# Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2001

### done BCECE Engineering Solved Paper-2001

• question_answer1) A thin circular ring of mass M and radius R is rotating about its axis with a constant angular speed $\omega .$ Two blocks, each of mass m are attached gently to the opposite ends of a diameter of the ring the angular. speed of the ring will be:

A) $\frac{M+2m}{M}\omega$

B) $\frac{M}{M+2m}\omega$

C) $\frac{M-2m}{M+2m}\omega$

D) $\frac{2M}{M+2m}\omega$

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• question_answer2) In a pressure cooker, the food is prepared quickly, the reason is that the:

A) boiling point of water is raised due to increase in volume

B) boiling point of water is raised due to the increase in pressure

C) boiling point of water decreases due to increase in pressure

D) none of the above

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• question_answer3) In the equation$\left( P+\frac{a}{{{V}^{2}}} \right)(V-b)=RT,$ where P = pressure, V= volume, a and b are constants, the dimensions of a are:

A) $\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{5}}}{{\text{T}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }$

B) $\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{-5}}}{{\text{T}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }$

C) $\text{ }\!\![\!\!\text{ M}{{\text{L}}^{5}}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }$

D) $\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{-1}}}{{\text{L}}^{5}}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }$

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• question_answer4) Two bulbs have wattage 250 W and 100 W respectively, each rated at 220 V. The ratio of resistances between the two bulbs will be:

A) 2 : 5

B) 5 : 2

C) 3 : 4

D) 4 : 3

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• question_answer5) When a current in coil changes from 4 A to 2 A in 0.05 s, emf of 8 V is induced in the coil. The coefficient of self-inductance in the coil is:

A) 0.8 H

B) 0.4 H

C) 0.2 H

D) 0.1 H

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• question_answer6) If a sphere is rolling, the ratio of its rotational to total energy is given by:

A) 2 : 7

B) 10 : 7

C) 7 : 10

D) 2 : 5

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• question_answer7) Water is flowing on the blades of a turbine at a rate of 100 kg/s from a certain spring. If the height of the spring be 100 m, the power transferred to the turbine will be:

A) 100 W

B) 1 Kw

C) 10 kW

D) 100 kW

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• question_answer8) A bullet $({{m}_{1}}=25g)$ fired with a velocity 400 m/s gets embedded into a bag of sand $({{m}_{2}}=4.9\,kg)$ suspended by a rope. The velocity gained by the bag is nearly:

A) 2 m/s

B) 4 m/s

C) 8 m/s

D) 0.2 m/s

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• question_answer9) The work done to form a layer of soap solution of size $10\times 10\,cm$ will be: (surface tension of soap solution is $3\times {{10}^{-2}}\,N/m$)

A) $\text{6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-2}}}\text{J}$

B) $\text{6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\text{J}$

C) $\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-2}}}\text{J}$

D) $\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\text{J}$

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• question_answer10) In a transistor $\beta =100$. The value of $\alpha$ is:

A) 1

B) 0.99

C) 0.1

D) 0.01

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• question_answer11) A bomb of mass 9 kg at rest explodes into two pieces of mass 4 kg and 5 kg. The velocity of 4 kg mass is 15 m/s. What is the kinetic energy of 5 kg mass?

A) Zero

B) 562.5 J

C) 360 J

D) 180 J

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• question_answer12) The velocity of sound at $0{}^\circ C$ is 332 m/s. At what temperature will it be 664 m/s?

A) $273{}^\circ C$

B) $546{}^\circ C$

C) $1092{}^\circ C$

D) $819{}^\circ C$

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• question_answer13) The equation of a wave moving on a string may be written as$y=3\,\cos \,\pi (100t-x)$where x, y are in cm and t in second. Its wavelength will be:

A) 5 cm

B) 2 cm

C) 100 cm

D) 3 cm

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• question_answer14) A train mover towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is ${{f}_{1.}}$ If the trains speed is reduced to 17 m/s, the frequency registered is ${{f}_{2}}$If the speed of round is 340 m/s, the ratio ${{f}_{1}}/{{f}_{2}}$ is:

A) $\frac{19}{18}$

B) $\frac{18}{19}$

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

D) $2$

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• question_answer15) In a closed organ pipe which of the following notes is not present, if fundamental note is 50 Hz?

A) 100 Hz

B) 150 Hz

C) 250 Hz

D) None of these

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• question_answer16) A monoatomic gas $(\gamma =5/3)$ at pressure P is suddenly compressed to $\frac{1}{8}$th of its volume adiabatically, the pressure of gas is :

A) $\frac{43}{3}P$

B) $8P$

C) $32P$

D) $\frac{24}{5}P$

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• question_answer17) An ideal Carnot engine whose efficiency is 40% receives heat at 500 K. If the efficiency is to be 50% the intake temperature for this same exhaust temperature is :

A) 600 K

B) 800 K

C) 900 K

D) 1000 K

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• question_answer18) A mixture of gas contains 8 g of oxygen and 7 g of nitrogen. To use the equation PV = nRT, the value of n of such mixture will be:

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

B) $\frac{1}{4}$

C) 2

D) 4

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• question_answer19) How many times is diatomic gas should be expanded adiabatically, so as to reduce the root mean square velocity to half?

A) 64

B) 32

C) 16

D) 8

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• question_answer20) The masses of three wires of copper are in the ratio 1 : 2 : 3 and their lengths are in the ratio 3 : 2 : 1. The ratio of their resistances is:

A) 3 : 2 : 1

B) 1 : 2 : 3

C) 27 : 6 : 1

D) 1 : 6 : 27

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• question_answer21) If the length of a conductor is halved, then the conductance will be:

A) quadrupled

B) doubled

C) halved

D) unchanged

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• question_answer22) The vertical component of earths magnetic field is zero at a place whose angle of dip is:

A) $90{}^\circ$

B) $60{}^\circ$

C) $45{}^\circ$

D) $0{}^\circ$

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• question_answer23) Energy stored in a coil of self-inductance 40 mH carrying a steady current of 2 A is:

A) 80 J

B) 0.08 J

C) 0.8 J

D) 8 J

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• question_answer24) Resistance of rod is $1\Omega$. It is bent in the form of square. What is the resistance across adjoint corners ?

A) $1\,\Omega$

B) $3\,\Omega$

C) $\frac{3}{16}\Omega$

D) $\frac{3}{4}\Omega$

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• question_answer25) A capacitor of capacitance$1\,\mu F$ is filled with two dielectrics of dielectric constants 4 and 6. What is the new capacitance? A) $10\,\mu F$

B) $5\,\mu F$

C) $4\,\mu F$

D) $7\,\mu F$

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• question_answer26) The focal length of lens is 5 cm. If die least distance of distinct vision is 25 cm the magnification is:

A) 2.1

B) 1

C) 1.1

D) 6

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• question_answer27) The critical angle for a medium is $45{}^\circ$. The refractive index will be:

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

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

C) $\sqrt{2}$

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

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• question_answer28) The specific resistance of wire of length 1 m, area .of cross-section $0.5\,{{m}^{2}}$ is $25\,\mu \Omega \,m$. The resistance of the wire will be:

A) $5\times {{10}^{-5}}\,\Omega$

B) $3\times {{10}^{-6}}\,\Omega$

C) $46\times {{10}^{6}}\,\Omega$

D) $2\times {{10}^{6}}\,\Omega$

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• question_answer29) Two identical wires A and B have the same length L and carry the same current $\text{I}$ Wire A is bent into a circle of radius R and wire B is bent to form a square of side a. If ${{B}_{1}}$ and${{B}_{2}}$ are the values of magnetic induction at the centre of the circle and the centre of the square respectively, then the ratio of${{\text{B}}_{\text{1}}}\text{/}{{\text{B}}_{\text{2}}}$ is :

A) $\frac{{{\pi }^{2}}}{8}$

B) $\frac{{{\pi }^{2}}}{8\sqrt{2}}$

C) $\frac{{{\pi }^{2}}}{16}$

D) $\frac{{{\pi }^{2}}}{16\sqrt{2}}$

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• question_answer30) The force acting on a pole of pole strength 1 Am is ${{10}^{-4}}N$. The magnetic field at that point is:

A) $\text{11 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\text{T}$

B) $\text{10 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\text{T}$

C) $\text{0}\text{.1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\text{T}$

D) $\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\text{T}$

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• question_answer31) A tuning fork produces S beats/s with another tuning fork B of frequency 256 Hz. On filing fork A only 2 beats are heard per second, the frequency of A before filing is:

A) 251 Hz

B) 254 Hz

C) 261 Hz

D) 256 Hz

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• question_answer32) Number of photons of wavelength 600 nm emitted per second by an electric bulb of power 50 W is: (Take $h=6.6\times {{10}^{-34}}J-s$)

A) ${{10}^{19}}$

B) $2\times {{10}^{20}}$

C) 60

D) zero

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• question_answer33) Half-life of radioactive substance is 3.20 h. What is the time taken for a 75% of substance to be used ?

A) 6.38 h

B) 12 h

C) 4.18 days

D) 1.2 days

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• question_answer34) TV waves have wavelength range of 1-10 m. Their frequency range will be:

A) 3-30 MHz

B) 30-300 MHz

C) 3-3000 MHz

D) 300-3000 MHz

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• question_answer35) Reactance of a capacitor of capacitance$C\mu F$ for AC frequency$\frac{400}{\pi }$0 Hz is$25\,\Omega .$The value of C is:

A) $50\,\mu F$

B) $25\,\mu F$

C) $100\,\mu F$

D) $75\,\mu F$

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• question_answer36) An electron and a proton have same de-Broglie wavelength, then kinetic energy of the electron is:

A) infinite

B) equal to KE of proton

C) zero

D) greater than KE of proton

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• question_answer37) Relative permeability of iron is 5500. Its magnetic susceptibility is:

A) 5501

B) $5500\times {{10}^{-7}}$

C) $5500\times {{10}^{7}}$

D) 5499

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• question_answer38) An example for diamagnetic substances is :

A) gold

B) nickel

C) aluminium

D) iron

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• question_answer39) The impurity atom that should be added to germanium to make it n-type semiconductor

A) aluminium

B) phosphorus

C) boron

D) indium

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• question_answer40) An atom of mass number A and atomic number Z emits successively an $\alpha$-particle and a $\text{-}$particle and $\text{-}$rays. The mass number and atomic number of the end product, will be:

A) A - 4, 7 - 1

B) A - 4, Z - 2

C) A - 1, Z - 4

D) A, Z + 1

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• question_answer41) When R is Rydbergs constant for hydrogen, the wave number of the first line in the Lyman series is:

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

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

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

D) $2R$

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• question_answer42) A source of sound of frequency 256 Hz is moving towards a wall with a velocity of 5 m/s. The velocity of sound is 330 m/s. The number of beats heard by an observer moving along with the sounding object is:

A) $256\times \frac{330}{325}-256$

B) $256-\frac{256\times 330}{335}$

C) $\frac{256\times 330}{325}-\frac{256\times 330}{325}$

D) $256\times \frac{335}{325}-256$

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• question_answer43) The effective capacitance between the points P and Q in the circuit shown in figure, is (capacitance of each capacitor is$1\mu F$): A) $0.4\mu F$

B) $3\mu F$

C) $4\mu F$

D) $2\mu F$

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• question_answer44) What is the resistance of a 40 W lamp which is lighted at full brilliance by a current of $\frac{\text{1}}{\text{3}}\text{A}$?

A) $450\,\Omega$

B) $360\,\Omega$

C) $120\,\Omega$

D) $13.33\,\Omega$

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• question_answer45) The energy gap of silicon is 1.14 eV. The maximum wavelength at which silicon will begin absorbing energy is:

A) $18.855\,\overset{\text{o}}{\mathop{\text{A}}}\,$

B) $108.55\,\overset{\text{o}}{\mathop{\text{A}}}\,$

C) $1085.5\,\overset{\text{o}}{\mathop{\text{A}}}\,$

D) $10855\,\overset{\text{o}}{\mathop{\text{A}}}\,$

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• question_answer46) Assuming that the junction diode is ideal, the current through the diode is: A) 0.02 A

B) 2 A

C) 0.2 A

D) None of these

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• question_answer47) With a resistance R connected in series with galvanometer of resistance $100\,\Omega ,$ it acts as a voltmeter of range 0 - V. to double the range a resistance of $1000\Omega ,$ is to be connected in series with R. then the value of R is:

A) $400\,\Omega$

B) $900\,\Omega$

C) $1100\,\Omega$

D) $1000\,\Omega$

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• question_answer48) An $\alpha$-particle can be represented by a:

A) hydrogen atom

B) helium ion

C) hydrogen ion

D) helium nucleus

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• question_answer49) Coefficients of coupling between two coils of self-inductances ${{L}_{1}}$ and ${{L}_{1}}$ is unity. It means:

A) 50% flux of ${{L}_{1}}$ is linked with ${{L}_{2}}$

B) 100% flux of ${{L}_{1}}$ is linked with ${{L}_{2}}$

C) $\sqrt{{{L}_{1}}}$ time of flux ${{L}_{1}}$ is linked with ${{L}_{2}}$

D) None of above

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• question_answer50) State which of the following is correct?

A) ${{g}_{m}}=\mu \times {{r}_{p}}$

B) ${{r}_{p}}=\mu \times {{g}_{r}}$

C) $\mu ={{r}_{p}}\times {{g}_{m}}$

D) $\mu =\frac{{{r}_{p}}}{{{g}_{m}}}$

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• question_answer51) Modem periodic table is based on atomic number of the elements. The significance of atomic number was proved by the experiment of:

A) discovery of X-ray by Roentgen

B) Mullikans oil drop experiment

C) Braggs work on X-ray diffraction

D) Mosleys work on X-ray spectra

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• question_answer52) The shape of $\text{Xe}{{\text{O}}_{\text{4}}}$molecule is tetrahedral due to:

A) $sp$

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

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

D) none of these

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• question_answer53) The monomer of natural rubber is:

A) isoprene

B) adipic acid

C) vinyl chloride

D) acrylonitrile

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• question_answer54) lodoform test is given by:

A) 1-propanol

B) methanol

C) 2-butanol

D) 1-butanol

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• question_answer55) $\text{0}\text{.3M }{{\text{H}}_{\text{3}}}\text{P}{{\text{O}}_{\text{3}}}$shows the normality of:

A) 0.3

B) 0.6

C) 0.9

D) 0.1

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• question_answer56) At 300 K, the ratio of the average molecular kinetic energy of $\text{U}{{\text{F}}_{\text{6}}}$to that of ${{\text{H}}_{2}}$is:

A) 2 : 7

B) 7 : 2

C) 6 : 2

D) 1 : 1

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• question_answer57) Graphite and diamond are:

A) polymorphs

B) allotropes

C) different crystal structure

D) all of the above

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• question_answer58) The correct alternate for the cells spontaneous reaction is:

A) $\text{E}_{\text{cell}}^{\text{o}}$cell should be infinite

B) $\text{E}_{\text{cell}}^{\text{o}}$cell should be zero,

C) $\text{E}_{\text{cell}}^{\text{o}}$ cell should be positive

D) $\text{E}_{\text{cell}}^{\text{o}}$ cell should be negative

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• question_answer59) The maximum amount of sulphur is given by:

A) $AgS({{K}_{sp}}=6\times {{10}^{-29}})$

B) $CuS\,({{K}_{sp}}=4\times {{10}^{-27}})$

C) $PbS\,({{K}_{sp}}=8\times {{10}^{-28}})$

D) $ZnS\,({{K}_{sp}}=8\times {{10}^{-30}})$

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• question_answer60) The highest electronegative element is:

A) carbon

B) oxygen

C) fluorine

D) nitrogen

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• question_answer61) Bromine can be liberated from $KBr$ solution by the action of:

A) chlorine

B) $\text{ }\!\!~\!\!\text{ NaCl}$

C) $\text{KI}$

D) iodine solution

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• question_answer62) The aldehyde can be detected by which of the following?

A) Tollens reagent

B) Fehlings solution

C) Schiffs reagent

D) All of the above

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• question_answer63) Froth floatation method is used for the concentration of:

A) sulphide ore

B) oxide ore

C) chloride ore

D) amalgams

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• question_answer64) The zero dipole moment is shown by:

A) $cis-$1, 2-dichloroethylene

B) trans-1, 2- dichloroethylene

C) 1, 1- dichloroethylene

D) none of the above

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• question_answer65) The correct order of electron affinities of S, N,O and Cl is:

A) $O=Cl<S=N$

B) $O<S<Cl<N$

C) $N<O<S<Cl$

D) $O<N<Cl<S$

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• question_answer66) In isotones the atomic number and mass numbers are:

A) same

B) different

C) equal

D) zero

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• question_answer67) One mole of $C{{O}_{2}}$contains:

A) $18.1\times {{10}^{23}}$molecules of$\text{C}{{\text{O}}_{\text{2}}}$

B) $~6.02\text{ }\times \,\,{{10}^{23}}$ atom of carbon

C) 3 g of carbon

D) $~6.02\times {{10}^{23}}$ atoms of oxygen

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• question_answer68) The interhalogen compound not formed is:

A) $ICl$

B) $I{{F}_{5}}$

C) $Br{{F}_{5}}$

D) $BrC{{l}_{7}}$

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• question_answer69) The element prepared by electrolysis is:

A) sodium

B) chlorine

C) fluorine

D) bromine

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• question_answer70) The element chlorine consists of a mixture of $\text{75}\text{.53 }\!\!%\!\!\text{ }\,{{\,}_{\text{17}}}\text{C}{{\text{l}}^{\text{35}}}$and $24.47%\,{{\,}_{17}}C{{l}^{37}}$having a mass of 34.97 amu and 36.95 amu, respectively. The atomic weight of chloride is:

A) 35.25

B) 35.45

C) 36.25

D) 36.45

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• question_answer71) The solubility of $A{{g}_{2}}S$is $[{{K}_{sp}}=256\times {{10}^{-6}}]:$

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

B) $4\times {{10}^{-3}}$

C) $0.4\times {{10}^{-2}}$

D) $0.4\times {{10}^{-3}}$

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• question_answer72) Marsh gas contains:

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

B) ${{C}_{2}}{{H}_{6}}$

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

D) $C{{H}_{4}}$

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• question_answer73) The ion present in Nesslers reagent is:

A) $Hg{{I}_{2}}$

B) $HgI_{4}^{2-}$

C) $H{{g}^{2+}}$

D) $H{{g}^{+}}$

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• question_answer74) Vitamin ${{\text{B}}_{\text{12}}}$ contains:

A) Cu

B) Fe

C) Mg

D) Co

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• question_answer75) 720 g of water contains how many moles of water:

A) 20

B) 40

C) 60

D) 80

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• question_answer76) $Zn(s)+C{{u}^{2+}}(aq)\xrightarrow{{}}Cu(s)+Z{{n}^{2+}}(aq)$ The emf of above reaction is 1.10 V at $\text{25}{{\,}^{\text{o}}}\text{C}\text{.}$ Find emf of cell well when $[Z{{n}^{2+}}]=0.1\,M$$[C{{u}^{2+}}]=0.1\,M$

A) $1.10\text{ V}$

B) $~-1.10\text{ V}$

C) $~0.110\text{ V}$

D) $~-0.110\text{ V}$

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• question_answer77) The colour of iodine solution is discharged by shaking it with aqueous solution of:

A) sodium sulphite

B) sulphuric acid

C) sodium sulphate

D) sodium thiosulphite

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• question_answer78) Nitrobenzene on treatment with $\text{B}{{\text{r}}_{\text{2}}}$produce

A) o, p-bromobenzene

B) p-bromonitrobenzene

C) m-bromonitrobenzene

D) none of the above

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• question_answer79) The entropy change $(\Delta S)$ in a system increase as:

A) solid < liquid < gas

B) liquid < gas < solid

C) solid < gas < liquid

D) gas < solid < liquid

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• question_answer80) The element having maximum hydration energy is:

A) Na

B) K

C) Rb

D) Cs

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• question_answer81) The total number of electrons present in all the p-orbitals of bromine is:

A) 7

B) 17

C) 27

D) 37

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• question_answer82) The rate constant of third order reaction is:

A) $\text{mol}\,{{\text{L}}^{-1}}{{\text{S}}^{-1}}$

B) $\text{mo}{{\text{l}}^{-2}}\,{{\text{L}}^{2}}{{T}^{-1}}$

C) $\text{mo}{{\text{l}}^{-1}}\,\text{L}{{\text{s}}^{-1}}$

D) $mo{{l}^{-2}}{{L}^{-1}}{{S}^{-1}}$

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• question_answer83) By the reduction of carbonyl compounds the alcohol not obtained is:

A) primary alcohol

B) secondary alcohol

C) tertiary alcohol

D) all of the above

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• question_answer84) The mixture of gases used for asthma patients is:

A) ${{O}_{2}}+He$

B) ${{O}_{2}}+Ne$

C) ${{O}_{2}}+{{H}_{2}}$

D) ${{O}_{2}}+Ar$

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• question_answer85) Acetate ion have:

A) two carbon, oxygen double bond

B) two carbon, oxygen single bond

C) one carbon, oxygen single bond and on carbon, oxygen double bond

D) none of the above

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• question_answer86) The difference between energy of product an energy of reactant is called:

A) entropy

B) heat content

C) heat of fusion

D) activation energy

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• question_answer87) The most covalent bond is:

A) $C-S$

B) $C-O$

C) $C-F$

D) $C-Br$

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• question_answer88) A Solution is made up of 10 mL of $\text{0}\text{.1}\,\text{N}\,\text{NaOH}$and 10 mL of $\text{0}\text{.05}\,\text{N}{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\text{.}$The $\text{pH}$of solution is:

A) 7

B) $>7$

C) $<7$

D) None of these

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• question_answer89) The addition of 1% alcohol to chloroform acts as a:

A) positive catalyst

B) negative catalyst

C) autocatalyst

D) none of these

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• question_answer90) $C{{H}_{3}}-CH=CH-C{{H}_{3}}$on ozonolysis produce:

A) acetaldehyde

B) mixture of acetaldehyde and ethyl alcohol

C) ethyl alcohol

D) mixture of acetone and acetaldehyde

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• question_answer91) Nitroalkane which do not exhibit tautomerism is:

A) ${{3}^{o}}-$nitroalkane

B) ${{2}^{o}}-$nitroalkane

C) ${{1}^{o}}-$nitroalkane

D) all of these

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• question_answer92) The paramagnetic element is:

A) $N{{i}^{2+}}$

B) $S{{c}^{3+}}$

C) $C{{u}^{+}}$

D) $Z{{n}^{2+}}$

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• question_answer93) Addition of HBr on propene produce:

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

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

C) $C{{H}_{3}}-\underset{Br}{\mathop{\underset{|}{\mathop{CH}}\,}}\,-C{{H}_{3}}$

D) none of the above

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• question_answer94) Which of the following is not a planar compound?

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

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

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

D) None of these

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• question_answer95) The saturated pentane have total number of isomers are:

A) 5

B) 4

C) 6

D) 3

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• question_answer96) $Mn{{O}_{2}}(s)+4HCl(aq)\xrightarrow{Heat}$ $MnC{{l}_{2}}(aq)+2{{H}_{2}}O+C{{l}_{2}}(g)$ The equivalent weight of $Mn{{O}_{2}}$in the above reaction is:

A) 23.4

B) 33.6

C) 43.5

D) 53.6

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• question_answer97) Tetraethyl lead is used as:

A) fire extinguisher

B) mosquito repellent

C) petroleum additive

D) none of the above

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• question_answer98) 4 moles of A are mixed with 4 moles of B and 2 moles of C are formed at equilibrium according to following reaction, $A+BC+D.$The value of equilibrium constant is:

A) 1

B) 4

C) $\frac{1}{4}$

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

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• question_answer99) The vapour pressure of benzene at a certain temperature is 200 mm Hg. At the same temperature the vapour pressure of a solution containing 2 g of non volatile non electrolyte solid in 78 g of benzene is 195 mm Hg. The molecular weight of solid is:

A) 20

B) 40

C) 60

D) 80

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• question_answer100) The metal not present in hard water is:

A) Ca

B) Na

C) Mg

D) Fe

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• question_answer101) The value of ${{(-i)}^{1/3}}$ is:

A) $\frac{1+\sqrt{3}i}{2}$

B) $\frac{1-\sqrt{3}i}{2}$

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

D) None of these

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• question_answer102) If $i=\sqrt{-1},$then $1+{{i}^{2}}+{{i}^{3}}-{{i}^{6}}+{{i}^{8}}$ is equal to:

A) $2-i$

B) 1

C) 3

D) $-1$

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• question_answer103) The series $\frac{5}{\sqrt{7}},\frac{6}{\sqrt{7}},\sqrt{7},...$is:

A) HP

B) GP

C) AP

D) none of these

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• question_answer104) 8th term of the series $2\sqrt{2}+\sqrt{2}+0+...$will be:

A) $-5\sqrt{2}$

B) $5\sqrt{2}$

C) $-10\sqrt{2}$

D) $10\sqrt{2}$

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• question_answer105) The roots of the equation $a({{x}^{2}}+1)-({{a}^{2}}+1)x=0$are:

A) $a,\frac{1}{a}$

B) $a,2a$

C) $a,\frac{1}{2a}$

D) none of these

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• question_answer106) The boolean function of the input/output table as shown below is:

 Input Output ${{x}_{1}}$ ${{x}_{2}}$ ${{x}_{3}}$ S 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1

A) $f({{x}_{1}},{{x}_{2}},{{x}_{3}})={{x}_{1}}{{x}_{2}}{{x}_{3}}+{{x}_{1}}{{x}_{2}}x_{3}^{}$$+\,{{x}_{1}}x{{}_{2}}{{x}_{3}}+x{{}_{1}}x{{}_{2}}x{{}_{3}}$

B) $f({{x}_{1}},{{x}_{2}}{{x}_{3}})=x{{}_{1}}x{{}_{2}}x{{}_{3}}+x{{}_{1}}x{{}_{2}}x{{}_{3}}$$+\,x{{}_{1}}x{{ }_{2}}x{{}_{3}}+{{x}_{1}}{{x}_{2}}{{x}_{3}}$

C) $f({{x}_{1}},{{x}_{2}},{{x}_{3}})={{x}_{1}}x{{}_{2}}x{{}_{3}}+x{{}_{1}}{{x}_{2}}x{{}_{3}}$

D) $f({{x}_{1}},{{x}_{2}},{{x}_{3}})=x{{}_{1}}{{x}_{2}}{{x}_{3}}+{{x}_{1}}x{{}_{2}}{{x}_{3}}$

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• question_answer107) The number of a triangle that can be formed by 5 points in a line and 3 points on a parallel line, is:

A) ${{\,}^{8}}{{C}_{3}}$

B) ${{\,}^{8}}{{C}_{3}}-{{\,}^{5}}{{C}_{3}}$

C) ${{\,}^{8}}{{C}_{3}}-{{\,}^{5}}{{C}_{3}}-1$

D) none of these

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• question_answer108) In how many ways can 5 keys be put in a ring:

A) $\frac{1}{2}4!$

B) $\frac{1}{2}5!$

C) $4!$

D) $5!$

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• question_answer109) The 6th term in expansion of ${{\left( 2{{x}^{2}}-\frac{1}{3{{x}^{2}}} \right)}^{10}},$is:

A) $\frac{4580}{17}$

B) $-\frac{896}{27}$

C) $\frac{5580}{17}$

D) none of these

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• question_answer110) If $n=2m,$then the middle term in the expansion of ${{(x+a)}^{n}}$will be:

A) $m\,th$

B) $(n-1)\,th$

C) $(m+1)th$

D) $(m+2)th$

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• question_answer111) In the expailsion of$\frac{{{e}^{4x}}-1}{{{e}^{2x}}}$the coefficient of ${{x}^{2}}$is:

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

B) 1

C) 0

D) none of these

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• question_answer112) $\left( \frac{a-b}{a} \right)+\frac{1}{2}{{\left( \frac{a-b}{a} \right)}^{2}}+\frac{1}{3}{{\left( \frac{a-b}{a} \right)}^{3}}+...$

A) ${{\log }_{e}}(a-b)$

B) ${{\log }_{e}}\left( \frac{a}{b} \right)$

C) ${{\log }_{e}}\left( \frac{b}{a} \right)$

D) ${{e}^{\left( \frac{a-b}{a} \right)}}$

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• question_answer113) The number of solutions of equations $x+y-z=0,3x-y-z=0,x-3y+1=0$is:

A) 0

B) 1

C) 2

D) infinite

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• question_answer114) If A is involutory matrix and I is unit matrix of same order, then $(I-A)(I+A)$ is:

A) zero matrix

B) A

C) $I$

D) 2A

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• question_answer115) If $\sin \theta +\cos ec\theta =2,$then ${{\sin }^{2}}\theta +\cos {{\sec }^{2}}\theta$ is equal to:

A) 1

B) 4

C) 2

D) none of these

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• question_answer116) If $(A-B)=\frac{\pi }{4},$then $(1+\tan A)(1-\tan B)$ equal to:

A) 1

B) 2

C) $~-1$

D) $-2$

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• question_answer117) If $\sin \theta +\cos \theta =1,$ then the general value of $\theta$ is:

A) $2n\pi$

B) $n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{4}$

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

D) none of these

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• question_answer118) If$\sin \theta =\sqrt{3}\cos \theta ,-\pi <\theta <0,$ then $\theta$is equal to:

A) $-\frac{5\pi }{6}$

B) $-\frac{4\pi }{6}$

C) $\frac{4\pi }{6}$

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

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• question_answer119) If ${{\cos }^{-1}}\left( \frac{1}{x} \right)=\theta ,$ then tan 9is equal to:

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

B) $\sqrt{{{x}^{2}}+1}$

C) $\sqrt{1-{{x}^{2}}}$

D) $\sqrt{{{x}^{2}}-1}$

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• question_answer120) If$\cos (2{{\sin }^{-1}}x)=\frac{1}{9},$ then $x$ is equal to:

A) only$2/3$

B) only$-2/3$

C) $-2/3$or $2/3$

D) neither 2/3 nor $-2/3$

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• question_answer121) If p and q are two statements, then statement $p\Rightarrow q\wedge \tilde{\ }q$is:

A) tautology

B) contradiction

C) neither tautology nor contradiction

D) none of the above

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• question_answer122) Three points $(p+1,1),(2p+1,3)$ and $(2p+2,2p)$ are collinear, the value of p is equal to:

A) $-1$

B) 1

C) 2

D) 0

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• question_answer123) The distance between the lines $y=mx+{{c}_{1}}$and $y=m\text{ }x+{{C}_{2}}$is:

A) $\frac{{{c}_{1}}-{{c}_{2}}}{\sqrt{{{m}^{2}}+1}}$

B) $\frac{{{c}_{2}}-{{c}_{1}}}{\sqrt{{{m}^{2}}+1}}$

C) $\frac{{{c}_{2}}\tilde{\ }{{c}_{1}}}{\sqrt{{{m}^{2}}+1}}$

D) 0

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• question_answer124) The lines $(p-q)x+(q-r)y+(r-p)=0$ $(q-r)x+(r-p)y+(p-q)=0$ $(r-p)x+(p-q)y+(q-r)=0$are:

A) parallel

B) perpendicular

C) concurrent

D) none of these

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• question_answer125) The equation ${{(x+y)}^{2}}-({{x}^{2}}+{{y}^{2}})=0$ represents:

A) a circle

B) two lines

C) two parallel lines

D) two mutually perpendicular lines

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• question_answer126) Two lines represented by equation ${{x}^{2}}++xy+{{y}^{2}}=0$ are:

A) coincident

B) parallel

C) mutually perpendicular

D) imaginary

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• question_answer127) The equation of the diameter of the circle ${{x}^{2}}+{{y}^{2}}+2x-4y-11=0$ which bisects the chords intercepted on the line $2x-y+3=0$ is:

A) $x+y-7=0$

B) $2x-y-5=0$

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

D) none of these

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• question_answer128) The angle between the two tangents from the origin to the circle ${{(x-1)}^{2}}+{{(y+1)}^{2}}=25$is:

A) 0

B) $\pi /3$

C) $\pi /6$

D) $\pi /2$

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• question_answer129) The equation $13[{{(x-1)}^{2}}+{{(y-2)}^{2}}]=3{{(2x+3y-2)}^{2}}$ represents:

A) parabola

B) ellipse

C) hyperbola

D) none of these

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• question_answer130) The equation of the hyperbola whose directrix is $x+2y=1,$focus $(2,1)$ and eccentricity 2 will be:

A) ${{x}^{2}}-16xy-11{{y}^{2}}-12x+6y+21=0$

B) $3{{x}^{2}}+16xy+15{{y}^{2}}-4x-14y+1=0$

C) ${{x}^{2}}+16xy+11{{y}^{2}}-12x+6y+21=0$

D) none of the above

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• question_answer131) The angle between the lines whose direction ratios are $a,\text{ }b,\text{ }c$and $b-c,c-a,a-b$is:

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

B) ${{\sin }^{-1}}\left( \frac{1}{abc} \right)$

C) ${{0}^{o}}$

D) ${{90}^{o}}$

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• question_answer132) The angle between the planes $3x-4y+5z=0$ and $2x-y-2z=5$is:

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

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

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

D) none of these

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• question_answer133) The vector $2\hat{i}+\hat{j}-\hat{k}$is perpendicular to $\hat{i}-4\hat{j}+\lambda \hat{k},$then $\lambda$ is equal to:

A) 0

B) 1

C) $-2$

D) $-3$

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• question_answer134) If the angle between the unit vectors $\vec{a}$and $\vec{b}$be ${{60}^{o}},$ then $(2\vec{a}-3\vec{b}).(4\vec{a}+\vec{b})$is equal to:

A) 0

B) 5

C) 15

D) none of these

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• question_answer135) $\underset{x\to 0}{\mathop{\lim }}\,\frac{x({{e}^{x}}-1)}{1-\cos x}$is equal to:

A) 0

B) $\infty$

C) 2

D) ${{e}^{2}}$

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• question_answer136) Domain of the function $f(x)=\frac{1}{\sqrt{x+2}}$is:

A) R

B) $(-2,\infty )$

C) $(2,\infty )$

D) $(0,\infty )$

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• question_answer137) The derivative of $\log (\tan x)$is equal to:

A) $2\text{ }sec\text{ }2x$

B) $2\cos ec2x$

C) $\sec 2x$

D) $\cos ec2x$

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• question_answer138) The derivative of ${{\cos }^{-1}}\frac{x-{{x}^{-1}}}{x+{{x}^{-1}}}$is equal to:

A) $\frac{1}{1+{{x}^{2}}}$

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

C) $\frac{2}{1+{{x}^{2}}}$

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

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• question_answer139) $\int_{{}}^{{}}{\frac{{{x}^{2}}dx}{{{(a+bx)}^{2}}}}$is equal to:

A) $\frac{1}{{{b}^{2}}}\left[ x+\frac{2a}{b}log(a+bx)-\frac{{{a}^{2}}}{b}\left( \frac{1}{a+bx} \right) \right]+c$

B) $\frac{1}{{{b}^{2}}}\left[ x-\frac{2a}{b}log(a+bx)+\frac{{{a}^{2}}}{b}\left( \frac{1}{a+bx} \right) \right]+c$

C) $\frac{1}{{{b}^{2}}}\left[ x+\frac{2a}{b}log(bx+a)+\frac{{{a}^{2}}}{b}.\frac{1}{a+bx} \right]+c$

D) $\frac{1}{{{b}^{2}}}\left[ x+\frac{a}{b}-\frac{2a}{b}\log (a+bx)-\frac{{{a}^{2}}}{b}\left( \frac{1}{a+bx} \right) \right]+c$

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• question_answer140) $\int_{{}}^{{}}{\frac{dx}{1+{{e}^{x}}}}$is equal to:

A) $\log (1+{{e}^{x}})+c$

B) $-\log (1+{{e}^{-x}})+c$

C) $-\log (1-{{e}^{-x}})+c$

D) $\log ({{e}^{-x}}+{{e}^{-2x}})+c$

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• question_answer141) $\,\int_{0}^{a}{\frac{{{x}^{4}}dx}{{{({{a}^{2}}+{{x}^{2}})}^{4}}}}$is equal to:

A) $\frac{1}{16{{a}^{3}}}\left( \frac{\pi }{4}-\frac{1}{3} \right)$

B) $\frac{1}{16{{a}^{3}}}\left( \frac{\pi }{4}+\frac{1}{3} \right)$

C) $\frac{1}{16}{{a}^{3}}\left( \frac{\pi }{4}-\frac{1}{3} \right)$

D) $\frac{{{a}^{3}}}{16}\left( \frac{\pi }{4}+\frac{1}{3} \right)$

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• question_answer142) Area bounded by the curve ${{x}^{4}}=4y$and the straight line $x=4y-2$is:

A) $\frac{\text{8}}{\text{9}}\,\text{sq}\,\text{unit}$

B) $\frac{9}{8}\,\text{sq}\,\text{unit}$

C) $\frac{4}{3}\,\text{sq}\,\text{unit}$

D) none of these

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• question_answer143) The order and degree of the differential equation $y=x\frac{dy}{dx}+\sqrt{{{a}^{2}}{{\left( \frac{dy}{dx} \right)}^{2}}+{{b}^{2}}}$are:

A) 1, 2

B) 2, 1

C) 1, 1

D) 2, 2

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• question_answer144) $y=4\sin 3x$is a solution of the differential equation:

A) $\frac{dy}{dx}+8y=0$

B) $\frac{dy}{dx}-8y=0$

C) $\frac{{{d}^{2}}y}{d{{x}^{2}}}+9y=0$

D) $\frac{{{d}^{2}}y}{d{{x}^{2}}}-9y=0$

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• question_answer145) If A and B are two events such that $A\subseteq B,$then $p\left( \frac{B}{A} \right)$is equal to:

A) 0

B) $1$

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

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

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• question_answer146) In shuffling a pack of playing cards, four are accidently dropped. The probability that the missing cards should be one from each suit, is:

A) $\frac{1}{{{\,}^{52}}{{C}_{4}}}$

B) $\frac{{{({{\,}^{13}}{{C}_{1}})}^{4}}}{{{\,}^{52}}{{C}_{4}}}$

C) $\frac{{{({{\,}^{13}}{{C}_{2}})}^{2}}}{{{\,}^{52}}{{C}_{4}}}$

D) $\frac{{{({{\,}^{13}}{{C}_{4}})}^{4}}}{{{\,}^{52}}{{C}_{4}}}$

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• question_answer147) If a point moves in a straight line so that its displacement s at time t is given by ${{s}^{2}}=1+{{t}^{2}},$then its acceleration at time t is:

A) $\frac{1}{{{s}^{3}}}$

B) $-\frac{1}{{{s}^{2}}}$

C) $\frac{1}{s}-\frac{{{t}^{2}}}{{{s}^{3}}}$

D) $\frac{1}{s}-\frac{1}{{{s}^{2}}}$

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• question_answer148) A stone is thrown vertically upwards with an initial velocity $u.$From the top of a tower reaches the ground with a velocity $3u.$ The height of the tower is:

A) $\frac{3{{u}^{2}}}{g}$

B) $\frac{4{{u}^{2}}}{g}$

C) $\frac{6{{u}^{2}}}{g}$

D) $\frac{9{{u}^{2}}}{g}$

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• question_answer149) Two forces P and Q have a resultant R and the resolved part of R in the direction of P is of magnitude Q. Then the angle between the forces is:

A) ${{\sin }^{-1}}{{\left( \frac{P}{2Q} \right)}^{1/2}}$

B) $2{{\sin }^{-1}}{{\left( \frac{P}{2Q} \right)}^{1/2}}$

C) ${{\cos }^{-1}}{{\left( \frac{P}{2Q} \right)}^{1/2}}$

D) $2{{\cos }^{-1}}{{\left( \frac{P}{2Q} \right)}^{1/2}}$

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• question_answer150) The resultant of two like parallel forces is 12N. The distance between the forces is 18 m. If one force is of 4N, then the distance of the resultant from the smaller force is:

A) 4 m

B) 8 m

C) 12 m

D) none of these

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