BCA Entrance Exam 2080 (2023 AD) Questions with Answers

1. aHe asked what my name is.
2. bHe asked what my name was.
3. cHe asked what my was my name.
4. dHe asked what were my name.

Answer (b): In reported speech the verb moves back a tense (is becomes was) and the question takes statement word order: what my name was.

Revise: Grammar and Usage (Class 11 notes)

1. awould recognize
2. bwould have recognize
3. cwould have recognized
4. drecognizes

Answer (c): A past unreal condition (if + past perfect) takes would have + past participle in the main clause.

Revise: Grammar and Usage (Class 11 notes)

1. ato do
2. bdo
3. cdone
4. ddid

Answer (b): After make + object in the active voice we use the bare infinitive, so make me do.

Revise: Grammar and Usage (Class 11 notes)

1. aseparate
2. brecommendation
3. caccommodation
4. danxietie

Answer (d): The correct spelling is anxiety. The other three are spelled correctly.

Revise: Grammar and Usage (Class 11 notes)

1. aweren't they
2. bwere they
3. cwas he
4. dwasn't he

Answer (b): Nobody is negative in meaning, so the tag is positive. Nobody takes the plural pronoun they, giving were they.

Revise: Grammar and Usage (Class 11 notes)

1. ashe is an actress
2. bactress
3. cfamous
4. dacting

Answer (a): As if needs a full clause (subject + verb), so she is an actress.

Revise: Grammar and Usage (Class 11 notes)

1. averb
2. bnoun
3. cadjective
4. dadverb

Answer (d): Well tells how she performed, so it modifies a verb and is an adverb.

Revise: Grammar and Usage (Class 11 notes)

1. aconcrete noun
2. babstract noun
3. ccollective noun
4. dcountable noun

Answer (b): Creativity is a quality or idea that cannot be touched, so it is an abstract noun.

Revise: Grammar and Usage (Class 11 notes)

1. aSuffix
2. bPrefix
3. cRoot word
4. dNew word

Answer (a): An affix added at the end of a word is a suffix: punish + ment.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. afor
2. bsince
3. cin
4. dat

Answer (a): For is used with a length of time (a long time); since is used with a point in time.

Revise: Grammar and Usage (Class 11 notes)

1. ahas go
2. bhas gone
3. cwent
4. dhas been going

Answer (b): The present result (he is away now) needs the present perfect: has gone.

Revise: Grammar and Usage (Class 11 notes)

1. aan
2. ba
3. cthe
4. dnone of above

Answer (b): Headache begins with a consonant sound, and it is a singular countable noun here, so a.

Revise: Grammar and Usage (Class 11 notes)

1. apass
2. bcan pass
3. cwould pass
4. dwill pass

Answer (c): Wish about a future wanted outcome takes would + verb. Pass, can pass and will pass do not follow the wish pattern.

Revise: Grammar and Usage (Class 11 notes)

1. aThe Conservationist was written by Nadine Gordimer.
2. bThe Conservationist has been written by Nadine Gordimer.
3. cThe Conservationist written by Nadine Gordimer.
4. dThe Conservationist was wrote by Nadine Gordimer.

Answer (a): Simple past active becomes was/were + past participle: was written by.

Revise: Grammar and Usage (Class 11 notes)

1. abecause
2. bbecause of
3. calthough
4. ddespite

Answer (d): A noun phrase (the hard labor) follows despite, which shows contrast. Although needs a clause.

Revise: Grammar and Usage (Class 11 notes)

1. ahad seen
2. bsaw
3. chas seen
4. dsees

Answer (b): Both actions are in the past and follow quickly, so simple past: saw.

Revise: Grammar and Usage (Class 11 notes)

1. aare
2. bis
3. chave
4. dhas

Answer (a): Two subjects joined by and take a plural verb: are.

Revise: Grammar and Usage (Class 11 notes)

1. aeither
2. bneither
3. ceither or
4. dneither nor

Answer (a): With a negative verb, either at the end of the sentence adds a second negative idea.

Revise: Grammar and Usage (Class 11 notes)

1. aheavy
2. bheavily
3. cwith heavy
4. dwith heavily

Answer (b): An adverb is needed to modify the verb raining, and heavily fits.

Revise: Grammar and Usage (Class 11 notes)

1. aI visit him in the supermarket sometimes.
2. bI visit him sometimes in the supermarket.
3. cI visit sometimes him in the supermarket.
4. dI sometimes visit him in the supermarket.

Answer (d): Frequency adverbs such as sometimes usually come before the main verb.

Revise: Grammar and Usage (Class 11 notes)

1. ais
2. bare
3. cwas
4. dwere

Answer (a): Travelling is a gerund subject, singular, and the statement is a general truth, so is.

Revise: Grammar and Usage (Class 11 notes)

1. alasting only for a short time
2. bthe state of being alike
3. cvictory over a place or people by use of military force
4. dliquid that is believed to cure all ills

Answer (b): Resemblance is similarity between things, or being alike.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. ado not enjoy
2. bdid not enjoy
3. chas not enjoyed
4. denjoyed

Answer (b): The sentence is in the past and but shows contrast, so did not enjoy.

Revise: Grammar and Usage (Class 11 notes)

1. ainteresting
2. binterested
3. cinterest
4. dall of them

Answer (b): Be interested in is the fixed phrase for a person's feeling.

Revise: Grammar and Usage (Class 11 notes)

1. aDeciding
2. bThreatening
3. cPredicting a future action
4. dPromising

Answer (b): Telling parents about someone's wrongdoing as a warning is a threat.

Revise: Grammar and Usage (Class 11 notes)

1. ahas
2. bhave
3. chad
4. dhas had

Answer (a): Everyone is singular and the statement is a general truth in the present: has.

Revise: Grammar and Usage (Class 11 notes)

1. aCollin was eager to read Science.
2. bCollin was not eager to read Science.
3. cCollin was eager to read Science for father
4. dCollin was eager to read not Science but Math.

Answer (b): Reluctantly means unwillingly, so she was not eager.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. ahowever
2. balthough
3. cin spite of
4. dbecause

Answer (c): A noun phrase (the fact that ...) follows in spite of. Although and however do not fit this structure.

Revise: Grammar and Usage (Class 11 notes)

1. acan go
2. bshould go
3. cwill go
4. dmay

Answer (b): Giving advice uses should.

Revise: Grammar and Usage (Class 11 notes)

1. aits
2. bit's
3. cits'
4. dit

Answer (a): Its is the possessive form. It's means it is.

Revise: Grammar and Usage (Class 11 notes)

1. athere
2. bwhere
3. cthat
4. dwhich

Answer (b): Where is the relative adverb for a place.

Revise: Grammar and Usage (Class 11 notes)

1. abreak
2. bbrake
3. cbroke
4. dbreek

Answer (a): After could not use the base verb: break. Brake is a different word.

Revise: Grammar and Usage (Class 11 notes)

1. aOscar Wilde
2. bLeo Tolstoy
3. cChinua Achebe
4. dR.K. Narayan

Answer (a): The Selfish Giant is a fairy tale by Oscar Wilde.

Revise: The Selfish Giant (Class 11 notes)

1. aup
2. binto
3. cto
4. dabout

Answer (a): Bring up means to raise a topic for discussion.

Revise: Grammar and Usage (Class 11 notes)

1. aTeaching as public profession
2. bTeaching as private profession
3. cTeaching as dream
4. dTeaching as anxiety

Answer (b): Palmer calls teaching the most privatized of the public professions, because teachers work alone behind closed doors.

Revise: Reading Comprehension (Class 11 notes)

1. ateach in isolation
2. bteach in collaboration with other teachers
3. cteach sharing experiences
4. dteach in semester class

Answer (a): The passage says teachers almost always teach solo and close the door on colleagues.

Revise: Reading Comprehension (Class 11 notes)

1. aInternet
2. bonline classes
3. chigher education
4. dnew syllabus

Answer (a): The passage names widespread use of the internet to circulate syllabi and publish course evaluations.

Revise: Reading Comprehension (Class 11 notes)

1. aalways
2. bsometimes
3. cseldom
4. dnever

Answer (c): Rarely means not often, which is seldom.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. aLawyers
2. bSurgeons
3. cTeachers
4. dAll of them

Answer (c): Palmer says 'we teach in front of students', so we means teachers.

Revise: Reading Comprehension (Class 11 notes)

1. a$45$
2. b$50$
3. c$55$
4. d$30$

Answer (d): $n(A\cap B)=30+50-55=25$. So $n(A-B)=5$, $n(B-A)=25$ and the sum is $30$.

Revise: Algebra (Class 11 notes)

1. a$\frac{20\times21}{2}$
2. b$\frac{19\times21}{2}$
3. c$\frac{1\times20}{2}$
4. d$200$

Answer (a): Sum of first $n$ natural numbers is $\frac{n(n+1)}{2}$, so $\frac{20\times21}{2}=210$.

Revise: Algebra (Class 11 notes)

1. a$26$
2. b$58$
3. c$32$
4. d$6$

Answer (a): The intersection cannot be larger than the smaller set, so the maximum is $26$.

Revise: Algebra (Class 11 notes)

1. a$n$
2. b$n+1$
3. c$2n$
4. d$2n+1$

Answer (d): $2n$ is always even, so $2n+1$ is always odd.

Revise: Algebra (Class 11 notes)

1. a$[1,\infty)$
2. b$(-\infty,+\infty)$
3. c$(-1,\infty)$
4. d$[0,\infty)$

Answer (d): A square root gives non-negative values, and it takes every value from 0 upward, so the range is $[0,\infty)$. ($[1,\infty)$ is the domain.)

Revise: Algebra (Class 11 notes)

1. aless than 0
2. bless than $-1$
3. cbetween $1$ and $-1$
4. dgreater than 1

Answer (c): The infinite sum converges only when $|r|<1$, that is, $-1<r<1$.

Revise: Algebra (Class 11 notes)

1. a$38$
2. b$90$
3. c$22$
4. d$70$

Answer (c): $90-x=4x-20$, so $5x=110$ and $x=22$.

Revise: Trigonometry (Class 11 notes)

1. a$\frac{-1\pm i\sqrt3}{2}$
2. b$\frac{-1-i\sqrt3}{2}$
3. c$\frac{-1\pm i\sqrt2}{2}$
4. d$\frac{-1+i\sqrt3}{2}$

Answer (a): $x=\frac{-1\pm\sqrt{1-4}}{2}=\frac{-1\pm i\sqrt3}{2}$. Both signs are roots, so option a is complete.

Revise: Algebra (Class 11 notes)

1. a$\frac{4x-1}{3}$
2. b$\frac{4x+1}{3}$
3. c$\frac{3x-1}{4}$
4. d$\frac{3x+1}{4}$

Answer (a): Put $y=\frac{3x+1}{4}$, so $x=\frac{4y-1}{3}$. Swap to get $f^{-1}(x)=\frac{4x-1}{3}$.

Revise: Algebra (Class 11 notes)

1. a$(x+1)(x-3)$
2. b$(x+2)(x-2)$
3. c$(x+3)(x-1)$
4. d$(x+4)(x+1)$

Answer (a): Dividing by $(x-2)$ gives $x^2-2x-3=(x-3)(x+1)$.

Revise: Algebra (Class 11 notes)

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

Answer (c): Here $a=1$, $r=\frac12$, so $S=\frac{a}{1-r}=\frac{1}{1/2}=2$.

Revise: Algebra (Class 11 notes)

1. a$661$
2. b$551$
3. c$441$
4. d$331$

Answer (c): $\left(\frac{6\cdot7}{2}\right)^2=21^2=441$.

Revise: Algebra (Class 11 notes)

1. a$25$
2. b$25\sqrt3$
3. c$\frac{25}{2}$
4. d$50\sqrt3$

Answer (b): $h=25\tan60^\circ=25\sqrt3$.

Revise: Trigonometry (Class 11 notes)

1. a$7550$
2. b$7650$
3. c$7750$
4. d$7850$

Answer (b): Discount $=850$, so selling price $=8500-850=7650$.

Revise: Algebra (Class 11 notes)

1. a$750$
2. b$650$
3. c$700$
4. d$850$

Answer (c): Rs. 117150 equals $\frac{117150\times2}{213}=1100$ US dollars. Then the pounds are $\frac{1100\times7}{11}=700$.

Revise: Algebra (Class 11 notes)

1. a$9\%$
2. b$10\%$
3. c$12\%$
4. d$14\%$

Answer (b): Cost price $=11000-1000=10000$. Profit % $=\frac{1000}{10000}\times100=10%$.

Revise: Algebra (Class 11 notes)

1. a$2$
2. b$4$
3. c$5$
4. d$3$

Answer (d): 12 girls equal 8 boys, so 6 girls equal 4 boys. Then 4 boys and 6 girls equal 8 boys, who need 3 days.

Revise: Algebra (Class 11 notes)

1. a$2x^2-3xy+y^2=0$
2. b$x^2-3xy+2y^2=0$
3. c$2x^2-xy+2y^2=0$
4. d$2x^2-5xy+2y^2=0$

Answer (d): $(x-2y)(2x-y)=2x^2-xy-4xy+2y^2=2x^2-5xy+2y^2=0$.

Revise: Analytic geometry (Class 11 notes)

1. aThe angle at the center is double the angle at the circumference.
2. bThe angle at the circumference is double the angle at the center.
3. cThe angle at the center is half the angle at the circumference.
4. dThe angle at the circumference is equal to the angle at the center.

Answer (a): Circle theorem: the angle at the centre is twice the angle at the circumference on the same arc.

Revise: Analytic geometry (Class 11 notes)

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

Answer (d): $f(g(x))=4(x+1)=20$, so $x+1=5$ and $x=4$.

Revise: Algebra (Class 11 notes)

1. a$\frac12$
2. b$\frac13$
3. c$\frac14$
4. d$\frac23$

Answer (c): Outcomes: GG, GB, BG, BB. Only one is GG, so $\frac14$.

Revise: Statistics and Probability (Class 11 notes)

1. a$\sqrt3$
2. b$2+\sqrt3$
3. c$2-\sqrt3$
4. d$2$

Answer (b): $\tan(45+30)=\frac{1+1/\sqrt3}{1-1/\sqrt3}=\frac{\sqrt3+1}{\sqrt3-1}=2+\sqrt3$.

Revise: Trigonometry (Class 11 notes)

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

Answer (d): $\frac{15}{2}(2a+14\cdot4)=435$ gives $2a+56=58$, so $a=1$.

Revise: Algebra (Class 11 notes)

1. a$\log4+\log2$
2. b$\log4+\log4$
3. c$2\log4$
4. d$4\log2$

Answer (a): $\log4+\log2=\log(4\times2)=\log8$.

Revise: Algebra (Class 11 notes)

1. a$\begin{pmatrix}6&-10\9&-13\end{pmatrix}$
2. b$\begin{pmatrix}6&10\9&-13\end{pmatrix}$
3. c$\begin{pmatrix}6&-10\9&13\end{pmatrix}$
4. d$\begin{pmatrix}6&0\9&3\end{pmatrix}$

Answer (a): $AB=\begin{pmatrix}6&9\-10&-13\end{pmatrix}$. Its transpose swaps rows and columns.

Revise: Algebra (Class 11 notes)

1. a$-\frac{3}{\sqrt2}$
2. b$\frac{3}{\sqrt2}$
3. c$-\frac{3}{5\sqrt2}$
4. d$\frac{3}{5\sqrt2}$

Answer (c): $\vec a\cdot\vec b=0-6+0=-6$, $|\vec a|=5$, $|\vec b|=2\sqrt2$, so $\cos\theta=\frac{-6}{10\sqrt2}=-\frac{3}{5\sqrt2}$. The paper prints options c and d identically as $\frac{3}{5\sqrt2}$, a lost minus sign in one of them, so option c is restored as $-\frac{3}{5\sqrt2}$.

Revise: Vectors (Class 11 notes)

1. a$\frac{a+b}{2ab}$
2. b$\frac{a-b}{2ab}$
3. c$\frac{2ab}{a+b}$
4. d$\frac{2ab}{a-b}$

Answer (c): Harmonic mean is the reciprocal of the mean of the reciprocals: $\frac{2ab}{a+b}$.

Revise: Algebra (Class 11 notes)

1. a$80$
2. b$90$
3. c$125$
4. d$100$

Answer (d): The sum of the first $n$ odd numbers is $n^2=100$.

Revise: Algebra (Class 11 notes)

1. a$1$
2. b$-1$
3. c$0$
4. d$\pm i$

Answer (d): $x^2=-1$, so $x=\pm i$.

Revise: Algebra (Class 11 notes)

1. a$15$
2. b$16$
3. c$17$
4. d$22$

Answer (b): The differences are 1, 2, 3, 4, so the next difference is 5 and the term is $11+5=16$.

Revise: Algebra (Class 11 notes)

1. a$\frac1{\sqrt2}$
2. b$-\frac1{\sqrt2}$
3. c$\frac1{\sqrt2}$ or $-\frac1{\sqrt2}$
4. d$1$

Answer (c): $4a^2-6a+1=2a^2-6a+2$ gives $2a^2=1$, so $a=\pm\frac1{\sqrt2}$.

Revise: Algebra (Class 11 notes)

1. a$x$
2. b$-x$
3. c$x^2$
4. d$-x^2$

Answer (b): For negative $x$, the absolute value is $-x$, which is positive.

Revise: Algebra (Class 11 notes)

1. ano solution
2. bunique solution
3. cinfinite solution
4. dtwo solution

Answer (a): The coefficients are in ratio $3:1$ but the constants are not ($5\cdot3\ne14$), so the lines are parallel and distinct: no solution.

Revise: Analytic geometry (Class 11 notes)

1. a$(1,1)$
2. b$(8,2)$
3. c$(-2,6)$
4. d$(0,1)$

Answer (a): Rotation by $90^\circ$ gives $(x,y)\to(-y,x)=(-4,3)$. Adding $(5,-2)$ gives $(1,1)$.

Revise: Analytic geometry (Class 11 notes)

1. a$5$
2. b$6$
3. c$7$
4. d$9$

Answer (b): By the remainder theorem $R=f(1)=2-7+1+10=6$.

Revise: Algebra (Class 11 notes)

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

Answer (d): $5^{x+3}=5^{2x}$, so $x+3=2x$ and $x=3$.

Revise: Algebra (Class 11 notes)

1. a$1$
2. b$2$
3. c$3$
4. d$453$

Answer (b): $(x+y)^2=x^2+y^2+2xy$ gives $9=5+2xy$, so $xy=2$.

Revise: Algebra (Class 11 notes)

1. a$\frac{2h}{b}$
2. b$ab$
3. c$a-b$
4. d$\frac ab$

Answer (d): Putting $y=mx$ gives $bm^2+2hm+a=0$, so the product of roots is $\frac ab$.

Revise: Analytic geometry (Class 11 notes)

1. a$(g,f)$
2. b$(f,g)$
3. c$(-g,-f)$
4. d$(-f,-g)$

Answer (c): Completing the squares gives $(x+g)^2+(y+f)^2=g^2+f^2-c$, so the centre is $(-g,-f)$. The paper prints 'radius', a misprint for 'centre', since every option is a coordinate pair.

Revise: Analytic geometry (Class 11 notes)

1. a$0$
2. b$-1$
3. c$1$
4. d$2$

Answer (c): By definition $0!=1$.

Revise: Algebra (Class 11 notes)

1. a$\sin^2x$
2. b$\cos^2x$
3. c$\csc^2x$
4. d$\sec^2x$

Answer (d): Standard result: $\frac{d}{dx}\tan x=\sec^2x$.

Revise: Calculus (Class 11 notes)

1. a$5$
2. b$4$
3. c$1$
4. d$3$

Answer (d): $\sqrt{1+4+4}=3$.

Revise: Vectors (Class 11 notes)

1. a$3\times3$
2. b$4\times4$
3. c$4\times3$
4. d$3\times4$

Answer (a): $(3\times4)(4\times3)$ gives rows of $A$ by columns of $B$: $3\times3$.

Revise: Algebra (Class 11 notes)

1. aidentity
2. bscalar
3. csymmetric
4. dskew-symmetric

Answer (c): $A^T=A$ is the definition of a symmetric matrix.

Revise: Algebra (Class 11 notes)

1. a$\left(\frac{n(n+1)}{2}\right)^3$
2. b$\left(\frac{n(n+1)}{2}\right)^2$
3. c$\left(\frac{n(n+1)}{3}\right)^2$
4. d$\left(\frac{n(n-1)}{2}\right)^2$

Answer (b): The sum of cubes equals the square of the sum of the first $n$ numbers.

Revise: Algebra (Class 11 notes)

1. a$\frac{11}{12}$
2. b$\frac{12}{13}$
3. c$\frac{13}{14}$
4. d$\frac{14}{15}$

Answer (c): Numerators go 1, 4, 7 (add 3) and denominators 2, 5, 8 (add 3). The fifth term is $\frac{13}{14}$.

Revise: Algebra (Class 11 notes)

1. a$442\ cm^3$
2. b$452\ cm^3$
3. c$462\ cm^3$
4. d$472\ cm^3$

Answer (c): $V=\pi r^2h=\frac{22}{7}\times49\times3=462$.

Revise: Algebra (Class 11 notes)

1. areal and equal
2. breal and unequal
3. cirrational
4. dimaginary

Answer (a): A zero discriminant means two equal real roots.

Revise: Algebra (Class 11 notes)

1. a$\frac13$
2. b$\frac12$
3. c$\frac34$
4. d$2$

Answer (b): Odd faces are 1, 3, 5, so $\frac36=\frac12$.

Revise: Statistics and Probability (Class 11 notes)

1. aJava
2. bPython
3. cHTML
4. dC++

Answer (c): HTML is the markup language every web page is built with, and it is the answer the paper intends. Java and Python are also used on the server side, but they are general-purpose languages, so HTML is the strongest fit for web development.

Revise: Web Technology I (Class 11 notes)

1. aUniform Resource Locator
2. bUniversal Routing Language
3. cUnique Resource Link
4. dUser Registration Link

Answer (a): URL means Uniform Resource Locator, the address of a web resource.

Revise: Web Technology I (Class 11 notes)

1. aRespiration
2. bPhotosynthesis
3. cDigestion
4. dFermentation

Answer (b): Plants use light, water and carbon dioxide to make glucose in photosynthesis.

1. aElephant
2. bBlue Whale
3. cGiraffe
4. dRhinoceros

Answer (b): The blue whale is the largest animal ever known, larger than any land mammal.

1. aBan Ki-moon
2. bAntonio Guterres
3. cKofi Annan
4. dNikki Haley

Answer (b): At the time of the exam, Antonio Guterres (Portugal) held the post, in office since 2017.

1. aAnnapurna Range
2. bLangtang Range
3. cKhumbu Himal
4. dDhaulagiri Range

Answer (c): Mount Everest lies in the Khumbu region, in the Khumbu Himal section of the Mahalangur Himal. Annapurna, Langtang and Dhaulagiri are different ranges.

1. a12
2. b15
3. c17
4. d20

Answer (c): The UN 2030 Agenda adopted 17 SDGs in 2015.