BIT Entrance Exam 2078 Model Questions Questions with Answers

1. aHigher than Nepal
2. bThe highest of Nepal.
3. cHigher than that of Nepal
4. dHighest than the Nepal.

Answer (c): Compare like with like: the standard of living is compared with 'that of Nepal', and 'higher than' is the correct comparative.

Revise: Grammar and Usage (Class 11 notes)

1. aThan
2. bto
3. cfrom
4. dnone

Answer (b): Adjectives such as superior, inferior, senior and junior take 'to', not 'than'.

Revise: Grammar and Usage (Class 11 notes)

1. aangry
2. bhappy
3. csad
4. dsleepy

Answer (d): Eyes that feel heavy are drooping from tiredness, so the idiom means sleepy.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. abecome angry
2. bbecome sad
3. cbecome firm
4. dbecome violent

Answer (c): 'Not to move a single hair' is about staying unmoved and steady, which is closest to becoming firm.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. afurtive
2. bsuccessful
3. cnon sense
4. drespectable

Answer (a): Surreptitious means done secretly or stealthily, which is the meaning of furtive.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. adoing
2. bIt was done
3. chow to do
4. dto do

Answer (c): 'Know' is followed by a question word plus infinitive, so 'how to do' is correct.

Revise: Grammar and Usage (Class 11 notes)

1. alook over
2. blook into
3. clook for
4. dlook after

Answer (b): 'Look into' means to investigate, which is what one does before entering a business.

Revise: Grammar and Usage (Class 11 notes)

1. aon July 25
2. bthe July 25th
3. cat July 25th
4. dJuly the 25th

Answer (a): Dates take the preposition 'on'.

Revise: Grammar and Usage (Class 11 notes)

1. ain, on
2. bon, on
3. cin, in
4. don, in

Answer (a): Live 'in water' and 'on land' are the standard prepositions.

Revise: Grammar and Usage (Class 11 notes)

1. awe'd taken off
2. bhad we taken off
3. cwe took off
4. dwe'd took off

Answer (b): 'No sooner' at the start requires inversion with the past perfect: had we taken off.

Revise: Grammar and Usage (Class 11 notes)

1. adoesn't he
2. bhadn't he
3. cdon't he
4. ddidn't he

Answer (a): The main verb 'has' is used in the present simple, so the tag is 'doesn't he'.

Revise: Grammar and Usage (Class 11 notes)

1. adon't they
2. bdo they
3. cdidn't they
4. ddid they

Answer (b): 'Seldom' is negative, so the tag is positive: 'do they'.

Revise: Grammar and Usage (Class 11 notes)

1. aBecause of
2. bsince
3. calthough
4. dIn spite of

Answer (d): The meaning is contrast followed by a noun, so 'in spite of' fits.

Revise: Grammar and Usage (Class 11 notes)

1. aa
2. ban
3. cthe
4. dnone

Answer (a): 'European' begins with the consonant sound /j/, so 'a' is used.

Revise: Grammar and Usage (Class 11 notes)

1. aa
2. ban
3. cthe
4. dnone

Answer (c): The job is specified by the clause 'she applied for', so 'the' is needed.

Revise: Grammar and Usage (Class 11 notes)

1. aa
2. band
3. cthe
4. dnone

Answer (d): A noun followed by a number (question 10) takes no article.

Revise: Grammar and Usage (Class 11 notes)

1. aa
2. ban
3. cthe
4. dNone

Answer (b): LLB is pronounced 'el-el-bee', starting with a vowel sound, so 'an' is used.

Revise: Grammar and Usage (Class 11 notes)

1. aA
2. bAn
3. cThe
4. dNone

Answer (d): A general statement about cows as a class takes no article ('Cows from Australia are known ...'); the singular 'cow' is a misprint for 'cows'.

Revise: Grammar and Usage (Class 11 notes)

1. amuch
2. ba few
3. ca large number
4. dmany

Answer (a): 'Speak' is used with the uncountable 'much' in a negative sentence.

Revise: Grammar and Usage (Class 11 notes)

1. aso diligently prepared
2. bas diligently prepared
3. csuch diligently prepared
4. dsuch prepared diligently

Answer (c): The pattern is 'such + adjective + noun + that', so 'such diligently prepared' fits.

Revise: Grammar and Usage (Class 11 notes)

1. amy brother
2. bof my brother
3. cof my brother's
4. dmy brother's

Answer (d): Possession is shown with the possessive form: my brother's.

Revise: Grammar and Usage (Class 11 notes)

1. awe
2. bus
3. cthey
4. dme

Answer (b): After a preposition the object form 'us' is used.

Revise: Grammar and Usage (Class 11 notes)

1. ashopping
2. bto shop
3. cto shopping
4. dshop

Answer (a): 'Go + verb-ing' is used for activities: go shopping.

Revise: Grammar and Usage (Class 11 notes)

1. adid
2. bhave done
3. cwas doing
4. dhad done

Answer (d): The thanking happened in the past, and the action thanked for happened earlier, so the past perfect 'had done'.

Revise: Grammar and Usage (Class 11 notes)

1. awent
2. bgone
3. cgoing
4. dbeen-gone

Answer (b): Present perfect needs the past participle: has gone.

Revise: Grammar and Usage (Class 11 notes)

1. awould he
2. bthought not he
3. cshall he
4. dshouldn't he

Answer (d): The tag for 'ought to' is 'shouldn't he'.

Revise: Grammar and Usage (Class 11 notes)

1. awouldn't buy
2. bwon't buy
3. cwould buy
4. ddon't buy

Answer (a): Second conditional: if + past, would + base verb. The coat is too expensive, so 'wouldn't buy'.

Revise: Grammar and Usage (Class 11 notes)

1. ais
2. bhas
3. care
4. dwas

Answer (c): 'Police' is a plural noun and takes 'are'.

Revise: Grammar and Usage (Class 11 notes)

1. ato solve
2. bsolved
3. csolving
4. dto solving

Answer (a): 'Help' is followed by an infinitive (with or without to), so 'to solve'.

Revise: Grammar and Usage (Class 11 notes)

1. athird
2. bfirst
3. csecond
4. dfourth

Answer (c): The adjective approximate is pronounced ap-PROX-i-mate, with stress on the second syllable.

Revise: Grammar and Usage (Class 11 notes)

1. arising
2. bfalling
3. cfalling and rising
4. dnone of these

Answer (b): Commands normally have a falling intonation.

Revise: Grammar and Usage (Class 11 notes)

1. acomes
2. bhad come
3. ccame
4. dwas coming

Answer (c): Second conditional with 'I'd throw' needs the simple past in the if-clause: came.

Revise: Grammar and Usage (Class 11 notes)

1. ayearn at
2. byearn of
3. cyearn for
4. dyearn with

Answer (c): The verb 'yearn' takes the preposition 'for'.

Revise: Grammar and Usage (Class 11 notes)

1. aHe told them that they don't make a noise.
2. bHe told them not to make a noise.
3. cHe told them to don't make a noise.
4. dHe told them that they didn't make a noise.

Answer (b): A negative command in direct speech becomes 'told + object + not to + verb' in reported speech.

Revise: Grammar and Usage (Class 11 notes)

1. aShe said to please not to go away.
2. bShe requested me not to go away.
3. cShe begged me that I not go away.
4. dShe begged that to don't go away.

Answer (b): A polite negative request is reported with 'requested + object + not to + verb'.

Revise: Grammar and Usage (Class 11 notes)

1. aSociable
2. baggravate
3. castute
4. dStipulate

Answer (a): Affable means friendly and easy to talk to, which is sociable.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. aSinecure
2. bmiser
3. cgenerous
4. dstingy

Answer (c): Benevolent means kind and giving, so generous is the nearest.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. ato be the son of
2. bto be the father of
3. cto be the daughter of
4. dto be friend of

Answer (b): To beget is to father, that is, to bring a child into existence as its father.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. a$\text{Profit},% = 50%$
2. b$\text{loss},% = 30%$
3. cNeither profit or loss
4. d$\text{Profit},% = \frac{100}{3}%$

Answer (a): Take CP = 2 and SP = 3. Profit = 1, so profit % = $\frac{1}{2}\times 100 = 50%$.

Revise: Algebra (Class 11 notes)

1. a$0$
2. b$\infty$
3. c$2$
4. d$\frac{1}{3}$

Answer (d): $\sum n^2=\frac{n(n+1)(2n+1)}{6}$, so the ratio is $\frac{(1+1/n)(2+1/n)}{6}\to\frac{2}{6}=\frac13$.

Revise: Calculus (Class 11 notes)

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

Answer (a): Put $x-1=h$: $\tan(\frac{\pi}{2}+\frac{\pi h}{2})=-\cot\frac{\pi h}{2}$. So the limit is $-\lim h\cot\frac{\pi h}{2}=-\frac{2}{\pi}$.

Revise: Calculus (Class 11 notes)

1. a$0$
2. b$1$
3. cnot defined
4. d$-1$

Answer (d): $\frac{1+\cos2x}{1-\cos2x}=\cot^2x$, so $y=\cot x$ and $\frac{dy}{dx}=-\csc^2x=-1$ at $x=\frac{\pi}{2}$.

Revise: Calculus (Class 11 notes)

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

Answer (d): Let $u=\sqrt{x^2+a^2}$. Then $\frac{d}{du}e^u=e^u=e^{\sqrt{x^2+a^2}}$.

Revise: Calculus (Class 11 notes)

1. a$1$ and $-2$
2. b$1$ and $\frac{c}{a}$
3. c$-\frac{b}{a}$ and $\frac{c}{a}$
4. d$0$ and $1$

Answer (b): Since $a+b+c=0$, $x=1$ is a root. The product of roots is $\frac{c}{a}$, so the other root is $\frac{c}{a}$.

Revise: Algebra (Class 11 notes)

1. a$\sqrt{pq}$
2. b$\frac{p+q}{2}$
3. c$\sqrt{(p+q)}$
4. d$pq$

Answer (a): $p=ar^{m+n-1}$ and $q=ar^{m-n-1}$, so $pq=(ar^{m-1})^2$. Hence the $m^{th}$ term is $\sqrt{pq}$.

Revise: Algebra (Class 11 notes)

1. arational
2. birrational
3. cimaginary
4. dReal and equal

Answer (a): The coefficients sum to $a+b+c=0$, so $x=1$ is a root. The other root is $\frac{b+c-a}{a+b-c}=\frac{-2a}{-2c}=\frac{a}{c}$, which is rational.

Revise: Algebra (Class 11 notes)

1. a$25x^2-30x+7=0$
2. b$25x^2-120x+63=0$
3. c$25x^2+120x-63=0$
4. dnone of these

Answer (b): The roots of $x^2-8x+7=0$ are 1 and 7, so the new roots are $\frac35$ and $\frac{21}{5}$. Sum $=\frac{24}{5}$ and product $=\frac{63}{25}$, giving $25x^2-120x+63=0$.

Revise: Algebra (Class 11 notes)

1. a$|r|>1$
2. b$|r|<1$
3. c$|r|=1$
4. d$|r^n|\le 1$

Answer (b): The sum formula is used in its closed form for $|r|<1$, where $r^n\to0$ for the infinite series; this is the textbook convention.

Revise: Algebra (Class 11 notes)

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

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

Revise: Algebra (Class 11 notes)

1. aalways $(1,0)$
2. balways $(0,0)$
3. cdoes not exist
4. d$(-\infty,0)$

Answer (c): The second derivative of a quadratic is a nonzero constant, so it never changes sign and there is no point of inflection.

Revise: Calculus (Class 11 notes)

1. a0 sq. unit
2. b1 sq. unit
3. c2 sq. unit
4. d3 sq. unit

Answer (a): Area $=\frac12|1(3-4)+2(4-2)+3(2-3)|=\frac12|-1+4-3|=0$. The points are collinear.

Revise: Analytic geometry (Class 11 notes)

1. a$(\frac{\pi}{3},2)$
2. b$(2,\frac{\pi}{3})$
3. c$(2,\frac{4\pi}{3})$
4. d$(\frac{4\pi}{3},2)$

Answer (c): $r=\sqrt{1+3}=2$. The point is in the third quadrant with reference angle $\frac{\pi}{3}$, so $\theta=\pi+\frac{\pi}{3}=\frac{4\pi}{3}$.

Revise: Analytic geometry (Class 11 notes)

1. a$6$
2. b$-6$
3. c$0$
4. d$-1$

Answer (c): $\sin^7x$ is an odd function, so its integral over a symmetric interval is 0.

Revise: Calculus (Class 11 notes)

1. a$(a-x)$ if $x>a$
2. b$\pm(x-a)$ if $x\ge a$
3. c$(x-a)$ if $x<a$
4. d$(a-x)$ if $x<a$

Answer (d): By definition $|x-a|=a-x$ when $x<a$ (the value is positive) and $x-a$ when $x\ge a$.

Revise: Algebra (Class 11 notes)

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

Answer (b): Write $\frac{x}{x+1}=1-\frac{1}{x+1}$ and integrate: $x-\log(1+x)+c$.

Revise: Calculus (Class 11 notes)

1. aAll scalar matrix are diagonal matrix
2. bAll diagonal matric are scalar matric but not vice-versa
3. cif $a_{ij}=-a_{ji}$ $\forall$ $i$ and $j$ and $a_{ij}=0$ for $i=j$ then matrix is called skew-symmetric matrix
4. dboth a and c

Answer (c): Statement a is false in the stated form (scalar matrices are diagonal, but a is not the full picture here), and b is false because it reverses the relation. Statement c is the correct definition of a skew-symmetric matrix, so only c is true.

Revise: Algebra (Class 11 notes)

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

Answer (b): Let $y=3x^4+2$. Then $x^4=\frac{y-2}{3}$, so $f^{-1}(x)=\sqrt[4]{\frac{x-2}{3}}$.

Revise: Algebra (Class 11 notes)

1. a$R-{2}$
2. b$R$
3. c$R-{4}$
4. d$[0,\infty]$

Answer (a): The function is undefined only where the denominator is zero, that is at $x=2$.

Revise: Algebra (Class 11 notes)

1. a$\frac{31}{32}$
2. b$2^{31}$
3. c$\frac{63}{64}$
4. d$2^{64}$

Answer (c): Working from the inside: each extra layer gives exponent $1-\frac{1}{2^k}$. With six 2's the exponent is $1-\frac{1}{64}=\frac{63}{64}$.

Revise: Algebra (Class 11 notes)

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

Answer (a): $R_3-R_2=R_2-R_1$ (both give 3,3,3), so the rows are dependent and the determinant is 0.

Revise: Algebra (Class 11 notes)

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

Answer (b): $\tan15^\circ=\tan(45^\circ-30^\circ)=\frac{1-1/\sqrt3}{1+1/\sqrt3}=2-\sqrt3$. Options a and b are equal.

Revise: Trigonometry (Class 11 notes)

1. a$\hat\eta$ is the unit vector along $\vec a$
2. b$\hat\eta$ is the unit vector along $\vec b$
3. c$\hat\eta$ is the unit vector along $\vec a\times\vec b$
4. d$\hat\eta$ is the unit vector along $\vec a$ and $\vec b$

Answer (c): The cross product points along the direction perpendicular to both vectors, and $\hat\eta$ is the unit vector in that direction, that is along $\vec a\times\vec b$.

Revise: Vectors (Class 11 notes)

1. aFinite set with elements $\pm1$
2. bnull set
3. cinfinite set
4. ddata insufficient

Answer (b): A square root is never negative, so $\sqrt{2x^2-1}=-1$ has no real solution and A is empty.

Revise: Algebra (Class 11 notes)

1. a$\frac{\pi}{2}-\tan^{-1}x$
2. b$\frac{\pi}{2}-2\tan^{-1}x$
3. c$\pi-2\tan^{-1}x$
4. dnone of these

Answer (d): With $x=\tan\theta$: $\sin^{-1}(\cos2\theta)=\frac{\pi}{2}-2\theta$ and $\cos^{-1}(\sin2\theta)=\frac{\pi}{2}-2\theta$, giving $\pi-4\tan^{-1}x$, which matches none of a, b, c.

Revise: Trigonometry (Class 11 notes)

1. a$2\cos^2\frac x2-1$
2. b$1-2\sin^2\frac x2$
3. c$\frac{1-\tan^2\frac x2}{1+\tan^2\frac x2}$
4. dAll of these

Answer (d): All three are standard half-angle forms of $\cos x$.

Revise: Trigonometry (Class 11 notes)

1. aconsistent and dependent
2. bInconsistent and independent
3. cInconsistent and dependent
4. dconsistent and independent

Answer (b): Parallel lines never meet, so the system has no solution (inconsistent), and the two equations are not multiples of each other (independent).

Revise: Algebra (Class 11 notes)

1. a20%
2. b25%
3. c30%
4. d35%

Answer (a): Reduction $=\frac{25}{100+25}\times100=20%$.

Revise: Algebra (Class 11 notes)

1. a23%
2. b24%
3. c20%
4. d25%

Answer (d): If B earns 3, A earns 4. B earns less by $\frac{1}{4}\times100=25%$.

Revise: Algebra (Class 11 notes)

1. a1:1:2
2. b1:1:1
3. c1:2:1
4. d2:1:1

Answer (b): The expression equals $\frac12[(a-b)^2+(b-c)^2+(c-a)^2]=0$, so $a=b=c$.

Revise: Algebra (Class 11 notes)

1. a30km/hr
2. b2km/hr
3. c3km/hr
4. d34km/hr

Answer (a): Speed in still water $=\frac{32+28}{2}=30$ km/hr.

Revise: Algebra (Class 11 notes)

1. a$64\text{ cm}^2$
2. b$125\text{cm}^3$
3. c$150\text{cm}^3$
4. d$216\text{cm}^3$

Answer (b): $6a^2=150$ gives $a=5$, so volume $=a^3=125\text{ cm}^3$.

Revise: Algebra (Class 11 notes)

1. a192
2. b194
3. c190
4. d180

Answer (a): Set $160+2Q^2=240-3Q^2$: $5Q^2=80$, $Q=4$. Price $=160+2(16)=192$.

Revise: Algebra (Class 11 notes)

1. a$1\le\varepsilon(x)$
2. b$0\le p(\varepsilon)\le1$
3. c$0\le p(\varepsilon)$
4. d$-1\le p(\varepsilon)\le1$

Answer (b): Probability always lies between 0 and 1 inclusive.

Revise: Statistics and Probability (Class 11 notes)

1. a9
2. b6
3. c8
4. d11

Answer (d): These are consecutive prime numbers, and the prime after 7 is 11.

1. a4
2. b5
3. c3
4. d9

Answer (a): The code equals the number of vowels: SUN (U) = 1, RAM (A) = 1, MADHU (A, U) = 2. UNIVERSITY has U, I, E, I = 4.

1. a68
2. b70
3. c71
4. d69

Answer (d): Total $=21+49-1=69$.

1. aKamirita Sherpa
2. bSudarshan Gautam
3. cKami Rita Sherpa
4. dNawang Gombu Sherpa

Answer (c): Kami Rita Sherpa holds the record for the most Everest summits.

1. a3
2. b11
3. c17
4. d18

Answer (d): The 18th SAARC summit was held in Kathmandu in 2014, the most recent hosted by Nepal.

1. adata
2. boperating systems
3. chardware
4. dsoftware

Answer (c): Hardware is the physical, touchable part of a computer.

Revise: Computer System (Class 11 notes)

1. acomputer
2. bprocessor
3. ccase
4. dstylus

Answer (a): This is the textbook definition of a computer.

Revise: Computer System (Class 11 notes)

1. aWindows 98
2. bBSD Unix
3. cMicrosoft Office XP
4. dRed Hat Linux

Answer (c): Microsoft Office XP is an application suite, not an operating system.

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

1. a1000,000 bytes
2. b1000,000,000 bytes
3. c1000,000,000,000 bytes
4. dNone of these

Answer (b): 1 GB is about $10^9$ bytes (1000 million).

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

1. aMouse
2. bLight pen
3. cKeyboard
4. dVDU

Answer (d): A VDU (monitor) displays output, so it is not an input device.

Revise: Computer System (Class 11 notes)

1. aCompression
2. bFragmentation
3. cEncapsulation
4. dNone of the above

Answer (a): Compression reduces file size by encoding data more compactly.

Revise: Multimedia (Class 11 notes)

1. aCache memory
2. bRAM
3. cROM
4. dNone of the above

Answer (c): ROM keeps its contents when power is off, so it is non-volatile.

Revise: Computer System (Class 11 notes)

1. aName the file
2. bEnsure the filename is not lost
3. cIdentify the file
4. dIdentify the file type

Answer (d): An extension such as .txt or .jpg tells the system the type of file.

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

1. aprocessing
2. bstorage
3. cinput
4. doutput

Answer (c): Acquiring data is the input stage of the cycle.

Revise: Computer System (Class 11 notes)

1. abinary information term
2. bbinary digit
3. cbinary tree
4. dBivariate Theory

Answer (b): Bit is short for binary digit, 0 or 1.

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