BSc CSIT Entrance Exam 2074 Questions with Answers

1. a$p\ne 0,\ q=0$
2. b$p=0,\ q=0$
3. c$p\ne 0,\ q\ne 0$
4. d$p=0,\ q\ne 0$

Answer (a): A fraction is undefined exactly when its denominator is zero, so $q=0$ with $p\ne 0$ gives an undefined value.

Revise: Algebra (Class 11 notes)

1. a${x: a\le x\le b}$
2. b${x: a<x<b}$
3. c${x: a<x\le b}$
4. d${x: a\le x<b}$

Answer (a): Square brackets mean both end points are included, so the closed interval is $a\le x\le b$.

Revise: Algebra (Class 11 notes)

1. aUndefined
2. b$\sqrt{13}$
3. c$i\sqrt5$
4. d$-\sqrt{13}$

Answer (a): For $x=-3$, $f(-3)=\sqrt{4-9}=\sqrt{-5}$, which is not real. Since $f:R\to R$, the function is undefined at $-3$.

Revise: Algebra (Class 11 notes)

1. a${1}$
2. b${-1}$
3. c${-1,1}$
4. d${-1,-1}$

Answer (c): $|x|=1$ means $x=1$ or $x=-1$.

Revise: Algebra (Class 11 notes)

1. aNot known
2. b$8$
3. c$6$
4. d$9$

Answer (d): $x-7=2^1=2$, so $x=9$.

Revise: Algebra (Class 11 notes)

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

Answer (b): If $\cos\theta=4/5$ then $\sin\theta=\sqrt{1-16/25}=3/5$.

Revise: Trigonometry (Class 11 notes)

1. a$n\pi+\frac\pi3$
2. b$n\pi-\frac\pi3$
3. c$n\pi\pm\frac\pi3$
4. d$n\pi$

Answer (c): $\tan x=\pm\sqrt3$, which is $\tan^2x=\tan^2\frac\pi3$, so $x=n\pi\pm\frac\pi3$.

Revise: Trigonometry (Class 11 notes)

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

Answer (c): In an AP $2b=a+c$: $2(4k-6)=(k+2)+(3k-2)=4k$, so $8k-12=4k$ and $k=3$.

Revise: Algebra (Class 11 notes)

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

Answer (b): GP with $a=1$, $r=-1/2$: $S=\frac{a}{1-r}=\frac{1}{3/2}=\frac23$.

Revise: Algebra (Class 11 notes)

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

Answer (d): A $3\times1$ matrix times a $1\times3$ matrix is $3\times3$ with entries $a_ib_j$, giving the matrix in option d.

Revise: Algebra (Class 11 notes)

1. a$10$
2. b$1$
3. c$0$
4. d$-1$

Answer (c): Row 3 is $4$ times row 2, so two rows are proportional and the determinant is $0$.

Revise: Algebra (Class 11 notes)

1. aDiagonal
2. bSymmetric
3. cSkew symmetric
4. dUnit

Answer (b): The entries satisfy $a_{ij}=a_{ji}$ (2,3 and 3,4), so the matrix equals its transpose.

Revise: Algebra (Class 11 notes)

1. a$64i$
2. b$64$
3. c$0$
4. d$-64i$

Answer (a): By De Moivre: $2^6(\cos90^\circ+i\sin90^\circ)=64i$.

Revise: Algebra (Class 11 notes)

1. a$16$
2. b$16\omega$
3. c$-8$
4. d$16\omega^2$

Answer (c): $1+\omega+\omega^2=0$ and $1+\omega=-\omega^2$, so the second bracket is $-2\omega^2$; its cube is $-8\omega^6=-8$.

Revise: Algebra (Class 11 notes)

1. a$x^2+x-6=0$
2. b$x^2+x+6=0$
3. c$x^2-x-6=0$
4. d$x^2-x+6=0$

Answer (a): Sum $=-1$, product $=-6$, so $x^2-(-1)x+(-6)=x^2+x-6=0$.

Revise: Algebra (Class 11 notes)

1. a$6/5$
2. b$-6/5$
3. c$3/5$
4. d$-3/5$

Answer (a): Slopes are $-k/3$ and $5/2$. Perpendicular: $(-k/3)(5/2)=-1$, so $k=6/5$.

Revise: Analytic geometry (Class 11 notes)

1. a$5$
2. b$3$
3. c$0$
4. d$-5$

Answer (d): Pair of lines $ax^2+2hxy+by^2=0$ is perpendicular when $a+b=0$: $5+k=0$, so $k=-5$.

Revise: Analytic geometry (Class 11 notes)

1. a$x+y=2$
2. b$x-y=2$
3. c$2x+2y=3$
4. d$-x-y=2$

Answer (a): Tangent at $(x_1,y_1)$ is $xx_1+yy_1=r^2$: $x+y=2$.

Revise: Analytic geometry (Class 11 notes)

1. a$2$
2. b$3$
3. c$5/7$
4. d$\frac12$

Answer (d): Divide by $x^2$: the limit is the ratio of leading coefficients, $3/6=\frac12$.

Revise: Calculus (Class 11 notes)

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

Answer (a): Using $1-\cos ax=2\sin^2\frac{ax}{2}$, the limit is $2\cdot\frac{a^2}{4}=\frac{a^2}{2}$.

Revise: Calculus (Class 11 notes)

1. a$\tan t$
2. b$\tan\frac t2$
3. c$-\tan t$
4. d$-\tan\frac t2$

Answer (b): $dy/dt=\sin t$, $dx/dt=1+\cos t$, so $dy/dx=\frac{2\sin\frac t2\cos\frac t2}{2\cos^2\frac t2}=\tan\frac t2$.

Revise: Calculus (Class 11 notes)

1. a$-\tan x$
2. b$\tan x$
3. c$\cot x$
4. d$-\cot x$

Answer (a): $\frac{d(\cos x)}{d(\sin x)}=\frac{-\sin x}{\cos x}=-\tan x$.

Revise: Calculus (Class 11 notes)

1. a$12$
2. b$-12$
3. c$4$
4. d$0$

Answer (c): $y''=6x-24=0$ gives $x=4$, and $y''$ changes sign there.

Revise: Calculus (Class 11 notes)

1. a$\cot x+C$
2. b$-\cot x+C$
3. c$\tan x+C$
4. d$-\tan x+C$

Answer (b): $\int\csc^2x,dx=-\cot x+C$.

Revise: Calculus (Class 11 notes)

1. a$\frac\pi4$
2. b$\frac\pi2$
3. c$0$
4. d$1$

Answer (a): $\tan^{-1}x\Big|_0^1=\frac\pi4-0=\frac\pi4$.

Revise: Calculus (Class 11 notes)

1. afirst
2. bsecond
3. cfourth
4. dthird

Answer (b): The word is stressed as com-MEM-o-rate, on the second syllable.

Revise: Grammar and Usage (Class 11 notes)

1. anor
2. bfour
3. csew
4. dtour

Answer (c): 'Go' has the vowel /əʊ/, the same as 'sew'. 'Nor' and 'four' have /ɔː/ and 'tour' has /ʊə/.

Revise: Grammar and Usage (Class 11 notes)

1. aopens
2. bis opened
3. chas to be opened
4. dbe opened

Answer (b): A school does not open itself, so the passive is needed, and it follows "hope that" in the present form: "is opened".

Revise: Grammar and Usage (Class 11 notes)

1. aBellicose
2. bbigot
3. cpacifist
4. dfatalist

Answer (a): "Bellicose" describes a person eager to fight.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. arash
2. bauspicious
3. cfolly
4. dfictitious

Answer (b): Ominous means threatening; the opposite is auspicious (promising).

Revise: Vocabulary and Word Formation (Class 11 notes)

1. aOf, from
2. bFrom, of
3. cof, at
4. don at

Answer (a): Idiom: die of a disease, die from (loss of blood) an injury or cause.

Revise: Grammar and Usage (Class 11 notes)

1. aAt
2. bfor
3. cfrom
4. dto

Answer (d): The verb 'give' takes 'to' for the recipient: Whom did you give it to?

Revise: Grammar and Usage (Class 11 notes)

1. aUpon
2. bon
3. cat
4. dfrom

Answer (a): "Spring upon" means to leap at and attack.

Revise: Grammar and Usage (Class 11 notes)

1. aare
2. bhas
3. cis
4. dam

Answer (c): Rice and curry is thought of as one single dish, so the verb is singular: "is".

Revise: Grammar and Usage (Class 11 notes)

1. adrawback
2. bInsect
3. cprofit
4. dGarland

Answer (a): A snag is a hidden difficulty, that is, a drawback.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. aBigamy
2. bpolygamy
3. cmonogamy
4. dmatrimony

Answer (b): Polygamy is having many spouses; bigamy is exactly two.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. aGrowl
2. bgibber
3. cyelp
4. dhowl

Answer (b): Monkeys gibber (chatter rapidly). Growl, yelp and howl belong to other animals such as dogs and wolves.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. aComplement
2. bdirect object
3. cadjunct
4. dIndirect object

Answer (d): "To his sister" names the receiver of the book, so it is the indirect object.

Revise: Grammar and Usage (Class 11 notes)

1. aIts
2. bit's
3. citself
4. dthere

Answer (a): A possessive determiner is needed before 'hood', so 'its'. 'It's' means 'it is'.

Revise: Grammar and Usage (Class 11 notes)

1. aA
2. ban
3. cthe
4. dsame

Answer (c): "The same" is a fixed phrase.

Revise: Grammar and Usage (Class 11 notes)

1. aBad
2. bgifted
3. cclumsy
4. dunlucky

Answer (b): Versatile means able to do many things well, so gifted fits best.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. aNon
2. bun
3. cin
4. dil

Answer (a): The standard word is "non-aggression".

Revise: Vocabulary and Word Formation (Class 11 notes)

1. asitophobia
2. bpyrophobia
3. ctrichophobia
4. dmonomania

Answer (b): Pyro means fire, so pyrophobia.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. aReal
2. breadable
3. creadable
4. dreality

Answer (d): "Reality" is formed with the noun suffix -ity; the others are adjectives.

Revise: Grammar and Usage (Class 11 notes)

1. aFill
2. buntil
3. cwhile
4. dunless

Answer (b): "Until" links waiting with the time the bus came.

Revise: Grammar and Usage (Class 11 notes)

1. aItinerant
2. bmendicant
3. ctramp
4. dtourist

Answer (a): Itinerant means moving from place to place, especially for work.

Revise: Vocabulary and Word Formation (Class 11 notes)

1. aaren't you
2. bcan't you
3. cwon't it
4. dIsn't you

Answer (a): Positive statement takes a negative tag: "aren't you".

Revise: Grammar and Usage (Class 11 notes)

1. arising and rising
2. brising and falling
3. crising
4. dfalling and falling

Answer (b): An alternative question rises on the first option and falls on the last.

Revise: Grammar and Usage (Class 11 notes)

1. a$10^{-7}$ m
2. b$10^{-10}$ m
3. c$10^{-12}$ m
4. d$10^{-15}$ m

Answer (b): Atomic radii are about $1$ angstrom, i.e. $10^{-10}$ m.

Revise: Physical Quantities (Class 11 notes)

1. a$0^\circ$
2. b$45^\circ$
3. c$90^\circ$
4. d$120^\circ$

Answer (c): The distance from the earth is greatest when the maximum height is greatest, $H=u^2\sin^2\theta/2g$, which occurs at $90^\circ$. The $45^\circ$ angle only maximizes horizontal range.

Revise: Kinematics (Class 11 notes)

1. afriction of air
2. btension of air
3. cgravity
4. dits mass

Answer (a): Air friction dissipates its energy, damping the oscillation.

Revise: Periodic Motion (Class 12 notes)

1. acompression
2. bcohesion
3. cadhesion
4. dcapillarity

Answer (c): Attraction between unlike molecules (powder and skin) is adhesion.

Revise: Elasticity (Class 11 notes)

1. ainertia
2. bshearing strain
3. ctransfer of momentum
4. dsurface tension

Answer (c): Viscosity arises from momentum transfer between adjacent layers of a fluid moving at different speeds, so it is most closely related to transfer of momentum.

Revise: Fluid Statics (Class 12 notes)

1. a15.4 cm
2. b15.4 cm
3. c15.8 cm
4. d86.24 cm

Answer (d): $\Delta L=L\alpha\Delta T=700\times11\times10^{-6}\times(243-131)=700\times11\times10^{-6}\times112=0.8624$ m, which is 86.24 cm.

Revise: Thermal Expansion (Class 11 notes)

1. aadiabatic process
2. bisothermal process
3. cisobaric process
4. disochoric process

Answer (b): Internal energy of an ideal gas depends only on temperature, which is constant in an isothermal process.

Revise: First Law of Thermodynamics (Class 12 notes)

1. a10%
2. b20%
3. c60%
4. d100%

Answer (a): Real steam engines convert only a small fraction of heat to work, of the order of 10 percent.

Revise: Second Law of Thermodynamics (Class 12 notes)

1. aisothermally
2. bisobarically
3. cadiabatically
4. disochorically

Answer (b): For the same initial state and the same final volume, an isobaric expansion keeps pressure at its highest value, so its area under the P-V curve is larger than for isothermal or adiabatic expansion.

Revise: First Law of Thermodynamics (Class 12 notes)

1. aThe interference is constructive.
2. bThe interference is destructive.
3. cThe interference depends on the type of wave.
4. dAll of the above

Answer (a): A large resultant amplitude comes from constructive interference.

Revise: Interference (Class 12 notes)

1. a500 Hz
2. b420 Hz
3. c520 Hz
4. d532 Hz

Answer (d): $f'=f\frac{v+v_o}{v}=524\times\frac{345}{340}\approx531.7\approx532$ Hz.

Revise: Acoustic Phenomena (Class 12 notes)

1. aparallel to the wave velocity
2. banti-parallel to the wave velocity
3. cperpendicular to the wave velocity
4. dparallel or anti-parallel to the wave velocity

Answer (d): In a longitudinal wave the particles oscillate along the direction of propagation, moving both forward and backward, so parallel or anti-parallel.

Revise: Wave Motion (Class 12 notes)

1. a10 lux
2. b15 lux
3. c25 lux
4. d100 lux

Answer (c): $E=I/r^2=100/4=25$ lux.

Revise: Nature and Propagation of Light (Class 12 notes)

1. aLateral shift
2. bdispersion only
3. cdeviation only
4. ddispersion and deviation both

Answer (d): White light is bent (deviated) and split into colours (dispersed).

Revise: Refraction Through Prisms (Class 11 notes)

1. a2
2. b0.5
3. c1.5
4. d2.5

Answer (a): $n=1/\sin C=1/\sin30^\circ=2$.

Revise: Refraction at Plane Surface (Class 11 notes)

1. a$6.25\times10^{18}$
2. b$6.25\times10^{-19}$
3. c$1.6\times10^{-19}$
4. d$1.6\times10^{18}$

Answer (a): $n=Q/e=1/(1.6\times10^{-19})=6.25\times10^{18}$.

Revise: Electric Charges (Class 11 notes)

1. adoes not change
2. bdecreases
3. cincreases
4. dmay increase or decrease depending on the rate of heat

Answer (b): Heating lowers the density, so light travels faster and the refractive index decreases.

Revise: Refraction at Plane Surface (Class 11 notes)

1. a$P/E$
2. b$E/P$
3. c$P\cdot E$
4. d$PE\tan\theta$

Answer (c): $\tau=pE\sin\theta$, proportional to the product of $p$ and $E$.

Revise: Electric Field (Class 11 notes)

1. aemf
2. bpotential
3. ccurrent
4. dresistance

Answer (d): The bridge balances ratios of resistances to find an unknown resistance.

Revise: Electrical Circuit One (Class 12 notes)

1. ais zero at absolute zero temperature
2. bincreases with temperature
3. cis maximum at Curie temperature
4. dbecomes practically zero at Curie temperature

Answer (d): Above the Curie temperature a ferromagnet turns paramagnetic and loses its magnetism.

Revise: Magnetic Properties of Materials (Class 12 notes)

1. a0.02 Wb
2. b0.01 Wb
3. c0.05 Wb
4. d10 Wb

Answer (a): $\Phi=LI=10\times10^{-3}\times2=0.02$ Wb.

Revise: Electromagnetic Induction (Class 12 notes)

1. aelectromagnetic waves
2. bpositrons
3. cions
4. dprotons

Answer (c): Positive rays are streams of positive ions.

Revise: Electrons (Class 12 notes)

1. a3 KeV
2. b4000 eV
3. c3.1 J
4. d3.09 eV

Answer (d): $E=\frac{12375}{4000}\text{ eV}\approx3.09$ eV.

Revise: Photons (Class 12 notes)

1. a$1/n$
2. b$n^2$
3. c$n$
4. d$\frac1{n^2}$

Answer (b): $r_n=n^2a_0$.

Revise: Quantization of Energy (Class 12 notes)

1. asemiconductors
2. bconductors
3. cinsulators
4. ddielectrics

Answer (a): At very low temperatures carriers freeze out in semiconductors, so they stop conducting.

Revise: Semiconductor Devices (Class 12 notes)

1. a$1.505\times10^{23}$
2. b$1.005\times10^{23}$
3. c$1.205\times10^{23}$
4. d$1.303\times10^{23}$

Answer (a): $25/100=0.25$ mol, and each formula unit has one C: $0.25\times6.022\times10^{23}=1.505\times10^{23}$.

Revise: Stoichiometry (Class 11 notes)

1. a$[Ar]3d^54s^1$
2. b$[Ar]3d^64s^2$
3. c$[Ar]3d^74s^2$
4. d$[Ar]3d^44s^2$

Answer (a): Half-filled $d$ subshell is extra stable, so one $4s$ electron moves to $3d$.

Revise: Atomic Structure (Class 11 notes)

1. alinear
2. btetrahedral
3. cangular
4. dpyramidal

Answer (a): Two bond pairs and no lone pairs on C give a linear shape.

Revise: Chemical Bonding (Class 11 notes)

1. achlorine
2. bbromine
3. ciodine
4. dfluorine

Answer (a): Chlorine has the highest value; fluorine's small size causes repulsion in its compact shell.

Revise: Classification of Elements (Class 11 notes)

1. a1.3333333
2. b+4/3
3. c+2/3
4. d+8/3

Answer (d): $3x+4(-2)=0$ so $x=+8/3$.

Revise: Oxidation and Reduction (Class 11 notes)

1. abasic oxide
2. bamphoteric oxide
3. cneutral oxide
4. dacidic oxide

Answer (a): A metal oxide of an alkaline earth metal reacts with acids to form salts.

Revise: Chemistry of Non-Metals (Class 11 notes)

1. asodium
2. bsodium hydroxide
3. csodium carbonate
4. dammonia

Answer (a): Sodium is obtained by electrolysis of fused NaCl in the Down's cell.

Revise: Chemistry of Metals (Class 11 notes)

1. a2,2 dimethyl propane
2. b2-methyl butane
3. c2-methyl propane
4. dPentane

Answer (a): A propane chain with two methyl groups on carbon 2.

Revise: Fundamental Principles (Class 11 notes)

1. a$CH_4$
2. b$C_2H_2$
3. c$H_2$
4. d$C_2H_4$

Answer (a): $Al_4C_3+12H_2O\to4Al(OH)_3+3CH_4$.

Revise: Hydrocarbons (Class 11 notes)

1. aglycol
2. bglucose
3. cα-amino acid
4. dphthalic acid

Answer (c): Proteins are chains of $\alpha$-amino acids joined by peptide bonds.

Revise: Amines (Class 12 notes)

1. aglucose
2. bfructose
3. cgalactose
4. dmaltose

Answer (a): Glucose has a free aldehyde group, a reducing sugar giving Tollens' test.

Revise: Aldehydes and Ketones (Class 12 notes)

1. ainsecticide
2. bherbicide
3. cfungicide
4. drodenticide

Answer (a): DDT kills insects.

Revise: Chemistry in the Service to Mankind (Class 12 notes)

1. acancer
2. bmental anxiety
3. cphysical disorder
4. dmalaria

Answer (b): Tranquilizers calm the nervous system in mental stress.

Revise: Chemistry in the Service to Mankind (Class 12 notes)

1. a$sp^2$ hybridized
2. bsp hybridized
3. c$sp^3$ hybridized
4. d$sp^3$ d hybridized

Answer (a): Each C forms three sigma bonds in a planar ring, so it is $sp^2$.

Revise: Aromatic Hydrocarbons (Class 11 notes)

1. aHoffman's test
2. bFehling's solution
3. cVictor Meyer's test
4. dBrillstein's test

Answer (c): Victor Meyer's test gives red, blue and no colour for the three classes.

Revise: Alcohols (Class 12 notes)

1. aClemenssion reduction
2. bWolf-Kishner reduction
3. cCannizaro's reduction
4. dPerkin's reaction

Answer (a): Zn-Hg with conc. HCl is the Clemmensen reduction.

Revise: Aldehydes and Ketones (Class 12 notes)

1. a$NH_3$
2. b$CH_3NH_2$
3. c$(CH_3)_2NH$
4. d$(CH_3)_3N$

Answer (c): In aqueous solution basicity depends on both the +I effect and solvation, and the secondary amine $(CH_3)_2NH$ is the strongest base. The tertiary amine is less solvated and weaker; the gas-phase order would differ.

Revise: Amines (Class 12 notes)

1. a$ZnSO_4.7H_2O$
2. b$Zn(OH)_2$
3. c$ZnCO_3$
4. dZnO

Answer (a): White vitriol is hydrated zinc sulphate.

Revise: Chemistry of Metals (Class 11 notes)

1. azinc
2. bcopper
3. cmercury
4. diron

Answer (c): Cinnabar is HgS.

Revise: Chemistry of Metals (Class 11 notes)

1. a1.4
2. b2
3. c3
4. d4

Answer (a): $[H^+]=0.04$, $pH=-\log0.04=1.4$.

Revise: Ionic Equilibrium (Class 12 notes)

1. a$Sm^{-1}$
2. bohm
3. c$cm^{-1}$
4. d$ohm^{-1}cm^{-1}$

Answer (c): Cell constant = $l/A$, in $cm^{-1}$.

Revise: Electrochemistry (Class 12 notes)

1. a$mol\ s^{-1}$
2. b$L\ mol^{-2}s^{-1}$
3. c$s^{-1}$
4. d$mol\ L^{-1}s^{-1}$

Answer (c): Rate $=k[A]$, so $k$ has units of $s^{-1}$.

Revise: Chemical Kinetics (Class 12 notes)

1. aVolume
2. bmass
3. carea
4. dconcentration

Answer (d): Concentration does not depend on the amount of substance.

Revise: Chemical Thermodynamic (Class 12 notes)

1. acurie
2. bnik/L
3. cgauss
4. dg/L

Answer (a): The curie is a unit of radioactivity.

Revise: Nuclear Chemistry (Class 12 notes)

1. asodium nitroprusside
2. bPrussian blue
3. cTollen's reagent
4. dBayer's reagent

Answer (a): This complex is sodium nitroprusside.

Revise: Study of Heavy Metals (Class 12 notes)