TU FoHSS | notesharu model set

BCA Entrance Model Set 2 with Answers

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

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Mathematics

Q1Logarithms

The value of $\log_2 64 + \log_3 81$ is

Answer (c): $\log_2 64=6$ since $2^6=64$, and $\log_3 81=4$ since $3^4=81$. Sum $=10$.

Revise: Algebra (Class 11 notes)

Q2Logarithms

If $\log_x 125 = 3$, then $x$ equals

Answer (a): $\log_x 125=3$ means $x^3=125$, so $x=5$.

Revise: Algebra (Class 11 notes)

Q3Logarithms

The value of $\log_{10} 2 + \log_{10} 5$ is

a0
b10
c$\frac{1}{10}$
d1

Answer (d): $\log 2+\log 5=\log(2\times5)=\log 10=1$.

Revise: Algebra (Class 11 notes)

Q4Logarithms

If $\log_3 (x-1) = 2$, then $x$ is

Answer (c): $x-1=3^2=9$, so $x=10$.

Revise: Algebra (Class 11 notes)

Q5Determinants

The determinant of the matrix $\begin{bmatrix}1&2\3&4\end{bmatrix}$ is

a $2$
b $10$
c $-2$
d $-10$

Answer (c): $\det=1\cdot4-2\cdot3=4-6=-2$.

Revise: Algebra (Class 12 notes)

Q6Matrices

If $A=\begin{bmatrix}2&1\0&3\end{bmatrix}$ and $B=\begin{bmatrix}1&0\4&2\end{bmatrix}$, the element in the second row and first column of $AB$ is

Answer (d): Row 2 of $A$ is $(0,3)$ and column 1 of $B$ is $(1,4)$: $0\cdot1+3\cdot4=12$.

Revise: Algebra (Class 12 notes)

Q7Determinants

If $\begin{vmatrix}x&2\3&4\end{vmatrix}=2$, then $x$ is

Answer (b): $4x-6=2\Rightarrow 4x=8\Rightarrow x=2$.

Revise: Algebra (Class 12 notes)

Q8Matrices

The matrix $\begin{bmatrix}k&2\4&8\end{bmatrix}$ is singular when $k$ equals

Answer (d): Singular means determinant $0$: $8k-8=0\Rightarrow k=1$.

Revise: Algebra (Class 12 notes)

Q9Compound interest

The compound interest on Rs 10,000 for 2 years at 10% per annum, compounded annually, is

aRs 2,000
bRs 2,100
cRs 2,200
dRs 2,210

Answer (b): $A=10000(1.1)^2=12100$, so $CI=12100-10000=2100$.

Q10Compound interest

The difference between compound interest and simple interest on Rs 4,000 for 2 years at 10% per annum is

aRs 20
bRs 40
cRs 400
dRs 80

Answer (b): Difference for 2 years $=P\left(\frac{r}{100}\right)^2=4000\times0.01=40$.

Q11Mensuration

The volume of a cylinder of radius 7 cm and height 10 cm is (take $\pi=\frac{22}{7}$)

a770 cm$^3$
b440 cm$^3$
c1540 cm$^3$
d1100 cm$^3$

Answer (c): $V=\pi r^2h=\frac{22}{7}\times49\times10=1540$.

Q12Mensuration

A cone has base radius 5 cm and slant height 13 cm. Its volume is

a$300\pi$ cm$^3$
b$100\pi$ cm$^3$
c$65\pi$ cm$^3$
d$125\pi$ cm$^3$

Answer (b): Height $=\sqrt{13^2-5^2}=12$. $V=\frac13\pi r^2h=\frac13\pi\cdot25\cdot12=100\pi$.

Q13Mensuration

The surface area of a sphere is 616 cm$^2$. Its radius is (take $\pi=\frac{22}{7}$)

a7 cm
b14 cm
c3.5 cm
d49 cm

Answer (a): $4\pi r^2=616\Rightarrow r^2=\frac{616\times7}{88}=49$, so $r=7$.

Q14Mensuration

The diagonal of a rectangle is 13 cm and one side is 12 cm. Its area is

a156 cm$^2$
b30 cm$^2$
c65 cm$^2$
d60 cm$^2$

Answer (d): Other side $=\sqrt{13^2-12^2}=5$. Area $=12\times5=60$.

Q15Probability

Two dice are thrown together. The probability that the sum is 8 is

a$\frac{5}{36}$
b$\frac{1}{6}$
c$\frac{1}{9}$
d$\frac{7}{36}$

Answer (a): Favourable: (2,6),(3,5),(4,4),(5,3),(6,2) = 5 out of 36.

Revise: Statistics and Probability (Class 11 notes)

Q16Probability

A bag has 3 red and 5 blue balls. Two balls are drawn one after another without replacement. The probability that both are red is

a$\frac{9}{64}$
b$\frac{3}{8}$
c$\frac{3}{28}$
d$\frac{1}{4}$

Answer (c): $\frac38\times\frac27=\frac{6}{56}=\frac{3}{28}$.

Revise: Statistics and Probability (Class 11 notes)

Q17Probability

If $A$ and $B$ are independent events with $P(A)=0.4$ and $P(B)=0.5$, then $P(A\cup B)$ is

a0.9
b0.2
c0.6
d0.7

Answer (d): $P(A\cap B)=0.4\times0.5=0.2$. $P(A\cup B)=0.4+0.5-0.2=0.7$.

Revise: Statistics and Probability (Class 11 notes)

Q18Probability

A fair coin is tossed three times. The probability of getting at least one head is

a$\frac{1}{8}$
b$\frac{7}{8}$
c$\frac{3}{8}$
d$\frac{1}{2}$

Answer (b): $P=1-P(\text{no head})=1-\left(\frac12\right)^3=\frac78$.

Revise: Statistics and Probability (Class 11 notes)

Q19Coordinate geometry

The distance between the points $(1,2)$ and $(4,6)$ is

Answer (c): $\sqrt{(4-1)^2+(6-2)^2}=\sqrt{9+16}=5$.

Revise: Analytic geometry (Class 11 notes)

Q20Straight line

The equation of the line through $(2,3)$ with slope 2 is

a$2x-y+1=0$
b$x-2y+4=0$
c$2x-y-1=0$
d$2x+y-7=0$

Answer (c): $y-3=2(x-2)\Rightarrow y=2x-1\Rightarrow 2x-y-1=0$.

Revise: Analytic geometry (Class 11 notes)

Q21Circle

The radius of the circle $x^2+y^2-6x+8y=0$ is

Answer (b): Centre $(3,-4)$, so $r^2=9+16-0=25$ and $r=5$.

Revise: Analytic geometry (Class 11 notes)

Q22Coordinate geometry

The area of the triangle with vertices $(0,0)$, $(4,0)$ and $(0,6)$ is

a24 square units
b12 square units
c10 square units
d6 square units

Answer (b): Right triangle with legs 4 and 6: $\frac12\times4\times6=12$.

Revise: Analytic geometry (Class 11 notes)

Q23Straight line

The perpendicular distance of the point $(3,4)$ from the line $3x+4y-5=0$ is

a20
b5
c$\frac45$
d4

Answer (d): $d=\frac{|3(3)+4(4)-5|}{\sqrt{3^2+4^2}}=\frac{20}{5}=4$.

Revise: Analytic geometry (Class 11 notes)

Q24Straight line

The slope of the line $3x-6y+5=0$ is

a$\frac12$
b $2$
c$-\frac12$
d $-2$

Answer (a): $y=\frac{3x+5}{6}$, so slope $=\frac36=\frac12$.

Revise: Analytic geometry (Class 11 notes)

Q25Trigonometric ratios

The value of $\sin30^\circ\cos60^\circ+\cos30^\circ\sin60^\circ$ is

a1
b$\frac12$
c$\frac{\sqrt3}{2}$
d0

Answer (a): It equals $\sin(30^\circ+60^\circ)=\sin90^\circ=1$. Check: $\frac14+\frac34=1$.

Revise: Trigonometry (Class 11 notes)

Q26Trigonometric ratios

If $\sin\theta=\frac35$ and $\theta$ is acute, then $\tan\theta$ is

a$\frac43$
b$\frac45$
c$\frac34$
d$\frac54$

Answer (c): $\cos\theta=\frac45$, so $\tan\theta=\frac{3/5}{4/5}=\frac34$.

Revise: Trigonometry (Class 11 notes)

Q27Multiple angles

If $\cos A=\frac45$ and $A$ is acute, then $\sin2A$ is

a$\frac{12}{25}$
b$\frac{7}{25}$
c$\frac{24}{25}$
d$\frac85$

Answer (c): $\sin A=\frac35$. $\sin2A=2\sin A\cos A=2\cdot\frac35\cdot\frac45=\frac{24}{25}$.

Revise: Trigonometry (Class 11 notes)

Q28Product to sum

The value of $\cos75^\circ\cos15^\circ$ is

a$\frac12$
b$\frac{\sqrt3}{4}$
c1
d$\frac14$

Answer (d): Use $\cos A\cos B=\frac12[\cos(A+B)+\cos(A-B)]=\frac12[\cos90^\circ+\cos60^\circ]=\frac12\cdot\frac12=\frac14$.

Revise: Trigonometry (Class 11 notes)

Q29Trigonometric functions

The period of the function $\sin3x$ is

a $3\pi$
b $2\pi$
c$\frac{2\pi}{3}$
d$\frac{\pi}{3}$

Answer (c): Period of $\sin kx$ is $\frac{2\pi}{k}$, so here $\frac{2\pi}{3}$.

Revise: Trigonometry (Class 11 notes)

Q30Differentiation

The derivative of $x^2e^x$ with respect to $x$ is

a$2xe^x$
b$x^2e^x$
c$e^x(x^2+2x)$
d$e^x(x^2+2)$

Answer (c): Product rule: $2x\cdot e^x+x^2\cdot e^x=e^x(x^2+2x)$.

Revise: Calculus (Class 11 notes)

Q31Integration

The value of $\int_0^2(3x^2+2x),dx$ is

Answer (d): $[x^3+x^2]_0^2=8+4=12$.

Revise: Calculus (Class 12 notes)

Q32Limits

The value of $\lim_{x\to0}\frac{\sin5x}{3x}$ is

a$\frac35$
b$\frac53$
c1
d15

Answer (b): $\frac{\sin5x}{3x}=\frac53\cdot\frac{\sin5x}{5x}\to\frac53\cdot1$.

Revise: Calculus (Class 11 notes)

Q33Maxima and minima

The local maximum value of $f(x)=x^3-3x$ is

a $-2$
b2
c0
d4

Answer (b): $f'(x)=3x^2-3=0\Rightarrow x=\pm1$. $f''(-1)=-6<0$, so maximum at $x=-1$: $f(-1)=-1+3=2$.

Revise: Calculus (Class 11 notes)

Q34Mean

The mean of six numbers is 15. When one number is removed, the mean of the remaining five becomes 14. The number removed is

Answer (b): Total $=6\times15=90$; remaining total $=5\times14=70$. Removed $=90-70=20$.

Revise: Statistics and Probability (Class 11 notes)

Q35Median

The median of the data 3, 7, 5, 13, 9, 11 is

a7
b9
c8
d8.5

Answer (c): Sorted: 3, 5, 7, 9, 11, 13. Median is the mean of the 3rd and 4th: $\frac{7+9}{2}=8$.

Revise: Statistics and Probability (Class 11 notes)

Q36Dispersion

A data set has mean 50 and standard deviation 10. Its coefficient of variation is

a20%
b5%
c40%
d0.2%

Answer (a): $CV=\frac{\sigma}{\bar x}\times100=\frac{10}{50}\times100=20%$.

Revise: Statistics and Probability (Class 11 notes)

Q37Vectors

If $\vec a=2\hat i+\hat j-\hat k$ and $\vec b=\hat i+3\hat j+\hat k$, then $\vec a\cdot\vec b$ is

Answer (d): $2(1)+1(3)+(-1)(1)=2+3-1=4$.

Revise: Vectors (Class 11 notes)

Q38Vectors

The vectors $2\hat i+p\hat j$ and $3\hat i-6\hat j$ are perpendicular when $p$ equals

a $-1$
b2
c1
d3

Answer (c): Dot product zero: $2(3)+p(-6)=0\Rightarrow p=1$.

Revise: Vectors (Class 11 notes)

Q39Quadratic equations

If $\alpha$ and $\beta$ are the roots of $x^2-5x+6=0$, then $\alpha^2+\beta^2$ is

Answer (a): $\alpha+\beta=5$, $\alpha\beta=6$. $\alpha^2+\beta^2=25-12=13$.

Revise: Algebra (Class 11 notes)

Q40Arithmetic progression

The sum of the first 20 terms of the AP 3, 7, 11, ... is

a800
b840
c780
d820

Answer (d): $S_n=\frac n2[2a+(n-1)d]=10[6+19\cdot4]=10\times82=820$.

Revise: Algebra (Class 11 notes)

Q41Geometric progression

The sum to infinity of the series $8+4+2+1+\dots$ is

Answer (a): $a=8$, $r=\frac12$: $S_\infty=\frac{a}{1-r}=\frac{8}{1/2}=16$.

Revise: Algebra (Class 11 notes)

Q42Permutations

The number of different arrangements of the letters of the word LEVEL is

a60
b120
c30
d15

Answer (c): Five letters with E repeated twice and L twice: $\frac{5!}{2!,2!}=30$.

Revise: Algebra (Class 11 notes)

Q43Combinations

The value of $^8C_3$ is

a56
b336
c24
d28

Answer (a): $^8C_3=\frac{8\cdot7\cdot6}{3\cdot2\cdot1}=56$.

Revise: Algebra (Class 11 notes)

Q44Binomial theorem

The coefficient of $x^2$ in the expansion of $(1+x)^6$ is

Answer (c): Coefficient is $^6C_2=\frac{6\cdot5}{2}=15$.

Revise: Algebra (Class 11 notes)

Q45Inequalities

The solution set of $|2x-3|<5$ is

a$-4<x<1$
b$1<x<4$
c$-1<x<4$
d$x<-1$ or $x>4$

Answer (c): $-5<2x-3<5\Rightarrow -2<2x<8\Rightarrow -1<x<4$.

Revise: Algebra (Class 11 notes)

Q46Profit and loss

A shopkeeper marks an article 40% above its cost price and allows a 10% discount. His profit percent is

a30%
b26%
c50%
d25%

Answer (b): Let CP $=100$. Marked $=140$. Selling $=140\times0.9=126$. Profit $=26%$.

Q47Number series

What comes next in the series 2, 6, 12, 20, 30, ... ?

Answer (a): Terms are $n(n+1)$: $1\cdot2,2\cdot3,3\cdot4,4\cdot5,5\cdot6$, so next is $6\cdot7=42$. Differences 4, 6, 8, 10, 12 agree.

Q48Clocks

What is the angle between the hour hand and the minute hand of a clock at 4:30?

a$30^\circ$
b$60^\circ$
c$45^\circ$
d$15^\circ$

Answer (c): Hour hand: $4\times30+15=135^\circ$. Minute hand: $180^\circ$. Difference $=45^\circ$.

Q49Coding-decoding

In a certain code, CAT is written as ECV. How is DOG written in that code?

aEPH
bFPI
cFQH
dFQI

Answer (d): Each letter moves 2 places forward: D to F, O to Q, G to I.

Q50Ranking

Ram is 7th from the top and 12th from the bottom in a class. How many students are in the class?

Answer (a): Total $=7+12-1=18$ (Ram is counted in both ranks).

English

Q51Conditionals

If I ____ you, I would apologise to her at once.

aam
bwere
cwas being
dwill be

Answer (b): Second conditional (unreal present) uses 'were' for all persons after 'if': If I were you, I would...

Revise: Grammar and Usage (Class 11 notes)

Q52Conditionals

Had she studied harder, she ____ the examination.

awould pass
bwould have passed
cwill pass
dhad passed

Answer (b): Inverted third conditional (Had + subject + past participle) takes 'would have + past participle' in the result clause.

Revise: Grammar and Usage (Class 11 notes)

Q53Conditionals

Unless you hurry, you ____ the last bus.

awon't miss
bwould miss
cmissed
dwill miss

Answer (d): First conditional: 'unless' (= if not) with a present verb takes 'will + base verb'.

Revise: Grammar and Usage (Class 11 notes)

Q54Gerunds

He carefully avoided ____ the question.

ato answer
banswer
canswering
danswered

Answer (c): 'Avoid' is followed by a gerund (verb + -ing).

Revise: Grammar and Usage (Class 11 notes)

Q55Gerunds

I am looking forward to ____ you again next week.

asee
bseeing
csaw
dbe seeing

Answer (b): In 'look forward to', 'to' is a preposition, so a gerund follows.

Revise: Grammar and Usage (Class 11 notes)

Q56Gerunds

It is no use ____ over spilt milk.

ato cry
bcry
ccrying
dcried

Answer (c): The fixed pattern 'It is no use + gerund' needs the -ing form.

Revise: Grammar and Usage (Class 11 notes)

Q57Causative verbs

I had my car ____ yesterday.

arepair
brepairing
cto repair
drepaired

Answer (d): Causative 'have + object + past participle' shows someone else did the action for you.

Revise: Grammar and Usage (Class 11 notes)

Q58Causative verbs

She got her brother ____ the broken lamp.

afix
bto fix
cfixed
dfixing

Answer (b): Causative 'get + person + to-infinitive' (get someone to do something).

Revise: Grammar and Usage (Class 11 notes)

Q59Phrasal verbs

The cricket match was ____ because of heavy rain.

acalled on
bcalled up
ccalled off
dcalled in

Answer (c): 'Call off' is a phrasal verb meaning to cancel.

Revise: Grammar and Usage (Class 11 notes)

Q60Phrasal verbs

Rita takes ____ her mother; both are very patient.

aafter
bover
cup
doff

Answer (a): 'Take after' means to resemble a family member in looks or character.

Revise: Grammar and Usage (Class 11 notes)

Q61Phrasal verbs

We ran ____ an old friend at the market today.

aaway
bout
coff
dinto

Answer (d): 'Run into' means to meet someone by chance.

Revise: Grammar and Usage (Class 11 notes)

Q62Phrasal verbs

Please ____ this form and return it to the office.

afill with
bfill at
cfill by
dfill in

Answer (d): 'Fill in' (a form) means to complete it by writing the required details.

Revise: Grammar and Usage (Class 11 notes)

Q63Articles

She is ____ honest girl.

aan
ba
cthe
dno article

Answer (a): 'Honest' starts with a vowel sound (the 'h' is silent), so we use 'an'.

Revise: Grammar and Usage (Class 11 notes)

Q64Articles

____ Himalayas lie in the north of Nepal.

aA
bThe
cAn
dNo article

Answer (b): Names of mountain ranges take 'the'.

Revise: Grammar and Usage (Class 11 notes)

Q65Prepositions

He has been living in Pokhara ____ 2015.

afor
bsince
cfrom
dat

Answer (b): 'Since' is used with a point in time; 'for' is used with a period.

Revise: Grammar and Usage (Class 11 notes)

Q66Prepositions

The textbook is divided ____ ten chapters.

ainto
bby
cof
dto

Answer (a): 'Divided into' is used for splitting something into parts.

Revise: Grammar and Usage (Class 11 notes)

Q67Tenses

By the time we reached the hall, the programme ____.

ahas already started
bhad already started
cwas already starting
dalready starts

Answer (b): An action completed before another past action takes the past perfect.

Revise: Grammar and Usage (Class 11 notes)

Q68Tenses

I ____ this novel since last Monday.

aam reading
bhave been reading
cread
dhad read

Answer (b): 'Since' with a continuing action up to now takes the present perfect continuous.

Revise: Grammar and Usage (Class 11 notes)

Q69Voice

Choose the correct passive form of: "They are building a new bridge."

aA new bridge is built by them.
bA new bridge has been built by them.
cA new bridge was being built by them.
dA new bridge is being built by them.

Answer (d): Present continuous passive: is/are + being + past participle.

Revise: Grammar and Usage (Class 11 notes)

Q70Reported speech

Choose the correct reported form of: He said, "I am tired."

aHe said that he is tired.
bHe said that I was tired.
cHe said that he was tired.
dHe said that he had been tired.

Answer (c): In indirect speech the present tense backshifts to the past and 'I' changes to 'he'.

Revise: Grammar and Usage (Class 11 notes)

Q71Subject-verb agreement

Neither the teacher nor the students ____ present at the assembly.

awas
bwere
cis
dhas been

Answer (b): With neither...nor, the verb agrees with the nearer subject, 'students', which is plural.

Revise: Grammar and Usage (Class 11 notes)

Q72Subject-verb agreement

The number of applicants ____ increasing every year.

ais
bare
cwere
dhave been

Answer (a): 'The number of' takes a singular verb (unlike 'a number of').

Revise: Grammar and Usage (Class 11 notes)

Q73Question tags

She can swim, ____?

acan she
bisn't she
cdoesn't she
dcan't she

Answer (d): A positive statement takes a negative tag with the same auxiliary: can ... can't she.

Revise: Grammar and Usage (Class 11 notes)

Q74Modals

You ____ smoke here; it is strictly prohibited.

amust not
bneed not
cmay
dought

Answer (a): 'Must not' expresses prohibition.

Revise: Grammar and Usage (Class 11 notes)

Q75Degrees of comparison

Sita is ____ than her younger sister.

amost intelligent
bintelligenter
cmuch intelligent
dmore intelligent

Answer (d): Longer adjectives form the comparative with 'more' before the adjective, followed by 'than'.

Revise: Grammar and Usage (Class 11 notes)

Q76Synonyms

Choose the word closest in meaning to ABUNDANT.

ascarce
bplentiful
crare
dtiny

Answer (b): 'Abundant' means existing in large quantities, which is 'plentiful'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q77Antonyms

Choose the word opposite in meaning to TRANSPARENT.

aopaque
bclear
cthin
dglassy

Answer (a): 'Transparent' lets light through; its antonym 'opaque' does not.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q78One-word substitution

A person who can speak two languages fluently is called

apolyglot
bbilingual
clinguist
dinterpreter

Answer (b): 'Bilingual' = able to speak two languages ('polyglot' means many).

Revise: Vocabulary and Word Formation (Class 11 notes)

Q79Idioms

The idiom "to bite the bullet" means

ato eat very fast
bto speak angrily
cto face a painful situation bravely
dto avoid a difficult task

Answer (c): It means to endure something unpleasant with courage.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q80Idioms

The idiom "once in a blue moon" means

avery rarely
bevery month
cvery quickly
dat midnight

Answer (a): A blue moon is a rare event, so the phrase means very seldom.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q81Spelling

Choose the correctly spelt word.

aAccomodation
bAccommodation
cAcommodation
dAccommodetion

Answer (b): 'Accommodation' has double c and double m.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q82Word formation

The noun form of the verb 'decide' is

adecision
bdecidence
cdecideness
ddecided

Answer (a): Decide takes the suffix change -ide to -ision: decision.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q83Confused words

The teacher gave the students some good ____ about the exam.

aadvise
badvices
cadvisor
dadvice

Answer (d): 'Advice' is the uncountable noun; 'advise' is the verb.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q84Concord

Choose the grammatically correct sentence.

aEach of the boys have finished his work.
bEach of the boys have finished their works.
cEach of the boys has finished his work.
dEach of the boys are finished his work.

Answer (c): 'Each' is singular, so it takes 'has'; 'work' is uncountable here.

Revise: Grammar and Usage (Class 11 notes)

Q85Conjunctions

____ it was raining heavily, we went out for a walk.

aBecause
bUnless
cAlthough
dSince

Answer (c): The two clauses contrast, so the concessive conjunction 'although' fits.

Revise: Grammar and Usage (Class 11 notes)

Q86Relative pronouns

The man ____ car was stolen reported it to the police.

awhose
bwho
cwhom
dwhich

Answer (a): 'Whose' shows possession for a person (the man's car).

Revise: Grammar and Usage (Class 11 notes)

Q87Reading comprehension

Read the passage and answer. Bamboo is one of the fastest growing plants in the world. Some species can grow almost one metre in a single day. Because its roots hold the soil firmly, bamboo is often planted on hillsides to prevent landslides. It is also strong yet light, so people use it to build houses, furniture and scaffolding. Unlike trees, bamboo does not die when it is harvested; new shoots keep rising from the same roots. Which of the following best expresses the main idea of the passage?

aBamboo is a fast-growing and very useful plant.
bBamboo can only grow on hillsides.
cTrees are more useful than bamboo.
dBamboo houses are always heavy.

Answer (a): The passage covers growth speed, soil protection and uses, so the main idea is that bamboo is fast-growing and useful.

Revise: Reading Comprehension (Class 11 notes)

Q88Reading comprehension

aIts roots hold the soil and prevent landslides.
bIt needs very little water.
cIt gives shade to travellers.
dIt grows only on slopes.

Answer (a): The passage says its roots hold the soil firmly to prevent landslides.

Revise: Reading Comprehension (Class 11 notes)

Q89Reading comprehension

aIt dies completely.
bIt must be replanted from seed.
cNew shoots rise from the same roots.
dIt stops growing for years.

Answer (c): The last sentence: unlike trees, it does not die; new shoots keep rising.

Revise: Reading Comprehension (Class 11 notes)

Q90Reading comprehension

Read the passage and answer. Bamboo is one of the fastest growing plants in the world. Some species can grow almost one metre in a single day. Because its roots hold the soil firmly, bamboo is often planted on hillsides to prevent landslides. It is also strong yet light, so people use it to build houses, furniture and scaffolding. Unlike trees, bamboo does not die when it is harvested; new shoots keep rising from the same roots. The word 'harvested' in the passage most nearly means

acut and collected for use
bplanted in rows
cwatered regularly
dburnt for fuel

Answer (a): To harvest is to cut and gather a crop or plant for use.

Revise: Reading Comprehension (Class 11 notes)

General Knowledge and IT

Q91World geography

What is the capital city of Australia?

aCanberra
bSydney
cMelbourne
dPerth

Answer (a): Canberra, not Sydney, is the capital of Australia.

Q92Geography of Nepal

Which is the longest river within Nepal?

aKoshi
bGandaki
cMahakali
dKarnali

Answer (d): The Karnali is Nepal's longest river (about 507 km inside Nepal).

Q93Nepal general knowledge

The national flower of Nepal is

aLotus
bRose
cMarigold
dRhododendron (Lali Gurans)

Answer (d): Rhododendron (Lali Gurans) is Nepal's national flower.

Q94Science

Which is the largest planet of the solar system?

aJupiter
bSaturn
cNeptune
dEarth

Answer (a): Jupiter is the largest planet in our solar system.

Q95Nepal history

Nepal was declared a federal democratic republic in the year

a2006 AD
b2007 AD
c2015 AD
d2008 AD

Answer (d): The first Constituent Assembly declared the republic on 28 May 2008 (2065 BS).

Q96Computer memory

Which of the following is a volatile memory?

aROM
bRAM
cHard disk
dPen drive

Answer (b): RAM loses its content when power is off; ROM, disks and flash keep data.

Revise: Computer System (Class 11 notes)

Q97HTML

Which HTML tag creates the largest heading?

a<h6>
b<head>
c<title>
d<h1>

Answer (d): Headings run from <h1> (largest) to <h6> (smallest).

Revise: Web Technology I (Class 11 notes)

Q98Number systems

The decimal equivalent of the binary number 11010 is

Answer (d): $16+8+0+2+0=26$.

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

Q99Number systems

The hexadecimal equivalent of decimal 255 is

Answer (d): $255=15\times16+15$, and 15 is F, so FF.

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

Q100Operating system

Which of the following is an operating system?

aOracle
bLinux
cPython
dExcel

Answer (b): Linux is an operating system; Oracle is a DBMS, Python a language, Excel a spreadsheet.

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

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Mathematics

Q1Logarithms

The value of

\log_2 64 + \log_3 81

isThe value of $\log_2 64 + \log_3 81$ is

Answer (c): $\log_2 64=6$ since $2^6=64$ , and $\log_3 81=4$ since $3^4=81$ . Sum $=10$ .$\log_2 64=6$ since $2^6=64$, and $\log_3 81=4$ since $3^4=81$. Sum $=10$.

Revise: Algebra (Class 11 notes)

Q2Logarithms

\log_x 125 = 3

, then

x

equalsIf $\log_x 125 = 3$, then $x$ equals

Answer (a): $\log_x 125=3$ means $x^3=125$ , so $x=5$ .$\log_x 125=3$ means $x^3=125$, so $x=5$.

Revise: Algebra (Class 11 notes)

Q3Logarithms

The value of

\log_{10} 2 + \log_{10} 5

isThe value of $\log_{10} 2 + \log_{10} 5$ is

a0
b10
c $\frac{1}{10}$ $\frac{1}{10}$
d1

Answer (d): $\log 2+\log 5=\log(2\times5)=\log 10=1$ .$\log 2+\log 5=\log(2\times5)=\log 10=1$.

Revise: Algebra (Class 11 notes)

Q4Logarithms

\log_3 (x-1) = 2

, then

x

isIf $\log_3 (x-1) = 2$, then $x$ is

Answer (c): $x-1=3^2=9$ , so $x=10$ .$x-1=3^2=9$, so $x=10$.

Revise: Algebra (Class 11 notes)

Q5Determinants

The determinant of the matrix

\begin{bmatrix}1&2\\3&4\end{bmatrix}

isThe determinant of the matrix $\begin{bmatrix}1&2\3&4\end{bmatrix}$ is

a $2$
b $10$
c $-2$
d $-10$

Answer (c): $\det=1\cdot4-2\cdot3=4-6=-2$ .$\det=1\cdot4-2\cdot3=4-6=-2$.

Revise: Algebra (Class 12 notes)

Q6Matrices

A=\begin{bmatrix}2&1\\0&3\end{bmatrix}

and

B=\begin{bmatrix}1&0\\4&2\end{bmatrix}

, the element in the second row and first column of

AB

isIf $A=\begin{bmatrix}2&1\0&3\end{bmatrix}$ and $B=\begin{bmatrix}1&0\4&2\end{bmatrix}$, the element in the second row and first column of $AB$ is

Answer (d): Row 2 of $A$ is $(0,3)$ and column 1 of $B$ is $(1,4)$ : $0\cdot1+3\cdot4=12$ .Row 2 of $A$ is $(0,3)$ and column 1 of $B$ is $(1,4)$: $0\cdot1+3\cdot4=12$.

Revise: Algebra (Class 12 notes)

Q7Determinants

\begin{vmatrix}x&2\\3&4\end{vmatrix}=2

, then

x

isIf $\begin{vmatrix}x&2\3&4\end{vmatrix}=2$, then $x$ is

Answer (b): $4x-6=2\Rightarrow 4x=8\Rightarrow x=2$ .$4x-6=2\Rightarrow 4x=8\Rightarrow x=2$.

Revise: Algebra (Class 12 notes)

Q8Matrices

The matrix

\begin{bmatrix}k&2\\4&8\end{bmatrix}

is singular when

k

equalsThe matrix $\begin{bmatrix}k&2\4&8\end{bmatrix}$ is singular when $k$ equals

Answer (d): Singular means determinant $0$ : $8k-8=0\Rightarrow k=1$ .Singular means determinant $0$: $8k-8=0\Rightarrow k=1$.

Revise: Algebra (Class 12 notes)

Q9Compound interest

The compound interest on Rs 10,000 for 2 years at 10% per annum, compounded annually, is

aRs 2,000
bRs 2,100
cRs 2,200
dRs 2,210

Answer (b): $A=10000(1.1)^2=12100$ , so $CI=12100-10000=2100$ .$A=10000(1.1)^2=12100$, so $CI=12100-10000=2100$.

Q10Compound interest

The difference between compound interest and simple interest on Rs 4,000 for 2 years at 10% per annum is

aRs 20
bRs 40
cRs 400
dRs 80

Answer (b): Difference for 2 years $=P\left(\frac{r}{100}\right)^2=4000\times0.01=40$ .Difference for 2 years $=P\left(\frac{r}{100}\right)^2=4000\times0.01=40$.

Q11Mensuration

The volume of a cylinder of radius 7 cm and height 10 cm is (take

\pi=\frac{22}{7}

)The volume of a cylinder of radius 7 cm and height 10 cm is (take $\pi=\frac{22}{7}$)

a770 cm $^3$ 770 cm$^3$
b440 cm $^3$ 440 cm$^3$
c1540 cm $^3$ 1540 cm$^3$
d1100 cm $^3$ 1100 cm$^3$

Answer (c): $V=\pi r^2h=\frac{22}{7}\times49\times10=1540$ .$V=\pi r^2h=\frac{22}{7}\times49\times10=1540$.

Q12Mensuration

A cone has base radius 5 cm and slant height 13 cm. Its volume is

a $300\pi$ cm $^3$ $300\pi$ cm$^3$
b $100\pi$ cm $^3$ $100\pi$ cm$^3$
c $65\pi$ cm $^3$ $65\pi$ cm$^3$
d $125\pi$ cm $^3$ $125\pi$ cm$^3$

Answer (b): Height $=\sqrt{13^2-5^2}=12$ . $V=\frac13\pi r^2h=\frac13\pi\cdot25\cdot12=100\pi$ .Height $=\sqrt{13^2-5^2}=12$. $V=\frac13\pi r^2h=\frac13\pi\cdot25\cdot12=100\pi$.

Q13Mensuration

The surface area of a sphere is 616 cm

^2

. Its radius is (take

\pi=\frac{22}{7}

)The surface area of a sphere is 616 cm$^2$. Its radius is (take $\pi=\frac{22}{7}$)

a7 cm
b14 cm
c3.5 cm
d49 cm

Answer (a): $4\pi r^2=616\Rightarrow r^2=\frac{616\times7}{88}=49$ , so $r=7$ .$4\pi r^2=616\Rightarrow r^2=\frac{616\times7}{88}=49$, so $r=7$.

Q14Mensuration

The diagonal of a rectangle is 13 cm and one side is 12 cm. Its area is

a156 cm $^2$ 156 cm$^2$
b30 cm $^2$ 30 cm$^2$
c65 cm $^2$ 65 cm$^2$
d60 cm $^2$ 60 cm$^2$

Answer (d): Other side $=\sqrt{13^2-12^2}=5$ . Area $=12\times5=60$ .Other side $=\sqrt{13^2-12^2}=5$. Area $=12\times5=60$.

Q15Probability

Two dice are thrown together. The probability that the sum is 8 is

a $\frac{5}{36}$ $\frac{5}{36}$
b $\frac{1}{6}$ $\frac{1}{6}$
c $\frac{1}{9}$ $\frac{1}{9}$
d $\frac{7}{36}$ $\frac{7}{36}$

Answer (a): Favourable: (2,6),(3,5),(4,4),(5,3),(6,2) = 5 out of 36.

Revise: Statistics and Probability (Class 11 notes)

Q16Probability

A bag has 3 red and 5 blue balls. Two balls are drawn one after another without replacement. The probability that both are red is

a $\frac{9}{64}$ $\frac{9}{64}$
b $\frac{3}{8}$ $\frac{3}{8}$
c $\frac{3}{28}$ $\frac{3}{28}$
d $\frac{1}{4}$ $\frac{1}{4}$

Answer (c): $\frac38\times\frac27=\frac{6}{56}=\frac{3}{28}$ .$\frac38\times\frac27=\frac{6}{56}=\frac{3}{28}$.

Revise: Statistics and Probability (Class 11 notes)

Q17Probability

A

and

B

are independent events with

P(A)=0.4

and

P(B)=0.5

, then

P(A\cup B)

isIf $A$ and $B$ are independent events with $P(A)=0.4$ and $P(B)=0.5$, then $P(A\cup B)$ is

a0.9
b0.2
c0.6
d0.7

Answer (d): $P(A\cap B)=0.4\times0.5=0.2$ . $P(A\cup B)=0.4+0.5-0.2=0.7$ .$P(A\cap B)=0.4\times0.5=0.2$. $P(A\cup B)=0.4+0.5-0.2=0.7$.

Revise: Statistics and Probability (Class 11 notes)

Q18Probability

A fair coin is tossed three times. The probability of getting at least one head is

a $\frac{1}{8}$ $\frac{1}{8}$
b $\frac{7}{8}$ $\frac{7}{8}$
c $\frac{3}{8}$ $\frac{3}{8}$
d $\frac{1}{2}$ $\frac{1}{2}$

Answer (b): $P=1-P(\text{no head})=1-\left(\frac12\right)^3=\frac78$ .$P=1-P(\text{no head})=1-\left(\frac12\right)^3=\frac78$.

Revise: Statistics and Probability (Class 11 notes)

Q19Coordinate geometry

The distance between the points

(1,2)

and

(4,6)

isThe distance between the points $(1,2)$ and $(4,6)$ is

Answer (c): $\sqrt{(4-1)^2+(6-2)^2}=\sqrt{9+16}=5$ .$\sqrt{(4-1)^2+(6-2)^2}=\sqrt{9+16}=5$.

Revise: Analytic geometry (Class 11 notes)

Q20Straight line

The equation of the line through

(2,3)

with slope 2 isThe equation of the line through $(2,3)$ with slope 2 is

a $2x-y+1=0$ $2x-y+1=0$
b $x-2y+4=0$ $x-2y+4=0$
c $2x-y-1=0$ $2x-y-1=0$
d $2x+y-7=0$ $2x+y-7=0$

Answer (c): $y-3=2(x-2)\Rightarrow y=2x-1\Rightarrow 2x-y-1=0$ .$y-3=2(x-2)\Rightarrow y=2x-1\Rightarrow 2x-y-1=0$.

Revise: Analytic geometry (Class 11 notes)

Q21Circle

The radius of the circle

x^2+y^2-6x+8y=0

isThe radius of the circle $x^2+y^2-6x+8y=0$ is

Answer (b): Centre $(3,-4)$ , so $r^2=9+16-0=25$ and $r=5$ .Centre $(3,-4)$, so $r^2=9+16-0=25$ and $r=5$.

Revise: Analytic geometry (Class 11 notes)

Q22Coordinate geometry

The area of the triangle with vertices

(0,0)

(4,0)

and

(0,6)

isThe area of the triangle with vertices $(0,0)$, $(4,0)$ and $(0,6)$ is

a24 square units
b12 square units
c10 square units
d6 square units

Answer (b): Right triangle with legs 4 and 6: $\frac12\times4\times6=12$ .Right triangle with legs 4 and 6: $\frac12\times4\times6=12$.

Revise: Analytic geometry (Class 11 notes)

Q23Straight line

The perpendicular distance of the point

(3,4)

from the line

3x+4y-5=0

isThe perpendicular distance of the point $(3,4)$ from the line $3x+4y-5=0$ is

a20
b5
c $\frac45$ $\frac45$
d4

Answer (d): $d=\frac{|3(3)+4(4)-5|}{\sqrt{3^2+4^2}}=\frac{20}{5}=4$ .$d=\frac{|3(3)+4(4)-5|}{\sqrt{3^2+4^2}}=\frac{20}{5}=4$.

Revise: Analytic geometry (Class 11 notes)

Q24Straight line

The slope of the line

3x-6y+5=0

isThe slope of the line $3x-6y+5=0$ is

a $\frac12$ $\frac12$
b $2$
c $-\frac12$ $-\frac12$
d $-2$

Answer (a): $y=\frac{3x+5}{6}$ , so slope $=\frac36=\frac12$ .$y=\frac{3x+5}{6}$, so slope $=\frac36=\frac12$.

Revise: Analytic geometry (Class 11 notes)

Q25Trigonometric ratios

The value of

\sin30^\circ\cos60^\circ+\cos30^\circ\sin60^\circ

isThe value of $\sin30^\circ\cos60^\circ+\cos30^\circ\sin60^\circ$ is

a1
b $\frac12$ $\frac12$
c $\frac{\sqrt3}{2}$ $\frac{\sqrt3}{2}$
d0

Answer (a): It equals $\sin(30^\circ+60^\circ)=\sin90^\circ=1$ . Check: $\frac14+\frac34=1$ .It equals $\sin(30^\circ+60^\circ)=\sin90^\circ=1$. Check: $\frac14+\frac34=1$.

Revise: Trigonometry (Class 11 notes)

Q26Trigonometric ratios

\sin\theta=\frac35

and

\theta

is acute, then

\tan\theta

isIf $\sin\theta=\frac35$ and $\theta$ is acute, then $\tan\theta$ is

a $\frac43$ $\frac43$
b $\frac45$ $\frac45$
c $\frac34$ $\frac34$
d $\frac54$ $\frac54$

Answer (c): $\cos\theta=\frac45$ , so $\tan\theta=\frac{3/5}{4/5}=\frac34$ .$\cos\theta=\frac45$, so $\tan\theta=\frac{3/5}{4/5}=\frac34$.

Revise: Trigonometry (Class 11 notes)

Q27Multiple angles

\cos A=\frac45

and

A

is acute, then

\sin2A

isIf $\cos A=\frac45$ and $A$ is acute, then $\sin2A$ is

a $\frac{12}{25}$ $\frac{12}{25}$
b $\frac{7}{25}$ $\frac{7}{25}$
c $\frac{24}{25}$ $\frac{24}{25}$
d $\frac85$ $\frac85$

Answer (c): $\sin A=\frac35$ . $\sin2A=2\sin A\cos A=2\cdot\frac35\cdot\frac45=\frac{24}{25}$ .$\sin A=\frac35$. $\sin2A=2\sin A\cos A=2\cdot\frac35\cdot\frac45=\frac{24}{25}$.

Revise: Trigonometry (Class 11 notes)

Q28Product to sum

The value of

\cos75^\circ\cos15^\circ

isThe value of $\cos75^\circ\cos15^\circ$ is

a $\frac12$ $\frac12$
b $\frac{\sqrt3}{4}$ $\frac{\sqrt3}{4}$
c1
d $\frac14$ $\frac14$

Answer (d): Use $\cos A\cos B=\frac12[\cos(A+B)+\cos(A-B)]=\frac12[\cos90^\circ+\cos60^\circ]=\frac12\cdot\frac12=\frac14$ .Use $\cos A\cos B=\frac12[\cos(A+B)+\cos(A-B)]=\frac12[\cos90^\circ+\cos60^\circ]=\frac12\cdot\frac12=\frac14$.

Revise: Trigonometry (Class 11 notes)

Q29Trigonometric functions

The period of the function

\sin3x

isThe period of the function $\sin3x$ is

a $3\pi$
b $2\pi$
c $\frac{2\pi}{3}$ $\frac{2\pi}{3}$
d $\frac{\pi}{3}$ $\frac{\pi}{3}$

Answer (c): Period of $\sin kx$ is $\frac{2\pi}{k}$ , so here $\frac{2\pi}{3}$ .Period of $\sin kx$ is $\frac{2\pi}{k}$, so here $\frac{2\pi}{3}$.

Revise: Trigonometry (Class 11 notes)

Q30Differentiation

The derivative of

x^2e^x

with respect to

x

isThe derivative of $x^2e^x$ with respect to $x$ is

a $2xe^x$ $2xe^x$
b $x^2e^x$ $x^2e^x$
c $e^x(x^2+2x)$ $e^x(x^2+2x)$
d $e^x(x^2+2)$ $e^x(x^2+2)$

Answer (c): Product rule: $2x\cdot e^x+x^2\cdot e^x=e^x(x^2+2x)$ .Product rule: $2x\cdot e^x+x^2\cdot e^x=e^x(x^2+2x)$.

Revise: Calculus (Class 11 notes)

Q31Integration

The value of

\int_0^2(3x^2+2x)\,dx

isThe value of $\int_0^2(3x^2+2x),dx$ is

Answer (d): $[x^3+x^2]_0^2=8+4=12$ .$[x^3+x^2]_0^2=8+4=12$.

Revise: Calculus (Class 12 notes)

Q32Limits

The value of

\lim_{x\to0}\frac{\sin5x}{3x}

isThe value of $\lim_{x\to0}\frac{\sin5x}{3x}$ is

a $\frac35$ $\frac35$
b $\frac53$ $\frac53$
c1
d15

Answer (b): $\frac{\sin5x}{3x}=\frac53\cdot\frac{\sin5x}{5x}\to\frac53\cdot1$ .$\frac{\sin5x}{3x}=\frac53\cdot\frac{\sin5x}{5x}\to\frac53\cdot1$.

Revise: Calculus (Class 11 notes)

Q33Maxima and minima

The local maximum value of

f(x)=x^3-3x

isThe local maximum value of $f(x)=x^3-3x$ is

a $-2$
b2
c0
d4

Answer (b): $f'(x)=3x^2-3=0\Rightarrow x=\pm1$ . $f''(-1)=-6<0$ , so maximum at $x=-1$ : $f(-1)=-1+3=2$ .$f'(x)=3x^2-3=0\Rightarrow x=\pm1$. $f''(-1)=-6<0$, so maximum at $x=-1$: $f(-1)=-1+3=2$.

Revise: Calculus (Class 11 notes)

Q34Mean

The mean of six numbers is 15. When one number is removed, the mean of the remaining five becomes 14. The number removed is

Answer (b): Total $=6\times15=90$ ; remaining total $=5\times14=70$ . Removed $=90-70=20$ .Total $=6\times15=90$; remaining total $=5\times14=70$. Removed $=90-70=20$.

Revise: Statistics and Probability (Class 11 notes)

Q35Median

The median of the data 3, 7, 5, 13, 9, 11 is

a7
b9
c8
d8.5

Answer (c): Sorted: 3, 5, 7, 9, 11, 13. Median is the mean of the 3rd and 4th: $\frac{7+9}{2}=8$ .Sorted: 3, 5, 7, 9, 11, 13. Median is the mean of the 3rd and 4th: $\frac{7+9}{2}=8$.

Revise: Statistics and Probability (Class 11 notes)

Q36Dispersion

A data set has mean 50 and standard deviation 10. Its coefficient of variation is

a20%
b5%
c40%
d0.2%

Answer (a): $CV=\frac{\sigma}{\bar x}\times100=\frac{10}{50}\times100=20\%$ .$CV=\frac{\sigma}{\bar x}\times100=\frac{10}{50}\times100=20%$.

Revise: Statistics and Probability (Class 11 notes)

Q37Vectors

\vec a=2\hat i+\hat j-\hat k

and

\vec b=\hat i+3\hat j+\hat k

, then

\vec a\cdot\vec b

isIf $\vec a=2\hat i+\hat j-\hat k$ and $\vec b=\hat i+3\hat j+\hat k$, then $\vec a\cdot\vec b$ is

Answer (d): $2(1)+1(3)+(-1)(1)=2+3-1=4$ .$2(1)+1(3)+(-1)(1)=2+3-1=4$.

Revise: Vectors (Class 11 notes)

Q38Vectors

The vectors

2\hat i+p\hat j

and

3\hat i-6\hat j

are perpendicular when

p

equalsThe vectors $2\hat i+p\hat j$ and $3\hat i-6\hat j$ are perpendicular when $p$ equals

a $-1$
b2
c1
d3

Answer (c): Dot product zero: $2(3)+p(-6)=0\Rightarrow p=1$ .Dot product zero: $2(3)+p(-6)=0\Rightarrow p=1$.

Revise: Vectors (Class 11 notes)

Q39Quadratic equations

\alpha

and

\beta

are the roots of

x^2-5x+6=0

, then

\alpha^2+\beta^2

isIf $\alpha$ and $\beta$ are the roots of $x^2-5x+6=0$, then $\alpha^2+\beta^2$ is

Answer (a): $\alpha+\beta=5$ , $\alpha\beta=6$ . $\alpha^2+\beta^2=25-12=13$ .$\alpha+\beta=5$, $\alpha\beta=6$. $\alpha^2+\beta^2=25-12=13$.

Revise: Algebra (Class 11 notes)

Q40Arithmetic progression

The sum of the first 20 terms of the AP 3, 7, 11, ... is

a800
b840
c780
d820

Answer (d): $S_n=\frac n2[2a+(n-1)d]=10[6+19\cdot4]=10\times82=820$ .$S_n=\frac n2[2a+(n-1)d]=10[6+19\cdot4]=10\times82=820$.

Revise: Algebra (Class 11 notes)

Q41Geometric progression

The sum to infinity of the series

8+4+2+1+\dots

isThe sum to infinity of the series $8+4+2+1+\dots$ is

Answer (a): $a=8$ , $r=\frac12$ : $S_\infty=\frac{a}{1-r}=\frac{8}{1/2}=16$ .$a=8$, $r=\frac12$: $S_\infty=\frac{a}{1-r}=\frac{8}{1/2}=16$.

Revise: Algebra (Class 11 notes)

Q42Permutations

The number of different arrangements of the letters of the word LEVEL is

a60
b120
c30
d15

Answer (c): Five letters with E repeated twice and L twice: $\frac{5!}{2!\,2!}=30$ .Five letters with E repeated twice and L twice: $\frac{5!}{2!,2!}=30$.

Revise: Algebra (Class 11 notes)

Q43Combinations

The value of

^8C_3

isThe value of $^8C_3$ is

a56
b336
c24
d28

Answer (a): $^8C_3=\frac{8\cdot7\cdot6}{3\cdot2\cdot1}=56$ .$^8C_3=\frac{8\cdot7\cdot6}{3\cdot2\cdot1}=56$.

Revise: Algebra (Class 11 notes)

Q44Binomial theorem

The coefficient of

x^2

in the expansion of

(1+x)^6

isThe coefficient of $x^2$ in the expansion of $(1+x)^6$ is

Answer (c): Coefficient is $^6C_2=\frac{6\cdot5}{2}=15$ .Coefficient is $^6C_2=\frac{6\cdot5}{2}=15$.

Revise: Algebra (Class 11 notes)

Q45Inequalities

The solution set of

|2x-3|<5

isThe solution set of $|2x-3|<5$ is

a $-4<x<1$ $-4<x<1$
b $1<x<4$ $1<x<4$
c $-1<x<4$ $-1<x<4$
d $x<-1$ or $x>4$ $x<-1$ or $x>4$

Answer (c): $-5<2x-3<5\Rightarrow -2<2x<8\Rightarrow -1<x<4$ .$-5<2x-3<5\Rightarrow -2<2x<8\Rightarrow -1<x<4$.

Revise: Algebra (Class 11 notes)

Q46Profit and loss

A shopkeeper marks an article 40% above its cost price and allows a 10% discount. His profit percent is

a30%
b26%
c50%
d25%

Answer (b): Let CP $=100$ . Marked $=140$ . Selling $=140\times0.9=126$ . Profit $=26\%$ .Let CP $=100$. Marked $=140$. Selling $=140\times0.9=126$. Profit $=26%$.

Q47Number series

What comes next in the series 2, 6, 12, 20, 30, ... ?

Answer (a): Terms are $n(n+1)$ : $1\cdot2,2\cdot3,3\cdot4,4\cdot5,5\cdot6$ , so next is $6\cdot7=42$ . Differences 4, 6, 8, 10, 12 agree.Terms are $n(n+1)$: $1\cdot2,2\cdot3,3\cdot4,4\cdot5,5\cdot6$, so next is $6\cdot7=42$. Differences 4, 6, 8, 10, 12 agree.

Q48Clocks

What is the angle between the hour hand and the minute hand of a clock at 4:30?

a $30^\circ$ $30^\circ$
b $60^\circ$ $60^\circ$
c $45^\circ$ $45^\circ$
d $15^\circ$ $15^\circ$

Answer (c): Hour hand: $4\times30+15=135^\circ$ . Minute hand: $180^\circ$ . Difference $=45^\circ$ .Hour hand: $4\times30+15=135^\circ$. Minute hand: $180^\circ$. Difference $=45^\circ$.

Q49Coding-decoding

In a certain code, CAT is written as ECV. How is DOG written in that code?

aEPH
bFPI
cFQH
dFQI

Answer (d): Each letter moves 2 places forward: D to F, O to Q, G to I.

Q50Ranking

Ram is 7th from the top and 12th from the bottom in a class. How many students are in the class?

Answer (a): Total $=7+12-1=18$ (Ram is counted in both ranks).Total $=7+12-1=18$ (Ram is counted in both ranks).

English

Q51Conditionals

If I ____ you, I would apologise to her at once.

aam
bwere
cwas being
dwill be

Answer (b): Second conditional (unreal present) uses 'were' for all persons after 'if': If I were you, I would...

Revise: Grammar and Usage (Class 11 notes)

Q52Conditionals

Had she studied harder, she ____ the examination.

awould pass
bwould have passed
cwill pass
dhad passed

Answer (b): Inverted third conditional (Had + subject + past participle) takes 'would have + past participle' in the result clause.

Revise: Grammar and Usage (Class 11 notes)

Q53Conditionals

Unless you hurry, you ____ the last bus.

awon't miss
bwould miss
cmissed
dwill miss

Answer (d): First conditional: 'unless' (= if not) with a present verb takes 'will + base verb'.

Revise: Grammar and Usage (Class 11 notes)

Q54Gerunds

He carefully avoided ____ the question.

ato answer
banswer
canswering
danswered

Answer (c): 'Avoid' is followed by a gerund (verb + -ing).

Revise: Grammar and Usage (Class 11 notes)

Q55Gerunds

I am looking forward to ____ you again next week.

asee
bseeing
csaw
dbe seeing

Answer (b): In 'look forward to', 'to' is a preposition, so a gerund follows.

Revise: Grammar and Usage (Class 11 notes)

Q56Gerunds

It is no use ____ over spilt milk.

ato cry
bcry
ccrying
dcried

Answer (c): The fixed pattern 'It is no use + gerund' needs the -ing form.

Revise: Grammar and Usage (Class 11 notes)

Q57Causative verbs

I had my car ____ yesterday.

arepair
brepairing
cto repair
drepaired

Answer (d): Causative 'have + object + past participle' shows someone else did the action for you.

Revise: Grammar and Usage (Class 11 notes)

Q58Causative verbs

She got her brother ____ the broken lamp.

afix
bto fix
cfixed
dfixing

Answer (b): Causative 'get + person + to-infinitive' (get someone to do something).

Revise: Grammar and Usage (Class 11 notes)

Q59Phrasal verbs

The cricket match was ____ because of heavy rain.

acalled on
bcalled up
ccalled off
dcalled in

Answer (c): 'Call off' is a phrasal verb meaning to cancel.

Revise: Grammar and Usage (Class 11 notes)

Q60Phrasal verbs

Rita takes ____ her mother; both are very patient.

aafter
bover
cup
doff

Answer (a): 'Take after' means to resemble a family member in looks or character.

Revise: Grammar and Usage (Class 11 notes)

Q61Phrasal verbs

We ran ____ an old friend at the market today.

aaway
bout
coff
dinto

Answer (d): 'Run into' means to meet someone by chance.

Revise: Grammar and Usage (Class 11 notes)

Q62Phrasal verbs

Please ____ this form and return it to the office.

afill with
bfill at
cfill by
dfill in

Answer (d): 'Fill in' (a form) means to complete it by writing the required details.

Revise: Grammar and Usage (Class 11 notes)

Q63Articles

She is ____ honest girl.

aan
ba
cthe
dno article

Answer (a): 'Honest' starts with a vowel sound (the 'h' is silent), so we use 'an'.

Revise: Grammar and Usage (Class 11 notes)

Q64Articles

____ Himalayas lie in the north of Nepal.

aA
bThe
cAn
dNo article

Answer (b): Names of mountain ranges take 'the'.

Revise: Grammar and Usage (Class 11 notes)

Q65Prepositions

He has been living in Pokhara ____ 2015.

afor
bsince
cfrom
dat

Answer (b): 'Since' is used with a point in time; 'for' is used with a period.

Revise: Grammar and Usage (Class 11 notes)

Q66Prepositions

The textbook is divided ____ ten chapters.

ainto
bby
cof
dto

Answer (a): 'Divided into' is used for splitting something into parts.

Revise: Grammar and Usage (Class 11 notes)

Q67Tenses

By the time we reached the hall, the programme ____.

ahas already started
bhad already started
cwas already starting
dalready starts

Answer (b): An action completed before another past action takes the past perfect.

Revise: Grammar and Usage (Class 11 notes)

Q68Tenses

I ____ this novel since last Monday.

aam reading
bhave been reading
cread
dhad read

Answer (b): 'Since' with a continuing action up to now takes the present perfect continuous.

Revise: Grammar and Usage (Class 11 notes)

Q69Voice

Choose the correct passive form of: "They are building a new bridge."

aA new bridge is built by them.
bA new bridge has been built by them.
cA new bridge was being built by them.
dA new bridge is being built by them.

Answer (d): Present continuous passive: is/are + being + past participle.

Revise: Grammar and Usage (Class 11 notes)

Q70Reported speech

Choose the correct reported form of: He said, "I am tired."

aHe said that he is tired.
bHe said that I was tired.
cHe said that he was tired.
dHe said that he had been tired.

Answer (c): In indirect speech the present tense backshifts to the past and 'I' changes to 'he'.

Revise: Grammar and Usage (Class 11 notes)

Q71Subject-verb agreement

Neither the teacher nor the students ____ present at the assembly.

awas
bwere
cis
dhas been

Answer (b): With neither...nor, the verb agrees with the nearer subject, 'students', which is plural.

Revise: Grammar and Usage (Class 11 notes)

Q72Subject-verb agreement

The number of applicants ____ increasing every year.

ais
bare
cwere
dhave been

Answer (a): 'The number of' takes a singular verb (unlike 'a number of').

Revise: Grammar and Usage (Class 11 notes)

Q73Question tags

She can swim, ____?

acan she
bisn't she
cdoesn't she
dcan't she

Answer (d): A positive statement takes a negative tag with the same auxiliary: can ... can't she.

Revise: Grammar and Usage (Class 11 notes)

Q74Modals

You ____ smoke here; it is strictly prohibited.

amust not
bneed not
cmay
dought

Answer (a): 'Must not' expresses prohibition.

Revise: Grammar and Usage (Class 11 notes)

Q75Degrees of comparison

Sita is ____ than her younger sister.

amost intelligent
bintelligenter
cmuch intelligent
dmore intelligent

Answer (d): Longer adjectives form the comparative with 'more' before the adjective, followed by 'than'.

Revise: Grammar and Usage (Class 11 notes)

Q76Synonyms

Choose the word closest in meaning to ABUNDANT.

ascarce
bplentiful
crare
dtiny

Answer (b): 'Abundant' means existing in large quantities, which is 'plentiful'.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q77Antonyms

Choose the word opposite in meaning to TRANSPARENT.

aopaque
bclear
cthin
dglassy

Answer (a): 'Transparent' lets light through; its antonym 'opaque' does not.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q78One-word substitution

A person who can speak two languages fluently is called

apolyglot
bbilingual
clinguist
dinterpreter

Answer (b): 'Bilingual' = able to speak two languages ('polyglot' means many).

Revise: Vocabulary and Word Formation (Class 11 notes)

Q79Idioms

The idiom "to bite the bullet" means

ato eat very fast
bto speak angrily
cto face a painful situation bravely
dto avoid a difficult task

Answer (c): It means to endure something unpleasant with courage.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q80Idioms

The idiom "once in a blue moon" means

avery rarely
bevery month
cvery quickly
dat midnight

Answer (a): A blue moon is a rare event, so the phrase means very seldom.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q81Spelling

Choose the correctly spelt word.

aAccomodation
bAccommodation
cAcommodation
dAccommodetion

Answer (b): 'Accommodation' has double c and double m.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q82Word formation

The noun form of the verb 'decide' is

adecision
bdecidence
cdecideness
ddecided

Answer (a): Decide takes the suffix change -ide to -ision: decision.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q83Confused words

The teacher gave the students some good ____ about the exam.

aadvise
badvices
cadvisor
dadvice

Answer (d): 'Advice' is the uncountable noun; 'advise' is the verb.

Revise: Vocabulary and Word Formation (Class 11 notes)

Q84Concord

Choose the grammatically correct sentence.

aEach of the boys have finished his work.
bEach of the boys have finished their works.
cEach of the boys has finished his work.
dEach of the boys are finished his work.

Answer (c): 'Each' is singular, so it takes 'has'; 'work' is uncountable here.

Revise: Grammar and Usage (Class 11 notes)

Q85Conjunctions

____ it was raining heavily, we went out for a walk.

aBecause
bUnless
cAlthough
dSince

Answer (c): The two clauses contrast, so the concessive conjunction 'although' fits.

Revise: Grammar and Usage (Class 11 notes)

Q86Relative pronouns

The man ____ car was stolen reported it to the police.

awhose
bwho
cwhom
dwhich

Answer (a): 'Whose' shows possession for a person (the man's car).

Revise: Grammar and Usage (Class 11 notes)

Q87Reading comprehension

aBamboo is a fast-growing and very useful plant.
bBamboo can only grow on hillsides.
cTrees are more useful than bamboo.
dBamboo houses are always heavy.

Answer (a): The passage covers growth speed, soil protection and uses, so the main idea is that bamboo is fast-growing and useful.

Revise: Reading Comprehension (Class 11 notes)

Q88Reading comprehension

aIts roots hold the soil and prevent landslides.
bIt needs very little water.
cIt gives shade to travellers.
dIt grows only on slopes.

Answer (a): The passage says its roots hold the soil firmly to prevent landslides.

Revise: Reading Comprehension (Class 11 notes)

Q89Reading comprehension

aIt dies completely.
bIt must be replanted from seed.
cNew shoots rise from the same roots.
dIt stops growing for years.

Answer (c): The last sentence: unlike trees, it does not die; new shoots keep rising.

Revise: Reading Comprehension (Class 11 notes)

Q90Reading comprehension

Read the passage and answer. Bamboo is one of the fastest growing plants in the world. Some species can grow almost one metre in a single day. Because its roots hold the soil firmly, bamboo is often planted on hillsides to prevent landslides. It is also strong yet light, so people use it to build houses, furniture and scaffolding. Unlike trees, bamboo does not die when it is harvested; new shoots keep rising from the same roots. The word 'harvested' in the passage most nearly means

acut and collected for use
bplanted in rows
cwatered regularly
dburnt for fuel

Answer (a): To harvest is to cut and gather a crop or plant for use.

Revise: Reading Comprehension (Class 11 notes)

General Knowledge and IT

Q91World geography

What is the capital city of Australia?

aCanberra
bSydney
cMelbourne
dPerth

Answer (a): Canberra, not Sydney, is the capital of Australia.

Q92Geography of Nepal

Which is the longest river within Nepal?

aKoshi
bGandaki
cMahakali
dKarnali

Answer (d): The Karnali is Nepal's longest river (about 507 km inside Nepal).

Q93Nepal general knowledge

The national flower of Nepal is

aLotus
bRose
cMarigold
dRhododendron (Lali Gurans)

Answer (d): Rhododendron (Lali Gurans) is Nepal's national flower.

Q94Science

Which is the largest planet of the solar system?

aJupiter
bSaturn
cNeptune
dEarth

Answer (a): Jupiter is the largest planet in our solar system.

Q95Nepal history

Nepal was declared a federal democratic republic in the year

a2006 AD
b2007 AD
c2015 AD
d2008 AD

Answer (d): The first Constituent Assembly declared the republic on 28 May 2008 (2065 BS).

Q96Computer memory

Which of the following is a volatile memory?

aROM
bRAM
cHard disk
dPen drive

Answer (b): RAM loses its content when power is off; ROM, disks and flash keep data.

Revise: Computer System (Class 11 notes)

Q97HTML

Which HTML tag creates the largest heading?

a<h6>
b<head>
c<title>
d<h1>

Answer (d): Headings run from <h1> (largest) to <h6> (smallest).

Revise: Web Technology I (Class 11 notes)

Q98Number systems

The decimal equivalent of the binary number 11010 is

Answer (d): $16+8+0+2+0=26$ .$16+8+0+2+0=26$.

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

Q99Number systems

The hexadecimal equivalent of decimal 255 is

Answer (d): $255=15\times16+15$ , and 15 is F, so FF.$255=15\times16+15$, and 15 is F, so FF.

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

Q100Operating system

Which of the following is an operating system?

aOracle
bLinux
cPython
dExcel

Answer (b): Linux is an operating system; Oracle is a DBMS, Python a language, Excel a spreadsheet.

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

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