# Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2002

### done JCECE Engineering Solved Paper-2002

• question_answer1) A long spring is stretched by $2\,\,cm$. Its potential energy is $U$. If the spring is stretched by $10\,\,cm,$ the potential energy stored in it will be:

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

B) $\frac{U}{5}$

C) $3U$

D) $25U$

• question_answer2) The coefficient of restitution e for a perfectly elastic collision is:

A) $1$

B) zero

C) infinite

D) $-1$

• question_answer3) A soap bubble is given negative charge. Then its radius:

A) decreases

B) increases

C) remains unchanged

D) nothing can be said because sufficient information is not available

• question_answer4) Source of energy in sun is caused by:

A) fusion of heavy nuclei

B) fission of heavy nuclei

C) fusion of hydrogen nuclei

D) fission of hydrogen nuclei

• question_answer5) A particle moves along a circular path under the action of a force. The work done by the force is:

A) positive and non-zero

B) negative and non-zero

C) zero

D) none of the above

• question_answer6) A particle is moving in a circle with uniform speed. It has constant:

A) velocity

B) acceleration

C) kinetic energy

D) displacement

• question_answer7) If$|\overset{\to }{\mathop{\mathbf{A}}}\,+\overset{\to }{\mathop{\mathbf{B}}}\,|=|\overset{\to }{\mathop{\mathbf{A}}}\,-\overset{\to }{\mathop{\mathbf{B}}}\,|$,$A$ and $B$ are finite then:

A) $\overset{\to }{\mathop{\mathbf{A}}}\,$ is parallel to $\overset{\to }{\mathop{\mathbf{B}}}\,$

B) $\overset{\to }{\mathop{\mathbf{A}}}\,$ is anti-parallel to $\overset{\to }{\mathop{\mathbf{B}}}\,$

C) $\overset{\to }{\mathop{\mathbf{A}}}\,$ and $\overset{\to }{\mathop{\mathbf{B}}}\,$ are equal in magnitude

D) $\overset{\to }{\mathop{\mathbf{A}}}\,$ and $\overset{\to }{\mathop{\mathbf{B}}}\,$ are mutually perpendicular

• question_answer8) A number of small drops of mercury adiabatically coalesce to form a single drop. The temperature of the drop:

A) increases

B) remains same

C) decreases

D) depend on size

• question_answer9) Light waves can be polarised as they are:

A) transverse

B) of high frequency

C) longitudinal

D) reflected

• question_answer10) In which process the speed of transfer of heat is maximum?

A) Conduction

B) Convection

D) In all these heat is transferred with the same speed

• question_answer11) Young's experiment establishes that:

A) light consists of waves

B) light consists of particles

C) light is neither of particles nor waves

D) light consists of particles and waves both

• question_answer12) A heating coil is labelled $100\,\,W,\,\,\text{ }220\,\,V$. The coil is cut into two equal pieces and the two pieces are joined in parallel to the same source. The energy now liberated per second is:

A) $400\,\,J$

B) $25\,\,J$

C) $50\,\,J$

D) $200\,\,J$

• question_answer13) Bending of light rays around the edges of an obstacle is known as:

A) refraction

B) polarization

C) diffraction

D) reflection

• question_answer14) A convex lens of focal length $40\,\,cm$ is in contact with a concave lens of focal length$25\,\,cm$. The power of the combination of the two lenses is:

A) $-1.5\,\,D$

B) $-6.5\,\,D$

C) $6.5\,\,D$

D) $6.67\,\,D$

• question_answer15) Particle $A$ moves in $S\text{-}N$ direction and particle $B$ moves in $W\text{-}E$ direction. Then the .velocity of particle $A$ with respect to $B$ is:

A) $N\text{-}W$ direction

B) $N\text{-}E$ direction

C) $S\text{-}W$ direction

D) $S\text{-}E$direction

• question_answer16) Weightlessness experienced while orbiting the earth in space ships is the result of:

A) inertia

B) acceleration

C) zero gravity

D) centre of gravity

• question_answer17) If one mole of a monoatomic gas $(\gamma =5/3)$ is mixed with one mole of a diatomic gas $(\gamma =7/5)$, the value of $\gamma$ for the mixture is:

A) $1.40$

B) $1.50$

C) $1.53$

D) $3.07$

• question_answer18) Which of the following statements is wrong?

A) Sound travels in straight line

B) Sound travels as waves

C) Sound is a form of energy

D) Sound travels faster in vacuum than in air

• question_answer19) If momentum of a certain body is increased by $50%$, then increases in the KE of the body will be:

A) $25%$

B) $50%$

C) $100%$

D) $125%$

• question_answer20) A uniform chain of length $L$ and mass $M$ is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If $g$ is the acceleration due to gravity the work required to pull the hanging pan of the chain on the table is:

A) $MgL$

B) $\frac{1}{3}MgL$

C) $\frac{1}{9}MgL$

D) $\frac{1}{18}MgL$

• question_answer21) In the arrangement shown in the figure for vertical oscillations of the mass $m$, the period is: A) $T=2\pi \sqrt{\frac{m}{{{k}_{1}}+{{k}_{2}}}}$

B) $T=2\pi \sqrt{\frac{{{k}_{1}}+{{k}_{2}}}{m}}$

C) $T=2\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{{{k}_{1}}+{{k}_{2}}}}$

D) $T=2\pi \sqrt{\frac{mg}{{{k}_{1}}+{{k}_{2}}}}$

• question_answer22) A person completes half of its journey with speed vi and rest half with speed ${{v}_{2}}$. The average speed of the person is:

A) $v=\frac{1}{2}({{v}_{1}}+{{v}_{2}})$

B) $v=\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}$

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

D) $v=\sqrt{{{v}_{1}}{{v}_{2}}}$

• question_answer23) A particle moves along a straight line such that its displacement at any time $t$ is given by$s={{t}^{3}}-3{{t}^{2}}+2m$. The displacement when the acceleration becomes zero is:

A) $zero$

B) $2\,\,m$

C) $3\,\,m$

D) $-2\,\,m$

• question_answer24) $[M{{L}^{2}}{{T}^{-3}}]$ represents the dimensions of:

A) pressure

B) energy

C) power

D) force

• question_answer25) The time period of a simple pendulum in a lift descending with constant acceleration $g$ is:

A) $T=2\pi \sqrt{\frac{l}{8}}$

B) $T=2\pi \sqrt{\frac{l}{2g}}$

C) zero

D) infinite

• question_answer26) A transverse wave is given by$y=A\sin 2\pi \left( \frac{t}{T}-\frac{x}{\lambda } \right)$. The maximum particle, velocity is equal to 4 times the wave velocity, when:

A) $\lambda =2\pi A$

B) $\lambda =\frac{1}{2}\pi A$

C) $\lambda =\pi \,\,A$

D) $\lambda =\frac{1}{4}\pi A$

• question_answer27) A tuning fork gives $4$ beats with $50\,\,cm$ length of a sonometer wire. If the length of the wire is shortened by $1\,\,cm$ the number of beats is still the same. The frequency of the fork is:

A) $396\,\,Hz$

B) $400\,\,Hz$

C) $404\,\,Hz$

D) $384\,\,Hz$

• question_answer28) Electron volt is a unit of:

A) potential

B) charge

C) power

D) energy

• question_answer29) Light of frequency $v$ is incident on a certain photoelectric substance with threshold frequency ${{v}_{0}}$. The work function for the substance is:

A) $hv$

B) $h{{v}_{0}}$

C) $h(v-{{v}_{0}})$

D) $h(v+{{v}_{0}})$

• question_answer30) For principal quantum number $n=3$ the possible values of orbital quantum number$l$are:

A) $1,\,\,2,\,\,3$

B) $0,\,\,1,\,\,2,\,\,3$

C) $0,\,\,1,\,\,2$

D) $-1,\,\,0,\,\,+1$

• question_answer31) Certain radioactive substance reduces to $25%$ of its value in $16$ days. Its half-life is:

A) 32 days

B) 8 days

C) 64 days

D) 28 days

• question_answer32) Penetrating power of $X-$rays does not depend on:

A) wavelength

B) energy

C) potential difference

D) current in the filament

• question_answer33) The ratio of resistance for forward to reverse bias of $p-n$ junction is:

A) ${{10}^{2}}:1$

B) ${{10}^{-2}}:1$

C) $1:{{10}^{-4}}$

D) $1:{{10}^{4}}$

• question_answer34) If a current flows through an infinitely long straight wire, the magnetic field produced at a point $1\,\,m$ away from it, is:

A) $2\times {{10}^{-3}}T$

B) $2\times {{10}^{-1}}T$

C) $2\times {{10}^{-7}}T$

D) $2\pi \times {{10}^{-6}}T$

• question_answer35) Two circular discs $A$ and $B$ with equal radii are blackened. They are heated to same temperature and are cooled under identical conditions. What inference do you draw from their cooling curves? A) $A$ and $B$ have same specific heats

B) Specific heat of $A$ is less

C) Specific heat of $B$ is less

D) Nothing can be said

• question_answer36) When a charged particle, travelling with uniform speed enters a uniform magnetic field perpendicularly then, its kinetic energy:

A) remains constant

B) increases

C) decreases

D) becomes zero

• question_answer37) A circular coil of radius $4\,\,cm$ and number of turns $20$ carries a current of $3\,\,A$. It is placed in a magnetic field of $0.5\,\,T$. The magnetic dipole moment of the coil is:

A) $0.60\,\,A{{m}^{2}}$

B) $0.45\,\,A{{m}^{2}}$

C) $0.30\,\,A{{m}^{2}}$

D) $0.15\,\,A{{m}^{2}}$

• question_answer38) In a circuit 5% of total current passes through a galvanometer. If resistance of the galvanometer is $G$, then value of the shunt is:

A) $19\,\,G$

B) $20\,\,G$

C) $G/20$

D) $G/19$

• question_answer39) In a moving coil galvanometer, deflection $\phi$ and current $I$ flowing through it are related by:

A) $I\propto \tan \phi$

B) $I\propto \phi$

C) $I\propto {{\phi }^{2}}$

D) $I\propto 1/\phi$

• question_answer40) A solenoid of length $l$ metre has self-inductance $L$ henry. If number of turns are doubled, its self-inductance:

A) remains same

B) becomes $2L$ henry

C) becomes $4L$ henry

D) becomes $\frac{L}{\sqrt{2}}$ henry

• question_answer41) The voltage of an AC supply varies with time $(t)$ as $V=120\sin \,\,100\pi t\cos \,\,100\pi t$. The maximum voltage and frequency respectively are:

A) $120\,\,V,\,\,100\,\,Hz$

B) $120/\sqrt{2}V,\,\,100\,\,Hz$

C) $60\,\,V,\,\,200\,\,Hz$

D) $60\,\,V,\,\,100\,\,Hz$

• question_answer42) Two point charges of $+3\mu C$ and $-3\mu C$ are at a distance$2\times 10\,\,m$ apart from each other. The electric field at a distance of $0.6\,\,m$ from the dipole in broadside-on position is:

A) $150\,\,N{{C}^{-1}}$

B) $250\,\,N{{C}^{-1}}$

C) $60\,\,N{{C}^{-1}}$

D) $35\,\,N{{C}^{-1}}$

• question_answer43) Two parallel large thin metal sheets have equal surface charge densities $(\sigma =26.4\times {{10}^{-12}}C/{{m}^{2}})$ of opposite signs. The electric field between these sheets is:

A) $1.5\,\,N/C$

B) $1.5\times {{10}^{-10}}N/C$

C) $3\,\,N/C$

D) $3\times {{10}^{-10}}N/C$

• question_answer44) $N$ identical spherical drops are charged to the same potential $V$. They combine to form a bigger drop. The potential of the big drop will be:

A) $V{{N}^{1/3}}$

B) $V{{N}^{2/3}}$

C) $V$

D) $VN$

• question_answer45) Three condensers of capacitance $2\mu F$ each are connected in series. The resultant capacitance is:

A) $6\mu F$

B) $3/2\mu F$

C) $2/3\mu F$

D) $5\mu F$

• question_answer46) Two electric bulbs rated ${{P}_{1}}$ watt, $V$ volt and ${{P}_{2}}$ wan, $V$ volt are connected in parallel and $V$ volt supply is applied to them. The total power will be:

A) ${{P}_{1}}+{{P}_{2}}$

B) $\sqrt{{{P}_{1}}{{P}_{2}}}$

C) $\frac{{{P}_{1}}{{P}_{2}}}{{{P}_{1}}+{{P}_{2}}}$

D) $\frac{{{P}_{1}}+{{P}_{2}}}{{{P}_{1}}{{P}_{2}}}$

• question_answer47) A hole is in the bottom of the tank having water. If total pressure at the bottom is $3\,\,atm$ $(1\,\,atm={{10}^{5}}N{{m}^{-2}})$, then velocity of water flowing from hole is:

A) $\sqrt{400}m{{s}^{-1}}$

B) $\sqrt{600}m{{s}^{-1}}$

C) $\sqrt{60}m{{s}^{-1}}$

D) $\sqrt{40}m{{s}^{-1}}$

• question_answer48) A fluid of volume $1\,\,L$ is subjected to a pressure change of${{10}^{7}}N/{{m}^{2}}$. As a result its volume changes by $0.4\,\,c{{m}^{3}}$. The bulk modulus of the fluid is:

A) $2.5\times {{10}^{10}}N/{{m}^{2}}$

B) $2.5\times {{10}^{11}}N/{{m}^{2}}$

C) $2.5\times {{10}^{9}}N/{{m}^{2}}$

D) $2.5\times {{10}^{15}}N/{{m}^{2}}$

• question_answer49) Stationary waves are so called because in them:

A) the particles of the medium are not disturbed at all

B) the particles of the medium do not execute $SHM$

C) Particles do not correspond flow of energy along the wire

D) the interference effect cannot be observed

• question_answer50) If the degrees of freedom of the molecules of a gas are n, the ratio of its two specific heats$({{C}_{P}}/{{C}_{V}})$will be:

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

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

C) $1+\frac{1}{n}$

D) $2-\frac{1}{n}$

A) $\alpha$ then $\beta$ and then $\gamma$ emitted

B) $\alpha$ or $\beta$ and then $\gamma$ emitted

C) $\alpha$ and $\beta$ and $\gamma$ emitted simultaneously

D) $\alpha$ and $\beta$ emitted simultaneously

• question_answer52) The work function of a metal is $1\,\,eV$. If $3000\overset{\text{o}}{\mathop{\text{A}}}\,$ wavelength light is incident, the value of stopping voltage is:

A) $1\,\,V$

B) $3.75\,\,V$

C)  $3.2\,\,V$

D)  $0.75\,\,V$

• question_answer53) Equation for a real gas is$\left( P+\frac{a}{{{V}^{2}}} \right)(V-b)=RT$where P= pressure, $V=$ volume, $a,\,\,b$ and $R$ constants, dimensional formula of $a$ is:

A) ${{L}^{6}}$

B) ${{M}^{1}}{{L}^{-1}}{{T}^{2}}$

C) ${{M}^{1}}{{L}^{5}}{{T}^{-2}}$

D) ${{L}^{3}}$

• question_answer54) A monoatomic ideal gas is compressed to its $1/8$ volume adiabatically at ${{17}^{o}}C$. Temperature after compression will be:

A) ${{34}^{o}}C$

B) ${{17}^{o}}C$

C) ${{136}^{o}}C$

D) ${{887}^{o}}C$

A) Work

B) Heat

C) Temperature

D) All of these

• question_answer56) Which formula is incorrect for root mean square velocity?

A) $\sqrt{\frac{3RT}{M}}$

B) $\sqrt{\frac{3PV}{M}}$

C) $\sqrt{\frac{3d}{P}}$

D) $\sqrt{\frac{2KE}{M}}$

• question_answer57) If the number of molecules of hydrogen is double to that of oxygen, at the same temperature, the ratio of their average $KE$ per molecule is:

A) $1:1$

B) $2:3$

C) $1:2$

D) $1:4$

• question_answer58) A liquid boils at that temperature at which the pressure of saturated vapour is:

A) more than atmospheric pressure

B) double to atmospheric pressure

C) equal to atmospheric pressure

D) less than atmospheric pressure

• question_answer59) What is the value of $\frac{PV}{T}$ for a $1$ mole of gas?

A) $4.2\times {{10}^{7}}cal/K$

B) $4.2cal/K$

C) $8.31cal/K$

D) $2cal/K$

• question_answer60) If a proton totally converts into energy, the value of energy will be:

A) $190\,\,MeV$

B) $931\,\,MeV$

C) $93.1\,\,MeV$

D) $931\,\,J$

• question_answer61) Experimental verification of matter waves was done by:

A) de-Broglie

B) Rutherford

C) Bohr

D) Davisson and Germer

• question_answer62) In the following nuclear reaction$_{2}H{{e}^{3}}{{+}_{z}}{{X}^{a}}{{\xrightarrow{{}}}_{z+1}}{{Y}^{a+2}}+Q$. What is$Q$?

A) Neutron

B) Proton

C) Positron

D) Electron

• question_answer63) For the reaction$_{1}{{H}^{2}}{{+}_{1}}{{H}^{2}}{{\xrightarrow{{}}}_{2}}H{{e}^{4}}+v+$Energy, what is the required condition?

A) High temperature and pressure

B) High temperature and low pressure

C) Low temperature and high pressure

D) High temperature only

• question_answer64) Work function of photoelectric metal is$3.13\,\,eV$. Threshold frequency is:

A) $4\times {{10}^{11}}Hz$

B) $5\times {{10}^{14}}Hz$

C) $8\times {{10}^{15}}Hz$

D) $8\times {{10}^{10}}Hz$

• question_answer65) Nitro group of nitrobenzene is:

A) $o-$directing

B) $m-$directing

C) $p-$directing

D) $o,$and $p$ directing

• question_answer66) In which compound the number of ${{3}^{o}}$ carbon is maximum:

A) 2, 5 dimethyl hexane

B) 2, 3, 4-trimethyl pentane

C) 2, 2, 4, 4-tetramethyl pentane

D) 2, 2, 3-trimethyl pentane

• question_answer67) The $pH$ of a solution of concentration few less than$1\,\,N\,\,NaOH$:

A) between $13$ and $14$

B) between $12$ and $13$

C) between $0$ and $1$

D) between $1$ and$2$

A) a neutral divalent species

B) a carbonation

C) a carbanion

• question_answer69) The geometry of the hybrid orbital, which contains $20%$ $s-$character is:

A) octahedral

B) tetrahedral

C) trigonal bipyramidal

D) square planar

• question_answer70) Which test is not ideal to distinguish 2-butanol and $1-$propanol?

A) Hydrogenation

B) Iodoform test

C) Lucas test

D) Oxidation test

• question_answer71) In the reaction of $C{{H}_{2}}=C{{H}_{2}}$ and $HBr$ initial addition occurs of:

A) indefinite

B) ${{H}^{+}}+B{{r}^{-}}$ both at one time

C) ${{H}^{+}}$

D) $B{{r}^{-}}$

• question_answer72) The hydrocarbon formed by electrolysis of sodium propionate:

A) $C{{H}_{3}}CH=C{{H}_{2}}$

B) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}$

C) $C{{H}_{3}}C{{H}_{2}}C{{H}_{3}}$

D) $C{{H}_{3}}-C{{H}_{3}}$

• question_answer73) $0.1\,\,M\,\,C{{H}_{3}}COOH$ is $1.3%$ ionised. The dissociation constant of it will be:

A) $1.69\times {{10}^{-5}}$

B) $1.69\times {{10}^{-6}}$

C) $1.69\times {{10}^{-4}}$

D) None of these

• question_answer74) Which of the following give dye test?

A) Aniline

B) Methylamine

C) Diphenylamine

D) Ethylamine

• question_answer75) When ethanamide is heated with $NaOH$ and $B{{r}_{2}}$ the compound formed is:

A) $C{{H}_{3}}CON{{H}_{2}}$

B) ${{C}_{2}}{{H}_{5}}NC$

C) $C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}$

D) $C{{H}_{3}}N{{H}_{2}}$

• question_answer76) The chemical formula of potash alum is ${{K}_{2}}S{{O}_{4}}\cdot A{{l}_{2}}{{(S{{O}_{4}})}_{3}}x{{H}_{2}}O$, here $x$ is:

A) $7$

B) $12$

C) $6$

D) $24$

• question_answer77) Brass is an alloy of:

A) $Cu+Zn+Fe$

B) $Cu+Zn+Ni$

C) $Cu+Zn+Sn$

D) $Cu+Zn$

• question_answer78) The electronic configuration of$F{{e}_{26}}$is$[Ar]$:

A) $3{{d}^{8}}4{{s}^{2}}$

B) $3{{d}^{7}}4{{s}^{2}}$

C) $3{{d}^{6}}4{{s}^{2}}$

D) $3{{d}^{5}}4{{s}^{2}}$

• question_answer79) The rate constant of forward reaction is $2.38\times {{10}^{-4}}$ and the rate constant of backward reaction is $4.76\times {{10}^{-5}}$. The equilibrium constant for the reaction will be:

A) $5$

B) $5\times {{10}^{-2}}$

C) $2\times {{10}^{-4}}$

D) none of these

• question_answer80) The element with electronic configuration $1{{s}^{2}}2{{s}^{2}}2{{p}^{6}},\,\,3{{s}^{2}}3{{p}^{6}},\,\,4{{s}^{2}}$ shows same property as:

A) $Mo$

B) $Rb$

C) $Ca$

D) $Sr$

• question_answer81) How much volume of $0.4\,\,M\,\,NaOH$ is required to neutralise completely $200\,\,mL$$0.5\,\,M\,\,{{H}_{2}}S{{O}_{4}}$ solution?

A) $600\,\,mL$

B) $300\,\,mL$

C) $500\,\,mL$

D) $200\,\,mL$

• question_answer82) The formula of acetaldehyde semi car b a zone:

A) $C{{H}_{3}}-CH=NNHCONHC{{H}_{3}}$

B) $C{{H}_{3}}-CH=N-NHCON{{H}_{2}}$

C) $C{{H}_{3}}CH=N-NHCON{{H}_{2}}$

D) $C{{H}_{3}}-CH=N-NHCONH-CON{{H}_{2}}$

• question_answer83) One compound reacts with chloroform in presence of $KOH$ and produces a bad smell (nause odour) compound. The compound formed is:

A) $C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}$

B) ${{C}_{6}}{{H}_{5}}CN$

C) $C{{H}_{3}}C{{H}_{2}}NC$

D) ${{C}_{2}}{{H}_{5}}CN$

• question_answer84) Phenol, chloroform and caustic potash are heated. The compound formed is:

A) salicylic acid

B) $p-$hydroxy benzaldehyde

C) $m-$hydroxy benzaldehyde

D) salicylaldehyde

• question_answer85) $A+NaOH\xrightarrow{{}}C{{H}_{3}}OH+HCOONa$is the reaction, compound $A$ is:

A) $HCN$

B) $HCHO$

C) $C{{H}_{3}}CN$

D) $C{{H}_{3}}Cl$

• question_answer86) The compound obtained by the reaction of acetic anhydride and ammonia is:

A) $C{{H}_{3}}COON{{H}_{4}}$

B) $C{{H}_{3}}CN$

C) $C{{H}_{3}}CONHC{{H}_{3}}$

D) $C{{H}_{3}}CON{{H}_{2}}$

• question_answer87) Metal which does not react with aqueous solution of copper sulphate is:

A) $Pb$

B) $Ag$

C) $Zn$

D) $Fe$

• question_answer88) When aniline react with acetic anhydride the product formed is:

A) $p-$aminobenzoic acid

B) $m-$aminobenzoic acid

C) acetanilide

D) $o-$aminobenzoic acid

• question_answer89) $5SO_{2}^{-}+2MnO_{4}^{-}+6{{H}^{+}}\xrightarrow{{}}5SO_{4}^{2-}$$+2M{{n}^{2+}}+2{{H}_{2}}O$the oxidation number of $Mn$ changes from:

A) $+14$to$+4$

B) $+6$to$+2$

C) $-7$to$-2$

D) $+7$to$+2$

• question_answer90) Which has highest ionisation potential?

A) $N$

B) $O$

C) ${{O}^{+}}$

D) $Na$

• question_answer91) Formic acid and acetic acid may be distinguished by the reaction with:

A) sodium

B) 2, 4-dinitrophenyl hydrazine

C) litmus paper

D) Tollen's reagent

• question_answer92) Maximum melting point is of:

A) $MgC{{l}_{2}}$

B) $BaC{{l}_{2}}$

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

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

• question_answer93) The process requiring the absorption of energy is:

A) $F\xrightarrow{{}}{{F}^{-}}$

B) $Cl-C{{l}^{-}}$

C) $O\xrightarrow{{}}{{O}^{2-}}$

D) $H-{{H}^{-}}$

• question_answer94) The number of coordinate bond in a molecule of${{H}_{2}}S{{O}_{4}}$:

A) $4$

B) $3$

C) $2$

D) $1$

A) $KCl$

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

C) $Ge{{l}_{4}}$

D) $Pb{{I}_{4}}$

• question_answer96) A piece of magnesium ribbon was heated to redness in an atmosphere of nitrogen and on cooling water was added. The gas evolved was:

A) ammonia

B) hydrogen

C) nitrogen

D) oxygen

• question_answer97) Which of the following halides is least stable and doubtful existence?

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

B) ${{K}_{2}}S{{O}_{4}}$

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

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

• question_answer98) Lithopone is a mixture of:

A) $ZnS$and${{K}_{2}}S{{O}_{4}}$

B) $CaC{{l}_{2}}$and$C{{a}_{3}}{{F}_{2}}$

C) $Ca{{C}_{2}}$and$C{{a}_{3}}{{N}_{2}}$

D) $ZnS+BaS{{O}_{4}}$

• question_answer99) Iodine is liberated from $KI$ solution when treated with:

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

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

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

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

• question_answer100) Chlorine acts as a bleaching agent only in the presence of:

A) dry air

B) sun light

C) moisture

D) pure oxygen

• question_answer101) If$\sin x+{{\sin }^{2}}x=1$, then the value of${{\cos }^{12}}x+3{{\cos }^{10}}x+3{{\cos }^{8}}x+{{\cos }^{6}}x$is equal to:

A) $0$

B) $1$

C) $-1$

D) $2$

• question_answer102) The equations$\frac{2{{\cos }^{2}}x}{2{{\sin }^{2}}x}=\frac{{{x}^{2}}+1}{{{x}^{2}}},\,\,0\le x\le \frac{x}{2}$has:

A) one real solution

B) no real solution

C) more than one real solution

D) none of the above

• question_answer103) If$f(x)=\frac{2x+1}{3x-2}$,then$fof(2)$is equal to:

A) $1$

B) $3$

C) $4$

D) $2$

• question_answer104) Which one of the following objective function on the set of real numbers?

A) $2x-5$

B) $|x|$

C) ${{x}^{2}}$

D) ${{x}^{2}}+1$

• question_answer105) Let the function $f$be defined by$f(x)=\frac{2x+1}{1-3x},$ then${{f}^{-1}}(x)$is:

A) $\frac{x-1}{3x+2}$

B) $\frac{3x+2}{x-1}$

C) $\frac{x+1}{3x-2}$

D) $\frac{2x+1}{1-3x}$

• question_answer106) If$\sqrt{a+ib}=x+iy$, then possible value of$\sqrt{a-ib}$is:

A) ${{x}^{2}}+{{y}^{2}}$

B) $\sqrt{{{x}^{2}}-{{y}^{2}}}$

C) $x+iy$

D) $x-iy$

• question_answer107) If${{i}^{2}}=-1$. Then sum$i+{{i}^{2}}+{{i}^{3}}+....+{{i}^{1000}}$ term is equal to:

A) $1$

B) $-1$

C) $i$

D) $0$

• question_answer108) If$\alpha ,\,\,\beta$are the roots of the equation${{x}^{2}}+2x+4=0$, then$\frac{1}{{{\alpha }^{3}}}+\frac{1}{{{\beta }^{3}}}$is equal to:

A) $-1/2$

B) $1/4$

C) ${{3}^{2}}$

D) $1/{{3}^{2}}$

• question_answer109) The least integer $k$ which makes roots of the equation ${{x}^{2}}+5x+k=0$ become imaginary, is:

A) $4$

B) $5$

C) $6$

D) $\frac{25}{4}$

• question_answer110) The number of terms of the $AP\,\,3,\,\,7,\,\,11,\,\,15...$ to be taken so that the sum is$210,\,\,\,\text{is}:$

A) $10$

B) $12$

C) -1

D) 2

• question_answer111) If $a,\,\,b,\,\,c,$ are respectively the $pth,\,\,qth,\,\,rth$ terms of an$AP$, then $\left[ \begin{matrix} a & p & 1 \\ b & q & 1 \\ c & r & 1 \\ \end{matrix} \right]$ is equal to:

A) $1$

B) $-1$

C) $0$

D) $pqr$

• question_answer112) The two geometric means between the numbers $1$ and $64$ are:

A) $1$ and $64$

B) $4$ and $16$

C) $2$ and$16$

D) $8$ and $16$

• question_answer113) If $n$ and $r$ are two positive integers such that$n\ge r$, then$^{n}{{C}_{r-1}}{{+}^{n}}{{C}_{r}}$is equal to:

A) $^{n}{{C}_{r-1}}$

B) $^{n}{{C}_{r}}$

C) $^{n-1}{{C}_{r}}$

D) $^{n+1}{{C}_{r}}$

• question_answer114) The number of ways in which a committee of a $6$ members can be formed from $8$ gentlemen and $4$ ladies so that the committee contains atleast $3$ ladies, is:

A) $252$

B) $672$

C) $420$

D) $250$

• question_answer115) If $A$ and $B$ are $2$ square matrices of the same order, then${{(A-B)}^{2}}$is:

A) ${{A}^{2}}-AB-BA+{{B}^{2}}$

B) ${{A}^{2}}-2BA+{{B}^{2}}$

C) ${{A}^{2}}-2AB+{{B}^{2}}$

D) ${{A}^{2}}-{{B}^{2}}$

• question_answer116) If $I$ is a unit matrix of order $10$, then determinant of $I$ is equal to:

A) $10$

B) $1$

C) $1/10$

D) $9$

• question_answer117) If the vectors $3\widehat{\mathbf{i}}+\lambda \widehat{\mathbf{j}}+\widehat{\mathbf{k}}$ and $2\widehat{\mathbf{i}}-\widehat{\mathbf{j}}+8\widehat{\mathbf{k}}$ are perpendicular, then value of $\lambda$ is:

A) $-14$

B) $7$

C) $14$

D) $1/7$

• question_answer118) The unit vector perpendicular to both $\widehat{\mathbf{i}}-\widehat{\mathbf{j}}$ and $\widehat{\mathbf{j}}+\widehat{\mathbf{k}}$ is:

A) $\widehat{\mathbf{i}}-\widehat{\mathbf{j}}+\widehat{\mathbf{k}}$

B) $\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\mathbf{k}}$

C) $\frac{\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\mathbf{k}}}{\sqrt{3}}$

D) $\frac{\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-\widehat{\mathbf{k}}}{\sqrt{3}}$

• question_answer119) For any three vectors$\overset{\to }{\mathop{\mathbf{a}}}\,,\,\,\overset{\to }{\mathop{\mathbf{b}}}\,,\,\,\overset{\to }{\mathop{\mathbf{c}}}\,$;$\overset{\to }{\mathop{\mathbf{a}}}\,\times (\overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,)+\overset{\to }{\mathop{\mathbf{b}}}\,\times (\overset{\to }{\mathop{\mathbf{c}}}\,+\overset{\to }{\mathop{\mathbf{a}}}\,)+\overset{\to }{\mathop{\mathbf{c}}}\,\times (\overset{\to }{\mathop{\mathbf{a}}}\,+\overset{\to }{\mathop{\mathbf{b}}}\,)$is:

A) $\overset{\to }{\mathop{\mathbf{0}}}\,$

B) $\overset{\to }{\mathop{\mathbf{a}}}\,+\overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,$

C) $\overset{\to }{\mathop{\mathbf{a}}}\,\cdot (\overset{\to }{\mathop{\mathbf{b}}}\,\times \overset{\to }{\mathop{\mathbf{c}}}\,)$

D) none of these

• question_answer120) The point moves such that the area of the triangle formed by it with the points $(1,\,\,5)$ and $(3,\,\,-7)$ is$21\,\,sq\,\,unit$The locus of the point is:

A) $6x+y-32=0$

B) $6x-y+32=0$

C) $x+6y-32=0$

D) $6x+y+32=0$

• question_answer121) The line $\frac{x}{a}-\frac{y}{b}=1$ cuts the $x-$axis at $P$. The equation of the line through $P$ perpendicular to the given line is:

A) $x+y=ab$

B) $x+y=a+b$

C) $ax+by={{a}^{2}}$

D) $bx+ay={{b}^{2}}$

• question_answer122) Three vertices of a parallelogram taken in order are $(-1,\,\,-6),\,\,\,(2,\,\,-5)$ and $(7,\,\,2)$. The fourth vertex is:

A) $(1,\,\,4)$

B) $(4,\,\,1)$

C) $(1,\,\,1)$

D) $(4,\,\,4)$

• question_answer123) Distance between the lines $5x+3y-7=0$ and$15x+9y+14=0$ is:

A) $\frac{35}{\sqrt{34}}$

B) $\frac{1}{3\sqrt{34}}$

C) $\frac{35}{3\sqrt{34}}$

D) $\frac{35}{2\sqrt{34}}$

• question_answer124) If the equation$2{{x}^{2}}+7xy+3{{y}^{2}}-9x-7y+k=0$ represents a pair of lines, then $k$ is equal to:

A) $4$

B) $2$

C) $1$

D) None of these

• question_answer125) The centre of a circle $(2,\,\,-3)$ and the circumference is $10\pi$. The equation or the circle is:

A) ${{x}^{2}}+{{y}^{2}}+4x+6y+12=0$

B) ${{x}^{2}}+{{y}^{2}}-4x+6y+12=0$

C) ${{x}^{2}}+{{y}^{2}}-4x+6y-12=0$

D) ${{x}^{2}}+{{y}^{2}}-4x-6y-12=0$

• question_answer126) The equation of the parabola whose vertex is at $(2,\,\,-1)$ and focus at $(2,\,\,-3)$ is:

A) ${{x}^{2}}+4x-8y-12=0$

B) ${{x}^{2}}-4x+8y+12=0$

C) ${{x}^{2}}+8y=12$

D) ${{x}^{2}}-4x+12=0$

• question_answer127) The eccentricity of the conic $9{{x}^{2}}+25{{y}^{2}}=225$ is:

A) $2/5$

B) $4/5$

C) $1/3$

D) $1/5$

• question_answer128) If${{\tan }^{-1}}x+{{\tan }^{-1}}y+{{\tan }^{-1}}z=\pi$, then$x+y+z$is equal to:

A) $xyz$

B) $0$

C) $1$

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

• question_answer129) $\underset{x\to 0}{\mathop{\lim }}\,\frac{1-\cos mx}{1-\cos nx}$is:

A) $m/n$

B) ${{m}^{2}}/{{n}^{2}}$

C) $0$

D) $n/m$

• question_answer130) If$x={{\sin }^{-1}}(3t-4{{t}^{3}})$and$y={{\cos }^{-1}}\sqrt{(1-{{t}^{2}})}$, then $\frac{dy}{dx}$ is equal to:

A) $1/2$

B) $2/5$

C) $3/2$

D) $1/3$

• question_answer131) The second derivative of a sin31 with respect to$a{{\cos }^{3}}t$at$t=\frac{\pi }{4}$to:

A) $\frac{4\sqrt{2}}{3a}$

B) $2$

C) $\frac{1}{12a}$

D) None of these

• question_answer132) If$f(x)=\left\{ \begin{matrix} \frac{{{x}^{2}}-9}{x-3}, & if\,\,x\ne 3 \\ 2x+k, & if\,\,x=3 \\ \end{matrix} \right.$is continuous at$x=3$, then $k$ is equal to:

A) $3$

B) $0$

C) $-6$

D) $1/6$

• question_answer133) The function$y=a(1-\cos x),\,\,a>0$is maximum when $x$ is equal to:

A) $\pi$

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

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

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

• question_answer134) $\int_{0}^{\pi /2}{x\,\,\sin \,\,x\,\,dx}$is equal to:

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

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

C) $\pi$

D) $1$

• question_answer135) $\int_{0}^{\pi /2}{\frac{\sin x}{\sin x+\cos x}}dx$is equal to:

A) $\pi$

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

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

D) $\frac{\pi }{4}$

• question_answer136) The area bounded by the parabola ${{y}^{2}}=4ax$ and${{x}^{2}}=4ay$is:

A) $\frac{8{{a}^{2}}}{3}sq\,\,unit$

B) $\frac{16{{a}^{2}}}{3}sq\,\,unit$

C) $\frac{32{{a}^{2}}}{3}sq\,\,unit$

D) $\frac{64{{a}^{2}}}{3}sq\,\,unit$

• question_answer137) The degree of differential equation $\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{3}}+6y=0$is:

A) $1$

B) $3$

C) $2$

D) $5$

• question_answer138) The solution$\frac{dy}{dx}+P(x)y=0$is:

A) $y=c{{e}^{\int{P\,\,dx}}}$

B) $x=c{{e}^{-\int{P\,\,dx}}}$

C) $y=c{{e}^{-\int{P\,\,dx}}}$

D) None of these

• question_answer139) If$P(A)=2/3,\,\,P(B)=1/2$and$P(A\cup B)=5/6$, then events $A$ and $B$ are:

A) mutually, exclusive

B) independent as well as mutually exhaustive

C) independent

D) dependent only on$A$

• question_answer140) $\int_{-2}^{2}{|1-{{x}^{2}}|dx}$is equal to:

A) $4$

B) $2$

C) $-2$

D) $0$

• question_answer141) $\int_{2}^{4}{x}\sqrt{6-x}\,dx$is equal to:

A) $\frac{16}{5}(3-\sqrt{2})$

B) $\frac{32}{5}(3-\sqrt{2})$

C) $\frac{8}{5}(3-\sqrt{2})$

D) $\frac{64}{5}(3-\sqrt{2})$

• question_answer142) $\int_{a}^{b}{\frac{f(x)}{f(x)+f(a+b-x)}}dx$is equal to:

A) $\frac{b-a}{2}$

B) $\frac{a-b}{2}$

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

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

• question_answer143) The maximum value of the function$\sin x(1+\cos x)$is:

A) $3$

B) $\frac{3\sqrt{3}}{4}$

C) $4$

D) $3\sqrt{3}$

• question_answer144) Let$f(x)=\frac{1}{\sqrt{18-{{x}^{2}}}}$. The value of$\underset{x\to 3}{\mathop{\lim }}\,\frac{f(x)-f(3)}{x-3}$is:

A) $0$

B) $-1/9$

C) $-1/3$

D) $3\sqrt{3}$

• question_answer145) ${{x}^{y}}\cdot {{y}^{x}}=1$, then$\frac{dy}{dx}$is:

A) $\frac{y(y+x\log y)}{x(y\log x+x)}$

B) $\frac{y(x+y\log x)}{x(y+x\log y)}$

C) $\frac{-y(y+x\log y)}{x(x+y\log x)}$

D) None of these

• question_answer146) If in $\Delta ABC$, $a+\tan A+b\tan B$$=(a+b)\tan \frac{1}{2}(A+B)$, then:

A) $A=B$

B) $B=C$

C) $C=A$

D) $A=B=C$

• question_answer147) The centre of the ellipse$\frac{{{(x+y-2)}^{2}}}{9}+\frac{{{(x-y)}^{2}}}{16}=1$is:

A) $(0,\,\,0)$

B) $(1,\,\,1)$

C) $(1,\,\,0)$

D) $(0,\,\,1)$

• question_answer148) The angle between the pair of lines is given by the equation${{x}^{2}}+2xy-{{y}^{2}}=0$is:

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

B) $\frac{\pi }{6}$

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

D) $0$

• question_answer149) The term independent of$x$is${{\left( \frac{3}{2}{{x}^{2}}-\frac{1}{3x} \right)}^{9}}$, is:

A) $5/27$

B) $7/18$

C) $8/27$

D) $1/24$

• question_answer150) If$x$is real, then$\frac{{{x}^{2}}-2x+4}{{{x}^{2}}+2x+4}$takes values in the interval:

A) $[1/3,\,\,3]$

B) $(1/3,\,\,3)$

C) $(3,\,\,3)$

D) $(-1/3,\,\,3)$

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