# Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2006

### done JCECE Engineering Solved Paper-2006

• question_answer1) Which of the following rays can be polarised?

A) Water wave and sound wave

B) Sound wave and radio wave

C) $X-$rays and water wave

D) Light wave and $X-$ ray

• question_answer2) Quantum nature can prove :

A) interference

B) photoelectric effect

C) diffraction

D) polarisation

• question_answer3) Which one has highest binding energy per nucleon?

A) $F{{e}^{56}}$

B) $L{{i}^{6}}$

C) ${{U}^{235}}$

D) $C{{a}^{40}}$

• question_answer4) Huygen's wave theory can't explain:

A) interference

B) photoelectric effect

C) diffraction

D) all of these

• question_answer5) If the refractive index of a glass prism is $\cot (A/2)$ and $A$ is angle of prism, then angle of minimum deviation is:

A) $\left( \frac{\pi }{2}-A \right)$

B) $\left( 2\pi -\frac{A}{2} \right)$

C) $\left( \frac{\pi -A}{2} \right)$

D) $(\pi -2A)$

• question_answer6) If $f$ is the frequency when mass m is attached to a spring of spring constant $k$, then new frequency for this arrangement, is:

A) $f/2$

B) $\sqrt{2f}$

C) $f/\sqrt{2}$

D) $2\sqrt{2f}$

• question_answer7) What is equivalent capacitance of the network? Each capacitor has $1\mu F$ capacitance:

A) $\frac{1}{3}\mu F$

B) $2\mu F$

C) $\frac{3}{2}\mu F$

D) $3\mu F$

• question_answer8) The two capacitors ${{C}_{1}}$and${{C}_{2}}$are charged to potentials ${{V}_{1}}$ and ${{V}_{2}}$ then connected in parallel. There will be no flow of energy, if:

A) ${{C}_{1}}{{V}_{1}}={{C}_{2}}{{V}_{2}}$

B) ${{V}_{1}}={{V}_{2}}$

C) ${{C}_{1}}={{C}_{2}}$

D) $\frac{{{C}_{1}}}{{{V}_{1}}}=\frac{{{C}_{2}}}{{{V}_{2}}}$

• question_answer9) Which is not the unit of electric field?

A) $\frac{N}{C}$

B) $\frac{N-m}{C}$

C) $\frac{V}{m}$

D) $\frac{J}{C\text{-}m}$

• question_answer10) If a body moves for $2\,\,s$ with $15\,\,m/s$ velocity towards east and then moves with $5\,\,m/s$ velocity for $8\,\,s$ towards north, then average velocity is:

A) $5\,\,m/s$

B) $15\,\,m/s$

C) $30\,\,m/s$

D) $7.5\,\,m/s$

• question_answer11) For monoatomic gas which is correct?

A) $CV=\frac{3}{5}R$

B) ${{C}_{P}}=\frac{5}{2}R$

C) ${{C}_{P}}-{{C}_{V}}=2R$

D) $\frac{{{C}_{P}}}{{{C}_{V}}}=\frac{3}{5}$

• question_answer12) Which is correct relationship for diode?

A)

B)

C)

D)

• question_answer13) In a properly biased transistor:

A) both depletion layers are equally large

B) both depletion layers are equally small

C) emitter-base depletion layer is large but base-collector depletion layer is small

D) emitter-base depletion layer is small but base-collector depletion layer is large

• question_answer14) A wire has resistance $20\,\,\Omega$. If its length is increased three times its initial length, then new resistance is:

A) $40\Omega$

B) $80\Omega$

C) $60\Omega$

D) $180\Omega$

• question_answer15) A circular coil of diameter $d$ is rotated in electric field such that electric flux is changed from zero to maximum value $\phi$ then, electric field is:

A) $\frac{\phi }{\pi {{d}^{2}}}$

B) $\frac{2\phi }{\pi {{d}^{2}}}$

C) $\frac{4{{d}^{2}}}{\pi {{\phi }^{2}}}$

D) $\frac{4\phi }{\pi {{d}^{2}}}$

• question_answer16) Work done in rotating a bar magnet from $0$ to angle $\theta$ is:

A) $MH(1-\cos \theta )$

B) $\frac{M}{H}(1-\cos \theta )$

C) $\frac{M}{H}(\cos \theta -1)$

D) $MH(\cos \theta -1)$

• question_answer17) If a convex lens of refractive index $1.44$ is dipped in liquid of refractive index $1.49$, then it behaves as:

A) concave lens

B) convex lens

C) mirror

D) none of these

• question_answer18) If a source approaches and recedes from observer with same velocity, the ratio of frequencies (apparent) is $6:5$, then velocity of source is:$({{v}_{s}}=330\,\,m/s)$

A) $20\,\,m/s$

B) $10\,\,m/s$

C) $30\,\,m/s$

D) $33\,\,m/s$

• question_answer19) If a boy swings in a circle so the minimum and maximum height from ground is$3\,\,m$and$6\,\,m$, then, its maximum velocity is:

A) $5\sqrt{2}m/s$

B) $2\sqrt{5}m/s$

C) $3\sqrt{5}m/s$

D) $5\sqrt{3}m/s$

• question_answer20) If percentage decrease in radius of earth is $1%$ without changing its mass, then percentage change in acceleration due to gravity is:

A) $2%$ decrease

B) $2%$ increase

C) $1%$ decrease

D) $1%$ increase

• question_answer21) A black body radiates at two temperatures ${{T}_{1}}$ and ${{T}_{2}}$ such that${{T}_{1}}<{{T}_{2}}$. The frequency corresponding to maximum intensity is:

A) less at${{T}_{1}}$

B) more at${{T}_{1}}$

C) equally in the two cases

D) cannot say

• question_answer22) If temperature is increased by $1\,\,K$ at constant volume, then work done on the gas is:

A) $\frac{5}{2}R$

B) $\frac{3}{2}R$

C) $zero$

D) $\frac{1}{2}R$

• question_answer23) A body cools from${{75}^{o}}C$ to${{70}^{o}}C$ in time ${{t}_{1}}$, from ${{70}^{o}}C$ to ${{65}^{o}}C$ in time ${{t}_{2}}$ and from ${{65}^{o}}C$ to ${{60}^{o}}C$ in timer$3$, then:

A) ${{t}_{3}}>{{t}_{2}}>{{t}_{1}}$

B) ${{t}_{1}}>{{t}_{2}}>{{t}_{3}}$

C) ${{t}_{2}}>{{t}_{1}}={{t}_{3}}$

D) ${{t}_{1}}>{{t}_{2}}>{{t}_{3}}$

• question_answer24) A gas is at ${{27}^{o}}C$. Its volume is doubled keeping pressure constant, then final temperature is:

A) ${{600}^{o}}C$

B) $327\,\,K$

C) ${{327}^{o}}C$

D) ${{273}^{o}}C$

• question_answer25) If the volume of gas is changed from ${{V}_{1}}$ to ${{V}_{2}}$ isothermally, then work done is:

A) $RT\ln \frac{{{V}_{1}}}{{{V}_{2}}}$

B) $RT\ln \frac{{{V}_{2}}}{{{V}_{1}}}$

C) $R({{T}_{2}}-{{T}_{1}})\ln \frac{{{V}_{2}}}{{{V}_{1}}}$

D) $R({{V}_{2}}-{{V}_{1}})\ln \frac{{{T}_{2}}}{{{T}_{1}}}$

• question_answer26) If energy is supplied to a gas is ochorically, increase in internal energy is $dU$ then:

A) $dQ=dU+dW$

B) $dQ=dU-dW$

C) $dQ=dU$

D) $dQ=-dU$

• question_answer27) A nucleus $_{Z}^{A}X$ emits one a and $2\beta$ particles, then final nucleus is:

A) $Y_{Z-2}^{A}$

B) $Y_{Z-4}^{A-4}$

C) $Y_{Z}^{A-4}$

D) $X_{Z}^{A}$

• question_answer28) The fringe width for red light is approximately how many times that for violet light in Young's slit experiment?

A) $2$ times

B) $3$ times

C) Equal

D) $1/2$ times

• question_answer29) A person sees clearly at a distance of $100\,\,cm$, then power of lens used to see object at $40\,\,cm$ is:

A) $3D$

B) $-3D$

C) $-1.5D$

D) $+1.5D$

• question_answer30) The electric potential $V$ is given as a function of distance $x$ (metre) by$V=(5{{x}^{2}}+10x-4)V$. Value of electric field at $x=1\,\,m$ is:

A) $-23\,\,V/m$

B) $11\,\,V/m$

C) $6\,\,V/m$

D) $-20\,\,V/m$

• question_answer31) In an image converter tube fluorescent material is bombarded by:

• question_answer32) A particle executes simple harmonic motion with a frequency$f$. The frequency with which its kinetic energy oscillates is:

A) $f/2$

B) $f$

C) $2f$

D) $4f$

• question_answer33) The work done by the centripetal force $F$ when the body completes one rotation around the circle of radius $R$ is:

A) $2\pi RF$

B) $2RF$

C) $RF$

D) $zero$

• question_answer34) The unit mass having $\overset{\to }{\mathop{\mathbf{r}}}\,=8\widehat{\mathbf{i}}-4\widehat{\mathbf{j}}$ and $\overset{\to }{\mathop{\mathbf{v}}}\,=8\widehat{\mathbf{i}}+4\widehat{\mathbf{j}}$ in its angular momentum is:

A) $64$ unit in $-\mathbf{\hat{k}}$ direction

B) $64$unit in $+\mathbf{\hat{k}}$ direction

C) $64$unit in $+\widehat{\mathbf{j}}$ direction

D) $64$unit in $+\widehat{\mathbf{i}}$ direction

• question_answer35) Which is nuclear fusion direction?

A) Hydrogen to helium

B) Uranium to krypton

C) Hydrogen to water

D) Neutron to proton

• question_answer36) If an $AC$ produces same heat as that produced by a steady current of $4\,\,A$, then peak value of current is:

A) $4\,\,A$

B) $1.56\,\,A$

C) $5.6\,\,A$

D) $1.41\,\,A$

• question_answer37) In$LCR$circuit $f=\frac{50}{\pi }Hz,$ $V=50\,\,volt,$$R=300\Omega$. If$L=1\,\,H$and$C=20\,\,\mu C$, then voltage across capacitor is:

A) $zero$

B) $20\,\,V$

C) $30\,\,V$

D) $50\,\,V$

• question_answer38) If two forces each of $2\,\,N$ are inclined at ${{60}^{o}}$, then resultant force is:

A) $2\,\,N$

B) $2\sqrt{5}N$

C) $3\sqrt{2}N$

D) $4\sqrt{2}N$

• question_answer39) A block of mass $10\,\,kg$ is placed on a rough horizontal surface whose coefficient of friction is 0.5. If a horizontal force of $100\,\,N$ is applied on it, then acceleration of block will be:

A) $10\,\,m/{{s}^{2}}$

B) $5\,\,m/{{s}^{2}}$

C) $15\,\,m/{{s}^{2}}$

D) $0.5\,\,m/{{s}^{2}}$

• question_answer40) The potential difference across an instrument in a $AC$ circuit of frequency $f$ is $V$ and the current through it is $I$ such that $V=5\cos 2\pi ft\,\,volt$ and $I=2\sin 2\pi ft\,\,amp$. The power dissipated in the instrument is:

A) $zero$

B) $10\,\,W$

C) $5\,\,W$

D) $2.5\,\,W$

• question_answer41) If ratio of intensities of interfering waves is $16:9$, then ratio of maximum to minimum intensity is:

A) $49:1$

B) $225:81$

C) $3:1$

D) $9:1$

• question_answer42) The power of a lens, a short sighted person uses is $-2\,\,D$. Find the maximum distance of an object which he can see without spectacles:

A) $25\,\,cm$

B) $50\,\,cm$

C) $100\,\,cm$

D) $10\,\,cm$

• question_answer43) The first overtone frequency of a wave on string of length $2\,\,m$ is $250\,\,Hz$. Then, its velocity is:

A) $1000\,\,m/s$

B) $25\,\,m/s$

C) $100\,\,cm$

D) $10\,\,cm$

• question_answer44) What is the current flowing in arm$AB$?

A) $\frac{35}{4}A$

B) $\frac{13}{7}A$

C) $\frac{5}{7}A$

D) $\frac{7}{5}A$

• question_answer45) A projectile is fired making an angle $2\theta$ with horizontal with velocity$4\,\,m/s$. At any instant it makes an angle $\theta$, then its velocity is:

A) $4\cos \theta$

B) $4(2\cos \theta -\sec \theta )$

C) $2(\sec \theta +4\cos \theta )$

D) $4(\sec \theta +\cos \theta )$

• question_answer46) If path difference becomes $(2n-1)\frac{\lambda }{2}$ then:

A) white fringe is formed

B) bright fringe is formed

C) uniform illumination is obtained

D) dark fringe is formed

• question_answer47) If the intensity of fringe at wavelength$\lambda$is$K$, then its intensity at wavelength $\lambda /2$ is:

A) $\frac{K}{2}$

B) $K$

C) $zero$

D) $\sqrt{2}K$

• question_answer48) A positively charged particle moving with velocity $v$ enters a region of space having a uniform magnetic field $B$. The particle will experience the large deflecting force, when the angle between $v$ and $B$ is:

A) ${{0}^{o}}$

B) ${{45}^{o}}$

C) ${{90}^{o}}$

D) ${{180}^{o}}$

• question_answer49) In a step-up transformer the turn ratio is$1:8$. A lead accumulator $(emf=6\,\,V)$ is connected across the primary coil of the transformer. The voltage across the secondary coil is:

A) $48\,\,V$

B) $0.75\,\,V$

C) $14\,\,V$

D) $zero$

• question_answer50) The mass of a lift is$500\,\,kg$. When it ascends with an acceleration of $2m/{{s}^{2}}$ the tension in the cable will be:$(g=10\,\,m/{{s}^{2}})$

A) $6000\,\,N$

B) $5000\,\,N$

C) $4000\,\,N$

D) $1000\,\,N$

• question_answer51) A water molecule can form maximum number of $H-$bond which is equal to:

A) $1$

B) $2$

C) $3$

D) $4$

• question_answer52) Bond angle in ${{H}_{2}}O$ is:

A) ${{109}^{o}}28'$

B) ${{107}^{o}}10$

C) ${{104.5}^{o}}$

D) ${{92}^{o}}$

A) $ZnS$

B) $PbC{{O}_{3}}$

C) $ZnC{{O}_{3}}$

D) $MgC{{O}_{3}}$

• question_answer54) Which is extremely stable?

A) $N{{F}_{3}}$

B) $NC{{l}_{3}}$

C) $NB{{r}_{3}}$

D) $N{{H}_{3}}$

• question_answer55) $C{{H}_{3}}COCl$does not react with:

A) diethyl ether

B) phenol

C) ethanol

D) aniline

• question_answer56) In $S{{O}_{2}}$ hybridisation is:

A) $sp$

B) $s{{p}^{3}}$

C) $ds{{p}^{2}}$

D) $s{{p}^{2}}$

• question_answer57) Lowest melting point chloride is:

A) $LiCl$

B) $NaCl$

C) $KCl$

D) $CsCl$

• question_answer58) Half-life of a substance is$6\min$. If its initial amount is$32\,\,g$, then amount present after $18\,\,\min$ is:

A) $4\,\,g$

B) $8\,\,g$

C) $16\,\,g$

D) $2\,\,g$

• question_answer59) If calcium acetate and calcium for mate react, then product formed is:

A) acetaldehyde

B) acetic acid

C) formic acid

D) ethyl for mate

• question_answer60) Reduction with aluminium isopropoxide in excess of isopropyl alcohol is called Meer we in Pond or f Verley reduction$(MPV)$. What will be the firal product when cyclohex-2-enone is selectively reduced in $MPV$ reaction?

A) Cyclohexanol

B) Cyclohex-2-enol

C) Cyclohexanone

D) Benzene

• question_answer61) If $pH$ of a solution is$4$, then ${{H}^{+}}$ is:

A) ${{10}^{4}}$

B) ${{10}^{10}}$

C) ${{10}^{-4}}$

D) ${{10}^{-10}}$

• question_answer62) When sodium nitrate is heated above${{6000}^{o}}C$, then:

A) only $N{{a}_{2}}O$ is formed

B) only ${{N}_{3}}$ is formed

C) only ${{O}_{2}}$ is formed

D) all are formed

• question_answer63) Which of the following produces $C{{l}_{2}}$ gas?

A) $NaCl+HN{{O}_{3}}$

B) $Mn{{O}_{2}}+HCl$

C) $KMn{{O}_{4}}+HCl$

D) $HCl+HN{{O}_{3}}$

• question_answer64) Which is correctly arranged as increasing size?

A) $F<O<C<Cl<Br$

B) $C<O<F<Cl<Br$

C) $Cl<Br<F<C<O$

D) $O<F<C<Cl<Br$

• question_answer65) $N{{H}_{3}}$ is absorbed by:

A) ozone

B) $CaO$

C) pyrargallol

D) $CaC{{l}_{2}}$

• question_answer66) $1.25\,\,g$$N{{H}_{3}}$ contains how many atoms?

A) ${{10}^{23}}$

B) $2\times {{10}^{23}}$

C) $6\times {{10}^{13}}$

D) $4\times {{10}^{23}}$

• question_answer67) Which of the following has smallest bond angle?

A) Ethane

B) Ethene

C) Ethyne

D) Ethanol

• question_answer68) Chloroform in air is oxidised to :

A) $CC{{l}_{4}}$

B) dichloromethane

C) phosgene

D) oxygen

A) $CaS{{O}_{4}}\cdot 2{{H}_{2}}O$

B) $CaS{{O}_{4}}\cdot \frac{1}{2}{{H}_{2}}O$

C) $MgS{{O}_{4}}\cdot 2{{H}_{2}}O$

D) $CuS{{O}_{4}}$

• question_answer70) Which is not soluble in water?

A) $PbS{{O}_{4}}$

B) $CdS{{O}_{4}}$

C) $Bi{{(S{{O}_{4}})}_{2}}$

D) $CuS{{O}_{4}}$

• question_answer71) Which of the following is colour red?

A) $C{{u}_{2}}O$

B) $CuF$

C) $Zn{{F}_{2}}$

D) $ZnC{{l}_{2}}$

• question_answer72) How many unpaired electrons are present in$[Cr{{(N{{H}_{3}})}_{5}}]B{{r}_{3}}$?

A) $1$

B) $2$

C) $3$

D) $4$

• question_answer73) $S+\frac{3}{2}{{O}_{2}}\xrightarrow{{}}S{{O}_{3}}\Delta H=2x$,$S{{O}_{2}}+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}S{{O}_{3}}\Delta H=y$,then heat of formation of $S{{O}_{2}}$ is:

A) $2x-y$

B) $2x+y$

C) $x+y$

D) $\frac{2x-y}{2}$

• question_answer74) Reagent (catalyst) used in Friedel-Craft's alkylation reaction is:

A) $AlC{{l}_{3}}$

B) $anhyd.\,\,AlC{{l}_{3}}$

C) ${{N}_{2}}$

D) $He$

• question_answer75) Catalyst used in making ${{H}_{2}}S{{O}_{4}}$ in contact process is:

A) ${{V}_{2}}{{O}_{5}}$

B) $F{{e}_{2}}{{O}_{3}}$

C) $C{{r}_{2}}{{O}_{3}}$

D) $Cr{{O}_{3}}$

• question_answer76) When acetamide is reacted with $NaOBr$, then product formed is:

A) ethanamine

B) methanamine

C) methanamide

D) ethanenitrile

• question_answer77) Isocyanide is prepared by :

A) Friedel Craft's reaction

B) Wurtz's reacdon

C) Williamson synthesis

D) Carbylamine reaction

• question_answer78) If rate of diffusion of $C{{H}_{4}}$ is twice than that of a gas$x$, then its molecular mass is:

A) $64\,\,g$

B) $16\,\,g$

C) $32\,\,g$

D) $8\,\,g$

• question_answer79) Which one is not Lewis acid?

A) $Be{{F}_{2}}$

B) $SnC{{l}_{4}}$

C) $AlC{{l}_{3}}$

D) $B{{F}_{3}}$

• question_answer80) Natural gas mainly consists of:

A) methane

B) butane

C) propane

D) ethane $+$ octane

• question_answer81) Phenol is treated with $Zn$ to form:

A) benzoic acid

B) benzyl alcohol

C) benzene

D) benzoquinone

• question_answer82) Which one is isoelectronic with$CO?$

A) $N_{2}^{-}$

B) $N_{2}^{+}$

C) $C{{N}^{-}}$

D) $NO$

• question_answer83) How much volume of $1\,\,M\,\,{{H}_{2}}S{{O}_{4}}$ is required to neutralize $20\,\,mL$ of$1M\,\,NaOH$?

A) $10\,\,mL$

B) $20\,\,mL$

C) $5\,\,mL$

D) $15\,\,mL$

A) $SnC{{l}_{2}}+HCl$

B) $AgN{{O}_{3}}+N{{H}_{4}}OH$

C) $CuS{{O}_{4}}+NaOH$

D) $FeS{{O}_{4}}+{{H}_{2}}{{O}_{2}}$

• question_answer85) $C{{u}^{2+}}+Ag\xrightarrow{{}}Cu+A{{g}^{+}}$ oxidation half reaction is:

A) $C{{u}^{2+}}\to Cu$

B) $Ag\to A{{g}^{+}}$

C) $Cu\to C{{u}^{2+}}$

D) all of these

• question_answer86) ${{C}_{4}}{{H}_{10}}O$ has how many isomeric alcohols?

A) $1$

B) $2$

C) $3$

D) $4$

• question_answer87) $IUPAC$name of$C{{H}_{3}}-C\equiv C-HC-{{(C{{H}_{3}})}_{2}}$is:

A) 4-methyl-2-pentyne

B) 1, 1-dimethyl-2-butyne

C) 2-methyl-4-pentyne

D) 4, 4-dimethyl-2-butyne

• question_answer88) Fehling test is given by:

A) glucose

B) fructose

C) sucrose

D) all of these

• question_answer89) Number of isomeric primary amine of molecular formula ${{C}_{4}}{{H}_{11}}N$ is:

A) $1$

B) $2$

C) $3$

D) $4$

• question_answer90) For reaction$3X+Y{{X}_{3}}Y$$\Delta H=+ve$, amount of ${{X}_{3}}Y$ can be changed by:

A) changing temperature

B) changing pressure

C) changing temperature, pressure,

D) changing temperature, pressure, adding catalyst

• question_answer91) Which one is most ionic?

A) ${{P}_{2}}{{O}_{5}}$

B) $Mn{{O}_{2}}$

C) $M{{n}_{2}}{{O}_{7}}$

D) ${{P}_{2}}{{O}_{3}}$

• question_answer92) Which one gives ${{I}_{2}}$ on reaction with$KI?$

A) $A{{g}_{2}}S{{O}_{4}}$

B) $CuS{{O}_{4}}$

C) $PbS{{O}_{4}}$

D) $CdS{{O}_{4}}$

• question_answer93) Colour of the solution when $KI$ reacts with $B{{r}_{2}}$ is:

A) blue

B) black

C) red

D) no change

• question_answer94) Finely divided iron combines with $CO$ to give:

A) $Fe{{(CO)}_{5}}$

B) $F{{e}_{2}}{{(CO)}_{9}}$

C) $F{{e}_{3}}{{(CO)}_{12}}$

D) $Fe{{(CO)}_{6}}$

• question_answer95) Which of the following is pyramidal?

A) $PC{{l}_{3}}$

B) $CO_{3}^{2-}$

C) $S{{O}_{2}}$

D) $NO_{3}^{-}$

• question_answer96) Which of the following conducts electricity?

A) Crystal$NaCl$

B) Diamond

C) Molten$KBr$

D) Sulphur

• question_answer97) Ratio of kinetic energy of hydrogen and helium gas at $300\,\,K$ is:

A) $2:1$

B) $4:5$

C) $1:1$

D) $1:2$

• question_answer98) Which of the following has highest energy?

A) $n=2,\,\,l=1$

B) $n=3,\,\,l=2$

C) $n=3,\,\,l=1$

D) $n=2,\,\,l=0$

• question_answer99) Oxidation state of phosphorus in pyrophosphoric acid is:

A) $+5$

B) $+3$

C) $+4$

D) $+1$

• question_answer100) If the $75%$ of a first order reaction is complete in$8\min$, then time taken to decompose $50%$ of its initial amount is:

A) $2\min$

B) $4\min$

C) $12\min$

D) $1\min$

• question_answer101) If$a\ne \beta$and${{\alpha }^{2}}=5\alpha -3,\,\,{{\beta }^{2}}=5\beta -3$then the equation having $\alpha /\beta$ and $\beta /\alpha$ as its roots is:

A) $3{{x}^{2}}+19x+3=0$

B) $3{{x}^{2}}-19x+3=0$

C) $3{{x}^{2}}-19x-3=0$

D) ${{x}^{2}}-16x+1=0$

• question_answer102) If$y={{(x+\sqrt{1+{{x}^{2}}})}^{n}}$, then${{(1+x)}^{2}}\frac{{{d}^{2}}y}{d{{x}^{2}}}+x\frac{dy}{dx}$is

A) ${{n}^{2}}y$

B) $-{{n}^{2}}y$

C) $-y$

D) $2{{x}^{2}}y$

• question_answer103) If$1,\,\,{{\log }_{3}}\sqrt{({{3}^{1-x}}+2)},\,\,{{\log }_{3}}(4\cdot {{3}^{x}}-1)$are in $AP$, then $x$ equals:

A) ${{\log }_{3}}4$

B) $1-{{\log }_{3}}4$

C) $1-{{\log }_{4}}3$

D) ${{\log }_{4}}3$

• question_answer104) A problem in mathematics is given to three students $A,\,\,\,B,\,\,\,C$ and their respective probability of solving the problem is $\frac{1}{2},\,\,\,\frac{1}{3}$ and$\frac{1}{4}$. Probability that the problem is solved, is:

A) $\frac{3}{4}$

B) $\frac{1}{2}$

C) $\frac{2}{3}$

D) $\frac{1}{3}$

• question_answer105) The angle of elevation of a tower at a point distant $d$ metres from its base is${{30}^{o}}$. If the tower is $20\,\,m$ high, then the value of $d$ is:

A) $10\sqrt{3}m$

B) $\frac{20}{\sqrt{3}}m$

C) $20\sqrt{3}m$

D) $10\,\,m$

• question_answer106) $l,\,\,\,m,\,\,\,n$ are the $p\text{th}$, $q\text{th}$ and $r\text{th}$ terms of a $GP$ and all positive, then$\left| \begin{matrix} \log l & p & 1 \\ \log m & q & 1 \\ \log n & r & 1 \\ \end{matrix} \right|$equals:

A) $3$

B) $2$

C) $1$

D) $zero$

• question_answer107) $\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1-\cos 2x}}{\sqrt{2}x}$is equal to:

A) $\lambda$

B) $-1$

C) zero

D) does not exist

• question_answer108) A triangle with vertices$(4,\,\,0),\,\,(-1,\,\,-1),\,\,(3,\,\,5)$ is:

A) isosceles and right angled

B) isosceles but not right angled

C) right angled but not isosceles

D) neither right angled nor isosceles

• question_answer109) ${{\cot }^{-1}}(\sqrt{\cos \alpha })-{{\tan }^{-1}}(\sqrt{\cos \alpha })=x$, then$\sin x$is equal to:

A) ${{\tan }^{2}}\left( \frac{\alpha }{2} \right)$

B) ${{\cot }^{2}}\left( \frac{\alpha }{2} \right)$

C) $\tan \alpha$

D) $\cot \left( \frac{\alpha }{2} \right)$

• question_answer110) A plane which passes through the point $(3,\,\,2,\,\,0)$ and the line$\frac{x-3}{1}=\frac{y-6}{5}=\frac{z-4}{4}$is:

A) $x-y+z=1$

B) $x+y+z=5$

C) $x+2y-z=1$

D) $2x-y+z=5$

• question_answer111) The solution of the equation $\frac{{{d}^{2}}y}{d{{x}^{2}}}={{e}^{-2x}}$ is:

A) $\frac{{{e}^{-2x}}}{4}$

B) $\frac{{{e}^{-2x}}}{4}+cx+d$

C) $\frac{1}{4}{{e}^{-2x}}+c{{x}^{2}}+d$

D) $\frac{1}{4}{{e}^{-2x}}+c+d$

• question_answer112) $\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{{{x}^{2}}+5x+3}{{{x}^{2}}+x+2} \right)}^{x}}$is equal to:

A) ${{e}^{4}}$

B) ${{e}^{2}}$

C) ${{e}^{3}}$

D) $e$

• question_answer113) The domain of${{\sin }^{-1}}\left[ {{\log }_{3}}\left( \frac{x}{3} \right) \right]$is:

A) $[1,\,\,9]$

B) $[-1,\,\,9]$

C) $[-9,\,\,1]$

D) $[-9,\,\,-1]$

• question_answer114) The value of${{2}^{1/4}}\cdot {{4}^{1/8}}\cdot {{8}^{1/16}}...\infty$is

A) $1$

B) $2$

C) $3$

D) $4$

• question_answer115) Fifth term of a $GP$ is $2$, then the product of its $9$ terms is:

A) 256

B) 512

C) 1024

D) none of these

• question_answer116) $\int_{0}^{10\pi }{|\sin x|}\,\,dx$is:

A) $20$

B) $8$

C) $10$

D) $18$

• question_answer117) ${{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}x}\,\,dx$, then$\underset{n\to \infty }{\mathop{\lim }}\,n[{{I}_{n}}+{{I}_{n+2}}]$ equal to:

A) $\frac{1}{2}$

B) $1$

C) $\infty$

D) $zero$

• question_answer118) $\int_{-\pi }^{\pi }{\frac{2x(1+\sin x)}{1+{{\cos }^{2}}x}}dx$is:

A) $\frac{{{\pi }^{2}}}{4}$

B) ${{\pi }^{2}}$

C) $zero$

D) $\frac{\pi }{2}$

• question_answer119) The period of the function$f(x)={{\sin }^{4}}x+{{\cos }^{4}}x$ is:

A) $\pi$

B) $\frac{\pi }{2}$

C) $2\pi$

D) none of these

• question_answer120) If${{x}^{y}}={{e}^{x-y}}$, then$\frac{dy}{dx}$is:

A) $\frac{1+x}{1+\log x}$

B) $\frac{1-\log x}{1+\log x}$

C) not defined

D) $\frac{\log x}{{{(1+\log x)}^{2}}}$

• question_answer121) The two curves ${{x}^{3}}-3x{{y}^{2}}+2=0$ and$3{{x}^{2}}y-{{y}^{3}}-2=0$

A) cut at right angles

B) touch each other

C) cut at an angle$\frac{\pi }{3}$

D) cut at an angle$\frac{\pi }{4}$

• question_answer122) The function $f(x)={{\cot }^{-1}}x+x$ increases in the interval:

A) $(1,\,\,\infty )$

B) $(-1,\,\,\infty )$

C) $(-\infty ,\,\,\infty )$

D) $(0,\,\,\infty )$

• question_answer123) The greatest value of$f(x)={{(x+1)}^{1/3}}-{{(x-1)}^{1/3}}$on$[0,\,\,1]$is:

A) $1$

B) $2$

C) $3$

D) $1/3$

• question_answer124) $\int{\frac{dx}{x({{x}^{n}}+1)}}$is equal to:

A) $\frac{1}{n}\log \left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+c$

B) $\frac{1}{n}\log \left( \frac{{{x}^{n}}+1}{{{x}^{n}}} \right)+c$

C) $\log \left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+c$

D) none of the above

• question_answer125) The area bounded by the curve $y=2x-{{x}^{2}}$ and the straight line $y=-x$ is given by:

A) $\frac{9}{2}sq\,\,unit$

B) $\frac{43}{6}sq\,\,unit$

C) $\frac{35}{6}sq\,\,unit$

D) none of these

• question_answer126) The differential equation of all non-vertical lines in a plane is:

A) $\frac{{{d}^{2}}y}{d{{x}^{2}}}=0$

B) $\frac{{{d}^{2}}x}{d{{y}^{2}}}=0$

C) $\frac{dy}{dx}=0$

D) $\frac{dx}{dy}=0$

• question_answer127) Given two vectors $\widehat{\mathbf{i}}-\widehat{\mathbf{j}}$ and $\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}$ the unit vector coplanar with the two vectors and perpendicular to first is:

A) $\pm \frac{1}{\sqrt{2}}(\widehat{\mathbf{i}}+\widehat{\mathbf{j}})$

B) $\frac{1}{\sqrt{5}}(2\widehat{\mathbf{i}}+\widehat{\mathbf{j}})$

C) $\pm \frac{1}{\sqrt{2}}(\widehat{\mathbf{i}}+\widehat{\mathbf{k}})$

D) none of these

• question_answer128) The vector $\widehat{\mathbf{i}}+x\widehat{\mathbf{j}}+3\widehat{\mathbf{k}}$ is rotated through an angle $\theta$ and doubled in magnitude, then it becomes$4\widehat{\mathbf{i}}+(4x-2)\widehat{\mathbf{j}}+2\widehat{\mathbf{k}}$. The value of is:

A) $\left\{ -\frac{2}{3},\,\,2 \right\}$

B) $\left\{ \frac{1}{3},\,\,2 \right\}$

C) $\left\{ \frac{2}{3},\,\,0 \right\}$

D) $\{2,\,\,7\}$

• question_answer129) A parallelepiped is formed by planes drawn through the points $(2,\,\,3,\,\,5)$ and $(5,\,\,9,\,\,7)$ parallel to the coordinate planes. The length of a diagonal of the parallelepiped to piped is:

A) $7$

B) $\sqrt{38}$

C) $\sqrt{155}$

D) none of these

• question_answer130) The equation of the plane containing the line$\frac{x-{{x}_{1}}}{l}=\frac{y-{{y}_{1}}}{m}=\frac{z-{{z}_{1}}}{n}$is$a(x-{{x}_{1}})+b(y-{{y}_{1}})+c(z-{{z}_{1}})=0$, where:

A) $a{{x}_{1}}+b{{y}_{1}}+c{{z}_{1}}=0$

B) $al+bm+cn=0$

C) $\frac{a}{l}=\frac{b}{m}=\frac{c}{n}$

D) $l{{x}_{1}}+m{{y}_{1}}+n{{z}_{1}}=0$

• question_answer131) $A$ and $B$ play a game where each is asked to select a number from $1$ to$25$. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is:

A) $\frac{1}{25}$

B) $\frac{24}{25}$

C) $\frac{2}{25}$

D) none of these

• question_answer132) The equation of the directrix of the parabola ${{y}^{2}}+4y+4x+2=0$is:

A) $x=-1$

B) $x=1$

C) $x=-\frac{3}{2}$

D) $x=\frac{3}{2}$

• question_answer133) Let ${{T}_{n}}$ denote the number of triangles which can be formed using the vertices of a regular polygon of $n$ sides. If${{T}_{n+1}}-{{T}_{n}}=21$, then n equals:

A) $5$

B) $7$

C) $6$

D) $4$

• question_answer134) In a triangle $ABC$, $\frac{A-B+C}{2}$is equal to:

A) ${{a}^{2}}+{{b}^{2}}-{{c}^{2}}$

B) ${{c}^{2}}+{{a}^{2}}-{{b}^{2}}$

C) ${{b}^{2}}-{{c}^{2}}-{{a}^{2}}$

D) ${{c}^{2}}-{{a}^{2}}-{{b}^{2}}$

• question_answer135) For $x\in R,\,\,\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{x-3}{x+2} \right)}^{x}}$ is equal to:

A) $e$

B) ${{e}^{-1}}$

C) ${{e}^{-5}}$

D) ${{e}^{5}}$

• question_answer136) The in centre of the triangle with vertices $(1,\,\,\sqrt{3}),\,\,(0,\,\,0)$and$(2,\,\,0)$is:

A) $\left( 1,\,\,\frac{\sqrt{3}}{2} \right)$

B) $\left( \frac{2}{3},\,\,\frac{1}{\sqrt{3}} \right)$

C) $\left( \frac{2}{3},\,\,\frac{\sqrt{3}}{2} \right)$

D) $\left( 1,\,\,\frac{1}{\sqrt{3}} \right)$

• question_answer137) If the vectors $\overset{\to }{\mathop{\mathbf{a}}}\,,\,\,\,\overset{\to }{\mathop{\mathbf{b}}}\,$ and $\overset{\to }{\mathop{\mathbf{c}}}\,$ from the sides $BC,\,\,\,CA$ and $AB$ respectively, of a triangle $ABC$, then:

A) $\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{b}}}\,\cdot \overset{\to }{\mathop{\mathbf{c}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=0$

B) $\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{b}}}\,\times \overset{\to }{\mathop{\mathbf{c}}}\,=\overset{\to }{\mathop{\mathbf{c}}}\,\times \overset{\to }{\mathop{\mathbf{a}}}\,=0$

C) $\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{b}}}\,\cdot \overset{\to }{\mathop{\mathbf{c}}}\,=\overset{\to }{\mathop{\mathbf{c}}}\,\cdot \overset{\to }{\mathop{\mathbf{a}}}\,=0$

D) $\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{a}}}\,+\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{c}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,\times \overset{\to }{\mathop{\mathbf{a}}}\,=0$

• question_answer138) If $\omega$ is an imaginary cube root of unity, then ${{(1+\omega -{{\omega }^{2}})}^{7}}$equals:

A) $128\omega$

B) $-128\omega$

C) $128{{\omega }^{2}}$

D) $-128{{\omega }^{2}}$

• question_answer139) ${{\sin }^{2}}\theta =\frac{4xy}{{{(x+y)}^{2}}}$is true, if and only if:

A) $x+y\ne 0$

B) $x=y,\,\,x\ne 0,\,\,y\ne 0$

C) $x=y$

D) $x\ne 0,\,\,y\ne 0$

• question_answer140) The radius of the circle passing through the foci of the ellipse $\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1$ and having its centre at$(0,\,\,3)$ is:

A) $4$

B) $3$

C) $\sqrt{12}$

D) $\frac{7}{2}$

• question_answer141) If $(\omega \ne 1)$ is a cubic root of unity, then$\left| \begin{matrix} 1 & 1+1+{{\omega }^{2}} & {{\omega }^{2}} \\ 1-i & -1 & {{\omega }^{2}}-1 \\ -i & -1+\omega -i & -1 \\ \end{matrix} \right|$equals:

A) $zero$

B) $1$

C) $i$

D) $\omega$

• question_answer142) Let$f(2)=4$ and $f'(2)=4$. Then$\underset{x\to 2}{\mathop{\lim }}\,\frac{x\,\,f(2)-2f(x)}{x-2}$is given by:

A) $2$

B) $-2$

C) $-4$

D) $3$

• question_answer143) Three straight lines $2x+11y-5=0$,$24x+7y-20=0$and$4x-3y-2=0$:

A) form a triangle

B) are only concurrent

C) are concurrent with on line bisecting the angle between the other two

D) none of the above

• question_answer144) A straight line through the point$(2,\,\,2)$intersects the line$\sqrt{3}x+y=0$and$\sqrt{3}x-y=0$at the points$A$and$B$. The equation to the line$AB$, so that triangle$AOB$is equilateral is:

A) $x-2=0$

B) $y-2=0$

C) $x+y-4=0$

D) none of these

• question_answer145) The greatest distance of the point $P(10,\,\,7)$ from the circle ${{x}^{2}}+{{y}^{2}}-4x-2y-20=0$ is:

A) $10$

B) $15$

C) $5$

D) none of these

• question_answer146) The equation of the ellipse whose foci are $(\pm \,\,2,\,\,0)$and eccentricity $\frac{1}{2}$ is:

A) $\frac{{{x}^{2}}}{12}+\frac{{{y}^{2}}}{16}=1$

B) $\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{12}=1$

C) $\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{8}=1$

D) none of these

• question_answer147) The equation of the chord joining two points $({{x}_{1}},\,\,{{y}_{1}})$ and $({{x}_{2}},\,\,{{y}_{2}})$ on the rectangular hyperbola $xy={{c}^{2}}$ is:

A) $\frac{x}{{{x}_{1}}+{{x}_{2}}}+\frac{y}{{{y}_{1}}+{{y}_{2}}}=1$

B) $\frac{x}{{{x}_{1}}-{{x}_{2}}}+\frac{y}{{{y}_{1}}-{{y}_{2}}}=1$

C) $\frac{x}{{{y}_{1}}+{{y}_{2}}}+\frac{y}{{{x}_{1}}+{{x}_{2}}}=1$

D) $\frac{x}{{{y}_{1}}-{{y}_{2}}}+\frac{y}{{{x}_{1}}-{{x}_{2}}}=1$

• question_answer148) Let $R$ be the resultant of $P$ and $Q$ $\text{and}$ if $\frac{P}{3}=\frac{Q}{7}=\frac{R}{5}$, the angle between $P$ and $R$ is:

A) ${{\cos }^{-1}}\left( \frac{11}{14} \right)$

B) ${{\cos }^{-1}}\left( -\frac{11}{14} \right)$

C) $\frac{2\pi }{3}$

D) $\frac{5\pi }{6}$

• question_answer149) Two bodies of different masses ${{m}_{1}}$ and ${{m}_{2}}$ are dropped from different heights ${{h}_{1}}$ and ${{h}_{2}}$. The ratio of the time taken by the two bodies to fall through these distances is:

A) ${{h}_{1}}:{{h}_{2}}$

B) $\sqrt{{{h}_{1}}}:\sqrt{{{h}_{2}}}$

C) $h_{1}^{2}:h_{2}^{2}$

D) ${{h}_{2}}:{{h}_{1}}$

• question_answer150) If$\operatorname{var}(x)=8.25,\,\,\operatorname{var}(y)=33.96$and$\operatorname{cov}(x,\,\,y)=10.2$, then the correlation coefficient is:

A) $0.89$

B) $-0.98$

C) $0.61$

D) $-0.16$