# Solved papers for VIT Engineering VIT Engineering Solved Paper-2010

### done VIT Engineering Solved Paper-2010

• question_answer1) A straight wire carrying current $i$ is turned into a circular loop. If the magnitude of magnetic moment associated with it in MKS unit is $M$, the length of wire will be

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

B) $\sqrt{\frac{4\pi M}{i}}$

C) $\sqrt{\frac{4\pi i}{M}}$

D) $\frac{M\pi }{i}$

• question_answer2) The ratio of the amounts of heat developed in the four arms of a balance Wheatstone bridge, when the arms have resistances $P=100\,\Omega$, $Q=10\,\Omega$, $R=300\,\Omega$ and $S=30\,\Omega$ respectively is

A) 3 : 30 : 1 : 10

B) 30 : 3 : 10 : 1

C) 30 : 10 : 1 : 3

D) 30 : 1 : 3 : 10

• question_answer3) An electric kettle takes 4 A current at 220 V. How much time will it take to boil 1 kg of water from temperature$20{}^\circ C$? The temperature of boiling water is$100{}^\circ C$.

A) 12.6 min

B) 4.2 min

C) 6.3 min

D) 8.4 min

• question_answer4) Magnetic field at the center of a circular loop of area A is B. The magnetic moment of the loop will be

A) $\frac{B{{A}^{2}}}{{{\mu }_{0}}\pi }$

B) $\frac{B{{A}^{3/2}}}{{{\mu }_{0}}\pi }$

C) $\frac{B{{A}^{3/2}}}{{{\mu }_{0}}{{\pi }^{1/2}}}$

D) $\frac{2B{{A}^{3/2}}}{{{\mu }_{0}}{{\pi }^{1/2}}}$

• question_answer5) In Youngs double slit experiment, the spacing between the slits is d and wavelength of light used is $\text{6000}\overset{\text{o}}{\mathop{\text{A}}}\,$.If the angular width of a fringe formed on a distance screen is $1{}^\circ$, then value of $d$ is

A) 1 mm

B) 0.05 mm

C) 0.03mm

D) 0.01 mm

• question_answer6) An electric dipole consists of two opposite charges of magnitude $q=1\times {{10}^{-6}}C$ separated by 2.0 cm. The dipole is placed in an external field of$1\times {{10}^{5}}N{{C}^{-1}}$. What maximum torque does the field exert on the dipole? How much work must an external agent do to turn the dipole end to end, starring from position of alignment$(9=0{}^\circ )$?

A) $4.4\times {{10}^{6}}N-m,\text{ }3.2\times {{10}^{-4}}J$

B) $-2\times {{10}^{-3}}N-m,\text{ }-4\times {{10}^{3}}J$

C) $4\times {{10}^{3}},\text{ }2\times {{10}^{-3}}J$

D) $2\times {{10}^{-3}}N-m,\text{ }4\times {{10}^{-3}}J$

• question_answer7) The electron of hydrogen atom is considered to be revolving round a proton in circular orbit of radius ${{h}^{2}}/m{{e}^{2}}$ with velocity${{e}^{2}}/h$, where$h=h/2\pi$. The current $i$ is

A) $\frac{4{{\pi }^{2}}m{{e}^{5}}}{{{h}^{2}}}$

B) $\frac{4{{\pi }^{2}}m{{e}^{5}}}{{{h}^{3}}}$

C) $\frac{4{{\pi }^{2}}{{m}^{2}}{{e}^{5}}}{{{h}^{3}}}$

D) $\frac{4{{\pi }^{2}}{{m}^{2}}{{e}^{2}}}{{{h}^{3}}}$

• question_answer8) In a double slit experiment, 5th dark fringe is formed opposite to one of the slits, the wavelength of light is

A) $\frac{d{{e}^{2}}}{6D}$

B) $\frac{{{d}^{2}}}{9D}$

C) $\frac{{{d}^{2}}}{15D}$

D) $\frac{{{d}^{2}}}{9D}$

• question_answer9) Which of the following rays is emitted by a human body?

A) X-rays

B) UV rays

C) Visible rays

D) IR rays

• question_answer10) A proton of mass $1.67\times {{10}^{-27}}kg$ enters a uniform magnetic field of 1 T at point A as shown in figure, with a speed of${{10}^{7}}m{{s}^{-1}}$. The magnetic field is directed normal to the plane of paper downwards. The proton emerges out of the magnetic field at point$C$, then the distance $AC$ and the value of angle $\theta$ will respectively be

A) $0.7m,\text{ }45{}^\circ$

B) $0.7\text{ }m,\,\,90{}^\circ$

C) $0.14\text{ }m,\text{ }90{}^\circ$

D) $0.14\text{ }m,\text{ }45{}^\circ$

• question_answer11) A neutral water molecule$\text{(}{{\text{H}}_{\text{2}}}\text{O)}$in its vapour state has an electric dipole moment of magnitude$6.4\times {{10}^{-30}}C-m$. How far apart are the molecules centres of positive and negative charges?

A) 4m

B) 4 mm

C) $4\mu$m

D) 4 pm

• question_answer12) Figure shows a straight wire of length $l$ carrying current $i$. The magnitude of magnetic field produced by the current at point P is

A) $\frac{\sqrt{2}{{\mu }_{0}}i}{\pi l}$

B) $\frac{{{\mu }_{0}}i}{4\pi l}$

C) $\frac{\sqrt{2}{{\mu }_{0}}i}{8\pi l}$

D) $\frac{{{\mu }_{0}}i}{2\sqrt{2}\pi l}$

• question_answer13) Zener diode is used for

A) producing oscillations in an oscillator

B) amplification

C) stabilization

D) rectification

• question_answer14) Two light sources are said to be coherent if they are obtained from

A) two independent point sources emitting light of the same wavelength

B) a single point source

C) a wide source

D) two ordinary bulbs emitting light of different wavelengths

• question_answer15) A small coil is introduced between the poles of an electromagnet so that its axis coincides with the magnetic field direction. The number of turns is n and the cross-sectional area of the coil is A. When the coil turns through $180{}^\circ$ about its diameter, the charge flowing through the coil is Q. The total resistance of the circuit is R. What is the magnitude of the magnetic induction?

A) $\frac{QR}{nA}$

B) $\frac{2QR}{nA}$

C) $\frac{Qn}{2RA}$

D) $\frac{QR}{2nA}$

• question_answer16) The attenuation in optical fibre is mainly due to

A) absorption

B) scattering

C) neither absorption nor scattering

D) Both [a] and [b]

• question_answer17) An arc of radius r carries charge. The linear density of charge is $\lambda$ and the arc subtends an angle $\frac{\pi }{3}$at the centre. What is electric potential at the centre?

A) $\frac{\lambda }{4{{\varepsilon }_{0}}}$

B) $\frac{\lambda }{8{{\varepsilon }_{0}}}$

C) $\frac{\lambda }{12{{\varepsilon }_{0}}}$

D) $\frac{\lambda }{16{{\varepsilon }_{0}}}$

• question_answer18) Sinusoidal carrier voltage of frequency 1.5 MHz and amplitude 50 V is amplitude modulated by sinusoidal voltage of frequency 10 kHz producing 50% modulation. The lower and upper side-band frequencies in kHz are

A) 1490, 1510

B) 1510,1490

C) $\frac{1}{1490},\frac{1}{1510}$

D) $\frac{1}{1510},\frac{1}{1490}$

• question_answer19) 50$\Omega$ and 100$\Omega$ resistors are connected in series. This connection is connected with a battery of 2.4 V. When a voltmeter of 100$\Omega$resistance is connected across 100$\Omega$ resistor, then the reading of the voltmeter will be

A) 1.6 V

B) 1.0 V

C) 1.2 V

D) 2.0 V

• question_answer20) In space charge limited region, the plate current in a diode is 10 mA for plate voltage 150 V. If the plate voltage is increased to 600V, then the plate current will be

A) 10 mA

B) 40 mA

C) 80 mA

D) 160 mA

• question_answer21) Light of wavelength strikes a photo-sensitive surface and electrons are ejected with kinetic energy E. If. the kinetic energy is to be increased to 2E, the wavelength must be changed to $\lambda$where

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

B) ${{\lambda }^{}}=2\lambda$

C) $\frac{\lambda }{2}<{{\lambda }^{}}<\lambda$

D) ${{\lambda }^{}}>\lambda$

• question_answer22) The maximum velocity of electrons emitted from a metal surface is$v$, when frequency of light falling on it is$f$. The maximum velocity when frequency becomes $4f$is

A) $2v$

B) $>2v$

C) $<2v$

D) between $2v$ and $4v$

• question_answer23) The collector plate in an experiment on photoelectric effect is kept vertically above the emitter plate. Light source is put on and a saturation photo-current is recorded. An electric field is switched on which has a vertically downward direction, then

A) the photo- current will increase

B) the kinetic energy of the electrons will increase

C) the slopping potential will decrease

D) the threshold wavelength will increase

• question_answer24) A cylindrical conductor of radius R carries a current i. The value of magnetic field at a point which is $\frac{R}{4}$distance inside from the surface is 10 T. The value of magnetic field at point which is 4R distance outside from the surface

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

B) $\frac{8}{3}T$

C) $\frac{40}{3}T$

D) $\frac{80}{3}T$

• question_answer25) The power of a thin convex lens $\left( _{a}{{n}_{g}}=1.5 \right)$ is 5.0 D. When it is placed in a liquid of refractive index $_{a}{{n}_{l}},$ then it behaves as a concave lens of focal length 100 cm. The refractive index of the liquid$_{a}{{n}_{l}},$will be

A) 5/3

B) 4/3

C) $\sqrt{3}$

D) 5/4

• question_answer26) Find the value of magnetic field between plates of capacitor at a distance 1 m from centre, where electric field varies by ${{10}^{10}}V/m$per second.

A) $5.56\times {{10}^{-8}}T$

B) $5.56\times {{10}^{-3}}T$

C) $\text{5}\text{.56 }\!\!\mu\!\!\text{ T }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }$

D) $5.55\text{ }T$

• question_answer27) sing an AC voltmeter the potential difference in the electrical line in a house is read to be 234 V. If line frequency is known to be 50 cycles/s, the equation for the line voltage is

A) $\text{V }\!\!~\!\!\text{ = 165 sin (100 }\!\!\pi\!\!\text{ t)}$

B) $\text{V=331 sin}\,\text{(100 }\!\!\pi\!\!\text{ t)}$

C) $\text{V=220}\,\text{sin}\,\text{(100 }\!\!\pi\!\!\text{ t)}$

D) $\text{V=440 sin (100 }\!\!\pi\!\!\text{ t)}$

• question_answer28) There are a 25 W - 220 V bulb and a 100 W -220 V line. Which electric bulb will glow more brightly?

A) 25 W bulb

B) 100 W bulb

C) Both will have equal incandescence

D) Neither 25 W nor 100 W bulb will give light

• question_answer29) Silver has a work function of 4.7 eV. When ultraviolet light of wavelength 100 nm is incident upon it, potential of 7.7 V is required to stop photoelectrons from reaching the collector plate. The potential required to stop electrons when light of wavelength 200 nm is incident upon silver is

A) 1.5 V

B) 1.85 V

C) 1.95 V

D) 2.37 V

• question_answer30) Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii ${{R}_{1}}$ and ${{R}_{2}}$, respectively. The ratio of masses of X and Y is

A) $\left( {{R}_{1}}/{{R}_{2}} \right)$

B) $\left( {{R}_{2}}/{{R}_{1}} \right)$

C) ${{\left( {{R}_{1}}/{{R}_{2}} \right)}^{2}}$

D) $\left( {{R}_{1}}/{{R}_{2}} \right)$

• question_answer31) According to the Bohrs theory of hydrogen atom, the speed of the electron, energy and the radius of its orbit vary with the principal quantum number n, respectively, as

A) $\frac{1}{n},\frac{1}{{{n}^{2}}},{{n}^{2}}$

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

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

D) $n,\frac{1}{{{n}^{2}}},\frac{1}{{{n}^{2}}}$

• question_answer32) In the hydrogen atom, the electron is making$6.6\times {{10}^{15}}\,\text{rps}$. If the radius of the orbit is $0.53\times {{10}^{-10}}m$, then magnetic field produced at the centre of the orbit is

A) 140 T

B) 12.5 T

C) 1.4 T

D) 0.14 T

• question_answer33) Two identical light sources ${{S}_{1}}$ and ${{S}_{2}}$emit light of same wavelength$\lambda$. These light rays will exhibit interference if

A) their phase differences remain constant

B) their phases are distributed randomly

C) their light intensities remain constant

D) their light intensities change randomly

• question_answer34) In Meter bridge or Wheatstone bridge for measurement of resistance, the known and the unknown resistances are interchanged. The error so removed is

A) end correction

B) index errror

C) due to temperature effect

D) random error

• question_answer35) A fish, looking up through the water, sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm below the surface of water, the radius of the circle in centimetre is

A) $\frac{12\,\times \,3}{\sqrt{5}}$

B) $12\,\times \,3\,\times \,\sqrt{5}$

C) $\frac{12\,\times \,3}{\sqrt{7}}$

D) $12\,\times \,3\,\times \,\sqrt{7}$

• question_answer36) Radio waves diffract around building although light waves do not. The reason is that radio waves

A) travel with speed larger than c

B) have much larger wavelength than light

C) carry news

D) are not electromagnetic waves

• question_answer37) In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If ${{a}_{0}}$ is the radius of the ground state orbit, $m$ is the mass and $e$ is charge on the electron and ${{\varepsilon }_{0}}$ is the vacuum permittivity, the speed of the electron is

A) $0$

B) $\frac{e}{\sqrt{{{\varepsilon }_{0}}{{a}_{0}}m}}$

C) $\frac{e}{\sqrt{4\pi {{\varepsilon }_{0}}{{a}_{0}}m}}$

D) $\frac{\sqrt{4\pi {{\varepsilon }_{0}}{{a}_{0}}m}}{e}$

• question_answer38) A potential difference of $2V$ is applied between the opposite faces of a Ge crystal plate of area $1c{{m}^{2}}$ and thickness 0.5 mm. If the concentration of electrons in Ge is $2\times {{10}^{19}}/{{m}^{2}}$ and mobilitys of electrons and holes are $\text{0}\text{.36 }{{\text{m}}^{\text{2}}}{{\text{V}}^{\text{-1}}}{{\text{s}}^{\text{-1}}}$and $\text{0}\text{.14 }{{\text{m}}^{\text{2}}}{{\text{V}}^{\text{-1}}}{{\text{s}}^{\text{-1}}}$respectively, then the current flowing through the plate will be

A) 0.25 A

B) 0.45 A

C) 0.56 A

D) 0.64 A

• question_answer39) An AM wave has 1800 W of total power content. For 100% modulation the carrier should have power content equal to

A) 1000 W

B) 1200 W

C) 1500 W

D) 1600 W

• question_answer40) Two light rays having the same wavelength $\lambda$ in vacuum are in phase initially. Then the first ray travels a path ${{l}_{1}}$ through a medium of refractive index ${{n}_{1}}$ while the second ray travels a path of length ${{l}_{2}}$ through a median of refractive index${{n}_{2}}$. The two waves are then combined to observe interference. The phase difference between the two waves is

A) $\frac{2\pi }{\lambda }\left( {{l}_{2}}-{{l}_{1}} \right)$

B) $\frac{2\pi }{\lambda }\left( {{n}_{1}}{{l}_{1}}-{{n}_{2}}{{l}_{2}} \right)$

C) $\frac{2\pi }{\lambda }\left( {{n}_{2}}{{l}_{2}}-{{n}_{1}}{{l}_{1}} \right)$

D) $\frac{2\pi }{\lambda }\left( \frac{{{l}_{1}}}{{{n}_{1}}}-\frac{{{l}_{2}}}{{{n}_{2}}} \right)$

• question_answer41) The correct formula of the complex tetraammineaquachlorocobalt (III) chloride is

A) $[Cl({{H}_{2}}O){{(N{{H}_{3}})}_{4}}Co]Cl$

B) $[CoCl({{H}_{2}}O){{(N{{H}_{3}})}_{4}}]Cl$

C) $[Co{{(N{{H}_{3}})}_{4}}({{H}_{2}}O)Cl]Cl$

D) $[CoCl({{H}_{2}}O){{(N{{H}_{3}})}_{4}}]C{{l}_{2}}$

• question_answer42) The equivalent conductance at infinite dilution of a weak acid such as HF

A) can be determined by extrapolation of measurements on dilute solutions of $HCl$,$HBr$ and $HI$

B) can be determined by measurement on very dilute HF solutions

C) can best be determined from measurements on dilute solutions of $NaF$,$NaCl$ and $HCl$

D) is an undefined quantity

• question_answer43) The product A is

A) succinic acid

B) melonic acid

C) oxalic acid

D) maleic acid

• question_answer44) For a reaction of type $A+B\xrightarrow{{}}$ products, it is observed that doubling concentration of A causes the reaction rate to be four times as great, but doubling amount of B does not affect the rate. The unit of rate constant is

A) ${{s}^{-1}}$

B) ${{s}^{-1}}\,mol\,\,{{L}^{-1}}$

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

D) $s\,\,{{s}^{-1}}\,mo{{l}^{-2}}\,\,{{L}^{2}}$

• question_answer45) A chemical reaction was carried out at 320 K and 300 K. The rate constants were found to be ${{k}_{1}}$ and ${{k}_{2}}$ respectively. Then

A) ${{k}_{2}}=4{{k}_{1}}$

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

C) ${{k}_{2}}=0.25{{k}_{1}}$

D) ${{k}_{2}}=0.5{{k}_{1}}$

• question_answer46) The formula of ethyl carbinol is

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

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

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

D) ${{(C{{H}_{3}})}_{3}}COH$

• question_answer47) Which of the following gives red colour in Victor Meyers test?

A) n-propyl alcohol

B) Isopropyl alcohol

C) hert-butyl alcohol

D) sec-butyl alcohol

• question_answer48) Enthalpy of a compound is equal to its

A) heat of combustion

B) heat of formation

C) heat of reaction

D) heat of solution

• question_answer49) For which one of the following reactions will there be a positive $\Delta S$?

A) ${{H}_{2}}O(g)\xrightarrow{{}}{{H}_{2}}O(l)$

B) ${{H}_{2}}+{{I}_{2}}\xrightarrow{{}}2HI$

C) $CaC{{O}_{3}}(s)\xrightarrow{{}}CaO(s)+C{{O}_{2}}(g)$

D) ${{N}_{2}}(g)+3{{H}_{2}}(g)\xrightarrow{{}}2N{{H}_{3}}(g)$

• question_answer50) Across the lanthanide series, the basicity of the lanthanide hydroxides

A) increases

B) decreases

C) first increases and then decreases

D) first decreases and then increases

• question_answer51) When p-nitrobromobenzene reacts with sodium ethoxide, the product obtained is

A) p-nitroanisole

B) ethyl phenyl ether

C) p-nitrophenetole

D) no reaction occurs

• question_answer52) A radioactive element X emits $3\alpha$,$1\beta$ and $1\gamma$-particles and forms $_{76}{{Y}^{235}}$. Element X is

A) $_{81}{{X}^{247}}$

B) $_{80}{{X}^{247}}$

C) $_{81}{{X}^{246}}$

D) $_{80}{{X}^{246}}$

• question_answer53) For the reaction, $2A(g)+{{B}_{2}}(g)2A{{B}_{2}}(g)$ the equilibrium constant, ${{K}_{p}}$ at 300 K is 16.0. The value of ${{K}_{p}}$ for $A{{B}_{2}}(g)A(g)+1/2{{B}_{2}}(g)$

A) $8$

B) $0.25$

C) $0.125$

D) $32$

• question_answer54) Frenkel defect is generally observed in

A) $AgBr$

B) $AgI$

C) $ZnS$

D) All of the above

• question_answer55) Most crystals show good cleavage because their atoms, ions or molecules are weakly

A) bonded together

B) strongly bonded together

C) spherically symmetrical

D) arranged in planes

• question_answer56) $[Co{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]N{{O}_{2}}$and $[Co{{(N{{H}_{3}})}_{4}}ClN{{O}_{2}}]Cl$ exhibit which type of isomerism?

A) Geometrical

B) Optical

D) lonisation

• question_answer57) Which of the following compounds is not coloured?

A) $N{{a}_{2}}[Cu{{(Cl)}_{4}}]$

B) $Na[Cd{{(Cl)}_{4}}]$

C) ${{K}_{4}}[Fe{{(CN)}_{6}}]$

D) ${{K}_{3}}[Fe{{(CN)}_{6}}]$

• question_answer58) Which of the following is a Gattermann aldehyde synthesis?

A)

B)

C)

D)

A) $\beta$-hydroxybutyraldehyde

B) $\alpha$-hydroxybutanal

C) $\beta$-hydroxypropanal

D) None. of the above

• question_answer60) Nitrobenzene can be converted into azobenzene by reduction with

A) $Zn,\,N{{H}_{4}}Cl,\,\Delta$

B) $Zn/NaOH,\,C{{H}_{3}}OH$

C) $Zn/NaOH$

D) $LiAl{{H}_{4}}$, ether

• question_answer61) The one which is least basic is

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

B) ${{C}_{6}}{{H}_{5}}N{{H}_{2}}$

C) ${{({{C}_{6}}{{H}_{5}})}_{3}}N$

D) ${{({{C}_{6}}{{H}_{5}})}_{2}}NH$

• question_answer62) Coordination number of $Ni$ in ${{[Ni{{({{C}_{2}}{{O}_{4}})}_{3}}]}^{4-}}$is

A) 3

B) 6

C) 4

D) 5

• question_answer63) Mg. is an important component of which biomolecule occurring extensively in living world?

A) Haemoglobin

B) Chlorophyll

C) Florigen

D) ATP

A) $AgN{{O}_{3}}$

B) $A{{g}_{2}}S$

C) Alloy of 80% $Ag+20%\,Cu$

D) $AgCl$

• question_answer65) Identify the statement which is not correct regarding $CuS{{O}_{4}}$

A) It reacts with $KI$ to give iodine

B) It reacts with $KCl$ to give $C{{u}_{2}}C{{l}_{2}}$

C) It reacts with $NaOH$ and glucose to give$C{{u}_{2}}O$

D) It gives $CuO$ on strong heating in air

• question_answer66) Transition metals usually exhibit highest oxidation states in their

A) chlorides

B) fluorides

C) bromides

D) iodides

• question_answer67) The number of Faradays needed to reduce 4 g equivalents of $C{{u}^{2+}}$to $Cu$ metal will be

A) $1$

B) $2$

C) $1/2$

D) $4$

• question_answer68) Which one of the following cells can convert chemical energy of ${{H}_{2}}$ and ${{O}_{2}}$ directly into electrical energy?

A) Mercury cell

B) Daniell cell

C) Fuel cell

• question_answer69) On treatment of propanone with dilute $Ba{{(OH)}_{2}}$, the product formed is

A) aldol

B) phorone

C) propionaldehyde

D) 4-hydroxy-4-methyl-2-pentanone

• question_answer70) Which of the following converts $C{{H}_{3}}CON{{H}_{2}}$to $C{{H}_{3}}N{{H}_{2}}$?

A) $NaBr$

B) $NaOBr$

C) $B{{r}_{2}}$

D) None of the above

A) Mercury coated apron

C) Copper apron

D) Aluminimised apron

• question_answer72) The standard Gibbs free energy change, $\Delta {{G}^{o}}$ is related to equilibrium constant, ${{K}_{P}}$ as

A) ${{K}_{P}}=-RT$ In $\Delta {{G}^{o}}$

B) ${{K}_{P}}={{\left[ \frac{e}{RT} \right]}^{\Delta {{G}^{o}}}}$

C) ${{K}_{P}}=-\frac{\Delta G}{RT}$

D) ${{K}_{P}}={{e}^{-\Delta {{G}^{o}}/RT}}$

• question_answer73) The yield of the product in the reaction ${{A}_{2}}(g)+2B(g)C(g)+Q\,\,kJ$ would be higher at

A) high temperature and high pressure

B) high temperature and low pressure

C) low temperature and high pressure

D) low temperature and low pressure

• question_answer74) In which of the following case, does the reaction go farthest to completion?

A) $K={{10}^{2}}$

B) $K=10$

C) $K={{10}^{-2}}$

D) $K=1$

• question_answer75) Formation of cyanohydrin-from a ketone is an example of

C) nucleophilic substitution

D) electrophilic substitution

• question_answer76) Glycerol on treatment with oxalic acid at ${{110}^{o}}C$ forms

A) formic acid

B) allyl alcohol

C) $C{{O}_{2}}$ and $CO$

D) acrolein

• question_answer77) The activity of an old piece of wood is just 25% of the fresh piece of wood. If ${{t}_{1/2}}$ of C-14 is 6000 yr, the age of piece of wood is

A) $6000\text{ }yr$

B) $3000\text{ }yr$

C) $9000\text{ }yr$

D) $12000\text{ }yr$

• question_answer78) The radius of $N{{a}^{+}}$ is 95 pm and that of $C{{l}^{-}}$ ion is 181 pm. Hence, the coordination number of $N{{a}^{+}}$ will be

A) 4

B) 6

C) 8

D) unpredictable

• question_answer79) The reaction, $ROH+{{H}_{2}}C{{N}_{2}}$ in the presence of $HB{{F}_{4}}$, gives the following product

A) $ROC{{H}_{3}}$

B) $RC{{H}_{2}}OH$

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

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

• question_answer80) The fatty acid which shows reducing property is

A) acetic acid

B) ethanoic acid

C) oxalic acid

D) formic acid

• question_answer81) If $F$ is functions such that $F(0)=2,$$F(1)=3,$$F(x+2)=2F(x)-F(x+1)$ for $x\ge 0,$ than$F(5)$ is equal to

A) -7

B) -3

C) 17

D) 13

• question_answer82) Let$S$be a set containing $n$elements. Then, number of binary operations on $S$is

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

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

C) ${{n}^{{{n}^{2}}}}$

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

• question_answer83) The numerically greatest term in the expansion of ${{(2-5x)}^{11}}$when $x=\frac{1}{5},$is

A) $55\times {{3}^{9}}$

B) $55\times {{3}^{6}}$

C) $45\times {{3}^{6}}$

D) $45\times {{3}^{9}}$

• question_answer84) The number of solutions of the equation$\sin \,({{e}^{x}})={{5}^{x}}+{{5}^{-x}},$is

A) 0

B) 1

C) 2

D) infinitely many

• question_answer85) If ${{a}^{x}}={{b}^{y}}={{c}^{z}}={{d}^{u}}$and $a,b,c,d$are in GP, then $x,y,z,u$are in

A) AP

B) GP

C) HP

D) None of these

• question_answer86) If z satisfies the equation $\left| \,z\, \right|-z=1+2i,$then z is equal to

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

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

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

D) $2+\frac{3}{2}i$

• question_answer87) If $z=\frac{1-i\sqrt{3}}{1+i\sqrt{3}},$then arg (z) is

A) $60{}^\circ$

B) $120{}^\circ$

C) $240{}^\circ$

D) $300{}^\circ$

• question_answer88) If $f(x)=\sqrt{{{\log }_{10}}{{x}^{2}}}.$ The set of all values of $x$for which $f(x)$is real, is

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

B) $[1,\,\infty )$

C) $(-\infty ,\,-1]$

D) $(-\infty ,\,-1]\cup [1,\infty )$

• question_answer89) For what values of m can the expression $2{{x}^{2}}+mxy+3{{y}^{2}}-5y-2$ be expressed as the product of two linear factors?

A) $0$

B) $\pm 1$

C) $\pm 7$

D) $49$

• question_answer90) If $B$is non-singular matrix and$A$is a square matrix, then det$({{B}^{-1}}AB)$is equal to

A) $\det \,({{A}^{-1}})$

B) $\det \,({{B}^{-1}})$

C) $\det \,(A)$

D) $\det \,(B)$

• question_answer91) If $f(x),\,g(x)$and $h\,(x)$are three polynomials of degree 2 and $\Delta (x)=\left| \begin{matrix} f(x) & g(x) & h(x) \\ f(x) & g(x) & h(x) \\ f(x) & g(x) & h(x) \\ \end{matrix} \right|$ then $\Delta (x)$is a polynomial of degree

A) 2

B) 3

C) 0

D) atmost 3

• question_answer92) The chances of defective screws in three boxes A, B, C are $\frac{1}{5},\frac{1}{6},\frac{1}{7}$respectively. A box is selected at random and a screw drawn from it at random is found to be defective, Then, the probability that it came from box A, is

A) $\frac{16}{29}$

B) $\frac{1}{15}$

C) $\frac{27}{59}$

D) $\frac{42}{107}$

• question_answer93) The value of $\frac{\cos \theta }{1+\sin \theta }$is equal to

A) $\tan \left( \frac{\theta }{2}-\frac{\pi }{4} \right)$

B) $\tan \left( -\frac{\pi }{4}-\frac{\theta }{2} \right)$

C) $\tan \left( \frac{\pi }{4}-\frac{\theta }{2} \right)$

D) $\tan \left( \frac{\pi }{4}+\frac{\theta }{2} \right)$

• question_answer94) If $3\sin \theta +5cos\theta =5,$ then the value of $5\sin \theta -3cos\theta$is equal to

A) 5

B) 4

C) 3

D) None of these

• question_answer95) The principal value of ${{\sin }^{-1}}\left\{ \sin \frac{5\pi }{6} \right\}$is

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

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

C) $\frac{7\pi }{6}$

D) None of these

• question_answer96) A rod of length $l$slides with its ends of two perpendicular lines. Then, the locus of its mid-point is

A) ${{x}^{2}}+{{y}^{2}}=\frac{{{l}^{2}}}{4}$

B) ${{x}^{2}}+{{y}^{2}}=\frac{{{l}^{2}}}{2}$

C) ${{x}^{2}}-{{y}^{2}}=\frac{{{l}^{2}}}{4}$

D) None of these

• question_answer97) The equation of straight line through the intersection of line $2x+y=1$and $3x+2y=5$and passing through the origin is

A) $7x+3y=0$

B) $7x-y=0$

C) $3x+2y=0$

D) $x+y=0$

• question_answer98) The line joining (5, 0) to $(10\,\cos \theta ,\,10\sin \theta )$ is divided internally in the ratio 2 : 3 at P. If $\theta$varies, then the locus of P is

A) a straight line

B) a pair of straight lines

C) a circle

D) None of the above

• question_answer99) If $2x+y+k=0$is a normal to the parabola ${{y}^{2}}=-8x,$then the value of k, is

A) 8

B) 16

C) 24

D) 32

• question_answer100) $\underset{n\to \infty }{\mathop{\lim }}\,\left[ \frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+.....+\frac{1}{n\,(n+1)} \right]$ is equal to

A) 1

B) -1

C) 0

D) None of these

• question_answer101) The condition that the line $lx+my=1$may be normal to the curve${{y}^{2}}=4ax,$is

A) $a{{l}^{3}}-2al{{m}^{2}}={{m}^{2}}$

B) $a{{l}^{2}}+2al{{m}^{3}}={{m}^{2}}$

C) $a{{l}^{3}}+2al{{m}^{2}}={{m}^{3}}$

D) $a{{l}^{3}}+2al{{m}^{2}}={{m}^{2}}$

• question_answer102) If $\int{f(x)dx=f(x),}$ then $\int{{{\left\{ f(x) \right\}}^{2}}dx}$is equal to

A) $\frac{1}{2}{{\left\{ f(x) \right\}}^{2}}$

B) ${{\left\{ f(x) \right\}}^{3}}$

C) $\frac{{{\left\{ f(x) \right\}}^{3}}}{3}$

D) ${{\left\{ f(x) \right\}}^{2}}$

• question_answer103) $\int{{{\sin }^{-1}}\left\{ \frac{(2x+2)}{\sqrt{4{{x}^{2}}+8x+13}} \right\}}\,dx$is equal to

A) $(x+1){{\tan }^{-1}}\left( \frac{2x+2}{3} \right)$ $-\frac{3}{4}\log \left( \frac{4{{x}^{2}}+8x+13}{9} \right)+c$

B) $\frac{3}{2}{{\tan }^{-1}}\left( \frac{2x+2}{3} \right)$ $-\frac{3}{4}\log \left( \frac{4{{x}^{2}}+8x+13}{9} \right)+c$

C) $(x+1){{\tan }^{-1}}\left( \frac{2x+2}{3} \right)$ $-\frac{3}{2}\log \,(4{{x}^{2}}+8x+13)+c$

D) $\frac{3}{2}(x+1){{\tan }^{-1}}\left( \frac{2x+2}{3} \right)$ $-\frac{3}{4}\log \,(4{{x}^{2}}+8x+13)+c$

• question_answer104) If the equation of an ellipse is $3{{x}^{2}}+2{{y}^{2}}+6x-8y+5=0,$ then which of the following are true?

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

B) centre is $(-1,\,2)$

C) foci are $(-1,\,1)$are $(-1,\,3)$

D) All of the above

• question_answer105) The equation of the common tangents to the two hyperbolas $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$and $\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1,$are

A) $y=\pm \,\,x\,\,\pm \sqrt{{{b}^{2}}-{{a}^{2}}}$

B) $y=\pm \,\,x\,\,\pm \sqrt{{{a}^{2}}-{{b}^{2}}}$

C) $y=\pm \,\,x\,\,\pm \sqrt{{{a}^{2}}+{{b}^{2}}}$

D) $y=\pm \,\,x\,\,\pm \left( {{a}^{2}}-{{b}^{2}} \right)$

• question_answer106) Domain of the function $f(x)={{\log }_{x}}\cos x,$is

A) $\left( -\frac{\pi }{2},\frac{\pi }{2} \right)-\{\,1\,\}$

B) $\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]-\{\,1\,\}$

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

D) None of these

• question_answer107) Range of the function $y={{\sin }^{-1}}\left( \frac{{{x}^{2}}}{1+{{x}^{2}}} \right),$is

A) $\left( 0,\frac{\pi }{2} \right)$

B) $\left[ \underset{{}}{\mathop{0,}}\, \right.\left. \frac{\pi }{2} \right)$

C) $\left( \left. 0,\frac{\pi }{2} \right] \right.$

D) $\left[ 0,\,\frac{\pi }{2} \right]$

• question_answer108) If $x=\sec \theta -\cos \theta ,$ $y={{\sec }^{n}}\theta -{{\cos }^{n}}\theta ,$ then $({{x}^{2}}+4){{\left( \frac{dy}{dx} \right)}^{2}}$is equal to

A) ${{n}^{2}}({{y}^{2}}-4)$

B) ${{n}^{2}}(4-{{y}^{2}})$

C) ${{n}^{2}}({{y}^{2}}+4)$

D) None of these

• question_answer109) If $y=\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y+.....\infty }}}},$then $\frac{dy}{dx}$is equal to

A) $\frac{y+x}{{{y}^{2}}-2x}$

B) $\frac{{{y}^{3}}-x}{2{{y}^{2}}-2xy-1}$

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

D) None of these

• question_answer110) If $\int_{1}^{x}{\frac{dt}{\left| \,t\, \right|\sqrt{{{t}^{2}}-1}}}=\frac{\pi }{6},$then $x$can be equal to

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

B) $\sqrt{3}$

C) $2$

D) None of these

• question_answer111) The area bounded by the curve $y=\left| \,\sin x\, \right|,$$x\text{-}$axis and the lines $\left| \,x\, \right|=\pi ,$is

A) 2 sq unit

B) 1 sq unit

C) 4 sq unit

D) None of these

• question_answer112) The degree of the differential equation of all curves having normal of constant length c is

A) 1

B) 3

C) 4

D) None of these

• question_answer113) If $\overrightarrow{a}=2\hat{i}+2\hat{j}+3\hat{k},$ $\overrightarrow{b}=-\hat{i}+2\hat{j}+\hat{k}$ and $\overrightarrow{c}=3\hat{i}+\hat{j},$ then $\overrightarrow{a}+t\,\overrightarrow{b}$ is perpendicular to $\overrightarrow{c},$if t is equal to

A) 2

B) 4

C) 6

D) 8

• question_answer114) The distance between the line $\overrightarrow{r}=2\hat{i}-2\hat{j}+3\hat{k}+\lambda (\hat{i}-\hat{j}+4\hat{k})$ and the plane $\overrightarrow{r}\cdot (\hat{i}+5\hat{j}+\hat{k})=5,$is

A) $\frac{10}{3}$

B) $\frac{10}{\sqrt{3}}$

C) $\frac{10}{3\sqrt{3}}$

D) $\frac{10}{9}$

• question_answer115) The equation of sphere concentric with the sphere ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-4x-6y-8z-5=0$and which passes through the origin is

A) ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-4x-6y-8z=0$

B) ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-6y-8z=0$

C) ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}=0$

D) ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-4x-6y-8z-6=0$

• question_answer116) If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect, then the value of k, is

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

B) $\frac{9}{2}$

C) $-\frac{2}{9}$

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

• question_answer117) The two curves $y={{3}^{x}}$and $y={{5}^{x}}$intersect at an angle

A) ${{\tan }^{-1}}\left( \frac{\log 3-\log 5}{1+\log 3\,\,\log 5} \right)$

B) ${{\tan }^{-1}}\left( \frac{\log 3+\log 5}{1-\log 3\,\,\log 5} \right)$

C) ${{\tan }^{-1}}\left( \frac{\log 3+\log 5}{1+\log 3\,\,\log 5} \right)$

D) ${{\tan }^{-1}}\left( \frac{\log 3-\log 5}{1-\log 3\,\,\log 5} \right)$

• question_answer118) The equation $\lambda {{x}^{2}}+4xy+{{y}^{2}}+\lambda x+3y+2=0$ represents a parabola, if $\lambda$ is

A) 0

B) 1

C) 2

D) 4

• question_answer119) If two circles $2{{x}^{2}}+2{{y}^{2}}-3x+6y+k=0$ and ${{x}^{2}}+{{y}^{2}}-4x+10y+16=0$ cut orthogonally, then the value of k is

A) 41

B) 14

C) 4

D) 1

• question_answer120) If $A\,(-2,\,1),$ $B\,(2,\,3)$ and $C\,(-2,\,-4)$ are three points. Then the angle between $BA$and $BC$is

A) ${{\tan }^{-1}}\left( \frac{2}{3} \right)$

B) ${{\tan }^{-1}}\left( \frac{3}{2} \right)$

C) ${{\tan }^{-1}}\left( \frac{1}{3} \right)$

D) ${{\tan }^{-1}}\left( \frac{1}{2} \right)$