# Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2009

### done BCECE Engineering Solved Paper-2009

• question_answer1) A rectangular coil of 100 turns and size $0.1\times 0.05$ m is placed perpendicular to a magnetic field of 0.1 T. The induced emf when the field drops to 0.05 T in 0.05 s is

A) 0.5 V

B) 1.0 V

C) 1.5 V

D) 2.0 V

• question_answer2) A paramagnetic substance is placed in a weak magnetic field and its absolute temperature T is increased. As a result, its magnetization

A) increases in proportion to T

B) decreases in proportion to $\frac{1}{T}$

C) increases in proportion to${{T}^{2}}$

D) decreases in proportion to $\frac{1}{{{T}^{2}}}$

• question_answer3) The current through n bulb is increased by. Assuming that the resistance of the filament remains unchanged the power of the bulb will

A) increase by 1%

B) decrease by 1%

C) increase by 2%

D) decrease by 2%

• question_answer4) You are given two resistances ${{R}_{1}}$ and${{R}_{2}}$ By using them singly in series and In parallel you can obtain four resistances of $1.5\,\Omega ,\,2\,\Omega ,\,6\,\Omega$ and 8 $\Omega .$ The values of ${{R}_{1}}$ and ${{R}_{2}}$ are

A) $1\,\,\Omega ,\,7\,\Omega$

B) $1.5\,\,\Omega ,\,6.5\,\Omega$

C) $3\,\,\Omega ,\,5\,\Omega$

D) $2\,\,\Omega ,\,6\,\Omega$

• question_answer5) A wire often the $l$ carrying a current $I$ A is bent into a circle. The magnitude of the magnetic moment is

A) $\frac{l{{I}^{2}}}{2\pi }$

B) $\frac{l{{I}^{2}}}{4\pi }$

C) $\frac{{{l}^{2}}I}{2\pi }$

D) $\frac{{{l}^{2}}I}{4\pi }$

• question_answer6) A parallel beam of white light is reflected from a thin wedge-shaped film. The colour of the fringe the edge of the wedge will be

A) white

B) red

C) black

D) violet

• question_answer7) An object is placed at the focus of a convex mirror. If its focal length is 20 cm, the distance of mirror is

A) 20 cm

B) 10 cm

C) 40 cm

D) None of these

• question_answer8) A convex lens of glass ($\mu =1$ of 8 cm when place in has a focal length of lens when air. What is the focal $\left( \mu =\frac{4}{3} \right)?$

A) $4cm$

B) $8\,cm$

C) $16\,cm$

D) $32\,cm$

• question_answer9) An LCR series circuit, connected to a source E, is resonance. Then

A) the voltage across R is zero

B) the voltage across R equals applied voltage

C) the voltage across C is zero

D) the voltage across L equals applied voltage

• question_answer10) What will be the colour of the sky as seen from the earth if there were no atmosphere?

A) Black

B) Blue

C) Orange

D) Red

• question_answer11) In a single slit diffraction experiment, the width of the slit is made double its original width. Then the central maximum on the diffraction pattern will become

A) narrower and fainter

B) narrower and brighter

• question_answer12) An $\alpha -$particle and a deuteron projected with equal kinetic energies describe circular paths or radii ${{r}_{1}}$ and${{r}_{2}}$ respectively in a uniform magnetic field. The ratio${{\text{r}}_{\text{1}}}\text{/}{{\text{r}}_{\text{2}}}$ is

A) 1

B) 2

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

D) $\sqrt{2}$

• question_answer13) The energy in monochromatic X-rays of wavelength $1\,\overset{\text{o}}{\mathop{\text{A}}}\,$ is roughly equal to

A) $\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-15}}}\text{J}$

B) $\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-16}}}\text{J}$

C) $\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-17}}}\text{J}$

D) $\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-18}}}\text{J}$

• question_answer14) The de-Broglie wavelength of a neutron at 927?C is $\lambda$. What will be its wavelength at 27?C?

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

B) $\lambda$

C) $2\lambda$

D) None of these

• question_answer15) A telescope has an objective of focal length 100 cm and an eye-piece of focal length 5 cm. What is the magnifying power of the telescope when it is in normal adjustment?

A) 0.2

B) 2.0

C) 20

D) 200

• question_answer16) An isotropic source of 2 candela produces a light flux equal to

A) $2\pi$ lumen

B) $4\pi$ lumen

C) $6\pi$ lumen

D) $8\pi$ lumen

• question_answer17) No photoelectrons are emitted from a metal if the wavelength of the light exceeds 600 nm. The work function of the metal is approximately equal to

A) $\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-16}}}\text{J}$

B) $\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-19}}}\text{J}$

C) $\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-20}}}\text{J}$

D) $\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-22}}}\text{J}$

• question_answer18) In Rutherfords$\alpha -$particle experiment with thin gold foil, 8100 scintillations per minute are observed at an angle of 60?. The number of scintillations per minute at an angle of 120? will be

A) 900

B) 2025

C) 32400

D) 4050

• question_answer19) Which of the following gates has the truth table

 A B X 0 0 1 1 0 1 0 1 1 1 1 0

A) NAND

B) NOR

C) XOR

D) AND

• question_answer20) Which of the junction diodes shown below are forward biased?

A) B) C) D) • question_answer21) A uniform rod or mass m and length l is held ${{60}^{\text{o}}}$ with the vertical. . What will be the potential this position?

A) Zero

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

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

D) $mgl$

• question_answer22) A sphere roils down an inclined plane without slipping. What fraction of its total energy is rotational?

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

B) $\frac{3}{7}$

C) $\frac{4}{7}$

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

• question_answer23) 23. From the top of a building 40 m tall, a boy projects a Stone vertically upwards with an initial velocity $10\,m{{s}^{-1}}$ such that it eventually falls to the ground. After how long will the stone strike the ground? Take $g=10\,m{{s}^{-2}}$

A) 1 s

B) 2 s

C) 3 s

D) 4 s

• question_answer24) A 150 m long train is travelling from east to west at a speed of $20\,m{{s}^{-1}}$. A bird is flying from west to east at a speed of $5\,m{{s}^{-1}}$. How long wilt the bird take to cross the train?

A) 6 s

B) 7.5 s

C) 10 s

D) 30 s

• question_answer25) An elastic spring has a length ${{l}_{1}}$ when it is stretched with a force of 2 N and a length of ${{l}_{2}}$ when it is stretched with a force of 3N. What will be the length of the spring if it is stretched with force of 5N?

A) $(l{{ }_{1}}+{{l}_{2}})$

B) $\frac{1}{2}(l{{ }_{1}}+{{l}_{2}})$

C) $(3l{{ }_{2}}-2{{l}_{1}})$

D) $(3l{{ }_{1}}-2{{l}_{2}})$

• question_answer26) The density of water at the surface of ocean is $\rho$ If the bulk modulus of water is B, what is the density of ocean water at a depth where the pressure is$n{{p}_{0,}}$ where${{p}_{0,}}$ is the atmospheric pressure?

A) $\frac{\rho B}{B-(n-1){{P}_{0}}}$

B) $\frac{\rho B}{B+(n-1)P0}$

C) $\frac{\rho B}{B-n{{P}_{0}}}$

D) $\frac{\rho B}{B+n{{P}_{0}}}$

• question_answer27) What is the torque of force $\mathbf{\hat{F}}=-3\mathbf{\hat{i}}+\mathbf{\hat{j}}+5\mathbf{\hat{k}}$ acting at point whose position vector is$\mathbf{\vec{r}}=7\mathbf{\hat{i}}+3\mathbf{\hat{j}}+\mathbf{\hat{k}}?$

A) $14\mathbf{\hat{i}}-38\mathbf{\hat{j}}+16\mathbf{\hat{k}}$

B) $4\mathbf{\hat{i}}+4\mathbf{\hat{j}}+6\mathbf{\hat{k}}$

C) $-14\mathbf{\hat{i}}+38\mathbf{\hat{j}}-6\mathbf{\hat{k}}$

D) $-21\mathbf{\hat{i}}+3\mathbf{\hat{j}}+5\mathbf{\hat{k}}$

• question_answer28) Two satellites of masses 3M and M orbit the earth in circular orbits of radii r and 3r respectively. The ratio of their speeds is

A) 1 : 1

B) $\sqrt{3}$: 1

C) 3 : 1

D) 9 : 1

• question_answer29) The dimensions of Reynoldss constant are

A) $\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{o}}}{{\text{L}}^{\text{o}}}{{\text{T}}^{\text{o}}}\text{ }\!\!]\!\!\text{ }$

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

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

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

• question_answer30) The surface tension of soap solution is $\sigma$. What is the work done in blowing soap bubble of radius r?

A) $\pi {{r}^{2}}\sigma$

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

C) $4\pi {{r}^{2}}\sigma$

D) $8\pi {{r}^{2}}\sigma$

• question_answer31) The ratio of nns speed of ${{O}_{2}}$ to ${{H}_{2}}$ is

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

B) 4

C) 2

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

• question_answer32) Two rods A and B of different materials are welded together as shown in figure. If their thermal conductivities are ${{K}_{1}}$ and${{K}_{2}}$ the thermal conductivity of the composite rod will be

A) $2({{K}_{1}}+{{K}_{2}})$

B) $\frac{3}{2}({{K}_{1}}+{{K}_{2}})$

C) $({{K}_{1}}+{{K}_{2}})$

D) $\frac{1}{2}({{K}_{1}}+{{K}_{2}})$

• question_answer33) The wavelength of the radiation emitted by a body depends upon

A) the nature of its surface

B) the area of its surface

C) the temperature of its surface

D) All the above factors

• question_answer34) An ideal monoatomic gas is taken around the cycle ABCDA as shown in the p- V diagram. The work done during the cycle is given by A) $\frac{1}{2}pV$

B) $pV$

C) $2pV$

D) $4pV$

• question_answer35) An ideal gas at pressure p is adiabaticalty compressed so that its density becomes n times the initial value. The final pressure of the gas will be$\left( \gamma =\frac{{{C}_{P}}}{{{C}_{V}}} \right)$

A) ${{n}^{\gamma }}P$

B) ${{n}^{-\gamma }}P$

C) ${{n}^{(-\gamma -1)}}P$

D) ${{n}^{(1-\gamma )}}P$

• question_answer36) The displacement of a travelling wave is given by$y=2\,\cos \,2\pi \,(10t-\,0.008\,x\,+\,.35)$ where, x and y are in centimetre and t in second. What is the phase difference between oscillatory motion at two points separated by a distance of 4 m?

A) $2\pi$

B) $4\pi$

C) $6\pi$

D) $8\pi$

• question_answer37) A bimetallic strip consists of brass and iron when it is heated it bends into an arc with brass on the convex and iron on the concave side of the arc. This happens because

A) brass has a higher specific heat capacity than iron

B) density of brass is more than that of iron

C) it is easier to bend an iron strip than a brass strip of the same size

D) brass has a higher coefficient of linear expansion than iron

• question_answer38) Three sound waves of equal amplitudes have frequencies (v -1), v, (v + 1). They superpose to give beats. The number of beats produced per second will be

A) v

B) v/2

C) 2

D) 1

• question_answer39) Which of the following functions does not represent a stationary wave? Here a, b and c are constants.

A) $y=a\,\cos bx\,\sin ct$

B) $y=a\sin bx\,\cos \,ct$

C) $y=a\,\sin (bx+ct)$

D) $y=a\sin (bx+ct)\,+a\,\sin \,(bx-ct)$

• question_answer40) The velocity of sound is greatest in

A) water

B) air

C) vacuum

D) steel

• question_answer41) Due to Doppler effect, the shift in wavelength observed is $0.1\,\overset{\text{o}}{\mathop{\text{A}}}\,,$ for a star producing wavelength $6000\overset{\text{o}}{\mathop{\text{A}}}\,$. The velocity of recession of star will be

A) $2.5\,km{{s}^{-1}}$

B) $10\,km{{s}^{-1}}$

C) $5\,km{{s}^{-1}}$

D) $20\,km{{s}^{-1}}$

• question_answer42) A body executing linear simple harmonic motion has a velocity of $3\,m{{s}^{-1}}$ when its displacement is 4 cm and a velocity of $4\,m{{s}^{-1}}$ when its displacement is 3 cm. What is the amplitude of oscillation?

A) 5 cm

B) 7.5 cm

C) 10 cm

D) 12.5 cm

• question_answer43) Two masses ${{m}_{1}}$ and${{m}_{2}}$ are suspended together by a massless spring of force constant k, as shown in figure. When the masses are in equilibrium, mass ${{m}_{1}}$is removed without disturbing the system. The angular frequency of oscillation of mass ${{m}_{2}}$ is

A) $\sqrt{\frac{k}{{{m}_{2}}}}$

B) $\sqrt{\frac{k}{{{m}_{1}}}}$

C) $\sqrt{\frac{k{{m}_{1}}}{m\,_{2}^{2}}}$

D) $\sqrt{\frac{k{{m}_{2}}}{m_{1}^{2}\,}}$

• question_answer44) The intensity level of a sound wave is defined by an arbitrary scale. The zero of the scale is taken at the sound wave intensity

A) $\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-10}}}\,\text{W}{{\text{m}}^{\text{-2}}}$

B) $\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-12}}}\,\text{W}{{\text{m}}^{\text{-2}}}$

C) $\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-14}}}\,\text{W}{{\text{m}}^{\text{-2}}}$

D) $\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-16}}}\,\text{W}{{\text{m}}^{\text{-2}}}$

• question_answer45) A pendulum bob of mass m carrying a charge q is at rest with its string making an angle $\theta$ with the vertical in a uniform horizontal electric field E. The tension in the siring is

A) $\frac{\text{mg}}{\text{sin}}\text{and}\frac{\text{qE}}{\text{cos}\,}$

B) $\frac{\text{mg}}{\text{cos}}\text{and}\frac{\text{qE}}{\sin \,}$

C) $\frac{\text{qE}}{mg}$

D) $\frac{mg}{\text{qE}}$

• question_answer46) A galvanometer of resistance 10 $\Omega$ gives full-scale deflection when 1 mA current passes through it. The resistance required to convert it into a voltmeter reading upto 2.5 V is

A) $24.9\,\Omega$

B) $249\,\Omega$

C) $2490\,\Omega$

D) $24900\,\Omega$

• question_answer47) The current inside an electrolytic cell is carried by

A) positive ions

B) negative ions

C) both positive and negative ions

D) electrons

• question_answer48) The electric potential V (in volt) varies with x (in metre) according to the relation $V=(5+4{{x}^{2}})$. The force experienced by a negative charge of 2x10-6C located at a =0.5 m is

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

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

C) $\text{6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-6}}}\text{N}$

D) $\text{8 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-6}}}\text{N}$

• question_answer49) A parallel plate capacitor of plate area A has a charge Q. The force on each plate of the capacitor is

A) $\frac{2{{Q}^{2}}}{{{\varepsilon }_{0}}A}$

B) $\frac{{{Q}^{2}}}{{{\varepsilon }_{0}}A}$

C) $\frac{{{Q}^{2}}}{2{{\varepsilon }_{0}}A}$

D) Zero

• question_answer50) In Millikans oil drop experiment, an oil drop is observed to move vertically upwards. The upward motion of the drop is due to

A) gravity

B) viscosity

C) buoyancy

D) electric field

• question_answer51) Which one of these is an important polysaccharide present in plants?

A) Glucose

B) Glycogen

C) Sucrose

D) Starch

• question_answer52) Cannizaro reaction would be given by

A) ${{C}_{6}}{{H}_{5}}CHO$

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

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

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

• question_answer53) $C{{H}_{3}}C\equiv CH\xrightarrow[+H{{g}^{2+}},60{{\,}^{o}}C]{{{H}_{2}}S{{O}_{4}}}$?

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

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

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

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

• question_answer54) In which of the following can peroxide effect operate?

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

B) $C{{H}_{3}}C{{H}_{2}}CH=C{{H}_{2}}+HBr$

C) $C{{H}_{3}}CH=CH.C{{H}_{3}}+HBr$

D) $C{{H}_{3}}C{{H}_{2}}CH=C{{H}_{2}}+HI$

• question_answer55) The term quaternary structure is used in the context of

A) carbohydrates

B) vitamins

C) proteins

D) nucleic acids

A) antibiotic

B) sedative

C) tranquilizer

D) antipyretic

• question_answer57) The following is a coordination compound of iron

A) chlorophyll

B) Mohrs salt

C) haemoglobin

D) vitamin ${{B}_{12}}$

• question_answer58) This metal is extracted from its ore by formation of a cyanide complex

A) $Ag$

B) $Cu$

C) $Al$

D) $Zn$

• question_answer59) Smoke is an example of

A) emulsion

B) aerosol

C) gel

D) foam

• question_answer60) Propan-2-ol + ethanoic acid$\xrightarrow{{}}$

A) ${{(C{{H}_{3}})}_{2}}CHCOOC{{H}_{3}}$

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

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

D) ${{(C{{H}_{3}})}_{2}}CHCOOC{{H}_{2}}C{{H}_{3}}$

• question_answer61) Which of the following gives RNC when treated with $CHC{{l}_{3}}$and KOH?

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

B) ${{R}_{2}}NH$

C) ${{R}_{4}}{{N}^{+}}C{{l}^{-}}$

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

• question_answer62) Which of the following is a soap?

A) Sodium acetate

B) Magnesium butyrate

C) Sodium palmitate

D) Palmitic acid

• question_answer63) The C-C bond dissociation energy in kcal/mol is

A) 8.1

B) 0.81

C) 81

D) 810

• question_answer64) A compound has four $s{{p}^{3}}$hybridized covalent bonds. Its shape is

A) linear

B) square planar

C) octahedral

D) tetrahedral

A) $\approx 20$

B) $\approx 40$

C) $\approx 60$

D) $\approx 80$

• question_answer66) 1 mole of $\text{C}{{\text{O}}_{\text{2}}}$contains

A) $6\times {{10}^{23}}$atoms of C

B) $6\times {{10}^{23}}$atoms of O

C) $18\times {{10}^{23}}$molecules of $C{{O}_{2}}$

D) 3 g-atoms of $C{{O}_{2}}$

• question_answer67) Rutherfords famous experiment with $\alpha -$particles used this metal

A) Ni

B) Au

C) Fe

D) Zn

• question_answer68) The charge on an electron in Coulombs is

A) $1.602\times {{10}^{-19}}$

B) $1.062\times {{10}^{-19}}$

C) $1.620\times {{10}^{-19}}$

D) $1.006\times {{10}^{-19}}$

• question_answer69) The number of subshells for a shell with principal quantum number $n$ is

A) $n$

B) $~n+1$

C) $n-1$

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

• question_answer70) Which of the following pairs of atomic numbers represents s-block elements?

A) 7, 15

B) 6, 12

C) 9, 17

D) 3, 11

• question_answer71) For a system in equilibrium

A) $\Delta G=0$

B) $\Delta G>0$

C) $\Delta G<0$

D) $\Delta H=0$

• question_answer72) Which of the following will produce the highest rise in temperature?

A) $\text{64}\,\text{mL}\,\text{1M}\,\text{NaOH}\,\text{+}\,\text{33}\,\text{mL}$of $\text{0}\text{.5}\,\text{M}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$

B) $\text{33}\,\text{mL}$of $\text{1}\,\text{M}\,\text{NaOH}\,\text{+}\,\text{67}\,\text{mL}\,$of $\text{0}\text{.5}\,\text{M}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$

C) $\text{40}\,\text{mL}$of $\text{1}\,\text{M}\,\text{NaOH}\,\text{+}\,\text{60}\,\text{mL}$of $\text{0}\text{.5}\,\text{M}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$

D) $\text{50}\,\text{mL}$of $\text{1}\,\text{M}\,\text{NaOH}\,\text{+}\,\text{50}\,\text{mL}$of $\text{0}\text{.5}\,\text{M}\,{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$

• question_answer73) The standard for atomic mass is

A) $_{1}^{1}H$

B) $_{6}^{12}C$

C) $_{6}^{14}C$

D) $_{8}^{16}O$

• question_answer74) Which of the following involves absorption of energy?

A) $Cl+{{e}^{-}}\xrightarrow{{}}C{{l}^{-}}$

B) ${{O}^{-}}+{{e}^{-}}\xrightarrow{{}}{{O}^{2-}}$

C) $O+{{e}^{-}}\xrightarrow{{}}{{O}^{-}}$

D) $S+{{e}^{-}}\xrightarrow{{}}{{S}^{-}}$

• question_answer75) The successive ionization energies of an element are 800, 2,000, 3,600, 25,000 and 32,000 kJ/mol. The number of valence electrons are

A) 5

B) 2

C) 3

D) 4

• question_answer76) The first order rate constant for the decomposition of ${{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}$is $6.2\times {{10}^{-4}}{{s}^{-1}}.$ The half-life in seconds is nearly

A) 1117.7

B) 111.7

C) 223

D) 160

• question_answer77) The rate constant of a reaction is $1\times {{10}^{-2}}mo{{l}^{-2}}{{L}^{2}}{{s}^{-1}}.$ The order of the reaction is

A) 0

B) 1

C) 2

D) 3

• question_answer78) The oxidation number of O in $\text{O}{{\text{F}}_{\text{2}}}$is

A) $-2$

B) $+\,1$

C) $+\,2$

D) $-1$

• question_answer79) The correct relationship is

A) ${{K}_{C}}=n\times {{K}_{p}}$

B) ${{K}_{p}}={{K}_{C}}{{(RT)}^{\Delta {{n}_{g}}}}$

C) ${{K}_{p}}=n\times {{K}_{C}}$

D) ${{K}_{C}}-{{K}_{p}}={{(RT)}^{\Delta N}}$

• question_answer80) W. For the reaction, $2B+AC,$ the equilibrium constant is

A) $\frac{[A]{{[B]}^{3}}}{[C]}$

B) $\frac{[C]}{[A][2B]}$

C) $\frac{[C]}{[A]{{[B]}^{2}}}$

D) $\frac{[A][B]}{[C]}$

• question_answer81) A buffer contains equal concentrations of ${{X}^{-}}$ and HX. The ${{K}_{a}}$for HX is ${{10}^{-8}}.$ The pH of the buffer is

A) 3

B) 8

C) 7

D) 11

• question_answer82) The metal which gives ${{\text{H}}_{\text{2}}}$on treatment with acid as well as $NaOH$ is

A) Fe

B) Cu

C) Zn

D) Hg

• question_answer83) Which is isoelectronic with hydride ion?

A) He

B) $\text{H}{{\text{e}}^{+}}$

C) Li

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

• question_answer84) A solution of Na in liquid$\text{N}{{\text{H}}_{\text{3}}}$ is

A) green

B) blue

C) pink

D) yellow

• question_answer85) The oxide which gives ${{\text{H}}_{\text{2}}}{{\text{O}}_{\text{2}}}$on treatment with dilute acid is

A) $Pb{{O}_{2}}$

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

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

D) $N{{a}_{2}}{{O}_{2}}$

• question_answer86) During the electrolysis of fused $NaCl,$ this happens at cathode

A) oxidation of$N{{a}^{+}}$

B) reduction of$N{{a}^{+}}$

C) reduction of $C{{l}^{-}}$

D) oxidation of $C{{l}^{-}}$

• question_answer87) Which of the following-s a colored gas?

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

B) $NO$

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

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

• question_answer88) This compound gives off ${{\text{O}}_{\text{2}}}$on moderate heating

A) $HgO$

B) $ZnO$

C) $CaO$

D) $A{{l}_{2}}{{O}_{3}}$

• question_answer89) Plaster of Paris is hardened by

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

B) hydration

C) dehydration

D) changing into $CaC{{O}_{3}}$

• question_answer90) The least ionic chloride is formed by

A) Mg

B) Ca

C) Be

D) Sr

A) 90% Cu

B) 50% Ni

C) 90% Sn

D) 50% Cu

• question_answer92) In the thermite welding, this is used

A) Ca

B) Al + Fe

C) Fe

D) $Al+F{{e}_{2}}{{O}_{3}}$

• question_answer93) ${{\text{K}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}$cannot be prepared by Solvay-ammonia process because

A) ${{\text{K}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}$is fairly soluble in water

B) it has no water of crystallization

C) $\text{KHC}{{\text{O}}_{\text{3}}}$ is highly soluble in water

D) ${{\text{K}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}$decomposes in ${{\text{H}}_{\text{2}}}\text{O}$

A) $N{{a}_{2}}S{{O}_{4}}.10{{H}_{2}}O$

B) $FeS{{O}_{4}}.7{{H}_{2}}O$

C) $ZnS{{O}_{4}}.7{{H}_{2}}O$

D) $MgS{{O}_{4}}.7{{H}_{2}}O$

• question_answer95) The salt responsible for permanent hardness of ${{\text{H}}_{\text{2}}}\text{O}$is

A) $N{{a}_{2}}S{{O}_{4}}$

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

C) $NaCl$

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

• question_answer96) Which of the following carbonium ion is most stable?

A) ${{C}_{6}}{{H}_{5}}\overset{+}{\mathop{C}}\,{{H}_{2}}$

B) ${{(C{{H}_{3}})}_{3}}\overset{+}{\mathop{C}}\,$

C) ${{(C{{H}_{3}})}_{2}}\overset{+}{\mathop{C}}\,H$

D) $C{{H}_{3}}\overset{+}{\mathop{C}}\,{{H}_{2}}$

• question_answer97) Which of the following reacts in presence of anhydrpus $\text{AlC}{{\text{l}}_{\text{3}}}$to give acetophenone?

A) ${{C}_{6}}{{H}_{6}}+C{{H}_{3}}COC{{H}_{3}}$

B) ${{C}_{6}}{{H}_{5}}OH+C{{H}_{3}}COC{{H}_{3}}$

C) ${{C}_{6}}{{H}_{5}}OH+C{{H}_{3}}COOH$

D) ${{C}_{6}}{{H}_{6}}+C{{H}_{3}}COCl$

• question_answer98) The isomers which can be interconverted through rotation around a single bond are

A) conformers

B) diastereoisomers

C) enantiomers

D) position isomers

• question_answer99) Phenol is the component of this fraction upon fractional distillation of petroleum

A) light oil

B) middle oil

C) heavy oil

D) pitch

• question_answer100) Ethyl chloride on treatment with alcoholic alkali gives

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

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

C) ${{C}_{2}}{{H}_{5}}OH$

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

• question_answer101) The area of the figure bounded by ${{y}^{2}}=2x+1$ and $x-y=1$is

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

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

C) $\frac{8}{3}$

D) $\frac{11}{3}$

• question_answer102) The order of the differential equation of all tangent lines to the parabola $y={{x}^{2}}$is

A) 1

B) 2

C) 3

D) 4

• question_answer103) $\int_{{}}^{{}}{\frac{dx}{\sqrt{(1-x)(x-2)}}}$is equal to

A) ${{\sin }^{-1}}(2x-3)+C$

B) ${{\sin }^{-1}}(2x+5)+C$

C) ${{\sin }^{-1}}(3-2x)+C$

D) ${{\sin }^{-1}}(5-2x)+C$

• question_answer104) $\int_{{}}^{{}}{\frac{({{\sec }^{2}}x-7)}{{{\sin }^{7}}x}}dx$is equal to

A) $\frac{\tan x}{{{\sin }^{7}}x}+C$

B) $\frac{\cos x}{{{\sin }^{7}}x}+C$

C) $\frac{\sin x}{{{\cos }^{7}}x}+C$

D) $\frac{\sin x}{{{\tan }^{7}}x}+C$

• question_answer105) $\int_{-3}^{2}{\{|x+1|+|x+2|+||x-1|\}}\,dx$is equal to

A) $\frac{31}{2}$

B) $\frac{35}{2}$

C) $\frac{37}{2}$

D) $\frac{39}{2}$

• question_answer106) The variance of first $n$natural numbers is

A) $\frac{{{n}^{2}}+1}{12}$

B) $\frac{{{n}^{2}}-1}{12}$

C) $\frac{(n+1)(2n+1)}{6}$

D) ${{\left[ \frac{n(n+1)}{2} \right]}^{2}}$

• question_answer107) A particular solution of $\log \left( \frac{dy}{dx} \right)=3x+4y,y(0)=0$is

A) ${{e}^{3x}}+3{{e}^{-4y}}=4$

B) $4{{e}^{3x}}-3{{e}^{-4y}}=3$

C) $3{{e}^{3x}}+4{{e}^{-4y}}=7$

D) $4{{e}^{3x}}+3{{e}^{-4y}}=7$

• question_answer108) The equation of the curve whose subnormal is equal to a constant a is

A) $y=ax+b$

B) ${{y}^{2}}=2ax+2b$

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

D) None of these

• question_answer109) If the standard deviation of a variable X is $\sigma ,$then the standard deviation of $\sigma ,$(a, b, c are constants) is

A) $\frac{a}{c}\sigma$

B) $\left| \frac{a}{c} \right|\sigma$

C) $\left| \frac{c}{a} \right|\sigma$

D) $\frac{c}{a}\sigma$

• question_answer110) If $\sin \alpha ,\cos \alpha$are the roots of the equation$a{{x}^{2}}+bx+c=0,(c\ne 0),$the

A) ${{a}^{2}}-{{b}^{2}}+2ac=0$

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

C) ${{a}^{2}}+{{b}^{2}}-2ac=0$

D) ${{(a-c)}^{2}}={{b}^{2}}+{{c}^{2}}$

• question_answer111) If $\alpha ,\beta ,\gamma$are such that $\alpha +\beta +\gamma =2,$${{\alpha }^{2}}+{{\beta }^{2}}+{{\gamma }^{2}}=6,$${{\alpha }^{3}}+{{\beta }^{3}}+{{\gamma }^{3}}=8,$then ${{\alpha }^{4}}+{{\beta }^{4}}+{{\gamma }^{4}}$is equal to

A) 7

B) 12

C) 18

D) 36

• question_answer112) The equation $\bar{z}=\bar{a}+\frac{{{r}^{2}}}{(z-a)},r>0$ represents

A) an ellipse

B) a parabola

C) a circle

D) _ a straight line through point $\bar{a}$

• question_answer113) If $\frac{3}{2+\cos \theta +i\sin \theta }=a+ib,$then $[{{(a-2)}^{2}}+{{b}^{2}}]$is equal to

A) 0

B) 1

C) $-1$

D) 2

• question_answer114) The value of $4+5{{\left( -\frac{1}{2}+\frac{i\sqrt{3}}{2} \right)}^{334}}+3{{\left( -\frac{1}{2}+\frac{i\sqrt{3}}{2} \right)}^{365}}$is

A) $1-i\sqrt{3}$

B) $-1+i\sqrt{3}$

C) $i\sqrt{3}$

D) $-i\sqrt{3}$

• question_answer115) If in the expansion of ${{(a-2b)}^{n}},$ the sum of 4th and 5th term is zero, then the value of$\frac{a}{b}$ is

A) $\frac{n-4}{5}$

B) $\frac{2(n-4)}{5}$

C) $\frac{5}{n-4}$

D) $\frac{5}{2(n-4)}$

• question_answer116) If$A=\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right]$is such that $|A|=0$ and${{A}^{2}}-(a+d)A+kI=0,$ then $k$is equal to

A) $b+c$

B) $a+d$

C) $ab+cd$

D) zero

• question_answer117) The sum of series$1+\frac{3}{2}+\frac{7}{4}+\frac{15}{8}+\frac{31}{16}+...$is equal to

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

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

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

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

• question_answer118) The number of meaningful solutions of ${{\log }_{4}}(x-1)={{\log }_{2}}(x-3)$is

A) 3

B) 2

C) 1

D) zero

• question_answer119) The number of ways of arranging letters of the word HAVANA so that V and N do not appear together is

A) 60

B) 80

C) 100

D) 120

• question_answer120) A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is

A) $\frac{3}{8}$

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

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

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

• question_answer121) The expression ${{\cos }^{2}}(A-B)+co{{s}^{2}}B-2\cos (A-B)cos\,A\,cos\,B$is independent of

A) A

B) B

C) both A and B

D) neither A nor B

• question_answer122) If the system of equations $ax+y=3,$$x+2y=3,3x+4y=7$is consistent, then value of a is equal to

A) 2

B) 1

C) -1

D) 0

• question_answer123) If $\left| \begin{matrix} x-1 & 5x & 7 \\ {{x}^{2}}-1 & x-1 & 8 \\ 2x & 3x & 0 \\ \end{matrix} \right|=a{{x}^{3}}+b{{x}^{2}}+cx+d,$then c is equal to

A) $-1$

B) 12

C) 15

D) 17

• question_answer124) If $a,b,c>0,$the minimum value of $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}$is

A) 1

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

C) 2

D) $\frac{5}{2}$

• question_answer125) If $\tan {{1}^{o}}\tan {{2}^{o}}...tan{{2}^{o}}....\tan {{89}^{o}}={{x}^{2}}-8,$then the value of $x$can be

A) $\pm \,1$

B) $\pm \,\,2$

C) $\pm \,\,3$

D) $\pm \,\,4$

• question_answer126) If $\sin (x+3\alpha )=3\sin (\alpha -x),$then

A) $\tan \,x=\tan \alpha$

B) $\tan \,x={{\tan }^{2}}\alpha$

C) $\tan x={{\tan }^{3}}\alpha$

D) $\tan x=3\tan \alpha$

• question_answer127) In a $\Delta ABC,2{{a}^{2}}+4{{b}^{2}}+{{c}^{2}}=4ab+2ac,$then $\cos \,B$is equal to

A) 0

B) $\frac{1}{8}$

C) $\frac{3}{8}$

D) $\frac{7}{8}$

• question_answer128) Let A and B be two events such that $P(A)=0.3$and $p(A\cup B)=0.8.$If A and B are independent events, then $P(B)$ is

A) $\frac{3}{7}$

B) $\frac{4}{7}$

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

D) $\frac{6}{7}$

• question_answer129) A bag contains 4 brown and 5 white balls. A man pulls two balls at random without replacement. The probability that the man gets both the balls of the same colour is

A) $\frac{5}{108}$

B) $\frac{1}{6}$

C) $\frac{5}{18}$

D) $\frac{4}{9}$

• question_answer130) The value of expression$\frac{1}{\cos {{290}^{o}}}+\frac{1}{\sqrt{3}\sin {{250}^{o}}}$ is equal to

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

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

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

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

• question_answer131) An equation of a line through the point (1, 2) whose distance from the point (3, 1) has the greatest value is

A) $y=2x$

B) $y=x+1$

C) $x+2y=5$

D) $y=3x-1$

• question_answer132) A line is drawn through the point P(3,11) to cut the circle ${{x}^{2}}+{{y}^{2}}=9$at A and B. Then, $PA.PB$is equal to

A) 9

B) 121

C) 205

D) 139

• question_answer133) If the tangent at point P on the circle ${{x}^{2}}+{{y}^{2}}+6x+6y-2=0$ meets the straight line $5x-2y+6=0$ at a point Q on the. $y-$axis, then length PQ is

A) 4

B) $2\sqrt{5}$

C) 5

D) $3\sqrt{5}$

• question_answer134) In a triangle ABC, $a:\text{ }b:\text{ }c\text{ }=\text{ }4:\text{ }5:\text{ }6.$The ratio of the radius of the circumcircle to that of the incircle is

A) $\frac{15}{4}$

B) $\frac{11}{5}$

C) $\frac{16}{7}$

D) $\frac{16}{3}$

• question_answer135) If $4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi ,$then $x$is equal to

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

B) 0

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

D) 1

• question_answer136) The Value of $\cos \left( \frac{1}{2}{{\cos }^{-1}}\frac{1}{8} \right)$ is equal to

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

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

C) $\frac{1}{16}$

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

• question_answer137) The vectors $\vec{a}=\hat{i}+\hat{j}+m\hat{k},$$\vec{b}=\hat{i}+\hat{j}+(m+1)\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}+m\hat{k}$ are coplanar, if $m$is equal to

A) 1

B) 4

C) 3

D) no value of m for which vectors are coplanar

• question_answer138) If|$|\vec{a}|=2,|\vec{b}|=3,|\vec{c}|=4$and $\vec{a}+\vec{b}+\vec{c}=0,$ then the value of $\vec{b}.\vec{c}+\vec{c}.\vec{a}+\vec{a}+\vec{a}.\vec{b}$is equal to

A) $\frac{19}{2}$

B) $-\frac{19}{2}$

C) $\frac{29}{2}$

D) $-\frac{29}{2}$

• question_answer139) The line $x+y=6$is a normal to the parabola ${{y}^{2}}=8x$at the point

A) $(18,-12)$

B) $(4,2)$

C) $(2,4)$

D) $(8,8)$

• question_answer140) If${{F}_{1}}=(3,0),{{F}_{2}}=(-3,0)$ and P is any point on the curve $16{{x}^{2}}+25{{y}^{2}}=400,$ then $P{{F}_{1}}+P{{F}_{2}}$is equal to

A) 6

B) 8

C) 10

D) 12

• question_answer141) If e and${{e}_{1}}$are the eccentricities of a hyperbola and its conjugate, then$\frac{1}{{{e}^{2}}}+\frac{1}{e_{1}^{2}}$ is equal to

A) $-1$

B) 0

C) 1

D) 2

• question_answer142) $\underset{x\to 0}{\mathop{\lim }}\,\frac{1-{{\cos }^{3}}x}{x\sin \cos x}$is equal to

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

B) $\frac{3}{5}$

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

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

• question_answer143) If $y={{\cos }^{-1}}(\cos \,x),$then $y(x)$is equal to

A) 1 for all $x$

B) $-1$for all $x$

C) 1 in 2nd and 3rd quadrant

D) $-1$in 3rd and 4th quadrant

• question_answer144) If the vectors $\overrightarrow{AB}=3\hat{i}+4\hat{k}$ and =$\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$are the sides of a $\Delta ABC,$ then the length of the median through A is

A) $\sqrt{14}$

B) $\sqrt{18}$

C) $\sqrt{29}$

D) 4

• question_answer145) The period of the function$f(x)=\cos e{{c}^{2}}3x+\cot 4x$is

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

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

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

D) $\pi$

• question_answer146) The graph of the function$f(x)={{\log }_{a}}(x+\sqrt{{{x}^{2}}+1})$ is symmetric about

A) $x-$axis

B) origin

C) $y-$axis

D) the line $y=x$

• question_answer147) The difference between the greatest and least values of the function$f(x)=\cos x+\frac{1}{2}\cos 2x-\frac{1}{3}\cos 3x$is

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

B) $\frac{8}{7}$

C) $\frac{3}{8}$

D) $\frac{9}{4}$

• question_answer148) $f(x)=\left\{ \begin{matrix} a{{x}^{2}}+b, & b\ne 0,x\le 1 \\ b{{x}^{2}}+ax+c, & x>1 \\ \end{matrix} \right.$ then$f(x)$ is continuous and differentiable at $x=1$if

A) $c=0,\,a=2b$

B) $a=b,\,c\in R$

C) $a=b,c=0$

D) $a=b,c\ne 0$

• question_answer149) Let $g(x)$be the inverse of function $f(x)$ and $f(x)=\frac{1}{1+{{x}^{3}}},$ then $g(x)$is equal to

A) $\frac{1}{1+{{\{g(x)\}}^{3}}}$

B) $\frac{1}{1+{{\{f(x)\}}^{3}}}$

C) $1+{{\{g(x)\}}^{3}}$

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

• question_answer150) If $\theta$ is the semi vertical angle of a cone of maximum volume and given slant height, then$\tan \,\theta$is given by

A) 2

B) 1

C) $\sqrt{2}$

D) $\sqrt{3}$

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