# Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2008

### done BCECE Engineering Solved Paper-2008

• question_answer1) If E = energy, G = gravitational constant, $I=$impulse and $M=$mass, then dimensions of $\frac{GI{{M}^{2}}}{{{E}^{2}}}$are same as that of

A) time

B) mass

C) length

D) force

• question_answer2) A point initially at rest moves along $x-$axis. Its acceleration varies with time as $a=(6t+5)m/{{s}^{2}}.$If it starts from origin, the distance covered in 2 s is

A) 20 m

B) 18 m

C) 16 m

D) 25 m

• question_answer3) Three blocks of masses 2 kg, 3 kg and 5 kg are connected to each other with light string and are then placed on a frictionless surface as shown in the figure. The system is pulled by a force $F=10N,$then tension ${{T}_{1}}=$

A) 1 N

B) 5 N

C) 8 N

D) 10 N

• question_answer4) A solid sphere rolls down two different inclined planes of same height, but of different inclinations. In both cases

A) speed and time of descent will be same

B) speed will be same, but time of descent will be different

C) speed will be different, but time of descent will be same

D) speed and time of descent both are different

• question_answer5) The angular amplitude of a simple pendulum is ${{\theta }_{0}}.$The maximum tension in its string will be

A) $mg(1-{{\theta }_{0}})$

B) $mg(1+{{\theta }_{0}})$

C) $mg(1-\theta _{0}^{2})$

D) $mg(1+\theta _{0}^{2})$

• question_answer6) An engine pumps up 100 kg of water through a height of 10 m in 5s. Given that the efficiency of engine is 60%. If $g=10\,m{{s}^{-2}},$ the power of the engine is

A) 3.3 kW

B) 0.33 kW

C) 0.033 kW

D) 33 kW

• question_answer7) At what speed, the velocity head of water is equal to pressure head of 40 cm of Hg?

A) 10.3 m/s

B) 2.8 m/s

C) 5.6 m/s

D) 8.4 m/s

• question_answer8) If the electric flux entering and leaving an enclosed surface respectively are ${{\phi }_{1}}$ and ${{\phi }_{2}}$ the electric charge inside the surface will be

A) $\frac{{{\phi }_{2}}-{{\phi }_{1}}}{{{\varepsilon }_{0}}}$

B) $\frac{{{\phi }_{1}}+{{\phi }_{2}}}{{{\varepsilon }_{0}}}$

C) $\frac{{{\phi }_{1}}-{{\phi }_{2}}}{{{\varepsilon }_{0}}}$

D) ${{\varepsilon }_{0}}\,({{\phi }_{1}}+{{\phi }_{2}})$

• question_answer9) In the propagation of light waves, the angle between the direction of vibration and plane of polarization is

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

B) ${{90}^{o}}$

C) ${{45}^{o}}$

D) ${{80}^{o}}$

• question_answer10) A light emitting diode (LED) has a voltage drop of 2 V across it and passes a current of 10 mA. When it operates with a 6 V battery through a limiting resistor R, the value of R is

A) $40\,k\Omega$

B) $4\,k\Omega$

C) $200\,\Omega$

D) $400\,\Omega$

• question_answer11) The minimum potential difference between the base and emitter required to switch a silicon transistor ON is approximately

A) 1 V

B) 3 V

C) 5 V

D) 4.2 V

• question_answer12) Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is $\pi /3$and the maximum height reached by it is 102 m. Then the maximum height reached by the other in metre is

A) 336

B) 224

C) 56

D) 34

• question_answer13) Which one of the following is a possible nuclear reaction?

A) $_{5}^{10}B+_{2}^{4}He\xrightarrow{{}}_{7}^{13}N+_{1}^{1}H$

B) $_{11}^{23}Na+_{1}^{1}H\xrightarrow{{}}_{10}^{20}Ne+_{2}^{4}He$

C) $_{93}^{239}Np+\xrightarrow{{}}_{94}^{239}Pu+{{\beta }^{-}}+\bar{v}$

D) $_{7}^{11}N+_{1}^{1}H\xrightarrow{{}}_{6}^{12}C+{{\beta }^{-}}+v$

• question_answer14) 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_answer15) During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio ${{C}_{p}}/{{C}_{v}}$for the gas is

A) 4/3

B) 2

C) 5/3

D) 3/2

• question_answer16) The sum of two vectors $\vec{A}$ and $\vec{B}$ is at right angles to their difference. Then

A) $A=B$

B) $A=2B$

C) $B=2A$

D) $\vec{A}$ and $\vec{B}$ have the same direction

• question_answer17) A ball is thrown up at an angle with the horizontal. Then the total change of momentum by the instant it returns to ground is

A) acceleration due to gravity $\times$ total time of flight

B) weight of the ball $\times$ half the time of flight

C) weight of the ball $\times$total time of flight

D) weight of the ball $\times$horizontal range

• question_answer18) When a spring is stretched by a distance $x,$it exerts a force, given by $F=(-5x-16{{x}^{3}})N$ The work done, when the spring is stretched from 0.1 m to 0.2 m is

A) $8.7\times {{10}^{-2}}J$

B) $12.2\times {{10}^{-2}}J$

C) $8.7\times {{10}^{-1}}J$

D) $12.2\times {{10}^{-1}}J$

• question_answer19) Time period of a simple pendulum of length$l$ is ${{T}_{1}}$and time period of a uniform rod of the same length $l$ pivoted about one end and oscillating in a vertical plane is ${{T}_{2}}.$Amplitude of oscillations in both the cases is small. Then${{T}_{1}}/{{T}_{2}}$is

A) $\frac{1}{\sqrt{3}}$

B) $1$

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

D) $\sqrt{\frac{3}{2}}$

• question_answer20) An insulator plate is passed between the plates of a capacitor. Then current

A) first flows from A to Band then from B to A

B) first flows from B to A and then from A to B

C) always flows from B to A

D) always flows from A to B

• question_answer21) 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_answer22) The electric current passes through a metallic wire produces heat because of

A) collisions of conduction electrons with each other

B) collisions of the atoms of the metal with each other

C) the energy released in the ionization of the atoms of the metal

D) collisions of the conduction electrons with the atoms of the metallic wire

• question_answer23) Two concentric circular coils of ten turns each are situated in the same plane. Their radii are 20 cm and 40 cm and they carry respectively 0.2 A and 0.3 A currents in opposite direction. The magnetic field in tesla at the centre is

A) $35\,{{\mu }_{0}}/4$

B) $\,{{\mu }_{0}}/80$

C) $7\,{{\mu }_{0}}/80$

D) $5\,{{\mu }_{0}}/4$

• question_answer24) Electromagnetic waves with frequencies greater than the critical frequency of ionosphere cannot be used for communication using sky wave propagation, because

A) the refractive Index of the ionosphere becomes very high for $f>{{f}_{c}}$

B) the refractive index of the ionosphere becomes very low for $f>{{f}_{c}}$

C) the refractive index of the ionosphere becomes very high for $f<{{f}_{c}}$

D) None of the above

• question_answer25) In a choke coil, the reactance ${{X}_{L}}$and resistance R are such that

A) ${{X}_{L}}=R$

B) ${{X}_{L}}>>R$

C) ${{X}_{L}}<<R$

D) ${{X}_{L}}=\infty$

• question_answer26) Reverberation time does not depend upon

A) temperature

B) volume of room

C) size of window

D) carpet and curtain

• question_answer27) In a potentiometer, the null point is received at 7th wire. If now we have to change the null point at 9th wire, what should we do?

A) Attach resistance in series with battery

B) Increase resistance in main circuit

C) Decrease resistance in main circuit

D) Decrease applied emf

• question_answer28) If average velocity becomes 4 times then what will be the effect on rms velocity at that temperature?

A) 1.4 times

B) 4 times

C) 2 times

D) $\frac{1}{4}$ times

• question_answer29) What is the Q-value of the reaction $p+{{\,}^{7}}Li\xrightarrow{{}}{{\,}^{4}}He+{{\,}^{4}}He$ The atomic masses of ${{\,}^{1}}H,{{\,}^{4}}He$ and ${{\,}^{7}}Li$ are 1.007825u, 4.002603 u and 7.016004 u respectively

A) 17.35 MeV

B) 18.06 MeV

C) 177.35 MeV

D) 170.35 MeV

• question_answer30) A Carots engine has an efficiency of 50% at sink temperature $50{{\,}^{o}}C.$ Calculate the temperature of source.

A) $133{{\,}^{o}}C$

B) $143{{\,}^{o}}C$

C) $100{{\,}^{o}}C$

D) $373{{\,}^{o}}C$

• question_answer31) $4{{m}^{3}}$of water is to be pumped to a height of 20 m and forced into a reservoir at a pressure of $2\times {{10}^{5}}N/{{m}^{2}}.$ The work done by the motor is (external pressure$={{10}^{5}}\,N/{{m}^{2}}$)

A) $8\times {{10}^{5}}J$

B) $16\times {{10}^{5}}\,J$

C) $12\times {{10}^{5}}\,J$

D) $32\times {{10}^{5}}\,J$

• question_answer32) Moment of inertia of ring about its diameter is $I.$ Then, moment of inertia about an axis passing through centre perpendicular to its plane is

A) $2I$

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

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

D) $I$

• question_answer33) When both the listener and source are moving towards each other, then which of the following is true regarding frequency and wavelength of wave observed by the observer?

A) More frequency, less wavelength

B) More frequency, more wavelength

C) Less frequency, less wavelength

D) More frequency, constant wavelength

• question_answer34) The coefficient of friction between the tyres and the road is 0.25. The maximum speed with which car can be driven round a curve of radius 40 m without skidding is (assume$g=10\,m{{s}^{-2}}$)

A) $40\,m{{s}^{-1}}$

B) $20\,m{{s}^{-1}}$

C) $15\,m{{s}^{-1}}$

D) $10\,m{{s}^{-1}}$

• question_answer35) A bomb of mass 3.0 kg explodes in air into two pieces of masses 2.0 kg and 1.0 kg. The smaller mass goes at a speed of 80 m/s. The total energy-.imparted, to the two fragments is

A) 1.07 kJ

B) 2.14 kJ

C) 2.4 kJ

D) 4.8 kJ

• question_answer36) If distance between earth and sun become four times, then time period becomes

A) 4 times

B) 8 times

C) 1/4 times

D) 1/8 times

• question_answer37) An air bubble is contained inside water. It behaves as a

A) concave lens

B) convex lens

C) Neither convex nor concave

D) Cannot say

• question_answer38) The power dissipated across resistance R which is connected across a battery of potential V is P. If resistance is doubled, then the power becomes

A) 1/2

B) 2

C) 1/4

D) 4

• question_answer39) A 100 V, AC source of frequency 500 Hz is connected to an LCR circuit with$L=8.1\,mH,$$C=12.5\mu F,R=10\,\Omega$all connected in series as shown in figure. What is the quality factor of circuit?

A) $2.02$

B) $2.5434$

C) $20.54$

D) $200.54$

• question_answer40) The inductance of a coil is $L=10\,H$and resistance $R=5\,\Omega .$If applied voltage of battery is 10 V and it switches off in 1 millisecond, find induced emf of inductor,

A) $2\times {{10}^{4}}V$

B) $1.2\times {{10}^{4}}V$

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

D) None of these

• question_answer41) A proton is moving in a uniform magnetic field in a circular path of radius a in a direction perpendicular to z-axis along which field B exists. Calculate the angular momentum, if the radius is a charge on proton is e.

A) $\frac{Be}{{{a}^{2}}}$

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

C) ${{a}^{2}}eB$

D) $aeB$

• question_answer42) We wish to see inside an atom. Assuming the atom to have a diameter of 100 pm, this means that one must be able to resolve a width of say 10 pm. If an electron microscope is used, the minimum electron energy required is about

A) 1.5 keV

B) 15 keV

C) 150 keV

D) 1.5 MeV

• question_answer43) A body from height h is dropped. If the coefficient of restitution is e, then calculate the height achieved after one bounce.

A) ${{h}_{1}}={{e}^{2}}h$

B) ${{h}_{1}}={{e}^{4}}h$

C) ${{h}_{1}}=eh$

D) ${{h}_{1}}=\frac{h}{e}$

• question_answer44) A beam of light travelling along $x-$axis is described by the electric field${{E}_{y}}=(600\,V{{m}^{-1}})\sin \omega (t-x/c)$ then maximum magnetic force on a charge $q=2e,$moving along $y-$axis with a speed of $3.0\times {{10}^{7}}\,m{{s}^{-1}}$ is $(e=1.6\times {{10}^{-19}}C)$

A) $19.2\times {{10}^{-17}}N$

B) $1.92\times {{10}^{-17}}\,N$

C) $0.192\,N$

D) None of these

• question_answer45) Equipotential surfaces associated with an electric field which is increasing in magnitude along the $x-$direction are

A) planes parallel to $yz-$plane

B) planes parallel to $xy-$plane

C) planes parallel to $xz-$plane

D) coaxial cylinders of increasing radii around the $x-$axis

• question_answer46) If 200 MeV energy is released in the fission of a single nucleus of ${{\,}_{92}}U{{\,}^{235}},$ how many fissions must occur per second to produce a power 1 kW?

A) $3.12\times {{10}^{13}}$

B) $3.12\times {{10}^{3}}$

C) $3.1\times {{10}^{17}}$

D) $3.12\times {{10}^{19}}$

• question_answer47) Find ratio of acceleration due to gravity g depth d and at height h, where d = 2h.

A) $1:1$

B) $1:2$

C) $2:1$

D) $1:4$

• question_answer48) A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power of combination is

A) $-1.5\,D$

B) $-6.5\,D$

C) $+6.5D$

D) $+\,6.67D$

• question_answer49) In a Youngs experiment, two coherent sources are placed 0.90 mm apart and the fringes are observed one metre away. If it produces the second dark fringe at a distance of 1 mm from the central fringe, the wavelength monochromatic light used would be

A) $60\times {{10}^{-4}}cm$

B) $10\times {{10}^{-4}}cm$

C) $10\times {{10}^{-5}}cm$

D) $6\times {{10}^{-5}}cm$

• question_answer50) A bar magnet when placed at an angle of ${{30}^{o}}$ the direction of magnetic field induction of $5\times {{10}^{-2}}T,$experiences a moment of couple $25\times {{10}^{-6}}\,N-m.$ If the length of the magnet is 5 cm its pole strength is

A) $2\times {{10}^{-2}}A-m$

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

C) $2\,A-m$

D) $5\,A-m$

• question_answer51) The number of moles of $\text{KMn}{{\text{O}}_{\text{4}}}$reduced by one mole of KI in alkaline medium is

A) 1

B) 5

C) 1/2

D) 1/5

• question_answer52) Value of $x$ in potash alum, ${{K}_{2}}S{{O}_{4}}.A{{l}_{x}}{{(S{{O}_{4}})}_{3}}.24{{H}_{2}}O$

A) 4

B) 1

C) 2

D) None of these

• question_answer53) Ozone is used for purifying water because

A) it dissociates and release oxygen

B) do not leave any foul smell like chlorine

C) kills bacteria, cyst, fungi and acts as a biocide

D) All of the above

• question_answer54) Internal energy is sum of

A) kinetic energy and potential energy

B) all types of energy of the system

C) energy of internal system

D) None of the above

• question_answer55) Total volume of atoms present in a face centred cubic unit cell of a metal is ($r=$atomic radius)

A) $\frac{20}{3}\pi {{r}^{3}}$

B) $\frac{24}{3}\pi {{r}^{3}}$

C) $\frac{12}{3}\pi {{r}^{3}}$

D) $\frac{16}{3}\pi {{r}^{3}}$

• question_answer56) If two molecules of A and B having mass 100 kg and 64 kg and rate of diffusion of A is $12\times {{10}^{-3}},$ then what will be the rate of diffusion of B?

A) $15\times {{10}^{-3}}$

B) $64\times {{10}^{-3}}$

C) $~5\times {{10}^{-3}}$

D) $~46\times {{10}^{-3}}$

• question_answer57) Aniline is prepared in presence of Fe/HCl from

A) benzene

B) nitrobenzene

C) dinitrobenzene

D) None of these

• question_answer58) Difference between S and ${{S}^{2-}}$as ${{S}^{2-}}$has

A) larger radii and larger size

B) smaller radii and larger size

C) larger radii and smaller size

D) smaller radii and smaller size

• question_answer59) Which of the following is not correct?

A) ${{t}_{1/2}}=\frac{0.693}{k}$

B) $N={{N}_{0}}{{e}^{-kt}}$

C) $\frac{1}{N}=\frac{1}{{{N}_{0}}}=\ln \,k{{t}_{1/2}}$

D) None of the above

• question_answer60) Which is not in accordance to aufbau principle?

A)

B)

C)

D)

• question_answer61) $C{{H}_{3}}C{{H}_{2}}Cl$undergoes homolytic fission, produces

A) $C{{H}_{3}}\overset{\centerdot }{\mathop{C}}\,{{H}_{2}}$and $\overset{\centerdot }{\mathop{C}}\,l$

B) $C{{H}_{3}}\overset{\oplus }{\mathop{C}}\,{{H}_{2}}$and $C{{l}^{\text{o}-}}$

C) $C{{H}_{3}}\overset{\oplus }{\mathop{C}}\,{{H}_{2}}$and $\overset{\centerdot }{\mathop{C}}\,l$

D) $C{{H}_{3}}\overset{\centerdot }{\mathop{C}}\,{{H}_{2}}$and $C{{l}^{\text{o}-}}$

• question_answer62) $C-C$bond order in benzene is

A) 1

B) 2

C) between 1 and 2

D) None of these

• question_answer63) In colloid particles, range of diameter is

A) 1 to 100 nm

B) 1 to 1000 cm

C) 1 to 1000 mm

D) 1 to 100 km

• question_answer64) $Z{{n}^{2+}}\xrightarrow{{}}Zn(s);{{E}^{o}}=-0.76\,V$ $C{{u}^{2+}}\xrightarrow{{}}Cu(s);{{E}^{o}}=-0.34\,V$ Which of the following is spontaneous?

A) $Z{{n}^{2+}}+Cu\xrightarrow{{}}Zn+C{{u}^{2+}}$

B) $C{{u}^{2+}}+Zn\xrightarrow{{}}Cu+Z{{n}^{2+}}$

C) $Z{{n}^{2+}}+C{{u}^{2+}}\xrightarrow{{}}Zn+Cu$

D) None of the above

• question_answer65) Highest electron affinity among the following is

A) fluorine

B) chlorine

C) sulphur

D) xenon

• question_answer66) Which of the following noble gases is most reactive?

A) He

B) Ne

C) Ar

D) Xe

• question_answer67) Which one of the following is a correct set with respect to molecule, hybridisation and shape?

A) $BeC{{l}_{2}},\text{ }s{{p}^{2}},\,$linear

B) $BeC{{l}_{2}},\text{ }s{{p}^{2}},$triangular planar

C) $~BC{{l}_{3}},\text{ }s{{p}^{2}},$ triangular planar

D) $BC{{l}_{3}},s{{p}^{3}},$tetrahedral

• question_answer68) ${{H}_{2}}S$is not a/an

A) reducing agent

B) acidic

C) oxidizing agent

D) None of the above

• question_answer69) On doubling p and V with constant temperature, the equilibrium constant will

A) remain constant

B) become double

C) become one-fourth

D) None of the above

• question_answer70) What is the electronic configuration of$M{{n}^{2+}}$?

A) $~[Ne]\text{ }3{{d}^{5}},\text{ }4{{s}^{o}}$

B) $\text{ }\!\![\!\!\text{ }Ar\text{ }\!\!]\!\!\text{ }3{{d}^{5}},\text{ }4{{s}^{2}}$

C) $\text{ }\!\![\!\!\text{ }Ar\text{ }\!\!]\!\!\text{ }3{{d}^{5}},\text{ }4{{s}^{0}}$

D) $\text{ }\!\![\!\!\text{ }Ne\text{ }\!\!]\!\!\text{ }3{{d}^{5}},\text{ }4{{s}^{2}}$

• question_answer71) Increase in atomic size down the group is due to

A) increase in number of electrons

B) increase in number of protons and neutrons

C) increase in number of protons

D) increase in number of protons, neutrons and electrons

• question_answer72) Which is tribasic acid?

A) ${{H}_{3}}P{{O}_{2}}$

B) ${{H}_{3}}P{{O}_{4}}$

C) ${{H}_{4}}{{P}_{2}}{{O}_{7}}$

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

• question_answer73) Highest ionizing power is exhibited by

A) $\alpha -$ rays

B) $\beta -$rays

C) $\gamma -$rays

D) $X-$rays

A) impure $Cu$

B) $Cu$alloy

C) pure $Cu$

D) Cu having 1% impurity

• question_answer75) Claisen condensation is not given by

A)

B)

C)

D)

• question_answer76) $AgN{{O}_{3}}$does not give precipitate with $CHC{{l}_{3}}$ because

A) $CHC{{l}_{3}}$ does not ionize in water

B) $Agn{{O}_{3}}$ is chemically inert

C) $CHC{{l}_{3}}$ is chemically inert

D) None of the above

• question_answer77) $_{90}T{{h}^{228}}\xrightarrow{{}}{{\,}_{83}}B{{i}^{212}}$by

A) $4\alpha ,1\beta$

B) $4\alpha ,2\beta ,$

C) $5\alpha ,1\beta$

D) $5\alpha ,2\beta ,$

• question_answer78) Blood cells do not shrink in blood because blood is

A) hypotonic

B) isotonic

C) equimolar

D) hypeitonic

• question_answer79) The compound in which underlined carbon uses only its $s{{p}^{3}}$hybrid orbitals for bond formation is

A) $C{{H}_{3}}\underset{\scriptscriptstyle-}{C}OOH$

B) $C{{H}_{3}}\underline{C}ON{{H}_{2}}$

C) $C{{H}_{3}}\underline{C}{{H}_{2}}OH$

D) $C{{H}_{3}}\underline{C}H=C{{H}_{2}}$

A) 2-methyl propan-2-ol

B) 2-methyl propan-1-ol

C) 3-methyl butan-1-ol

D) 3-methyl butan-2-ol

• question_answer81) Optical isomerism is shown by

A) propanol-2

B) butanol-2

C) ethanol

D) methanol

• question_answer82) When ${{C}_{2}}{{H}_{2}},C{{H}_{4}}$and ${{C}_{2}}{{H}_{4}}$passes through a test tube which have ammoniacal $C{{u}_{2}}C{{l}_{2}},$find out which gas comes out unaffected from test tube?

A) ${{C}_{2}}{{H}_{2}}$and $C{{H}_{4}}$

B) ${{C}_{2}}{{H}_{2}}$and ${{C}_{2}}{{H}_{4}}$

C) ${{C}_{2}}{{H}_{4}}$and $C{{H}_{4}}$

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

• question_answer83) When hydrogen molecules decomposed into its atoms which conditions gives maximum yield of H atoms?

A) High temperature and low pressure

B) Low temperature and high pressure

C) High temperature and high pressure

D) Low temperature and low pressure

• question_answer84) Natural rubber is a polymer of

A) styrene

B) chloroprene

C) $C{{H}_{2}}=\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,-CH=C{{H}_{2}}$or isoprene

• question_answer85) Which of the following compounds is aromatic?

A)

B)

C)

D)

• question_answer86) The value of $\Lambda _{eq}^{\infty }$ for$N{{H}_{4}}Cl,NaOH$ and$NaCl$ are respectively, 149.74, 248.1 and $126.4\,oh{{m}^{-1}}\,c{{m}^{2}}e{{q}^{-1}}.$ The value of $A_{eq}^{\infty }$of $N{{H}_{4}}OH$is

A) 371.44

B) 271.44

C) 71.44

D) Cannot be predicted from given data

• question_answer87) Number of atoms of He in 100 u of He (atomic wt of He is 4) are

A) 25

B) 100

C) 50

D) $100\times 6\times {{10}^{-23}}$

• question_answer88) Which has least gold number?

A) Gelatin

B) Starch

C) Albumin

D) Blood

• question_answer89) In a compound C, H and N are present in 9 : 1 : 3.5 by weight. If molecular weight of the compound is 108, then the molecular formula of the compound is

A) ${{C}_{2}}{{H}_{6}}{{N}_{2}}$

B) ${{C}_{3}}{{H}_{4}}N$

C) ${{C}_{6}}{{H}_{8}}{{N}_{2}}$

D) ${{C}_{9}}{{H}_{12}}{{N}_{3}}$

• question_answer90) In the following reaction ${{C}_{2}}{{H}_{2}}\xrightarrow[HgS{{O}_{4}}/{{H}_{2}}S{{O}_{4}}]{{{H}_{2}}O}X\rightleftharpoons C{{H}_{3}}CHO,$What is $X$?

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

B) $C{{H}_{3}}-O-C{{H}_{3}}$

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

D) $C{{H}_{2}}=CHOH$

• question_answer91) Which one of the following will most readily be dehydrated in acidic conditions?

A)

B)

C)

D)

• question_answer92) Which of the following solutions will have $pH=9$at 298 K?

A) $1\times {{10}^{-9}}\,M\,HCl$solution

B) $1\times {{10}^{-5}}\,M\,NaOH$solution

C) $1\times {{10}^{-9}}\,M\,KOH$solution

D) Both (a) and (b)

• question_answer93) The following data are for the decomposition of ammonium nitrite in aqueous solution.

 Vol. of ${{N}_{2}}$in cc Times (min) 6.25 10 9.00 15 11.40 20 13.65 25 35.65 Infinity
The order of reaction is

A) zero

B) one

C) two

D) three

• question_answer94) An alkyl halide by formation of its Grignard reagent and heating with water yields propane. What is the original alkyl halide?

A) Methyl iodide

B) Ethyl iodide

C) Ethyl bromide

D) Propyl bromide

• question_answer95) The following reaction is known as

A) Perkin reaction

B) Gattermann reaction

C) Kolbe reaction

D) Gattermann-aldehyde reaction

• question_answer96) Aldehyde with $N{{H}_{2}}.N{{H}_{2}}$forms

A) hydrazones

B) aniline

C) nitrobenzene

D) None of these

• question_answer97) Van t Hoff factor of $Ca{{(N{{O}_{3}})}_{2}}$us

A) one

B) two

C) three

D) four

• question_answer98) 1 mole of ${{H}_{2}}$and 2 moles of ${{I}_{2}}$are taken initially in a two litre vessel. The number of moles of ${{H}_{2}}$at equilibrium is 0.2. Then, the number of moles of ${{I}_{2}}$and HI at equilibrium are

A) 1.2, 1.6

B) 1.8, 1.0

C) 0.4, 2.4

D) 0.8, 2.0

• question_answer99) The volume of water to be added to 100 cm3 of $0.5\text{ }N\text{ }{{H}_{2}}S{{O}_{4}}$to get decinormal concentration is

A) $400\,c{{m}^{3}}$

B) $450\,c{{m}^{3}}$

C) $~500\,c{{m}^{3}}$

D) $100\,c{{m}^{3}}$

• question_answer100) 1.520 g of hydroxide of a metal on ignition gave 0.995 g of oxide. The equivalent weight of metal is

A) 1.52

B) 0.995

C) 190

D) 9

• question_answer101) If $f:R\to R$is defined by $f(x)=[2x]-2[x]$ for all $x\in R,$where $[x]$is the greatest integer not exceeding x, then the range of$f$is

A) $\{x\in R:0\le x\le 1\}$

B) $(0,1)$

C) $\{x\in R:x>0\}$

D) $\{x\in R:x\le 0\}$

• question_answer102) If $x=\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}},}$then ${{x}^{2}}{{(x-4)}^{2}}$ is equal to

A) 7

B) 4

C) 2

D) 1

• question_answer103) For all integers $n\ge 1,$which of the following is divisible by 9?

A) ${{8}^{n}}+1$

B) ${{4}^{n}}-3n-1$

C) ${{3}^{2n}}+3n+1$

D) ${{10}^{n}}+1$

• question_answer104) Eight different letters of an alphabet are given Words of four letters from these are formed The number of such words with at least one letter repeated is

A) $\left( _{4}^{8} \right)-{{\,}^{8}}{{P}_{4}}$

B) ${{8}^{4}}+\left( _{4}^{8} \right)$

C) ${{8}^{4}}-{{\,}^{8}}{{P}_{4}}$

D) ${{8}^{4}}-\left( _{4}^{8} \right)$

• question_answer105) The number of natural numbers less than 1000, in which no two digits are repeated is

A) 738

B) 792

C) 837

D) 720

• question_answer106) $1+\frac{2}{4}+\frac{2.5}{4.8}+\frac{2.5.8}{4.8.12}+\frac{2.5.8.11}{4.8.12.16}+...$is equal to

A) ${{4}^{-2/3}}$

B) $\sqrt[3]{16}$

C) $\sqrt[3]{4}$

D) ${{4}^{3/2}}$

• question_answer107) The coefficient of ${{x}^{n}}$in$\frac{1-2x}{{{e}^{x}}}$is

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

B) ${{(-1)}^{n}}.\frac{\left( 1+2n \right)}{n!}$

C) ${{(-1)}^{n}}.\frac{(1-2n)}{n!}$

D) ${{(-1)}^{n}}.\frac{(1+4n)}{n!}$

• question_answer108) If $\sqrt{9{{x}^{2}}+6x+1}<(2-x),$then

A) $x\in \left( -\frac{3}{2},\frac{1}{4} \right)$

B) $x\in \left( -\frac{3}{2},\frac{1}{4} \right]$

C) $x\in \left[ -\frac{3}{2},\frac{1}{4} \right)$

D) $x<\frac{1}{4}$

• question_answer109) The difference between two roots of the equation ${{x}^{3}}-13{{x}^{2}}+15x+189=0$ is$2.$Then, the roots of the equation are

A) $-3,5,7$

B) $-3,-7,-9$

C) $3,-5,7$

D) $-3,7,9$

• question_answer110) If $\alpha ,\beta ,\gamma$are the roots of the equation ${{x}^{3}}-6{{x}^{2}}+11x+6=0,$then $\sum {{\alpha }^{2}}\beta +\sum {{\alpha }^{2}}\beta +\sum \alpha {{\beta }^{2}}$is equal to

A) 80

B) 84

C) 90

D) - 84

• question_answer111) If A is an inverrible matrix of order n, then the determinant of $adj\,(A)$ is equal to

A) $|A{{|}^{n}}$

B) $|A{{|}^{n+1}}$

C) $|A{{|}^{n-1}}$

D) $|A{{|}^{n+2}}$

• question_answer112) $\left| \begin{matrix} \log e & \log {{e}^{2}} & \log {{e}^{3}} \\ \log {{e}^{2}} & \log {{e}^{3}} & \log {{e}^{4}} \\ \log {{e}^{3}} & \log {{e}^{4}} & \log {{e}^{5}} \\ \end{matrix} \right|$is equal to

A) 0

B) 1

C) 4 loge

D) 5 loge

• question_answer113) The equation of the locus of $z$ such that $\left| \frac{z-i}{z+i} \right|=2,$where $z=x+iy$is a complex number, is

A) $3{{x}^{2}}+\text{ }3{{y}^{2}}+10y\text{ }-3=0$

B) $~3{{x}^{2}}+3{{y}^{2}}+10y+3=0$

C) $3{{x}^{2}}-3{{y}^{2}}-10y-3=0$

D) ${{x}^{2}}+{{y}^{2}}-5y+3=0$

• question_answer114) If $5\cos x+12\cos y=13,$ then the maximum value of $5\,\sin x+12\sin y$is

A) 12

B) $\sqrt{120}$

C) $\sqrt{20}$

D) 13

• question_answer115) The quadratic equation whose roots are ${{\sin }^{2}}{{18}^{o}}$and ${{\cos }^{2}}{{36}^{o}}$is

A) $~16{{x}^{2}}-12x+1=0$

B) $16{{x}^{2}}+12x+1=0$

C) $16{{x}^{2}}-12x-1=0$

D) $16{{x}^{2}}+\text{10}x+1=0$

• question_answer116) For all values of $\theta ,$ the values of $3-\cos \theta +\cos \left( \theta +\frac{\pi }{3} \right)$ lie in the interval

A) $[-2,3]$

B) $[-2,1]$

C) $[2,4]$

D) $[1,5]$

• question_answer117) If $x=\tan {{15}^{o}},y=\cos ec{{75}^{o}}$and $z=4\sin {{18}^{o}},$then

A) $x<y<z$

B) $y<z<x$

C) $z<x<\text{ }y$

D) $~x<z<\text{ }y$

• question_answer118) If in $\Delta \,ABC,\,\,\tan \frac{A}{2}=\frac{5}{6}$ and $\tan \frac{C}{2}=\frac{2}{5},$then$a,b,c$ are such that

A) ${{b}^{2}}=ac$

B) $2b=a+c$

C) $2ac=b(a+c)$

D) $a+b=c$

• question_answer119) If $b+c=3a,$then $\cot \frac{B}{2}\cot \frac{C}{2}$is equal to

A) 3

B) 1

C) 4

D) 2

• question_answer120) The elevation of an object on a hill is observed from a certain point in the horizontal plane through its base, to be ${{30}^{o}}.$ After walking 120 m towards it on level ground the elevation is found to be ${{60}^{o}}.$ Then the height of the object (in metres) is

A) 120

B) $60\sqrt{3}$

C) $120\sqrt{3}$

D) $60$

• question_answer121) If $\vec{a}+\vec{b}+\vec{c}=\vec{o}$and $|\vec{a}|=3,|\vec{b}|=4$and $|\vec{c}|=\sqrt{37},$then the angle between $\vec{a}$and $\vec{b}$ is

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

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

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

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

• question_answer122) The position vector of a point lying on the line joining the points whose position vectors are $\hat{i}+\hat{j}-\hat{k}$and $\hat{i}-\hat{j}+\hat{k}$is

A) $\hat{j}$

B) $\hat{i}$

C) $\hat{k}$

D) $\vec{o}$

• question_answer123) If the volume of parallelepiped with$4\hat{i}+5\hat{j}+\hat{k},-\hat{j}+\hat{k}$with coterminous edges $4\hat{i}+5\hat{j}+\hat{k},-\hat{j}+\hat{k}$ and $3\hat{i}+9\hat{j}+p\hat{k}$is 34 cubic unit, then? is equal to

A) 4

B) -13

C) 13

D) 6

• question_answer124) If A and B are two independent events such that $P(B)=\frac{2}{7},P(A\cup {{B}^{c}})=0.8,$then $P(A)$ is equal to

A) 0.1

B) 0.2

C) 0.3

D) 0.4

• question_answer125) Seven balls are drawn simultaneoulsy from a bag containing 5 white and 6 green balls. The probability of drawing 3 white and 4 green balls is

A) $\frac{7}{{{\,}^{11}}{{C}_{7}}}$

B) $\frac{{{\,}^{5}}{{C}_{3}}+{{\,}^{6}}{{C}_{4}}}{{{\,}^{11}}{{C}_{7}}}$

C) $\frac{{{\,}^{5}}{{C}_{2}}+{{\,}^{6}}{{C}_{2}}}{{{\,}^{11}}{{C}_{7}}}$

D) $\frac{{{\,}^{6}}{{C}_{3}}+{{\,}^{5}}{{C}_{4}}}{{{\,}^{11}}{{C}_{7}}}$

• question_answer126) The equation of the line passing through the point of intersection of the lines$~x-3y+2=0$ and and perpendicular to the line $2x+5y-7=0$ is

A) $2x-3y+1=0$

B) $~6x-9y+11=0$

C) $~2x-3y+5=0$

D) $3x-2y+1=0$

• question_answer127) Let O be the origin and A be a point on the curve ${{y}^{2}}=4x.$Then the locus of the mid point of OA, is

A) ${{x}^{2}}=4y$

B) ${{x}^{2}}=2y$

C) ${{x}^{2}}=16y$

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

• question_answer128) The lines represented by the equation ${{x}^{2}}-\text{ }{{y}^{2}}-\text{ }x+3y-2=0$are

A) $x+y-1=0,\,x-y+2=0$

B) $x-y-2=0,x+y+1=0$

C) $x+y+2=,0,x-y-1=0$

D) $x-y+1=0,x+y-2=0$

• question_answer129) If OA is equally inclined to OX, OY and OZ and if A is $\sqrt{3}$unit from the origin, then A is

A) $(3,3,3)$

B) $(-1,1,-1)$

C) $(-1,1,1)$

D) $(1,1,1)$

• question_answer130) If the direction cosines of two lines are such that $l+m+n=0,{{l}^{2}}+{{m}^{2}}-{{n}^{2}}=,0$then the angle between them is

A) $\pi$

B) $\pi /3$

C) $\pi /4$

D) $\pi /6$

• question_answer131) The number of common tangents to the two circles ${{x}^{2}}+\text{ }{{y}^{2}}-\text{ }8x+2y=0$ and ${{x}^{2}}+{{y}^{2}}-2x-16y+25=0$is

A) 1

B) 2

C) 3

D) 4

• question_answer132) The length of the tangent drawn to the circle ${{x}^{2}}+{{y}^{2}}-2x+4y-11=0$from the point $(1,3)$is

A) 1

B) 2

C) 3

D) 4

• question_answer133) Equation of the latusrectum of the ellipse $9{{x}^{2}}+4{{y}^{2}}-18x-8y-23=0\text{ }$are

A) $y=\pm \text{ }\sqrt{5}$

B) $x=\pm \text{ }\sqrt{5}$

C) $y=1\pm 5$

D) $x=-1\pm \sqrt{5}$

• question_answer134) If the eccentricity of a hyperbola is$\sqrt{3},$, then the eccentricity of its conjugate hyperbola is

A) $\sqrt{2}$

B) $\sqrt{3}$

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

D) $2\sqrt{3}$

• question_answer135) If ${{x}^{y}}={{y}^{x}},$then $x(x-y\log x)\frac{dy}{dx}$is equal to

A) $y(y-x\log \,y)$

B) $y(y+x\,\log \,y)$

C) $x(x+y\log x)$

D) $x(y-x\log y)$

• question_answer136) $f(x)={{e}^{x}}\sin x,$then $f(x)$is equal to

A) ${{e}^{6x}}\sin 6x$

B) $2{{e}^{x}}\cos x$

C) $8{{e}^{x}}\sin x$

D) $8{{e}^{x}}\cos x$

• question_answer137) If $0<p<q,$then $\underset{n\to \infty }{\mathop{\lim }}\,{{({{q}^{n}}+{{p}^{n}})}^{1/n}}$is equal to

A) $e$

B) $p$

C) $q$

D) 0

• question_answer138) $\underset{x\to \infty }{\mathop{\lim }}\,[{{x}^{2}}+2x-1]$is equal to

A) $\infty$

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

C) 4

D) 1

• question_answer139) If $f(x)=\left\{ \begin{matrix} \frac{1-\sqrt{2}\sin x}{\pi -4x}, & if\,x\ne \frac{\pi }{4} \\ a & if\,x=\frac{\pi }{4} \\ \end{matrix} \right.$ is continuous at $\frac{\pi }{4},$ then a is equal to

A) 4

B) 2

C) 1

D) 1/4

• question_answer140) If $\theta$is the angle between the curves $xy=2$and ${{x}^{2}}+4y=0,$then $\tan \theta$is equal to

A) 1

B) -1

C) 2

D) 3

• question_answer141) In the interval $(-3,3)$ the function $f(x)=\frac{x}{3}+\frac{3}{x},x\ne 0$is

A) increasing

B) decreasing

C) neither increasing nor decreasing

D) partly increasing and partly decreasing

• question_answer142) If $\int_{{}}^{{}}{\,\sqrt{\frac{x}{{{a}^{3}}-{{x}^{3}}}}dx}=g(x)+c,$then $g(x)$is equal to

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

B) $\frac{2}{3}{{\sin }^{-1}}\left( \frac{{{x}^{3}}}{{{a}^{3}}} \right)$

C) $\frac{2}{3}{{\sin }^{-1}}\left( \sqrt{\frac{{{x}^{3}}}{{{a}^{3}}}} \right)$

D) $\frac{2}{3}{{\cos }^{-1}}\left( \frac{x}{a} \right)$

• question_answer143) If $\frac{dx}{{{x}^{2}}+2x+2}=f(x)+c,$then $f(x)$is equal to

A) ${{\tan }^{-1}}(x+1)$

B) $2{{\tan }^{-1}}(x+1)$

C) $-{{\tan }^{-1}}(x+1)$

D) $3{{\tan }^{-1}}(x+1)$

• question_answer144) $\int_{0}^{\pi /2}{\frac{dx}{1+{{\tan }^{3}}x}}$is equal to

A) $\pi$

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

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

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

• question_answer145) The solution of$(1+{{x}^{2}})\frac{dy}{dx}+2xy-4{{x}^{2}}=0$is

A) $3x(1+{{y}^{2}})=4{{y}^{3}}+c$

B) $3y(1+{{x}^{2}})=4{{x}^{3}}+c$

C) $3x(1-{{y}^{2}})=4{{y}^{3}}+c$

D) $3y(1+{{y}^{2}})=4{{x}^{3}}+c$

• question_answer146) The function $f(x)=\log (x+\sqrt{{{x}^{2}}+1})$is

A) an even function

B) an odd function

C) a periodic function

D) neither an even nor an odd function

• question_answer147) If p, q and rare simple propositions with truth values T, F, T, then the truth value of$(\tilde{\ }p\vee q)\wedge \tilde{\ }q\Rightarrow p$is

A) true

B) false

C) true, if r is false

D) None of these

• question_answer148) The dual of $x+(yx)=x$is

A) $(x+y).(x+x)=x$

B) $x.(y+x)=x$

C) $x.(y.x)=x$

D) None of the above

• question_answer149) Forces of magnitudes 5N, 10N, 15N and 20 N act on a particle in the direction of North, South, East and West respectively. The magnitude of their resultant is

A) $15\sqrt{2}N$

B) $10\,N$

C) $25\sqrt{2}\,N$

D) $5\sqrt{2}\,N$

• question_answer150) The value of $\int_{-\pi /2}^{\pi /2}{\log \left( \frac{2-\sin \theta }{2+\sin \theta } \right)}d\theta$is

A) 0

B) 1

C) 2

D) None of these