

Pick up the correct phrasal verb for the expression "It is not easy to....rebellion".

aput on
bput out
cput down
dput up

Answer (c): 'Put down' a rebellion means to suppress it.

Revise: Grammar and Usage (Class 11 notes)

Q65Phrasal verbs

Pick up the correct phrasal verb for the expression "Tom just ... and lets me do all the work.".

asit out
bsit in
csit on
dsit back

Answer (d): 'Sit back' means to relax and take no part, which suits letting someone else do the work.

Revise: Grammar and Usage (Class 11 notes)

Q66Phrasal verbs

Pick up the correct phrasal verb for the expression "everything will ... all right in the end".

awork up
bwork off
cwork on
dwork out

Answer (d): 'Work out' means to turn out well.

Revise: Grammar and Usage (Class 11 notes)

Q67Idioms

Choose the appropriate meaning to the idiomatic expression "a flash in the pan".

aa short lived success or enthusiasm
bsudden fortune
csuccessful life start
dnew day in life

Answer (a): The idiom describes something that starts promisingly but quickly fails, a short-lived success.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q68Idioms

Choose the appropriate meaning to the idiomatic expression "up and about".

arich once again
brecovered and in good health
cliked by everybody
dpurpose behind an action

Answer (b): 'Up and about' means out of bed and active again after illness.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q69Idioms

Choose the appropriate meaning to the idiomatic expression "the thrills and spills".

acritical mind set
bsuccessful person
csuccess and failures
dnew attempts

Answer (c): The phrase refers to the excitement (thrills) and mishaps (spills) of an activity, i.e. successes and failures; this is the closest option.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q70Idioms

Choose the appropriate meaning to the idiomatic expression "be out like a light".

afit and fine
bfeel great success
chappy and healthy
dfall quickly into a deep sleep

Answer (d): To be 'out like a light' is to fall asleep very fast.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q71Idioms

Choose the appropriate meaning to the idiomatic expression "mind over matter".

aovercome physical weakness by means of will power
bvery conscious person
cidealist person
dignore materiality

Answer (a): It means willpower can overcome physical limits or difficulties.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q72Prepositions

Choose the appropriate preposition/s to fill up the blank spaces "she was fined....parking her car... a no parking area."

afor, at
bfor, in
cby, with
don, in

Answer (b): One is fined 'for' an offence, and the car is parked 'in' an area.

Revise: Grammar and Usage (Class 11 notes)

Q73Prepositions

Choose the appropriate preposition/s to fill up the blank spaces "a patient died... cancer whereas other sick person died... the loss of blood."

afor, from
bby, by
cof, from
dof, by

Answer (c): Die 'of' a disease and die 'from' an injury or loss of blood.

Revise: Grammar and Usage (Class 11 notes)

Q75Prepositions

Choose the appropriate preposition/s to fill up the blank spaces "one must guard family members...any danger and live ...honest labour."

aagainst, by
bfor, by
cby, by
dfor, from

Answer (a): Guard 'against' danger and live 'by' honest labour.

Revise: Grammar and Usage (Class 11 notes)

Q76Prepositions

Choose the appropriate preposition/s to fill up the blank spaces "I am in dire need ...money ...the treatment of my sick wife."

aof, of
bof, for
cfor, for
dby, from

Answer (b): 'Need of money' and money 'for' the treatment.

Revise: Grammar and Usage (Class 11 notes)

Q77Word stress

The word "plutonium" gets its prime stress on :

a1st syllable
b3rd syllable
c2nd syllable
d4th syllable

Answer (c): Plu-TO-ni-um: words ending in -ium put stress on the syllable before the ending.

Q78Word stress

The word "cyber squatting" gets its prime stress on :

a4th syllable
b2nd syllable
c3rd syllable
d1st syllable

Answer (d): As a compound noun, the stress falls on the first element: CY-ber squatting.

Q79Word stress

The word "retractable" gets its prime stress on :

a1st syllable
b2nd syllable
c3rd syllable
d4th syllable

Answer (b): re-TRAC-ta-ble: stress falls on the root syllable after the prefix.

Q80Synonyms

Give similar meaning word to "bankruptcy".

ainsolvency
bcorrupt
cpoverty
deconomical

Answer (a): Bankruptcy is the legal state of being unable to pay debts, i.e. insolvency.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q81Idioms

Give a right meaning to the idiom "a baptism of fire".

astart a new work
ba difficult introduction to a new job or activity
cvery successful beginning
dremarkable initiation

Answer (b): The idiom means a harsh first experience of something new.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q82Idioms

Give a right meaning to the idiom "face the music".

aready for further action
bbold and decisive
clikes to dance
daccept the criticism or punishment for one's own work

Answer (d): To 'face the music' is to accept the consequences of what you did.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q83Conjunctions

Choose a correct conjunction for "he got the job... he had no suitable qualification".

aalthough
beven
cif
din spite of

Answer (a): 'Although' introduces a contrast with a full clause; 'in spite of' needs a noun phrase.

Revise: Grammar and Usage (Class 11 notes)

Q84Conjunctions

Choose a correct conjunction for "he broke the window...he was angry....soon realized the mistake".

ahowever, though
bbecause, but
cin spite of, even
dwhen, despite of

Answer (b): 'Because he was angry' gives the reason, and 'but' contrasts with realising the mistake.

Revise: Grammar and Usage (Class 11 notes)

Q85Conjunctions

Choose a correct conjunction for "Kanu is illiterate ..... he can read ...write a single word".

aeither, or
bif, even if
cneither, nor
dfor, but

Answer (c): The sense is that he can neither read nor write a word; 'neither...nor' is the matching correlative pair.

Revise: Grammar and Usage (Class 11 notes)

Q86Passive voice

The suitcase was left outside and was.... away by someone.

atakes
btaking
ctook
dtaken

Answer (d): Passive voice needs 'was' plus the past participle: 'taken'.

Revise: Grammar and Usage (Class 11 notes)

Q87Possessive adjectives

On ...trip to Pokhara we visited several wonderful natural sites.

aour
btheir
cwhose
dits

Answer (a): The subject is 'we', so the possessive is 'our'.

Revise: Grammar and Usage (Class 11 notes)

Q88Prepositions

The dog was killed by a lorry which went ....it.

aunder
bover
cthrough
dbelow

Answer (b): A vehicle running over an animal is 'went over it'.

Revise: Grammar and Usage (Class 11 notes)

Q89Adverbs of degree

The statue was ...heavy that a crane was brought to lift it.

atoo
bmuch
cso
dvery

Answer (c): 'So ... that' expresses result.

Revise: Grammar and Usage (Class 11 notes)

Q90Collocations

I put on warm clothes so that I might not....cold.

acatch
baffect
ctake
dattack

Answer (a): The collocation is 'catch cold'.

Revise: Grammar and Usage (Class 11 notes)

Q91One-word substitution

A short journey for pleasure is called......

ajaunt
bstroll
citinerary
djunta

Answer (a): A jaunt is a short pleasure trip.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q92One-word substitution

The state of not getting married is....

abachelor
bspinster
ccelibacy
dunmarried

Answer (c): The abstract noun for the state of remaining unmarried is 'celibacy'; the others are persons or adjectives.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q93One-word substitution

Gradual recovery from an illness is.....

aamnesia
bhysteria
cconvalescence
dsuperannuating

Answer (c): Convalescence is the period of recovery after illness.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q94Prepositions

It is much easier to run...debt than to get out of it.

adown
bout
cfor
dinto

Answer (d): The idiom is 'run into debt'.

Revise: Grammar and Usage (Class 11 notes)

Q95Collocations

Walking in the morning, I heard the.....of thunder.

acrackling
brippling
cclanking
drumbling

Answer (d): Thunder is described as 'rumbling'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q96Prefixes

Which of the following is not used as a prefix in forming a word.

atyro -
banti-
cpost-
dpre-

Answer (a): Anti-, post- and pre- are common prefixes; 'tyro-' is not.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q97Prefixes

The word "hearted" takes the prefix:

aup
bdown
cover
dunder

Answer (b): 'Downhearted' is the existing word.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q98Sentence types

John, who is wearing a white shirt, is my best friend. This is a ....sentence.

asimple
bcompound
ccomplex
dcomplex-compound

Answer (c): It has one main clause and one dependent relative clause, so it is complex.

Revise: Grammar and Usage (Class 11 notes)

Q99Intonation

The sentence "I saw a blackbird" has a ...tone.

afalling
brising
cfall-rise
dnone

Answer (a): A plain statement is normally said with a falling tone.

Q100One-word substitution

Belief in the existence of one God but without any religious dogma

aPantheism
bdeism
ctheism
dhenotheism

Answer (b): Deism is belief in one God based on reason, without organised religious doctrine.

Revise: Vocabulary and Word Formation (Class 11 notes)

Computer

Q101Computer buses

Which bus is bidirectional?

aData bus
bsystem bus
cAddress bus
dAll of the above

Answer (a): The data bus carries data both to and from the CPU, while the address bus is one-way (CPU to memory).

Revise: Computer System (Class 11 notes)

Q102Memory

Which of the following is also known as flash memory?

aROM
bPROM
cEPROM
dEEPROM

Answer (d): Flash memory is a type of electrically erasable programmable ROM (EEPROM).

Revise: Computer System (Class 11 notes)

Q103Computer architecture

Which of the following is based on separate storage and signal pathway?

aVon-Neumann
bCISC
cHarvard
dQueue

Answer (c): Harvard architecture uses separate memories and buses for instructions and data.

Revise: Computer System (Class 11 notes)

Q104Binary arithmetic

1000-100

binary subtraction is equivalent to......$1000-100$ binary subtraction is equivalent to......

a900
b010
c100
d001

Answer (c): $1000_2=8$ and $100_2=4$ , so the difference is $4=100_2$ .$1000_2=8$ and $100_2=4$, so the difference is $4=100_2$.

Revise: Number System and Boolean Logic (Class 11 notes)

Q105Types of software

Backberry is ..... software.

aSystem
bApplication
cUtility
dControl

Answer (a): BlackBerry (as an OS) is system software.

Revise: Computer Software and Operating System (Class 11 notes)

Q106Programming languages

Which of the following is high level procedural language?

aC++
bJava
cPython
dFortran

Answer (d): Fortran is a classic high-level procedural language, whereas C++ and Java are object-oriented.

Revise: Programming Concepts and Logic (Class 11 notes)

Q107Operators

Which of the following is logical operator

Answer (c): && is the logical AND; & is bitwise, = is assignment and == is relational.

Revise: Programming Concepts and Logic (Class 11 notes)

Q108Network types

Which of the following has smallest coverage?

aWAN
bLAN
cPAN
dMAN

Answer (c): A PAN covers only a few metres around a person.

Revise: Concept of Network and Data Communication (Class 12 notes)

Q109Transmission modes

Which among the following is full duplex transmission?

aWalkie-Talkie
bBluetooth
cKeyboard
dNone of the above

Answer (b): Bluetooth links can send and receive at the same time (full duplex); a walkie-talkie is half duplex and a keyboard is simplex.

Revise: Concept of Network and Data Communication (Class 12 notes)

Q110Networking

MAC stands for.....

aMedium Act Control
bMedia Act Control
cMedium Access Control
dMedia Access Control

Answer (d): MAC means Media Access Control.

Revise: Concept of Network and Data Communication (Class 12 notes)

Q111Cyber security

Which of the following is a component of cyber security?

aAI
bInternet of Things
cData warehouse
dRSA

Answer (d): RSA is a cryptographic algorithm, used for encryption in cyber security.

Revise: Information Security and Cyber Law (Class 11 notes)

Q112Hackers

Which among the following is not ethical hacker?

aBlack hat hacker
bGray hat hacker
cBiased hat hacker
dWhite hat hacker

Answer (a): Black hat hackers break in illegally, unlike ethical (white hat) hackers.

Revise: Information Security and Cyber Law (Class 11 notes)

Q113Types of computers

Which of the following is often used for automatic computation?

aHybrid
bAnalog
cDigital
dAll of the above

Answer (c): Digital computers perform automatic computation on discrete data.

Revise: Computer System (Class 11 notes)

Q114Memory hierarchy

Which of the following is the slowest memory?

aHard disk
bRAM
cCache
dRegister

Answer (a): Secondary storage such as a hard disk is much slower than RAM, cache and registers.

Revise: Computer System (Class 11 notes)

Q115CPU

aLogical Operation
bArithmetic Operation
cArithmetic and Logic operations
dNone of the above

Answer (c): The ALU of the CPU performs both arithmetic and logic operations.

Revise: Computer System (Class 11 notes)

Q116Application packages

Which key on the keyboard can be used to view slide show?

aF1
bF2
cF5
dF10

Answer (c): F5 starts a slide show from the beginning in presentation software.

Revise: Application Package (Class 11 notes)

Q117Units of memory

1 PB (pentabyte) is equivalent to

a1024 KB
b1024 MB
c1024 GB
d1000 TB

Answer (d): In SI usage 1 PB (petabyte) is $10^{15}$ bytes, which is 1000 TB; the other options are far too small.In SI usage 1 PB (petabyte) is $10^{15}$ bytes, which is 1000 TB; the other options are far too small.

Revise: Computer System (Class 11 notes)

Q118Character codes

ASCII used ...... bits to represent characters.

a8 Bits
b7 bits
c6 bits
d5 bits

Answer (b): Standard ASCII is a 7-bit code (128 characters).

Revise: Number System and Boolean Logic (Class 11 notes)

Q119Character codes

The code for the character "a" belongs to....... ASCII code.

Answer (b): Lowercase 'a' has ASCII code 97 (A is 65).

Revise: Number System and Boolean Logic (Class 11 notes)

Q120Number conversion

Which of the following Binary numbers is equivalent to the decimal number 24?

a110111
b111111
c11000
d11001

Answer (c): $24=16+8=11000_2$ .$24=16+8=11000_2$.

Revise: Number System and Boolean Logic (Class 11 notes)

Q121Number systems

The octal number system is called base-8 system as it has total eight digits

a1 to 8
b0 to 7
c2 to 9
dNone of the above

Answer (b): Octal digits run from 0 to 7.

Revise: Number System and Boolean Logic (Class 11 notes)

Q122Operating system

What else is a command interpreter called?

aprompt
bkernel
cshell
dcommand

Answer (c): The shell interprets the commands typed by the user.

Revise: Computer Software and Operating System (Class 11 notes)

Q123Booting

What is the meaning of the Booting in the operating system?

aRestarting computer
bInstall the program
cTo scan
dTo turn off

Answer (a): Booting is starting the computer and loading the OS; of the choices, restarting is the closest.

Revise: Computer Software and Operating System (Class 11 notes)

Q124Booting

What is bootstrapping called?

aCold boot
bCold hot boot
cCold hot strap
dHot boot

Answer (a): Bootstrapping starts the computer from a powered-off state, which is a cold boot.

Revise: Computer Software and Operating System (Class 11 notes)

Q125Types of OS

Which of the following is an example of a Real Time Operating System?

aMAC
bMS-DOS
cWindows 10
dProcess Control

Answer (d): Process control systems are classic real-time systems; the others are general-purpose OSs.

Revise: Computer Software and Operating System (Class 11 notes)

Q127Programming

What will be the output of the following code snippet? #include <stdio.h> int main() { int a = 3, b = 5; int t = a; a = b; b = t; printf("%d %d", a, b); return 0; }

Answer (d): The values are swapped using $t$ : $a$ becomes 5 and $b$ becomes 3, so it prints '5 3' (shown as 53).The values are swapped using $t$: $a$ becomes 5 and $b$ becomes 3, so it prints '5 3' (shown as 53).

Revise: Programming Concepts and Logic (Class 11 notes)

Q128Web technology

Which of the following can read and render HTML web pages?

aServer
bHead Tak
cWeb Browser
dEmpty

Answer (c): A web browser parses and displays HTML.

Revise: Web Technology I (Class 11 notes)

Q129Network protocols

Simple network management protocol uses which of the following port number

a161
b162
c163
d164

Answer (a): SNMP agents listen on UDP port 161 (traps use 162).

Revise: Concept of Network and Data Communication (Class 12 notes)

Q130HTML

Which of the following attributes defines the relationship between the current document and URL?

aURL
bREV
cREL
dUVL

Answer (c): The rel attribute specifies the relationship between the current document and the linked resource.

Revise: Web Technology I (Class 11 notes)

Q131HTML

How many sizes of headers are available in HTML by default?

Answer (d): HTML provides h1 to h6, six heading levels.

Revise: Web Technology I (Class 11 notes)

Q132Multimedia

Multimedia is also used for ....... communications and presentations.

aCorporate
bCompany
cCommunal
dCommercial

Answer (a): The standard phrase is 'corporate communications and presentations'.

Revise: Multimedia (Class 11 notes)

Q133Multimedia

A heavy video in a WBT may not load because of poor

aSignal
bKBPS
cPresentation
dBandwidth

Answer (d): Poor bandwidth limits how fast heavy media can load.

Revise: Multimedia (Class 11 notes)

Q134Cyber crimes

In which of the following, a person is constantly followed/chased by another person or group of several peoples?

aPhishing
bBulling
cStalking
dIdentity theft

Answer (c): Stalking is persistent following or harassment of a person.

Revise: Information Security and Cyber Law (Class 11 notes)

Q135Cyber ethics

Which of the following refers to exploring the appropriate, ethical behaviors related to the online environment and digital media platform?

aCyber Law
bCyber Ethics
cCyber Security
dCyber Safety

Answer (b): Cyber ethics concerns ethical behaviour online.

Revise: Information Security and Cyber Law (Class 11 notes)

Q136Malware

Code Red is a type of ........

aAn Antivirus Program
bA photo editing software
cA computer virus
dA video editing software

Answer (c): Code Red was a well-known computer worm/virus.

Revise: Information Security and Cyber Law (Class 11 notes)

Q137Firewall

Which of the following statements is correct about the firewall?

aIt is a device installed at the boundary of a company to prevent unauthorized physical access.
bIt is a device installed at the boundary of incorporation to protect it against unauthorized access.
cIt is a kind of wall built to prevent files from damaging the corporate.
dNone of the above.

Answer (b): A firewall sits at a network boundary and guards against unauthorised access; (a) wrongly says physical.

Revise: Information Security and Cyber Law (Class 11 notes)

Q138Malware

Which of the following is a type of independent malicious program that never requires any host program?

aTrojan Horse
bWorm
cTrap Door
dVirus

Answer (b): A worm is self-replicating and standalone; viruses need a host file.

Revise: Information Security and Cyber Law (Class 11 notes)

Q139Logic gates

How many AND gates are required to realize

Y=CD+EF+G

?How many AND gates are required to realize $Y=CD+EF+G$?

Answer (d): Two AND gates (for $CD$ and $EF$ ); $G$ goes straight to the OR gate.Two AND gates (for $CD$ and $EF$); $G$ goes straight to the OR gate.