TU IOST | Entrance paper

BSc CSIT Entrance Exam 2070 Questions with Answers

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

Mathematics

Q1Sets

If A and B are any two sets, then $A-(A-B)$ is equal to

a$B-A$
b$A\cap B$
c$A\cup B$
d $\phi$

Answer (b): $A-B$ is the part of $A$ outside $B$. Removing it from $A$ leaves the part of $A$ inside $B$, which is $A\cap B$.

Revise: Algebra (Class 11 notes)

Q2Functions

The range of the function $y=\sqrt{a^2-x^2}$, $a>0$ is equal to

a$[-a,a]$
b$(-a,a)$
c$[0,a]$
d$(0,a)$

Answer (c): $y=\sqrt{a^2-x^2}$ is defined for $-a\le x\le a$ and takes values from $0$ (at $x=\pm a$) up to $a$ (at $x=0$), so the range is $[0,a]$.

Revise: Algebra (Class 11 notes)

Q3Logarithms

What is the value of $\log_a\sqrt{a^3\sqrt{a^2}}$ ?

a $4$
b $3$
c $2$
d $1$

Answer (c): $\sqrt{a^2}=a$, so the expression is $\sqrt{a^4}=a^2$. Hence $\log_a a^2=2$.

Revise: Algebra (Class 11 notes)

Q4Matrices

If $A=\begin{pmatrix}0&1\-1&0\end{pmatrix}$, then $A^{100}$ is equal to

a $1$
b $0$
c $-1$
dNone

Answer (a): $A^2=-I$, so $A^4=I$ and $A^{100}=(A^4)^{25}=I$, the unit matrix, which the option '1' stands for. The printed 1 is read as the identity matrix.

Revise: Algebra (Class 11 notes)

Q5Sequences and series

If $a^x=b^y=c^z$ and $a,b,c$ are in G.P., then $x,y,z$ are in

aG.P.
bA.P.
cH.P.
dNone

Answer (c): Let each equal $k$: $\ln a=\frac{\ln k}{x}$ etc. $b^2=ac$ gives $\frac{2}{y}=\frac1x+\frac1z$, so $x,y,z$ are in H.P.

Revise: Algebra (Class 11 notes)

Q6Limits

$\lim_{x\to0}\frac{a^x-b^x}{x}$ is equal to

a $0$
b$\log(ab)$
c$\log(a/b)$
d$\log(b/a)$

Answer (c): Split as $\frac{a^x-1}{x}-\frac{b^x-1}{x}\to\ln a-\ln b=\ln(a/b)$.

Revise: Calculus (Class 12 notes)

Q7Derivatives

The derivative of $y=5^x$ with respect to $x$ is equal to

a$5^x\log_e5$
b$5^x$
c$\log_e5$
d$5\log_e5$

Answer (a): $\frac{d}{dx}a^x=a^x\ln a$, so $\frac{d}{dx}5^x=5^x\ln5$.

Revise: Calculus (Class 12 notes)

Q8Domain of a function

The function $f(x)=x-\frac{1}{x^2}$, $x\in R$, $x\neq0$ is defined for

a$(-\infty,0)\cup(0,\infty)$
b$(-\infty,0]\cup[0,\infty)$
c$[-1,1]$
d$(-\infty,\infty)$

Answer (a): The only restriction is $x\neq0$ (division by zero), so the domain is all reals except $0$.

Revise: Algebra (Class 11 notes)

Q9Integration

The integral $\int\frac{e^x,dx}{e^x+1}$ is equal to

a$\log(e^x+1)+C$
b$\frac{-1}{e^{2x}+1}+C$
c$\frac{-1}{2(e^x+e^{-x})}+C$
d$\frac{-1}{2(e^{2x}+1)}+C$

Answer (a): Put $u=e^x+1$, $du=e^x dx$. The integral becomes $\int\frac{du}{u}=\ln(e^x+1)+C$.

Revise: Calculus (Class 12 notes)

Q10Quadratic equations

For what value of $k$ will the equation $5x^2-kx+45=0$ have equal roots?

a $0$
b $\pm3$
c $\pm30$
d $\pm33$

Answer (c): Equal roots need $D=0$: $k^2-4(5)(45)=0$, so $k^2=900$ and $k=\pm30$.

Revise: Algebra (Class 11 notes)

Q11Quadratic equations

The quadratic equation whose one root is $2+\sqrt3$ is

a$x^2+4x+1=0$
b$x^2-4x+1=0$
c$x^2-4x-1=0$
d$-x^2-4x-1=0$

Answer (b): The conjugate root is $2-\sqrt3$. Sum $=4$, product $=4-3=1$, so $x^2-4x+1=0$.

Revise: Algebra (Class 11 notes)

Q12Straight lines

The distance between the parallel lines $y-2x=4$ and $6x-3y=5$ is

a$\frac{1}{\sqrt{45}}$
b$\frac{7}{\sqrt{45}}$
c$\frac{17}{\sqrt{45}}$
d$\frac{17}{2\sqrt{45}}$

Answer (c): Write the second as $2x-y-\frac53=0$ and the first as $2x-y+4=0$. Distance $=\frac{|4+5/3|}{\sqrt5}=\frac{17}{3\sqrt5}=\frac{17}{\sqrt{45}}$.

Revise: Analytic geometry (Class 11 notes)

Q13Circle

Radius of the circle $x^2+y^2-3x+2y-\frac34=0$ is

a $2$
b $1$
c $4$
d $3$

Answer (a): $r^2=g^2+f^2-c=\frac94+1+\frac34=4$, so $r=2$.

Revise: Analytic geometry (Class 11 notes)

Q14Complex numbers

The absolute value of the complex number $(1+i)^{-1}$ is

a $1$
b$\sqrt2$
c$\frac{1}{\sqrt2}$
d $2$

Answer (c): $|(1+i)^{-1}|=\frac{1}{|1+i|}=\frac{1}{\sqrt2}$.

Revise: Algebra (Class 11 notes)

Q15Complex numbers (De Moivre)

If $z=\cos\theta+i\sin\theta$, then $z^n+\frac{1}{z^n}$ is equal to

a$-2\cos n\theta$
b$2\cos n\theta$
c$2\sin n\theta$
d$-2\sin n\theta$

Answer (b): By De Moivre, $z^n=\cos n\theta+i\sin n\theta$ and $z^{-n}=\cos n\theta-i\sin n\theta$. The sum is $2\cos n\theta$.

Revise: Algebra (Class 11 notes)

Q16Sequences and series

The $n^{th}$ term of the series $2+6+12+20+\dots$ is

a$n(n+1)$
b$(n+1)(n+2)$
c$n(n-1)$
d $n$

Answer (a): The terms are $1\cdot2,\ 2\cdot3,\ 3\cdot4,\ 4\cdot5$, so $t_n=n(n+1)$.

Revise: Algebra (Class 11 notes)

Q17Infinite series

If $|x|<1$ and $y=x+x^2+x^3+x^4+\dots+\infty$, then $x$ is equal to

a$\frac{y}{1-y}$
b$\frac{y}{y-1}$
c$\frac{y+1}{y}$
d$\frac{y}{1+y}$

Answer (d): The infinite G.P. gives $y=\frac{x}{1-x}$. Then $y-xy=x$, so $x(1+y)=y$ and $x=\frac{y}{1+y}$.

Revise: Algebra (Class 11 notes)

Q18Chain rule

The derivative of $y=\cos(\cos\sqrt x)$ is

a$\frac{\sin(\cos\sqrt x)\cdot\sin\sqrt x}{2\sqrt x}$
b$\sin(\cos\sqrt x)$
c$\sin(\sin\sqrt x)$
d$\frac{\sin(\cos\sqrt x)}{2\sqrt x}$

Answer (a): Chain rule: $y'=-\sin(\cos\sqrt x)\cdot(-\sin\sqrt x)\cdot\frac{1}{2\sqrt x}=\frac{\sin(\cos\sqrt x)\sin\sqrt x}{2\sqrt x}$.

Revise: Calculus (Class 12 notes)

Q19Inverse trigonometric functions

$3\cos^{-1}x$ is equal to

a$\cos^{-1}(3x-4x^2)$
b$\cos^{-1}(4x^3-3x)$
c$\cos^{-1}(4x-3x^3)$
d$\cos^{-1}(3x^3-4x)$

Answer (b): Put $x=\cos\theta$. Then $\cos3\theta=4\cos^3\theta-3\cos\theta$, so $3\theta=\cos^{-1}(4x^3-3x)$.

Revise: Trigonometry (Class 11 notes)

Q20Trigonometric equations

Solution of $\tan ax=\cot bx$ is

a$\frac{2n+1}{a+b}\cdot\frac\pi4$
b$\frac{2n-1}{a-b}\cdot\frac\pi2$
c$\frac{2n+1}{a+b}\cdot\frac\pi2$
d$\frac\pi2$

Answer (c): $\tan ax=\tan(\frac\pi2-bx)$ gives $ax=n\pi+\frac\pi2-bx$, so $x=\frac{(2n+1)}{a+b}\cdot\frac\pi2$.

Revise: Trigonometry (Class 11 notes)

Q21Determinants

What is the value of $\begin{vmatrix}1&\omega&\omega^2\\omega&\omega^2&1\\omega^2&1&\omega\end{vmatrix}$, where $\omega$ is an imaginary cube root of unity?

a $1$
b $0$
c $3$
d $2$

Answer (b): Add all columns to the first: each row sum is $1+\omega+\omega^2=0$, so the first column becomes zero and the determinant is $0$.

Revise: Algebra (Class 11 notes)

Q22Pair of straight lines

The single equation representing the pair of lines $y=x$ and $y=-x$ is

a$y^2-x^2=0$
b$y-x=0$
c$x-y=0$
d$x^2+y^2=0$

Answer (a): Multiply $(y-x)(y+x)=0$ to get $y^2-x^2=0$.

Revise: Analytic geometry (Class 11 notes)

Q23Sets and intervals

Let $A=[-3,2]$ and $B=[2,3]$. Then $A-B$ is equal to

a$[-3,3)$
b$[-3,2)$
c$(-2,2)$
d$(-2,1)$

Answer (b): $A-B$ removes the point $2$ (the only common point) from $A$, leaving $[-3,2)$.

Revise: Algebra (Class 11 notes)

Q24Continuity

If $\lim_{x\to0^-}f(x)\neq\lim_{x\to0^+}f(x)$, then $f(x)$ is said to have

ainfinite discontinuity
bremovable discontinuity
cjump discontinuity
dnone

Answer (c): Both one-sided limits exist but differ, which is a jump discontinuity.

Revise: Calculus (Class 12 notes)

Q25Area under a curve

The area enclosed by the curve $y=3x$, the x-axis and the ordinates $x=0$, $x=4$ is

a $12$
b $16$
c $20$
d $24$

Answer (d): Area $=\int_0^4 3x,dx=\frac32x^2\Big|_0^4=24$.

Revise: Calculus (Class 12 notes)

English

Q26Vocabulary

Inscription on a tomb is called

aEpitaph
bcemetery
cMorgue
ddemagogue

Answer (a): An epitaph is the text written on a tombstone in memory of the dead.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q27Phrasal verbs

After he finished the exam, he ____ to the teacher.

aHanded over it
bhanded it over
chanded it out
dhanded out it

Answer (b): With a pronoun object, a phrasal verb is split: 'handed it over'. 'Handed over it' is wrong.

Revise: Grammar and Usage (Class 11 notes)

Q28Phrasal verbs

Every week she ____ her sister in her village to talk to her.

aCalls over
bcalls on
ccalls out
dcalls up

Answer (b): 'Call on' means to visit a person, which fits visiting her sister in the village.

Revise: Grammar and Usage (Class 11 notes)

Q29Prepositions

He has a coat ____ five pockets.

aof
babout
cwith
din

Answer (c): 'With' shows possession of a feature: a coat with five pockets.

Revise: Grammar and Usage (Class 11 notes)

Q30Idioms

To hit below the belt means:

ato use force
bto use unfair means
cto use energy
dto use leather

Answer (b): The idiom means to attack unfairly, against the rules.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q31Prepositions

I disapprove ____ his cheating on the exam.

aof
bat
cin
doff

Answer (a): The verb 'disapprove' is followed by the preposition 'of'.

Revise: Grammar and Usage (Class 11 notes)

Q32Phrasal verbs

The lights were ____ because the room was bright.

aPut off
btake off
cLeft off
dswitched off

Answer (d): 'Switched off' is the standard phrase for turning a light off. 'Take off' is wrong in form and 'left off' means stopped or omitted.

Revise: Grammar and Usage (Class 11 notes)

Q33Parts of speech

Which of the following is a noun?

aThicken
bimpoverish
cMercantile
dmercy

Answer (d): 'Mercy' is a noun. Thicken and impoverish are verbs and mercantile is an adjective.

Revise: Grammar and Usage (Class 11 notes)

Q34Parts of speech

Which of the underlined words is an adjective?

aSwimming is good for health.
bStudents are walking on the lawn.
cMany people like smoking.
dShe is taking knitting classes.

Answer (a): 'Good' describes 'swimming' and is a clear adjective. 'Lawn' is a noun; 'knitting' is a gerund used as a noun modifier.

Revise: Grammar and Usage (Class 11 notes)

Q35Voice

Which of the following is an active voice?

aThis work will be finished.
bThe suspect was seen.
cI know him.
dThe letter was posted.

Answer (c): In 'I know him' the subject performs the action. The others are passive.

Revise: Grammar and Usage (Class 11 notes)

Q36Subject-verb agreement

The memoranda ____ approved.

ahave been
bhas been
cwas
dis

Answer (a): 'Memoranda' is the plural of memorandum, so the plural verb 'have been' is used.

Revise: Grammar and Usage (Class 11 notes)

Q37Subject-verb agreement

Which of the following takes a singular verb?

apolice
bfurniture
cfamilies
dcommittees

Answer (b): 'Furniture' is an uncountable noun and takes a singular verb. Police is plural and the others are plural forms.

Revise: Grammar and Usage (Class 11 notes)

Q38Subject-verb agreement

Neither her nor they ____ going to the college.

ais
bare
chas
dwas

Answer (b): With 'neither...nor' the verb agrees with the nearer subject, 'they', so 'are'.

Revise: Grammar and Usage (Class 11 notes)

Q39Collective nouns

Which expression is incorrect?

aA pile of books
bA herd of cattle
cA herd of sheep
dA pack of wolves

Answer (c): The collective noun for sheep is a flock, not a herd. A herd of cattle, a pile of books and a pack of wolves are all correct.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q40Question tags

They daren't go ____?

adid they
bdo they
chasn't they
ddare they

Answer (d): 'Daren't' is a negative modal-like verb, so the positive question tag is 'dare they?'.

Revise: Grammar and Usage (Class 11 notes)

Q41Agreement with too/so

I am hungry and ____.

aShe is too
bthey are so
cso aren't they
dthey are too

Answer (d): 'They are too' completes the sentence meaning 'and they are hungry too'. The other options clash in subject or construction.

Revise: Grammar and Usage (Class 11 notes)

Q42Word stress

Which word has the stress on the first syllable?

aLikelihood
breligious
cfantastic
dorthography

Answer (a): LIKE-li-hood is stressed on the first syllable. Religious, fantastic and orthography are stressed on the second.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q43Syllables

How many syllables does the word 'economical' have?

afive
bfour
cthree
dsix

Answer (a): e-co-nom-i-cal has five syllables.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q44Pronunciation

The pair ____ has the same pronunciation.

apot, port
bso, sow
cpull, pool
ddid, dead

Answer (b): 'So' and 'sow' (to plant seeds) are both pronounced /soʊ/. The other pairs sound different.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q45Phonetics

The word 'they' has the same initial consonant sound as the word

aday
bdate
cthief
dthat

Answer (d): 'They' and 'that' both begin with the voiced sound /ð/.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q46Vocabulary

A professional horse rider is called

aJockey
brider
cCoach
dhorse courser

Answer (a): A jockey is a professional rider in horse races.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q47Antonyms

Give the opposite meaning of 'appropriate'.

aInevitable
blikely
cunsuitable
dsuitable

Answer (c): 'Appropriate' means suitable, so its opposite is unsuitable.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q48Synonyms

Select the right synonym of the word 'sporadic'.

aOccasional
bfrequently
ccontinuously
dnever ending

Answer (a): 'Sporadic' means happening at irregular, scattered times, i.e. occasional.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q49Punctuation

Which of the following is incorrectly punctuated?

aThe teacher said, "Honesty is the best policy".
bHe said to me "When did she come to the party"?
cThe man received a gift, the women, a book.
dThe man, whom he met, had excellent speech.

Answer (b): Option b is wrongly punctuated: it needs a comma after 'said to me' and the question mark belongs inside the quotation marks.

Revise: Grammar and Usage (Class 11 notes)

Q50Suffixes

The word 'father' takes the suffix:

a-is
b-some
c-ly
d-y

Answer (c): Father + ly gives the adjective 'fatherly'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Physics

Q51Dimensions

The dimensional formula for potential difference is

a$[ML^2T^{-3}I^{-1}]$
b$[ML^2T^{-3}I]$
c$[ML^2T^3I^{-1}]$
d$[ML^2T^{-2}I^{-2}]$

Answer (a): $V=\frac{W}{q}=\frac{ML^2T^{-2}}{IT}=ML^2T^{-3}I^{-1}$.

Revise: Physical Quantities (Class 11 notes)

Q52Motion under gravity

A stone is thrown vertically upward with a speed $u$ from the top of a tower and reaches the ground with a speed $3u$. The height of the tower is

a$\frac{3u^2}{g}$
b$\frac{4u^2}{g}$
c$\frac{6u^2}{g}$
d$\frac{9u^2}{g}$

Answer (b): Taking downward positive, $v^2=u^2+2gh$ gives $9u^2=u^2+2gh$, so $h=\frac{4u^2}{g}$.

Revise: Kinematics (Class 11 notes)

Q53Simple harmonic motion

The acceleration of a particle in SHM is

aAlways zero
balways constant
cMaximum at extreme position
dMaximum at the equilibrium position

Answer (c): $a=-\omega^2x$, which is largest when the displacement is largest, at the extreme position.

Revise: Periodic Motion (Class 12 notes)

Q54Thermal expansion

An iron ball is heated. The percentage increase will be largest in

avolume
bdensity
cdiameter
dsurface area

Answer (a): Fractional increase is $\alpha\Delta T$ for length, $2\alpha\Delta T$ for area and $3\alpha\Delta T$ for volume, so volume increases most.

Revise: Thermal Expansion (Class 11 notes)

Q55Elasticity

Two wires A and B of the same material have lengths in the ratio $1:2$ and diameters in the ratio $2:1$. If they are pulled by the same force, their increase in length will be in the ratio

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

Answer (c): $\Delta L=\frac{FL}{AY}\propto\frac{L}{d^2}$. Ratio $=\frac{1/4}{2/1}=\frac18$.

Revise: Elasticity (Class 11 notes)

Q56Equation of continuity

Water flows through a tube of non-uniform cross section. If the radius at the entrance and exit is $3:2$, the ratio of velocity of liquid entering and leaving the tube is

a$8:27$
b$4:9$
c$9:4$
d$1:1$

Answer (b): Continuity: $Av=$ constant, so $v\propto\frac{1}{r^2}$. $\frac{v_1}{v_2}=\frac{2^2}{3^2}=\frac49$.

Revise: Fluid Statics (Class 12 notes)

Q57Thermodynamic processes

The thermodynamic process in which the pressure of the system remains constant is called

aisothermal
badiabatic
cisochoric
disobaric

Answer (d): Constant pressure is an isobaric process.

Revise: First Law of Thermodynamics (Class 12 notes)

Q58Calorimetry

50 g of ice at $-6^\circ$C is dropped into water at $0^\circ$C. How many grams of water freeze? Specific heat capacity of ice $=2000,J,kg^{-1}C^{-1}$.

a1.785 g
b4.25 g
c3.16 g
d9.33 g

Answer (a): Heat to warm the ice: $0.05\times2000\times6=600$ J. Mass frozen $=\frac{600}{3.36\times10^5}\text{ kg}\approx1.785$ g.

Revise: Quantity of Heat (Class 11 notes)

Q59Concave mirror

The image of an object placed at the focus of a concave mirror is at

af
bInfinity
c2f
df/2

Answer (b): Rays from the focus become parallel after reflection, so the image forms at infinity.

Revise: Reflection at Curved Mirrors (Class 11 notes)

Q60Carnot engine

The temperature of source and sink of a Carnot engine are 400 K and 300 K respectively. What is its efficiency?

a100%
b75%
c33.3%
d25%

Answer (d): $\eta=1-\frac{T_2}{T_1}=1-\frac{300}{400}=0.25=25%$.

Revise: Second Law of Thermodynamics (Class 12 notes)

Q61Refractive index

The refractive index of air with respect to glass is $2/3$. The refractive index of diamond with respect to air is $12/5$. Then the refractive index of glass with respect to diamond will be

a $5/8$
b $8/9$
c $5/18$
d $18/5$

Answer (a): ${}_a n_g=\frac32$. ${}_d n_g=\frac{{}_a n_g}{{}_a n_d}=\frac{3/2}{12/5}=\frac{15}{24}=\frac58$.

Revise: Refraction at Plane Surface (Class 11 notes)

Q62Lens maker's formula

The focal length of a double convex lens for which the radius of curvature of each surface is $R$ will be ($\mu=1.5$)

a$R/2$
b $R$
c $2R$
d $4R$

Answer (b): $\frac1f=(\mu-1)\left(\frac2R\right)=0.5\cdot\frac2R=\frac1R$, so $f=R$.

Revise: Lenses (Class 11 notes)

Q63Refraction

Light of wavelength $7200$ Å in air has a wavelength in glass equal to (refractive index of glass with respect to air $=1.5$)

a7200 Å
b4800 Å
c1080 Å
d10800 Å

Answer (b): Wavelength in glass $=\lambda/n=7200/1.5=4800$ Å.

Revise: Refraction at Plane Surface (Class 11 notes)

Q64Capacitor combinations

Three capacitors of $3\mu F$, $9\mu F$ and $18\mu F$ are connected first in series and then in parallel. The ratio of $C$ equivalent capacitance in two cases ($C_s/C_p$) will be

a$1:15$
b$15:1$
c$1:1$
d$1:3$

Answer (a): $\frac1{C_s}=\frac13+\frac19+\frac1{18}=\frac12$, so $C_s=2\mu F$. $C_p=30\mu F$. Ratio $=\frac{2}{30}=1:15$.

Revise: Capacitor (Class 11 notes)

Q65Resistor combinations

Three equal resistors each of resistance $r$ are connected to form a triangle. The equivalent resistance across any two corners of the triangle is

a $2r$
b$r/3$
c$2r/3$
d $3r$

Answer (c): Across two corners, one resistor $r$ is in parallel with two in series ($2r$): $\frac{r\cdot2r}{3r}=\frac{2r}{3}$.

Revise: DC Circuit (Class 11 notes)

Q66Electric power

The resistances of two lamps are in the ratio $1:2$. Their wattage will be in the ratio of

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

Answer (b): On the same supply $P=\frac{V^2}{R}\propto\frac1R$, so the ratio is $2:1$.

Revise: DC Circuit (Class 11 notes)

Q67Inductor energy

The energy stored in a 50 mH inductor carrying a current of 4 A is

a0.1 J
b0.4 J
c0.3 J
d0.01 J

Answer (b): $U=\frac12LI^2=\frac12(0.05)(16)=0.4$ J.

Revise: Electromagnetic Induction (Class 12 notes)

Q68LCR resonance

The alternating current in an LCR circuit is maximum when

a$X_L=0$
b$X_C=0$
c$X_L=X_C$
d$\sqrt{X_L^2+X_C^2}=0$

Answer (c): At resonance $X_L=X_C$, impedance is minimum ($=R$) and current is maximum.

Revise: Alternating Currents (Class 12 notes)

Q69de Broglie wavelength

A particle of mass $10^{-31}$ kg is moving with a speed of $10^5$ m/s. The de Broglie wavelength of the particle is

a$6.63\times10^{-8}$ m
b $6.63$ Å
c $66.3$ Å
d$6.63\times10^{-7}$ m

Answer (a): $\lambda=\frac{h}{mv}=\frac{6.63\times10^{-34}}{10^{-31}\times10^5}=6.63\times10^{-8}$ m.

Revise: Quantization of Energy (Class 12 notes)

Q70Interference

Two waves of the same wavelength and amplitude interfere to give a minimum when their phase difference is

a $\pi$
b$\pi/2$
c$3\pi/2$
d $0$

Answer (a): Destructive interference needs a phase difference of an odd multiple of $\pi$; the smallest given is $\pi$.

Revise: Interference (Class 12 notes)

Q71X-rays

Hard X-rays as compared to soft X-rays have

aHigher intensity
blower frequency
cHigher frequency
dhigher speed

Answer (c): Hard X-rays have shorter wavelength and so higher frequency and penetrating power. All X-rays travel at $c$.

Revise: Electrons (Class 12 notes)

Q72Mass defect

The mass of an

\alpha

-particle is

aEqual to the mass of four protons
bEqual to the mass of four neutrons
cEqual to the masses of 2 protons and 2 neutrons
dLess than the sum of masses of 2 protons and 2 neutrons

Answer (d): An alpha particle is a helium nucleus; its mass is less than its separate nucleons by the mass defect (binding energy).

Revise: Radioactivity and Nuclear Reaction (Class 12 notes)

Q73Transistor amplifier

A common emitter transistor amplifier has a current gain of 50. If the load resistance is $4,k\Omega$ and the input resistance is $500,\Omega$, the voltage gain of the amplifier is

a400
b6.2
c500
d300

Answer (a): $A_v=\beta\frac{R_L}{R_{in}}=50\times\frac{4000}{500}=400$.

Revise: Semiconductor Devices (Class 12 notes)

Q74Resonance in pipes

A tube closed at one end has a length 1 meter. The air column in the pipe can resonate for sound of frequency ($v=320,ms^{-1}$)

a166 Hz
b249 Hz
c575 Hz
d80 Hz

Answer (d): Closed pipe: $f_1=\frac{v}{4L}=\frac{320}{4}=80$ Hz (other resonances are odd multiples: 240, 400 Hz...).

Revise: Wave in Pipes and Strings (Class 12 notes)

Q75Wave equation

A displacement wave is represented by $y=0.25\sin(500t-0.0025x)$, where $y$, $t$ and $x$ are in cm, second and meter respectively. The wavelength of the wave is

a $20\pi$ m
b $40\pi$ m
c $60\pi$ m
d $80\pi$ m

Revise: Wave Motion (Class 12 notes)

Chemistry

Q76Preparation of alkanes

The gas obtained by adding water on aluminium carbide is

aEthyne
bethane
cmethane
dethane

Answer (c): $\ce{Al4C3 + 12H2O -> 4Al(OH)3 + 3CH4}$, so methane is released.

Revise: Hydrocarbons (Class 11 notes)

Q77Alcohols

The mixture of HCl and $ZnCl_2$ is known as

aTollen's reagent
bBaeyer's reagent
cLucas reagent
dNessler's reagent

Answer (c): Concentrated HCl with anhydrous $\ce{ZnCl2}$ is Lucas reagent, used to distinguish 1, 2 and 3 degree alcohols.

Revise: Alcohols (Class 12 notes)

Q78Carboxylic acid nomenclature

The IUPAC name of n-valeric acid is

aPentanoic acid
bbutanoic acid
cPropanoic acid
dethanoic acid

Answer (a): Valeric acid is $\ce{CH3(CH2)3COOH}$, a five carbon acid: pentanoic acid.

Revise: Carboxylic Acids (Class 12 notes)

Q79Qualitative organic analysis

A blood red coloration of ferric sulphocyanide obtained by addition of ferric chloride in sodium extract confirms the presence of

aSulphur
bnitrogen
cboth a and b
dhalogens

Answer (c): Blood red $\ce{Fe(SCN)3}$ forms when both N and S are present in the sodium fusion extract (as NaSCN).

Revise: Fundamental Principles (Class 11 notes)

Q80Boiling point and hydrogen bonding

Which of the following compounds has the highest boiling point?

a$CH_4$
b$CH_3Cl$
c$CH_3Br$
d$CH_3OH$

Answer (d): Methanol has hydrogen bonding, which gives a much higher boiling point than the other compounds.

Revise: Chemical Bonding (Class 11 notes)

Q81Aldehydes

The compound that undergoes Cannizzaro reaction is

a$CH_3COOH$
b$C_2H_5CHO$
cHCHO
d$CH_3OCH_3$

Answer (c): Cannizzaro reaction needs an aldehyde with no alpha hydrogen. HCHO has none, so it qualifies.

Revise: Aldehydes and Ketones (Class 12 notes)

Q82Aromatic hydrocarbons

Benzene is converted to toluene by

aFriedel Craft reaction
bGrignard reaction
cWurtz reaction
dPerkin reaction

Answer (a): $\ce{C6H6 + CH3Cl ->[AlCl3] C6H5CH3 + HCl}$ is Friedel-Crafts alkylation.

Revise: Aromatic Hydrocarbons (Class 11 notes)

Q83Amines

The compound that gives positive carbylamine reaction is

a$(CH_3)_2NH$
b$(CH_3)_3N$
c$(CH_3)_4N^+$
d$(CH_3)NH_2$

Answer (d): Only primary amines give the carbylamine (isocyanide) test; $\ce{CH3NH2}$ is primary.

Revise: Amines (Class 12 notes)

Q84Metallurgy

Hematite is an ore of

aSilver
bIron
cMercury
dCopper

Answer (b): Hematite is $\ce{Fe2O3}$, an iron ore.

Revise: Chemistry of Metals (Class 11 notes)

Q85Oxides

$Na_2O$ is a

aNeutral oxide
bacidic oxide
cBasic oxide
damphoteric oxide

Answer (c): Oxides of strongly electropositive metals like sodium give alkali with water, so they are basic.

Revise: Classification of Elements (Class 11 notes)

Q86Periodic trends

Which of the following elements has highest electronegativity?

aBromine
bIodine
cChlorine
dFluorine

Answer (d): Electronegativity decreases down the halogen group, so fluorine is highest.

Revise: Classification of Elements (Class 11 notes)

Q87Compounds of metals

Zinc sulphate ($ZnSO_4\cdot7H_2O$) is also called

aWhite vitriol
bGreen vitriol
cBlue vitriol
dcorrosive sublimate

Answer (a): $\ce{ZnSO4.7H2O}$ is white vitriol. Green is $\ce{FeSO4.7H2O}$, blue is $\ce{CuSO4.5H2O}$.

Revise: Chemistry of Metals (Class 11 notes)

Q88Alloys

Brass is an alloy of

aCopper and Zinc
bCopper and Nickel
cCopper and Tin
dCopper and Lead

Answer (a): Brass is copper with zinc; bronze is copper with tin.

Revise: Chemistry of Metals (Class 11 notes)

Q89Ores

The formula of dolomite is

a$CaCO_3$
b$CaCO_3\cdot MgCO_3$
c$CaSO_4\cdot2H_2O$
d$CaF_2$

Answer (b): Dolomite is the double carbonate of calcium and magnesium.

Revise: Chemistry of Metals (Class 11 notes)

Q90Electronic configuration

The general electronic configuration of zinc is

a$[Ar]4s^23d^{10}$
b$[Ar]4s^13d^{10}$
c$[Ar]4s^23d^8$
d$[Ar]4s^23d^7$

Answer (a): Zinc ($Z=30$) has a full d subshell: $[Ar]3d^{10}4s^2$.

Revise: Transition Metals (Class 12 notes)

Q91Equivalent weight

Equivalent weight of $KMnO_4$ in neutral medium is

a52.6
b158.0
c31.6
d63.0

Answer (a): In neutral medium Mn changes from $+7$ to $+4$ (3 electrons): $\frac{158}{3}=52.67$.

Revise: Volumetric Analysis (Class 12 notes)

Q92Atomic models

Bohr's model was modified by

aRutherford
bSomerfield
cDalton
dPauli

Answer (b): Sommerfeld introduced elliptical orbits to improve Bohr's model.

Revise: Atomic Structure (Class 11 notes)

Q93Mole concept

How many oxygen atoms are there in 8.0 g of oxygen atoms?

a$3.011\times10^{23}$
b$3.011\times10^{22}$
c$3.011\times10^{20}$
d$3.011\times10^{19}$

Answer (a): Moles $=\frac{8}{16}=0.5$. Atoms $=0.5\times6.022\times10^{23}=3.011\times10^{23}$.

Revise: Stoichiometry (Class 11 notes)

Q94pH

What is the pH of 0.001 M HCl?

a2.0
b3.0
c4.0
d5.0

Answer (b): HCl is a strong acid: $[H^+]=10^{-3}$, so pH $=3$.

Revise: Ionic Equilibrium (Class 12 notes)

Q95Chemical kinetics

The rate of reaction is independent of

aTemperature
bconcentration
cParticle size of reactant
dMolecularity

Answer (d): Rate depends on temperature, concentration and surface area, but molecularity is a property of the elementary step, not a rate factor.

Revise: Chemical Kinetics (Class 12 notes)

Q96Conductance

The CGS unit of specific conductance is

aSiemen $cm^{-1}$
b$ohm^{-1}cm^2equiv^{-1}$
cSiemen
d$ohm^{-1}$

Answer (a): Specific conductance is $\frac1\rho$, with unit $ohm^{-1}cm^{-1}$, i.e. Siemen $cm^{-1}$.

Revise: Electrochemistry (Class 12 notes)

Q97Thermochemistry

Hess's law deals with

aTotal change in heat of reaction
bRate of reaction
cEquilibrium constant of reaction
dInfluence on pressure of volume of gas

Answer (a): Hess's law says the total heat change of a reaction is the same regardless of the path taken.

Revise: Chemical Thermodynamic (Class 12 notes)

Q98Ionic equilibrium

The degree of dissociation of an electrolyte

aDecreases with dilution
bIncreases with dilution
cMay increase or decrease with dilution
dIs not affected by dilution

Answer (b): By Ostwald's dilution law, $\alpha$ rises as concentration falls, so the degree of dissociation increases with dilution.

Revise: Ionic Equilibrium (Class 12 notes)

Q99Gas laws and moles

The weight of 100 ml of $NH_3$ gas at NTP is

a0.0759 g
b0.0579 g
c0.0459 g
d0.0359 g

Answer (a): Moles $=\frac{0.1}{22.4}=0.00446$; mass $=0.00446\times17=0.0759$ g.

Revise: Stoichiometry (Class 11 notes)

Q100Laws of chemical combination

The law of multiple proportions was given by

aRichter
bJohn Dalton
cAlbert Einstein
dGay Lussac

Answer (b): Dalton proposed the law of multiple proportions (1803).

Revise: Stoichiometry (Class 11 notes)

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Mathematics

Q1Sets

If A and B are any two sets, then

A-(A-B)

is equal toIf A and B are any two sets, then $A-(A-B)$ is equal to

a $B-A$ $B-A$
b $A\cap B$ $A\cap B$
c $A\cup B$ $A\cup B$
d $\phi$

Answer (b): $A-B$ is the part of $A$ outside $B$ . Removing it from $A$ leaves the part of $A$ inside $B$ , which is $A\cap B$ .$A-B$ is the part of $A$ outside $B$. Removing it from $A$ leaves the part of $A$ inside $B$, which is $A\cap B$.

Revise: Algebra (Class 11 notes)

Q2Functions

The range of the function

y=\sqrt{a^2-x^2}

a>0

is equal toThe range of the function $y=\sqrt{a^2-x^2}$, $a>0$ is equal to

a $[-a,a]$ $[-a,a]$
b $(-a,a)$ $(-a,a)$
c $[0,a]$ $[0,a]$
d $(0,a)$ $(0,a)$

Answer (c): $y=\sqrt{a^2-x^2}$ is defined for $-a\le x\le a$ and takes values from $0$ (at $x=\pm a$ ) up to $a$ (at $x=0$ ), so the range is $[0,a]$ .$y=\sqrt{a^2-x^2}$ is defined for $-a\le x\le a$ and takes values from $0$ (at $x=\pm a$) up to $a$ (at $x=0$), so the range is $[0,a]$.

Revise: Algebra (Class 11 notes)

Q3Logarithms

What is the value of

\log_a\sqrt{a^3\sqrt{a^2}}

?What is the value of $\log_a\sqrt{a^3\sqrt{a^2}}$ ?

a $4$
b $3$
c $2$
d $1$

Answer (c): $\sqrt{a^2}=a$ , so the expression is $\sqrt{a^4}=a^2$ . Hence $\log_a a^2=2$ .$\sqrt{a^2}=a$, so the expression is $\sqrt{a^4}=a^2$. Hence $\log_a a^2=2$.

Revise: Algebra (Class 11 notes)

Q4Matrices

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

, then

A^{100}

is equal toIf $A=\begin{pmatrix}0&1\-1&0\end{pmatrix}$, then $A^{100}$ is equal to

a $1$
b $0$
c $-1$
dNone

Answer (a): $A^2=-I$ , so $A^4=I$ and $A^{100}=(A^4)^{25}=I$ , the unit matrix, which the option '1' stands for. The printed 1 is read as the identity matrix.$A^2=-I$, so $A^4=I$ and $A^{100}=(A^4)^{25}=I$, the unit matrix, which the option '1' stands for. The printed 1 is read as the identity matrix.

Revise: Algebra (Class 11 notes)

Q5Sequences and series

a^x=b^y=c^z

and

a,b,c

are in G.P., then

x,y,z

are inIf $a^x=b^y=c^z$ and $a,b,c$ are in G.P., then $x,y,z$ are in

aG.P.
bA.P.
cH.P.
dNone

Answer (c): Let each equal $k$ : $\ln a=\frac{\ln k}{x}$ etc. $b^2=ac$ gives $\frac{2}{y}=\frac1x+\frac1z$ , so $x,y,z$ are in H.P.Let each equal $k$: $\ln a=\frac{\ln k}{x}$ etc. $b^2=ac$ gives $\frac{2}{y}=\frac1x+\frac1z$, so $x,y,z$ are in H.P.

Revise: Algebra (Class 11 notes)

Q6Limits

\lim_{x\to0}\frac{a^x-b^x}{x}

is equal to$\lim_{x\to0}\frac{a^x-b^x}{x}$ is equal to

a $0$
b $\log(ab)$ $\log(ab)$
c $\log(a/b)$ $\log(a/b)$
d $\log(b/a)$ $\log(b/a)$

Answer (c): Split as $\frac{a^x-1}{x}-\frac{b^x-1}{x}\to\ln a-\ln b=\ln(a/b)$ .Split as $\frac{a^x-1}{x}-\frac{b^x-1}{x}\to\ln a-\ln b=\ln(a/b)$.

Revise: Calculus (Class 12 notes)

Q7Derivatives

The derivative of

y=5^x

with respect to

x

is equal toThe derivative of $y=5^x$ with respect to $x$ is equal to

a $5^x\log_e5$ $5^x\log_e5$
b $5^x$ $5^x$
c $\log_e5$ $\log_e5$
d $5\log_e5$ $5\log_e5$

Answer (a): $\frac{d}{dx}a^x=a^x\ln a$ , so $\frac{d}{dx}5^x=5^x\ln5$ .$\frac{d}{dx}a^x=a^x\ln a$, so $\frac{d}{dx}5^x=5^x\ln5$.

Revise: Calculus (Class 12 notes)

Q8Domain of a function

The function

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

x\in R

x\neq0

is defined forThe function $f(x)=x-\frac{1}{x^2}$, $x\in R$, $x\neq0$ is defined for

a $(-\infty,0)\cup(0,\infty)$ $(-\infty,0)\cup(0,\infty)$
b $(-\infty,0]\cup[0,\infty)$ $(-\infty,0]\cup[0,\infty)$
c $[-1,1]$ $[-1,1]$
d $(-\infty,\infty)$ $(-\infty,\infty)$

Answer (a): The only restriction is $x\neq0$ (division by zero), so the domain is all reals except $0$ .The only restriction is $x\neq0$ (division by zero), so the domain is all reals except $0$.

Revise: Algebra (Class 11 notes)

Q9Integration

The integral

\int\frac{e^x\,dx}{e^x+1}

is equal toThe integral $\int\frac{e^x,dx}{e^x+1}$ is equal to

a $\log(e^x+1)+C$ $\log(e^x+1)+C$
b $\frac{-1}{e^{2x}+1}+C$ $\frac{-1}{e^{2x}+1}+C$
c $\frac{-1}{2(e^x+e^{-x})}+C$ $\frac{-1}{2(e^x+e^{-x})}+C$
d $\frac{-1}{2(e^{2x}+1)}+C$ $\frac{-1}{2(e^{2x}+1)}+C$

Answer (a): Put $u=e^x+1$ , $du=e^x dx$ . The integral becomes $\int\frac{du}{u}=\ln(e^x+1)+C$ .Put $u=e^x+1$, $du=e^x dx$. The integral becomes $\int\frac{du}{u}=\ln(e^x+1)+C$.

Revise: Calculus (Class 12 notes)

Q10Quadratic equations

For what value of

k

will the equation

5x^2-kx+45=0

have equal roots?For what value of $k$ will the equation $5x^2-kx+45=0$ have equal roots?

a $0$
b $\pm3$
c $\pm30$
d $\pm33$

Answer (c): Equal roots need $D=0$ : $k^2-4(5)(45)=0$ , so $k^2=900$ and $k=\pm30$ .Equal roots need $D=0$: $k^2-4(5)(45)=0$, so $k^2=900$ and $k=\pm30$.

Revise: Algebra (Class 11 notes)

Q11Quadratic equations

The quadratic equation whose one root is

2+\sqrt3

isThe quadratic equation whose one root is $2+\sqrt3$ is

a $x^2+4x+1=0$ $x^2+4x+1=0$
b $x^2-4x+1=0$ $x^2-4x+1=0$
c $x^2-4x-1=0$ $x^2-4x-1=0$
d $-x^2-4x-1=0$ $-x^2-4x-1=0$

Answer (b): The conjugate root is $2-\sqrt3$ . Sum $=4$ , product $=4-3=1$ , so $x^2-4x+1=0$ .The conjugate root is $2-\sqrt3$. Sum $=4$, product $=4-3=1$, so $x^2-4x+1=0$.

Revise: Algebra (Class 11 notes)

Q12Straight lines

The distance between the parallel lines

y-2x=4

and

6x-3y=5

isThe distance between the parallel lines $y-2x=4$ and $6x-3y=5$ is

a $\frac{1}{\sqrt{45}}$ $\frac{1}{\sqrt{45}}$
b $\frac{7}{\sqrt{45}}$ $\frac{7}{\sqrt{45}}$
c $\frac{17}{\sqrt{45}}$ $\frac{17}{\sqrt{45}}$
d $\frac{17}{2\sqrt{45}}$ $\frac{17}{2\sqrt{45}}$

Answer (c): Write the second as $2x-y-\frac53=0$ and the first as $2x-y+4=0$ . Distance $=\frac{|4+5/3|}{\sqrt5}=\frac{17}{3\sqrt5}=\frac{17}{\sqrt{45}}$ .Write the second as $2x-y-\frac53=0$ and the first as $2x-y+4=0$. Distance $=\frac{|4+5/3|}{\sqrt5}=\frac{17}{3\sqrt5}=\frac{17}{\sqrt{45}}$.

Revise: Analytic geometry (Class 11 notes)

Q13Circle

Radius of the circle

x^2+y^2-3x+2y-\frac34=0

isRadius of the circle $x^2+y^2-3x+2y-\frac34=0$ is

a $2$
b $1$
c $4$
d $3$

Answer (a): $r^2=g^2+f^2-c=\frac94+1+\frac34=4$ , so $r=2$ .$r^2=g^2+f^2-c=\frac94+1+\frac34=4$, so $r=2$.

Revise: Analytic geometry (Class 11 notes)

Q14Complex numbers

The absolute value of the complex number

(1+i)^{-1}

isThe absolute value of the complex number $(1+i)^{-1}$ is

a $1$
b $\sqrt2$ $\sqrt2$
c $\frac{1}{\sqrt2}$ $\frac{1}{\sqrt2}$
d $2$

Answer (c): $|(1+i)^{-1}|=\frac{1}{|1+i|}=\frac{1}{\sqrt2}$ .$|(1+i)^{-1}|=\frac{1}{|1+i|}=\frac{1}{\sqrt2}$.

Revise: Algebra (Class 11 notes)

Q15Complex numbers (De Moivre)

z=\cos\theta+i\sin\theta

, then

z^n+\frac{1}{z^n}

is equal toIf $z=\cos\theta+i\sin\theta$, then $z^n+\frac{1}{z^n}$ is equal to

a $-2\cos n\theta$ $-2\cos n\theta$
b $2\cos n\theta$ $2\cos n\theta$
c $2\sin n\theta$ $2\sin n\theta$
d $-2\sin n\theta$ $-2\sin n\theta$

Answer (b): By De Moivre, $z^n=\cos n\theta+i\sin n\theta$ and $z^{-n}=\cos n\theta-i\sin n\theta$ . The sum is $2\cos n\theta$ .By De Moivre, $z^n=\cos n\theta+i\sin n\theta$ and $z^{-n}=\cos n\theta-i\sin n\theta$. The sum is $2\cos n\theta$.

Revise: Algebra (Class 11 notes)

Q16Sequences and series

The

n^{th}

term of the series

2+6+12+20+\dots

isThe $n^{th}$ term of the series $2+6+12+20+\dots$ is

a $n(n+1)$ $n(n+1)$
b $(n+1)(n+2)$ $(n+1)(n+2)$
c $n(n-1)$ $n(n-1)$
d $n$

Answer (a): The terms are $1\cdot2,\ 2\cdot3,\ 3\cdot4,\ 4\cdot5$ , so $t_n=n(n+1)$ .The terms are $1\cdot2,\ 2\cdot3,\ 3\cdot4,\ 4\cdot5$, so $t_n=n(n+1)$.

Revise: Algebra (Class 11 notes)

Q17Infinite series

|x|<1

and

y=x+x^2+x^3+x^4+\dots+\infty

, then

x

is equal toIf $|x|<1$ and $y=x+x^2+x^3+x^4+\dots+\infty$, then $x$ is equal to

a $\frac{y}{1-y}$ $\frac{y}{1-y}$
b $\frac{y}{y-1}$ $\frac{y}{y-1}$
c $\frac{y+1}{y}$ $\frac{y+1}{y}$
d $\frac{y}{1+y}$ $\frac{y}{1+y}$

Answer (d): The infinite G.P. gives $y=\frac{x}{1-x}$ . Then $y-xy=x$ , so $x(1+y)=y$ and $x=\frac{y}{1+y}$ .The infinite G.P. gives $y=\frac{x}{1-x}$. Then $y-xy=x$, so $x(1+y)=y$ and $x=\frac{y}{1+y}$.

Revise: Algebra (Class 11 notes)

Q18Chain rule

The derivative of

y=\cos(\cos\sqrt x)

isThe derivative of $y=\cos(\cos\sqrt x)$ is

a $\frac{\sin(\cos\sqrt x)\cdot\sin\sqrt x}{2\sqrt x}$ $\frac{\sin(\cos\sqrt x)\cdot\sin\sqrt x}{2\sqrt x}$
b $\sin(\cos\sqrt x)$ $\sin(\cos\sqrt x)$
c $\sin(\sin\sqrt x)$ $\sin(\sin\sqrt x)$
d $\frac{\sin(\cos\sqrt x)}{2\sqrt x}$ $\frac{\sin(\cos\sqrt x)}{2\sqrt x}$

Answer (a): Chain rule: $y'=-\sin(\cos\sqrt x)\cdot(-\sin\sqrt x)\cdot\frac{1}{2\sqrt x}=\frac{\sin(\cos\sqrt x)\sin\sqrt x}{2\sqrt x}$ .Chain rule: $y'=-\sin(\cos\sqrt x)\cdot(-\sin\sqrt x)\cdot\frac{1}{2\sqrt x}=\frac{\sin(\cos\sqrt x)\sin\sqrt x}{2\sqrt x}$.

Revise: Calculus (Class 12 notes)

Q19Inverse trigonometric functions

3\cos^{-1}x

is equal to$3\cos^{-1}x$ is equal to

a $\cos^{-1}(3x-4x^2)$ $\cos^{-1}(3x-4x^2)$
b $\cos^{-1}(4x^3-3x)$ $\cos^{-1}(4x^3-3x)$
c $\cos^{-1}(4x-3x^3)$ $\cos^{-1}(4x-3x^3)$
d $\cos^{-1}(3x^3-4x)$ $\cos^{-1}(3x^3-4x)$

Answer (b): Put $x=\cos\theta$ . Then $\cos3\theta=4\cos^3\theta-3\cos\theta$ , so $3\theta=\cos^{-1}(4x^3-3x)$ .Put $x=\cos\theta$. Then $\cos3\theta=4\cos^3\theta-3\cos\theta$, so $3\theta=\cos^{-1}(4x^3-3x)$.

Revise: Trigonometry (Class 11 notes)

Q20Trigonometric equations

Solution of

\tan ax=\cot bx

isSolution of $\tan ax=\cot bx$ is

a $\frac{2n+1}{a+b}\cdot\frac\pi4$ $\frac{2n+1}{a+b}\cdot\frac\pi4$
b $\frac{2n-1}{a-b}\cdot\frac\pi2$ $\frac{2n-1}{a-b}\cdot\frac\pi2$
c $\frac{2n+1}{a+b}\cdot\frac\pi2$ $\frac{2n+1}{a+b}\cdot\frac\pi2$
d $\frac\pi2$ $\frac\pi2$

Answer (c): $\tan ax=\tan(\frac\pi2-bx)$ gives $ax=n\pi+\frac\pi2-bx$ , so $x=\frac{(2n+1)}{a+b}\cdot\frac\pi2$ .$\tan ax=\tan(\frac\pi2-bx)$ gives $ax=n\pi+\frac\pi2-bx$, so $x=\frac{(2n+1)}{a+b}\cdot\frac\pi2$.

Revise: Trigonometry (Class 11 notes)

Q21Determinants

What is the value of

\begin{vmatrix}1&\omega&\omega^2\\\omega&\omega^2&1\\\omega^2&1&\omega\end{vmatrix}

, where

\omega

is an imaginary cube root of unity?What is the value of $\begin{vmatrix}1&\omega&\omega^2\\omega&\omega^2&1\\omega^2&1&\omega\end{vmatrix}$, where $\omega$ is an imaginary cube root of unity?

a $1$
b $0$
c $3$
d $2$

Answer (b): Add all columns to the first: each row sum is $1+\omega+\omega^2=0$ , so the first column becomes zero and the determinant is $0$ .Add all columns to the first: each row sum is $1+\omega+\omega^2=0$, so the first column becomes zero and the determinant is $0$.

Revise: Algebra (Class 11 notes)

Q22Pair of straight lines

The single equation representing the pair of lines

y=x

and

y=-x

isThe single equation representing the pair of lines $y=x$ and $y=-x$ is

a $y^2-x^2=0$ $y^2-x^2=0$
b $y-x=0$ $y-x=0$
c $x-y=0$ $x-y=0$
d $x^2+y^2=0$ $x^2+y^2=0$

Answer (a): Multiply $(y-x)(y+x)=0$ to get $y^2-x^2=0$ .Multiply $(y-x)(y+x)=0$ to get $y^2-x^2=0$.

Revise: Analytic geometry (Class 11 notes)

Q23Sets and intervals

Let

A=[-3,2]

and

B=[2,3]

. Then

A-B

is equal toLet $A=[-3,2]$ and $B=[2,3]$. Then $A-B$ is equal to

a $[-3,3)$ $[-3,3)$
b $[-3,2)$ $[-3,2)$
c $(-2,2)$ $(-2,2)$
d $(-2,1)$ $(-2,1)$

Answer (b): $A-B$ removes the point $2$ (the only common point) from $A$ , leaving $[-3,2)$ .$A-B$ removes the point $2$ (the only common point) from $A$, leaving $[-3,2)$.

Revise: Algebra (Class 11 notes)

Q24Continuity

\lim_{x\to0^-}f(x)\neq\lim_{x\to0^+}f(x)

, then

f(x)

is said to haveIf $\lim_{x\to0^-}f(x)\neq\lim_{x\to0^+}f(x)$, then $f(x)$ is said to have

ainfinite discontinuity
bremovable discontinuity
cjump discontinuity
dnone

Answer (c): Both one-sided limits exist but differ, which is a jump discontinuity.

Revise: Calculus (Class 12 notes)

Q25Area under a curve

The area enclosed by the curve

y=3x

, the x-axis and the ordinates

x=0

x=4

isThe area enclosed by the curve $y=3x$, the x-axis and the ordinates $x=0$, $x=4$ is

a $12$
b $16$
c $20$
d $24$

Answer (d): Area $=\int_0^4 3x\,dx=\frac32x^2\Big|_0^4=24$ .Area $=\int_0^4 3x,dx=\frac32x^2\Big|_0^4=24$.

Revise: Calculus (Class 12 notes)

English

Q26Vocabulary

Inscription on a tomb is called

aEpitaph
bcemetery
cMorgue
ddemagogue

Answer (a): An epitaph is the text written on a tombstone in memory of the dead.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q27Phrasal verbs

After he finished the exam, he ____ to the teacher.

aHanded over it
bhanded it over
chanded it out
dhanded out it

Answer (b): With a pronoun object, a phrasal verb is split: 'handed it over'. 'Handed over it' is wrong.

Revise: Grammar and Usage (Class 11 notes)

Q28Phrasal verbs

Every week she ____ her sister in her village to talk to her.

aCalls over
bcalls on
ccalls out
dcalls up

Answer (b): 'Call on' means to visit a person, which fits visiting her sister in the village.

Revise: Grammar and Usage (Class 11 notes)

Q29Prepositions

He has a coat ____ five pockets.

aof
babout
cwith
din

Answer (c): 'With' shows possession of a feature: a coat with five pockets.

Revise: Grammar and Usage (Class 11 notes)

Q30Idioms

To hit below the belt means:

ato use force
bto use unfair means
cto use energy
dto use leather

Answer (b): The idiom means to attack unfairly, against the rules.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q31Prepositions

I disapprove ____ his cheating on the exam.

aof
bat
cin
doff

Answer (a): The verb 'disapprove' is followed by the preposition 'of'.

Revise: Grammar and Usage (Class 11 notes)

Q32Phrasal verbs

The lights were ____ because the room was bright.

aPut off
btake off
cLeft off
dswitched off

Answer (d): 'Switched off' is the standard phrase for turning a light off. 'Take off' is wrong in form and 'left off' means stopped or omitted.

Revise: Grammar and Usage (Class 11 notes)

Q33Parts of speech

Which of the following is a noun?

aThicken
bimpoverish
cMercantile
dmercy

Answer (d): 'Mercy' is a noun. Thicken and impoverish are verbs and mercantile is an adjective.

Revise: Grammar and Usage (Class 11 notes)

Q34Parts of speech

Which of the underlined words is an adjective?

aSwimming is good for health.
bStudents are walking on the lawn.
cMany people like smoking.
dShe is taking knitting classes.

Answer (a): 'Good' describes 'swimming' and is a clear adjective. 'Lawn' is a noun; 'knitting' is a gerund used as a noun modifier.

Revise: Grammar and Usage (Class 11 notes)

Q35Voice

Which of the following is an active voice?

aThis work will be finished.
bThe suspect was seen.
cI know him.
dThe letter was posted.

Answer (c): In 'I know him' the subject performs the action. The others are passive.

Revise: Grammar and Usage (Class 11 notes)

Q36Subject-verb agreement

The memoranda ____ approved.

ahave been
bhas been
cwas
dis

Answer (a): 'Memoranda' is the plural of memorandum, so the plural verb 'have been' is used.

Revise: Grammar and Usage (Class 11 notes)

Q37Subject-verb agreement

Which of the following takes a singular verb?

apolice
bfurniture
cfamilies
dcommittees

Answer (b): 'Furniture' is an uncountable noun and takes a singular verb. Police is plural and the others are plural forms.

Revise: Grammar and Usage (Class 11 notes)

Q38Subject-verb agreement

Neither her nor they ____ going to the college.

ais
bare
chas
dwas

Answer (b): With 'neither...nor' the verb agrees with the nearer subject, 'they', so 'are'.

Revise: Grammar and Usage (Class 11 notes)

Q39Collective nouns

Which expression is incorrect?

aA pile of books
bA herd of cattle
cA herd of sheep
dA pack of wolves

Answer (c): The collective noun for sheep is a flock, not a herd. A herd of cattle, a pile of books and a pack of wolves are all correct.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q40Question tags

They daren't go ____?

adid they
bdo they
chasn't they
ddare they

Answer (d): 'Daren't' is a negative modal-like verb, so the positive question tag is 'dare they?'.

Revise: Grammar and Usage (Class 11 notes)

Q41Agreement with too/so

I am hungry and ____.

aShe is too
bthey are so
cso aren't they
dthey are too

Answer (d): 'They are too' completes the sentence meaning 'and they are hungry too'. The other options clash in subject or construction.

Revise: Grammar and Usage (Class 11 notes)

Q42Word stress

Which word has the stress on the first syllable?

aLikelihood
breligious
cfantastic
dorthography

Answer (a): LIKE-li-hood is stressed on the first syllable. Religious, fantastic and orthography are stressed on the second.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q43Syllables

How many syllables does the word 'economical' have?

afive
bfour
cthree
dsix

Answer (a): e-co-nom-i-cal has five syllables.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q44Pronunciation

The pair ____ has the same pronunciation.

apot, port
bso, sow
cpull, pool
ddid, dead

Answer (b): 'So' and 'sow' (to plant seeds) are both pronounced /soʊ/. The other pairs sound different.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q45Phonetics

The word 'they' has the same initial consonant sound as the word

aday
bdate
cthief
dthat

Answer (d): 'They' and 'that' both begin with the voiced sound /ð/.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q46Vocabulary

A professional horse rider is called

aJockey
brider
cCoach
dhorse courser

Answer (a): A jockey is a professional rider in horse races.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q47Antonyms

Give the opposite meaning of 'appropriate'.

aInevitable
blikely
cunsuitable
dsuitable

Answer (c): 'Appropriate' means suitable, so its opposite is unsuitable.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q48Synonyms

Select the right synonym of the word 'sporadic'.

aOccasional
bfrequently
ccontinuously
dnever ending

Answer (a): 'Sporadic' means happening at irregular, scattered times, i.e. occasional.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q49Punctuation

Which of the following is incorrectly punctuated?

aThe teacher said, "Honesty is the best policy".
bHe said to me "When did she come to the party"?
cThe man received a gift, the women, a book.
dThe man, whom he met, had excellent speech.

Answer (b): Option b is wrongly punctuated: it needs a comma after 'said to me' and the question mark belongs inside the quotation marks.

Revise: Grammar and Usage (Class 11 notes)

Q50Suffixes

The word 'father' takes the suffix:

a-is
b-some
c-ly
d-y

Answer (c): Father + ly gives the adjective 'fatherly'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Physics

Q51Dimensions

The dimensional formula for potential difference is

a $[ML^2T^{-3}I^{-1}]$ $[ML^2T^{-3}I^{-1}]$
b $[ML^2T^{-3}I]$ $[ML^2T^{-3}I]$
c $[ML^2T^3I^{-1}]$ $[ML^2T^3I^{-1}]$
d $[ML^2T^{-2}I^{-2}]$ $[ML^2T^{-2}I^{-2}]$

Answer (a): $V=\frac{W}{q}=\frac{ML^2T^{-2}}{IT}=ML^2T^{-3}I^{-1}$ .$V=\frac{W}{q}=\frac{ML^2T^{-2}}{IT}=ML^2T^{-3}I^{-1}$.

Revise: Physical Quantities (Class 11 notes)

Q52Motion under gravity

A stone is thrown vertically upward with a speed

u

from the top of a tower and reaches the ground with a speed

3u

. The height of the tower isA stone is thrown vertically upward with a speed $u$ from the top of a tower and reaches the ground with a speed $3u$. The height of the tower is

a $\frac{3u^2}{g}$ $\frac{3u^2}{g}$
b $\frac{4u^2}{g}$ $\frac{4u^2}{g}$
c $\frac{6u^2}{g}$ $\frac{6u^2}{g}$
d $\frac{9u^2}{g}$ $\frac{9u^2}{g}$

Answer (b): Taking downward positive, $v^2=u^2+2gh$ gives $9u^2=u^2+2gh$ , so $h=\frac{4u^2}{g}$ .Taking downward positive, $v^2=u^2+2gh$ gives $9u^2=u^2+2gh$, so $h=\frac{4u^2}{g}$.

Revise: Kinematics (Class 11 notes)

Q53Simple harmonic motion

The acceleration of a particle in SHM is

aAlways zero
balways constant
cMaximum at extreme position
dMaximum at the equilibrium position

Answer (c): $a=-\omega^2x$ , which is largest when the displacement is largest, at the extreme position.$a=-\omega^2x$, which is largest when the displacement is largest, at the extreme position.

Revise: Periodic Motion (Class 12 notes)

Q54Thermal expansion

An iron ball is heated. The percentage increase will be largest in

avolume
bdensity
cdiameter
dsurface area

Answer (a): Fractional increase is $\alpha\Delta T$ for length, $2\alpha\Delta T$ for area and $3\alpha\Delta T$ for volume, so volume increases most.Fractional increase is $\alpha\Delta T$ for length, $2\alpha\Delta T$ for area and $3\alpha\Delta T$ for volume, so volume increases most.

Revise: Thermal Expansion (Class 11 notes)

Q55Elasticity

Two wires A and B of the same material have lengths in the ratio

1:2

and diameters in the ratio

2:1

. If they are pulled by the same force, their increase in length will be in the ratioTwo wires A and B of the same material have lengths in the ratio $1:2$ and diameters in the ratio $2:1$. If they are pulled by the same force, their increase in length will be in the ratio

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

Answer (c): $\Delta L=\frac{FL}{AY}\propto\frac{L}{d^2}$ . Ratio $=\frac{1/4}{2/1}=\frac18$ .$\Delta L=\frac{FL}{AY}\propto\frac{L}{d^2}$. Ratio $=\frac{1/4}{2/1}=\frac18$.

Revise: Elasticity (Class 11 notes)

Q56Equation of continuity

Water flows through a tube of non-uniform cross section. If the radius at the entrance and exit is

3:2

, the ratio of velocity of liquid entering and leaving the tube isWater flows through a tube of non-uniform cross section. If the radius at the entrance and exit is $3:2$, the ratio of velocity of liquid entering and leaving the tube is

a $8:27$ $8:27$
b $4:9$ $4:9$
c $9:4$ $9:4$
d $1:1$ $1:1$

Answer (b): Continuity: $Av=$ constant, so $v\propto\frac{1}{r^2}$ . $\frac{v_1}{v_2}=\frac{2^2}{3^2}=\frac49$ .Continuity: $Av=$ constant, so $v\propto\frac{1}{r^2}$. $\frac{v_1}{v_2}=\frac{2^2}{3^2}=\frac49$.

Revise: Fluid Statics (Class 12 notes)

Q57Thermodynamic processes

The thermodynamic process in which the pressure of the system remains constant is called

aisothermal
badiabatic
cisochoric
disobaric

Answer (d): Constant pressure is an isobaric process.

Revise: First Law of Thermodynamics (Class 12 notes)

Q58Calorimetry

50 g of ice at

-6^\circ

C is dropped into water at

0^\circ

C. How many grams of water freeze? Specific heat capacity of ice

=2000\,J\,kg^{-1}C^{-1}

.50 g of ice at $-6^\circ$C is dropped into water at $0^\circ$C. How many grams of water freeze? Specific heat capacity of ice $=2000,J,kg^{-1}C^{-1}$.

a1.785 g
b4.25 g
c3.16 g
d9.33 g

Answer (a): Heat to warm the ice: $0.05\times2000\times6=600$ J. Mass frozen $=\frac{600}{3.36\times10^5}\text{ kg}\approx1.785$ g.Heat to warm the ice: $0.05\times2000\times6=600$ J. Mass frozen $=\frac{600}{3.36\times10^5}\text{ kg}\approx1.785$ g.

Revise: Quantity of Heat (Class 11 notes)

Q59Concave mirror

The image of an object placed at the focus of a concave mirror is at

af
bInfinity
c2f
df/2

Answer (b): Rays from the focus become parallel after reflection, so the image forms at infinity.

Revise: Reflection at Curved Mirrors (Class 11 notes)

Q60Carnot engine

The temperature of source and sink of a Carnot engine are 400 K and 300 K respectively. What is its efficiency?

a100%
b75%
c33.3%
d25%

Answer (d): $\eta=1-\frac{T_2}{T_1}=1-\frac{300}{400}=0.25=25\%$ .$\eta=1-\frac{T_2}{T_1}=1-\frac{300}{400}=0.25=25%$.

Revise: Second Law of Thermodynamics (Class 12 notes)

Q61Refractive index

The refractive index of air with respect to glass is

2/3

. The refractive index of diamond with respect to air is

12/5

. Then the refractive index of glass with respect to diamond will beThe refractive index of air with respect to glass is $2/3$. The refractive index of diamond with respect to air is $12/5$. Then the refractive index of glass with respect to diamond will be

a $5/8$
b $8/9$
c $5/18$
d $18/5$

Answer (a): ${}_a n_g=\frac32$ . ${}_d n_g=\frac{{}_a n_g}{{}_a n_d}=\frac{3/2}{12/5}=\frac{15}{24}=\frac58$ .${}_a n_g=\frac32$. ${}_d n_g=\frac{{}_a n_g}{{}_a n_d}=\frac{3/2}{12/5}=\frac{15}{24}=\frac58$.

Revise: Refraction at Plane Surface (Class 11 notes)

Q62Lens maker's formula

The focal length of a double convex lens for which the radius of curvature of each surface is

R

will be (

\mu=1.5

)The focal length of a double convex lens for which the radius of curvature of each surface is $R$ will be ($\mu=1.5$)

a $R/2$ $R/2$
b $R$
c $2R$
d $4R$

Answer (b): $\frac1f=(\mu-1)\left(\frac2R\right)=0.5\cdot\frac2R=\frac1R$ , so $f=R$ .$\frac1f=(\mu-1)\left(\frac2R\right)=0.5\cdot\frac2R=\frac1R$, so $f=R$.

Revise: Lenses (Class 11 notes)

Q63Refraction

Light of wavelength

7200

Å in air has a wavelength in glass equal to (refractive index of glass with respect to air

=1.5

)Light of wavelength $7200$ Å in air has a wavelength in glass equal to (refractive index of glass with respect to air $=1.5$)

a7200 Å
b4800 Å
c1080 Å
d10800 Å

Answer (b): Wavelength in glass $=\lambda/n=7200/1.5=4800$ Å.Wavelength in glass $=\lambda/n=7200/1.5=4800$ Å.

Revise: Refraction at Plane Surface (Class 11 notes)

Q64Capacitor combinations

Three capacitors of

3\mu F

9\mu F

and

18\mu F

are connected first in series and then in parallel. The ratio of

C

equivalent capacitance in two cases (

C_s/C_p

) will beThree capacitors of $3\mu F$, $9\mu F$ and $18\mu F$ are connected first in series and then in parallel. The ratio of $C$ equivalent capacitance in two cases ($C_s/C_p$) will be

a $1:15$ $1:15$
b $15:1$ $15:1$
c $1:1$ $1:1$
d $1:3$ $1:3$

Answer (a): $\frac1{C_s}=\frac13+\frac19+\frac1{18}=\frac12$ , so $C_s=2\mu F$ . $C_p=30\mu F$ . Ratio $=\frac{2}{30}=1:15$ .$\frac1{C_s}=\frac13+\frac19+\frac1{18}=\frac12$, so $C_s=2\mu F$. $C_p=30\mu F$. Ratio $=\frac{2}{30}=1:15$.

Revise: Capacitor (Class 11 notes)

Q65Resistor combinations

Three equal resistors each of resistance

r

are connected to form a triangle. The equivalent resistance across any two corners of the triangle isThree equal resistors each of resistance $r$ are connected to form a triangle. The equivalent resistance across any two corners of the triangle is

a $2r$
b $r/3$ $r/3$
c $2r/3$ $2r/3$
d $3r$

Answer (c): Across two corners, one resistor $r$ is in parallel with two in series ( $2r$ ): $\frac{r\cdot2r}{3r}=\frac{2r}{3}$ .Across two corners, one resistor $r$ is in parallel with two in series ($2r$): $\frac{r\cdot2r}{3r}=\frac{2r}{3}$.

Revise: DC Circuit (Class 11 notes)

Q66Electric power

The resistances of two lamps are in the ratio

1:2

. Their wattage will be in the ratio ofThe resistances of two lamps are in the ratio $1:2$. Their wattage will be in the ratio of

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

Answer (b): On the same supply $P=\frac{V^2}{R}\propto\frac1R$ , so the ratio is $2:1$ .On the same supply $P=\frac{V^2}{R}\propto\frac1R$, so the ratio is $2:1$.

Revise: DC Circuit (Class 11 notes)

Q67Inductor energy

The energy stored in a 50 mH inductor carrying a current of 4 A is

a0.1 J
b0.4 J
c0.3 J
d0.01 J

Answer (b): $U=\frac12LI^2=\frac12(0.05)(16)=0.4$ J.$U=\frac12LI^2=\frac12(0.05)(16)=0.4$ J.

Revise: Electromagnetic Induction (Class 12 notes)

Q68LCR resonance

The alternating current in an LCR circuit is maximum when

a $X_L=0$ $X_L=0$
b $X_C=0$ $X_C=0$
c $X_L=X_C$ $X_L=X_C$
d $\sqrt{X_L^2+X_C^2}=0$ $\sqrt{X_L^2+X_C^2}=0$

Answer (c): At resonance $X_L=X_C$ , impedance is minimum ( $=R$ ) and current is maximum.At resonance $X_L=X_C$, impedance is minimum ($=R$) and current is maximum.

Revise: Alternating Currents (Class 12 notes)

Q69de Broglie wavelength

A particle of mass

10^{-31}

kg is moving with a speed of

10^5

m/s. The de Broglie wavelength of the particle isA particle of mass $10^{-31}$ kg is moving with a speed of $10^5$ m/s. The de Broglie wavelength of the particle is

a $6.63\times10^{-8}$ m$6.63\times10^{-8}$ m
b $6.63$ Å
c $66.3$ Å
d $6.63\times10^{-7}$ m$6.63\times10^{-7}$ m

Answer (a): $\lambda=\frac{h}{mv}=\frac{6.63\times10^{-34}}{10^{-31}\times10^5}=6.63\times10^{-8}$ m.$\lambda=\frac{h}{mv}=\frac{6.63\times10^{-34}}{10^{-31}\times10^5}=6.63\times10^{-8}$ m.

Revise: Quantization of Energy (Class 12 notes)

Q70Interference

Two waves of the same wavelength and amplitude interfere to give a minimum when their phase difference is

a $\pi$
b $\pi/2$ $\pi/2$
c $3\pi/2$ $3\pi/2$
d $0$

Answer (a): Destructive interference needs a phase difference of an odd multiple of $\pi$ ; the smallest given is $\pi$ .Destructive interference needs a phase difference of an odd multiple of $\pi$; the smallest given is $\pi$.

Revise: Interference (Class 12 notes)

Q71X-rays

Hard X-rays as compared to soft X-rays have

aHigher intensity
blower frequency
cHigher frequency
dhigher speed

Answer (c): Hard X-rays have shorter wavelength and so higher frequency and penetrating power. All X-rays travel at $c$ .Hard X-rays have shorter wavelength and so higher frequency and penetrating power. All X-rays travel at $c$.

Revise: Electrons (Class 12 notes)

Q72Mass defect

The mass of an

\alpha

-particle is

aEqual to the mass of four protons
bEqual to the mass of four neutrons
cEqual to the masses of 2 protons and 2 neutrons
dLess than the sum of masses of 2 protons and 2 neutrons

Answer (d): An alpha particle is a helium nucleus; its mass is less than its separate nucleons by the mass defect (binding energy).

Revise: Radioactivity and Nuclear Reaction (Class 12 notes)

Q73Transistor amplifier

A common emitter transistor amplifier has a current gain of 50. If the load resistance is

4\,k\Omega

and the input resistance is

500\,\Omega

, the voltage gain of the amplifier isA common emitter transistor amplifier has a current gain of 50. If the load resistance is $4,k\Omega$ and the input resistance is $500,\Omega$, the voltage gain of the amplifier is

a400
b6.2
c500
d300

Answer (a): $A_v=\beta\frac{R_L}{R_{in}}=50\times\frac{4000}{500}=400$ .$A_v=\beta\frac{R_L}{R_{in}}=50\times\frac{4000}{500}=400$.

Revise: Semiconductor Devices (Class 12 notes)

Q74Resonance in pipes

A tube closed at one end has a length 1 meter. The air column in the pipe can resonate for sound of frequency (

v=320\,ms^{-1}

)A tube closed at one end has a length 1 meter. The air column in the pipe can resonate for sound of frequency ($v=320,ms^{-1}$)

a166 Hz
b249 Hz
c575 Hz
d80 Hz

Answer (d): Closed pipe: $f_1=\frac{v}{4L}=\frac{320}{4}=80$ Hz (other resonances are odd multiples: 240, 400 Hz...).Closed pipe: $f_1=\frac{v}{4L}=\frac{320}{4}=80$ Hz (other resonances are odd multiples: 240, 400 Hz...).

Revise: Wave in Pipes and Strings (Class 12 notes)

Q75Wave equation

A displacement wave is represented by

y=0.25\sin(500t-0.0025x)

, where

y

t

and

x

are in cm, second and meter respectively. The wavelength of the wave isA displacement wave is represented by $y=0.25\sin(500t-0.0025x)$, where $y$, $t$ and $x$ are in cm, second and meter respectively. The wavelength of the wave is

a $20\pi$ m
b $40\pi$ m
c $60\pi$ m
d $80\pi$ m

Answer (d): Comparing with $y=A\sin(\omega t-kx)$ gives $\lambda=2\pi/k$ . The only option consistent with the intended $k=0.025$ is $\lambda=2\pi/0.025=80\pi$ , so the printed 0.0025 looks like a misprint for 0.025.Comparing with $y=A\sin(\omega t-kx)$ gives $\lambda=2\pi/k$. The only option consistent with the intended $k=0.025$ is $\lambda=2\pi/0.025=80\pi$, so the printed 0.0025 looks like a misprint for 0.025.

Revise: Wave Motion (Class 12 notes)

Chemistry

Q76Preparation of alkanes

The gas obtained by adding water on aluminium carbide is

aEthyne
bethane
cmethane
dethane

Answer (c): $\ce{Al4C3 + 12H2O -> 4Al(OH)3 + 3CH4}$ , so methane is released.$\ce{Al4C3 + 12H2O -> 4Al(OH)3 + 3CH4}$, so methane is released.

Revise: Hydrocarbons (Class 11 notes)

Q77Alcohols

The mixture of HCl and

ZnCl_2

is known asThe mixture of HCl and $ZnCl_2$ is known as

aTollen's reagent
bBaeyer's reagent
cLucas reagent
dNessler's reagent

Answer (c): Concentrated HCl with anhydrous $\ce{ZnCl2}$ is Lucas reagent, used to distinguish 1, 2 and 3 degree alcohols.Concentrated HCl with anhydrous $\ce{ZnCl2}$ is Lucas reagent, used to distinguish 1, 2 and 3 degree alcohols.

Revise: Alcohols (Class 12 notes)

Q78Carboxylic acid nomenclature

The IUPAC name of n-valeric acid is

aPentanoic acid
bbutanoic acid
cPropanoic acid
dethanoic acid

Answer (a): Valeric acid is $\ce{CH3(CH2)3COOH}$ , a five carbon acid: pentanoic acid.Valeric acid is $\ce{CH3(CH2)3COOH}$, a five carbon acid: pentanoic acid.

Revise: Carboxylic Acids (Class 12 notes)

Q79Qualitative organic analysis

A blood red coloration of ferric sulphocyanide obtained by addition of ferric chloride in sodium extract confirms the presence of

aSulphur
bnitrogen
cboth a and b
dhalogens

Answer (c): Blood red $\ce{Fe(SCN)3}$ forms when both N and S are present in the sodium fusion extract (as NaSCN).Blood red $\ce{Fe(SCN)3}$ forms when both N and S are present in the sodium fusion extract (as NaSCN).

Revise: Fundamental Principles (Class 11 notes)

Q80Boiling point and hydrogen bonding

Which of the following compounds has the highest boiling point?

a $CH_4$ $CH_4$
b $CH_3Cl$ $CH_3Cl$
c $CH_3Br$ $CH_3Br$
d $CH_3OH$ $CH_3OH$

Answer (d): Methanol has hydrogen bonding, which gives a much higher boiling point than the other compounds.

Revise: Chemical Bonding (Class 11 notes)

Q81Aldehydes

The compound that undergoes Cannizzaro reaction is

a $CH_3COOH$ $CH_3COOH$
b $C_2H_5CHO$ $C_2H_5CHO$
cHCHO
d $CH_3OCH_3$ $CH_3OCH_3$

Answer (c): Cannizzaro reaction needs an aldehyde with no alpha hydrogen. HCHO has none, so it qualifies.

Revise: Aldehydes and Ketones (Class 12 notes)

Q82Aromatic hydrocarbons

Benzene is converted to toluene by

aFriedel Craft reaction
bGrignard reaction
cWurtz reaction
dPerkin reaction

Answer (a): $\ce{C6H6 + CH3Cl ->[AlCl3] C6H5CH3 + HCl}$ is Friedel-Crafts alkylation.$\ce{C6H6 + CH3Cl ->[AlCl3] C6H5CH3 + HCl}$ is Friedel-Crafts alkylation.

Revise: Aromatic Hydrocarbons (Class 11 notes)

Q83Amines

The compound that gives positive carbylamine reaction is

a $(CH_3)_2NH$ $(CH_3)_2NH$
b $(CH_3)_3N$ $(CH_3)_3N$
c $(CH_3)_4N^+$ $(CH_3)_4N^+$
d $(CH_3)NH_2$ $(CH_3)NH_2$

Answer (d): Only primary amines give the carbylamine (isocyanide) test; $\ce{CH3NH2}$ is primary.Only primary amines give the carbylamine (isocyanide) test; $\ce{CH3NH2}$ is primary.

Revise: Amines (Class 12 notes)

Q84Metallurgy

Hematite is an ore of

aSilver
bIron
cMercury
dCopper

Answer (b): Hematite is $\ce{Fe2O3}$ , an iron ore.Hematite is $\ce{Fe2O3}$, an iron ore.

Revise: Chemistry of Metals (Class 11 notes)

Q85Oxides

Na_2O

is a$Na_2O$ is a

aNeutral oxide
bacidic oxide
cBasic oxide
damphoteric oxide

Answer (c): Oxides of strongly electropositive metals like sodium give alkali with water, so they are basic.

Revise: Classification of Elements (Class 11 notes)

Q86Periodic trends

Which of the following elements has highest electronegativity?

aBromine
bIodine
cChlorine
dFluorine

Answer (d): Electronegativity decreases down the halogen group, so fluorine is highest.

Revise: Classification of Elements (Class 11 notes)

Q87Compounds of metals

Zinc sulphate (

ZnSO_4\cdot7H_2O

) is also calledZinc sulphate ($ZnSO_4\cdot7H_2O$) is also called

aWhite vitriol
bGreen vitriol
cBlue vitriol
dcorrosive sublimate

Answer (a): $\ce{ZnSO4.7H2O}$ is white vitriol. Green is $\ce{FeSO4.7H2O}$ , blue is $\ce{CuSO4.5H2O}$ .$\ce{ZnSO4.7H2O}$ is white vitriol. Green is $\ce{FeSO4.7H2O}$, blue is $\ce{CuSO4.5H2O}$.

Revise: Chemistry of Metals (Class 11 notes)

Q88Alloys

Brass is an alloy of

aCopper and Zinc
bCopper and Nickel
cCopper and Tin
dCopper and Lead

Answer (a): Brass is copper with zinc; bronze is copper with tin.

Revise: Chemistry of Metals (Class 11 notes)

Q89Ores

The formula of dolomite is

a $CaCO_3$ $CaCO_3$
b $CaCO_3\cdot MgCO_3$ $CaCO_3\cdot MgCO_3$
c $CaSO_4\cdot2H_2O$ $CaSO_4\cdot2H_2O$
d $CaF_2$ $CaF_2$

Answer (b): Dolomite is the double carbonate of calcium and magnesium.

Revise: Chemistry of Metals (Class 11 notes)

Q90Electronic configuration

The general electronic configuration of zinc is

a $[Ar]4s^23d^{10}$ $[Ar]4s^23d^{10}$
b $[Ar]4s^13d^{10}$ $[Ar]4s^13d^{10}$
c $[Ar]4s^23d^8$ $[Ar]4s^23d^8$
d $[Ar]4s^23d^7$ $[Ar]4s^23d^7$

Answer (a): Zinc ( $Z=30$ ) has a full d subshell: $[Ar]3d^{10}4s^2$ .Zinc ($Z=30$) has a full d subshell: $[Ar]3d^{10}4s^2$.

Revise: Transition Metals (Class 12 notes)

Q91Equivalent weight

Equivalent weight of

KMnO_4

in neutral medium isEquivalent weight of $KMnO_4$ in neutral medium is

a52.6
b158.0
c31.6
d63.0

Answer (a): In neutral medium Mn changes from $+7$ to $+4$ (3 electrons): $\frac{158}{3}=52.67$ .In neutral medium Mn changes from $+7$ to $+4$ (3 electrons): $\frac{158}{3}=52.67$.

Revise: Volumetric Analysis (Class 12 notes)

Q92Atomic models

Bohr's model was modified by

aRutherford
bSomerfield
cDalton
dPauli

Answer (b): Sommerfeld introduced elliptical orbits to improve Bohr's model.

Revise: Atomic Structure (Class 11 notes)

Q93Mole concept

How many oxygen atoms are there in 8.0 g of oxygen atoms?

a $3.011\times10^{23}$ $3.011\times10^{23}$
b $3.011\times10^{22}$ $3.011\times10^{22}$
c $3.011\times10^{20}$ $3.011\times10^{20}$
d $3.011\times10^{19}$ $3.011\times10^{19}$

Answer (a): Moles $=\frac{8}{16}=0.5$ . Atoms $=0.5\times6.022\times10^{23}=3.011\times10^{23}$ .Moles $=\frac{8}{16}=0.5$. Atoms $=0.5\times6.022\times10^{23}=3.011\times10^{23}$.

Revise: Stoichiometry (Class 11 notes)

Q94pH

What is the pH of 0.001 M HCl?

a2.0
b3.0
c4.0
d5.0

Answer (b): HCl is a strong acid: $[H^+]=10^{-3}$ , so pH $=3$ .HCl is a strong acid: $[H^+]=10^{-3}$, so pH $=3$.

Revise: Ionic Equilibrium (Class 12 notes)

Q95Chemical kinetics

The rate of reaction is independent of

aTemperature
bconcentration
cParticle size of reactant
dMolecularity

Answer (d): Rate depends on temperature, concentration and surface area, but molecularity is a property of the elementary step, not a rate factor.

Revise: Chemical Kinetics (Class 12 notes)

Q96Conductance

The CGS unit of specific conductance is

aSiemen $cm^{-1}$ Siemen $cm^{-1}$
b $ohm^{-1}cm^2equiv^{-1}$ $ohm^{-1}cm^2equiv^{-1}$
cSiemen
d $ohm^{-1}$ $ohm^{-1}$

Answer (a): Specific conductance is $\frac1\rho$ , with unit $ohm^{-1}cm^{-1}$ , i.e. Siemen $cm^{-1}$ .Specific conductance is $\frac1\rho$, with unit $ohm^{-1}cm^{-1}$, i.e. Siemen $cm^{-1}$.

Revise: Electrochemistry (Class 12 notes)

Q97Thermochemistry

Hess's law deals with

aTotal change in heat of reaction
bRate of reaction
cEquilibrium constant of reaction
dInfluence on pressure of volume of gas

Answer (a): Hess's law says the total heat change of a reaction is the same regardless of the path taken.

Revise: Chemical Thermodynamic (Class 12 notes)

Q98Ionic equilibrium

The degree of dissociation of an electrolyte

aDecreases with dilution
bIncreases with dilution
cMay increase or decrease with dilution
dIs not affected by dilution

Answer (b): By Ostwald's dilution law, $\alpha$ rises as concentration falls, so the degree of dissociation increases with dilution.By Ostwald's dilution law, $\alpha$ rises as concentration falls, so the degree of dissociation increases with dilution.

Revise: Ionic Equilibrium (Class 12 notes)

Q99Gas laws and moles

The weight of 100 ml of

NH_3

gas at NTP isThe weight of 100 ml of $NH_3$ gas at NTP is

a0.0759 g
b0.0579 g
c0.0459 g
d0.0359 g

Answer (a): Moles $=\frac{0.1}{22.4}=0.00446$ ; mass $=0.00446\times17=0.0759$ g.Moles $=\frac{0.1}{22.4}=0.00446$; mass $=0.00446\times17=0.0759$ g.

Revise: Stoichiometry (Class 11 notes)

Q100Laws of chemical combination

The law of multiple proportions was given by

aRichter
bJohn Dalton
cAlbert Einstein
dGay Lussac

Answer (b): Dalton proposed the law of multiple proportions (1803).

Revise: Stoichiometry (Class 11 notes)

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