# Solved papers for Manipal Engineering Manipal Engineering Solved Paper-2015

### done Manipal Engineering Solved Paper-2015

• question_answer1) Two point charges 2q and 8q are placed at a distance r apart. Where should a third charge -q be placed between them, so that the electrical potential energy of the system is minimum?

A) At a distance of r/3 from 2q

B) At a distance of 2/73 from 2q

C) At a distance of r/16 from 2q

D) None of the above

• question_answer2) If levels 1 and 2 are separated by an energy $C\xrightarrow[{}]{{}}D;{{k}_{2}}={{10}^{12}}{{e}^{-24,606/T}}$ such that the corresponding transition frequency falls in the middle of the visible range, calculate the ratio of the populations of two levels in the thermal equilibrium at room temperature.

A) ${{k}_{1}}$

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

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

D) $C{{s}^{+}}$

• question_answer3) The energy of a hydrogen atom in its ground state is -13.6eV. The energy of the level corresponding to the quantum number n = 5 is

A) -5.40eV

B) -0.54eV

C) -8.5eV

D) -2.72eV

• question_answer4) We have a galvanometer of resistance 25 $C{{l}^{-}}$. It is shunted by 2.5 $9.2g{{N}_{2}}{{O}_{4}}$ wire. The part of the total current that flows through the galvanometer is given as

A) ${{N}_{2}}{{O}_{4}}(g)2N{{O}_{2}}(g)$

B) ${{N}_{2}}{{O}_{4}}$

C) ${{N}_{2}}{{O}_{4}}=92$

D) ${{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{p}}$

• question_answer5) Two moles of helium are mixed with n moles of hydrogen. The root mean square (rms) speed of gas molecules in the mixture is $-{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{p}}$ times the speed of sound in the mixture. Then, the value of n is

A) 1

B) 3

C) 2

D) 3/2

• question_answer6) A coil having n turns and resistance RQ, is connected with a galvanometer of resistance ${{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{v}}$ This combination is moved in time second from a magnetic field $-{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{v}}$ weber to $C{{l}_{2}}O,IC{{l}^{-}}_{2}$ weber. The induced current in the circuit is

A) $Cl_{2}^{-},Cl{{O}_{2}}$

B) $IF_{2}^{+},l_{3}^{-}$

C) $ClO_{2}^{-},ClF_{2}^{+}$

D) $C{{s}^{+}}$

• question_answer7) A thin film of soap solution $L{{i}^{+}}$lies on the top of a glass plate (a =1.5). When incident light is almost normal to the plate, two adjacent reflection maxima are observed at two wavelengths 420 nm and 630 nm. The minimum thickness of the soap solution is (a)

A) 420 nm

B) 450 nm

C) 630 nm

D) 1260nm

• question_answer8) A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that B is in the plane of the coil. If due to current i in the triangle, a torque t acts on it. The side I of the triangle is

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

B) ${{K}^{+}}$

C) ${{C}_{2}}{{H}_{4}}B{{r}_{2}}\xrightarrow[{}]{Alc.KOH}{{C}_{2}}{{H}_{2}}$

D) ${{I}_{2}}$

• question_answer9) The two blocks of masses $K{{l}_{2}}$ and ${{l}^{-}}$are kept on a smooth horizontal table as shown in the figure. Block of mass ${{K}^{+}};{{l}^{-}}$ but not ${{l}_{2}}$ is fastened to the spring. If now both the blocks are pushed to the left, so that the spring is compressed at a distance d. The amplitude of oscillation of block of mass $l_{3}^{-}$ after the system released, is A) ${{(1.0002)}^{3000}}$

B) $(a.\hat{i})(a\times \hat{i})+(a.\hat{j})(a\times \hat{j})+(a.\hat{k})(a\times \hat{k})$

C) $A=\{(x,y):{{x}^{2}}+{{y}^{2}}=25\}$

D) $B=\{(x,y):{{x}^{2}}+{{y}^{2}}=144\};$

• question_answer10) A juggler keeps on moving four balls in air throwing the balls after regular intervals. When one ball leaves his hand (speed $A\cap B$), the position of other balls (height in metre) will be $f(x)=\sqrt{{{x}^{2}}-4,}a=2$

A) 10,20,10

B) 15,20, 15

C) 5,15, 20

D) 5,10, 20

• question_answer11) Two coils have mutual inductance 0.005 H. The current changes in the first coil according to equation $\sqrt{5}$ where $\sqrt{3}$ A and $\sqrt{3}+1$. The maximum value of emf in the second coil is

A) 12 $n(n+1)d$

B) 8$\frac{n(n+1)d}{2n+1}$

C) 57$\frac{n(n+1)d}{2n}$

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

• question_answer12) A ball is projected from the point O with velocity 20 m/s at an angle of 60? with horizontal as shown in the figure. At highest point of its trajectory, it strikes a smooth plane of inclination 30? at point A. The collision is perfectly inelastic. The maximum height from the ground attained by the ball is A) 18.75m

B) 15m

C) 22.5m

D) 20.25m

• question_answer13) In a nuclear reactor, $f(x)=x{{e}^{x}}^{(1-x)},$ undergoes fission liberating 200 MeV of energy. The reactor has a 10% efficiency and produces 1000 MW power. If the reactor is to function for 10 yr, then find the total mass of uranium required.

A) $\left[ 1\frac{1}{2},1 \right]$

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

C) $\omega$

D) $(1+\omega )(1+{{\omega }^{2}}(1+{{\omega }^{3}})(1+{{\omega }^{4}})$

• question_answer14) A capacitor of capacitance $(1+{{\omega }^{5}})...(1+{{\omega }^{3n}})$ is charged to potential 50 V with a battery. The battery is now disconnected and an additional charge ${{2}^{3n}}$ is given to the positive plate of the capacitor. The potential difference across the capacitor will be

A) 50 V

B) 80 V

C) 100 V

D) 60 V

• question_answer15) The following configuration of gate is equivalent to A) NAND

B) XOR

C) OR

D) None of these

• question_answer16) Under what conditions current passing through the resistance R can be increased by short circuiting the battery of emf ${{2}^{2n}}$? The internal resistances of the two batteries are${{2}^{n}}$ and ${{x}^{2r}}$ respectively.

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

B) ${{\sin }^{-1}}\left\{ \cos \left( {{\sin }^{-1}}\sqrt{\frac{2-\sqrt{3}}{4}} \right. \right.$

C) $\left. \left. +{{\cos }^{-1}}\frac{\sqrt{12}}{4}+{{\sec }^{-1}}\sqrt{2} \right) \right\}$

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

• question_answer17) A rectangular glass slab ABCD of refractive index $\frac{\pi }{6}$ is immersed in water of refractive index $\frac{\pi }{2}$A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence ${{\cos }^{-1}}\frac{x}{2}+{{\cos }^{-1}}\frac{y}{3}=\theta ,$such the ray comes out only from the another surface CD is given by A) $9{{x}^{2}}-12xy\cos 6+4{{y}^{2}}$

B) $-36{{\sin }^{2}}\theta$

C) $36{{\sin }^{2}}\theta$

D) $36{{\cos }^{2}}\theta$

• question_answer18) A sinusoidal wave travelling in the positive direction on stretched string has amplitude 20 cm, wavelength 1 m and wave velocity 5 m/s. At x = 0 and t = 0, it is given that y = 0 and $\tan \left( {{\sec }^{-1}}x \right)=\sin \left( {{\cos }^{-1}}\frac{1}{\sqrt{5}} \right),$Find the wave function y (x,t).

A) $\pm \frac{3}{\sqrt{5}}$

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

C) $\pm \sqrt{\frac{3}{5}}$

D) $y=(2x-1){{e}^{2(1-x)}}$

• question_answer19) The length of a potentiometer wire is 7. A cell of emf E is balanced at length l/3 from the positive end of the wire. If the length of the wire is increased by l/2. Then, at what distance will the same cell give a balance point?

A) $y-1=0$

B) $x-1=0$

C) $x+y-1=0$

D) $x-y+1=0$

• question_answer20) Find the inductance of a unit length of two parallel wires, each of radius a, whose centres are at distance d apart and carry equal currents in opposite directions. Neglect the flux within the wire.

A) $(p\to \tilde{\ }p\wedge )(\tilde{\ }p\to p)$

B) $\frac{6!}{3!}$

C) $\underset{x\to -1}{\mathop{\lim }}\,\left( \frac{{{x}^{4}}+{{x}^{2}}=x+1}{{{x}^{2}}-x+1} \right)\frac{1-\cos (x+1)}{{{(x+1)}^{2}}}$

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

• question_answer21) Two wires of same lengths are shaped into a square and a circle. If they carry same current, then the ratio of their magnetic moments is

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

B) ${{e}^{1/2}}$

C) ${{\left( x-\frac{1}{x} \right)}^{4}}{{\left( x+\frac{1}{x} \right)}^{3}}.$

D) ${{A}^{2}}=A$

• question_answer22) A circular coil of 100 turns has an effective radius of 0.05 m and carries a current of How much work is required to turn it in an external magnetic field of 1.5 Wb/m2 through 180? about its axis perpendicular to the magnetic field? The plane of the coil is initially perpendicular to the magnetic field.

A) 0,456 J

B) 2.65 J

C) 0.2355 J

D) 3.95 J

• question_answer23) The time constant of L-R circuit is

A) LR

B) ${{(1+A)}^{n}}=I+\lambda A,$

C) $\lambda$

D) $2n-1$

• question_answer24) In wave mechanics, the angular momentum of an electron is given by

A) ${{2}^{n}}-1$

B) $u={{e}^{x}}\sin x$

C) $v={{e}^{x}}\cos x$

D) $v\frac{du}{dx}-u\frac{dv}{dx}={{u}^{2}}+{{v}^{2}}$

• question_answer25) The alternating voltage and current in an electric circuit are respectively given by $\frac{{{d}^{2}}u}{d{{x}^{2}}}=2v$ The reactance of the circuit will be

A) $\frac{{{d}^{2}}u}{d{{x}^{2}}}=-2u$

B) ${{\tan }^{-1}}\left( \frac{\sqrt{1+{{x}^{2}}}-1}{x} \right)$

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

D) zero

• question_answer26) The biological damage caused by 1 gray $\frac{1}{8}$radiation is compared with 1 gray $\frac{1}{4}$radiation in the same type of human tissue. The damage caused by the y-radiation is

A) more serious as compared to the damage caused by the $\text{ }\!\!\alpha\!\!\text{ -}$radiation.

B) less serious as compared to the damage caused by the a-radiation

C) equally serious as the damage caused by the $\frac{1}{2}$radiation

D) incomparable with the damage caused by the $\int_{{}}^{{}}{\frac{1-{{x}^{2}}}{(1+{{x}^{2}})\sqrt{1+{{x}^{4}}}}dx}$radiation, because $\sqrt{2}{{\sin }^{-1}}\left\{ \frac{\sqrt{2}x}{{{x}^{2}}+1} \right\}+C$radiation are not particles.

• question_answer27) Two identical coherent sources placed on a diameter of a circle of radius R at separation $\frac{1}{\sqrt{2}}{{\sin }^{-1}}\left\{ \frac{\sqrt{2}x}{{{x}^{2}}+1} \right\}+C$ symmetrically about the centre of the circle. The sources emit identical wavelength X each. The number of points on the circle with maximum intensity is $\frac{1}{2}{{\sin }^{-1}}\left\{ \frac{\sqrt{2}x}{{{x}^{2}}+1} \right\}+C$

A) 20

B) 22

C) 24

D) 26

• question_answer28) Two point masses 1 and 2 move with uniform velocities $\Delta ABC,\left| \begin{matrix} 1 & a & b \\ 1 & c & a \\ 1 & b & c \\ \end{matrix} \right|=0,$ and ${{\sin }^{2}}A+{{\sin }^{2}}B\text{ }+{{\sin }^{2}}C$ respectively. Their initial position vectors are $\frac{3\sqrt{3}}{2}$ and $\frac{9}{4}$ respectively. Which of the following should be satisfied for the collision of the point masses?

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

B) $y=x,x=e,y=\frac{1}{x}$

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

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

• question_answer29) A neutron moving with a speed v makes a head on collision with a hydrogen atom in ground state kept at rest. The minimum kinetic energy of neutron for which inelastic collision will take place is

A) 10.2eV

B) 20.4eV

C) 12.1eV

D) 16.8eV

• question_answer30) The specific heat at constant volume for the mono atomic argon is 0.075 kcal/kg-K, whereas its gram molecular specific heat is $\frac{5}{2}$ cal/mol K. The mass of the carbon atom is

A) $\underset{x\to \infty }{\mathop{\lim }}\,{{\left\{ \frac{a_{1}^{1/x}+a_{2}^{1/x}+...+a_{n}^{1/x}}{n} \right\}}^{nx}},$

B) ${{a}_{1}}+{{a}_{2}}+...+{{a}_{n}}$

C) ${{e}^{{{a}_{1}}+{{a}_{2}}+...+{{a}_{n}}}}$

D) $\frac{{{a}_{1}}+{{a}_{2}}+...+{{a}_{n}}}{n}$

• question_answer31) Order of magnitude of density of uranium nucleus is ${{a}_{1}}{{a}_{2}}...{{a}_{n}}$

A) $\int_{{}}^{{}}{\frac{{{\sec }^{2}}x}{{{(\sec x+\tan x)}^{9/2}}}dx}$

B) $-\frac{1}{{{(\sec x+\tan x)}^{11/2}}}\left\{ \frac{1}{11}-\frac{1}{7}{{(\sec x+\tan x)}^{2}} \right\}+K$

C) $\frac{1}{{{(\sec x+\tan x)}^{11/2}}}\left\{ \frac{1}{11}-\frac{1}{7}{{(\sec x+\tan x)}^{2}} \right\}+K$

D) $-\frac{1}{{{(\sec x+\tan x)}^{11/2}}}\left\{ \frac{1}{11}+\frac{1}{7}(\sec x+\tan x) \right\}+K$

• question_answer32) A block of mass m is lying on the edge having inclination angle ${{x}^{2}}+{{y}^{2}}=9,$Wedge is moving with a constant acceleration, a $\left( \frac{3}{2},\frac{1}{2} \right)$ The minimum value of coefficient of friction $\left( \frac{1}{2},\frac{3}{2} \right)$ so that m remains stationary with respect to wedge is A) $\left( \frac{1}{2},\frac{1}{2} \right)$

B) $\left( \frac{1}{2},\pm \sqrt{2} \right)$

C) ${{y}^{2}}-kx+8=0,$

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

• question_answer33) A small particle of mass m is released from rest from point A inside a smooth hemispherical bowl as shown in the figure. The ratio (x) of magnitude of centripetal force and normal reaction on the particle at any point B varies with 9 as A) (a) B) C) D) • question_answer34) A solid cylinder is rolling down on an inclined plane of angle $\frac{1}{4}$. The coefficient of static friction between the plane and the cylinder is ${{(y-2)}^{2}}=(x-1),$ The condition for the cylinder not to slip is

A) $x=1+xy\frac{dy}{dx}+\frac{{{(xy)}^{2}}}{2!}+{{\left( \frac{xy}{dx} \right)}^{2}}+\frac{{{(xy)}^{3}}}{3!}{{\left( \frac{dy}{dx} \right)}^{3}}$

B) $y={{\log }_{e}}(x)+C$

C) $y={{({{\log }_{e}}x)}^{2}}+C$

D) $y=\pm \sqrt{{{\log }_{e}}x{{)}^{2}}+2C}$

• question_answer35) For a given density of a planet, the orbital speed of satellite near 'the surface of the planet of radius R is proportional to

A) $xy={{x}^{y}}+C$

B) $\frac{4}{{{100}^{3}}}$

C) $\frac{3}{{{50}^{3}}}$

D) $\frac{3!}{{{100}^{3}}}$

• question_answer36) A large slab of mass 5 kg lies on a smooth horizontal surface, with a block of mass 4 kg lying on the top of it, the coefficient of friction between the block and the slab is 0.25. If the block is pulled horizontally by a force of F = 6N, the work done by the force of friction on the slab between the instants t = 2 s and t = 3 s is A) 2.4 J

B) 5.55 J

C) 4,44 J

D) -10 J

• question_answer37) Two unequal masses are connected on two sides of a light string passing over a light and smooth pulley as shown in the figure. The system is released from the rest. The larger mass is stoped for a moment, Is after the system is set into motion. The time elapsed before the string is tight again is A) 1/4 s

B) 1/2 s

C) 2/3 s

D) 1/3 s

• question_answer38) Figure shows an irregular block of material of refractive index $f(x)=\left\{ \begin{matrix} \frac{\sin (\cos x)-\cos x}{{{(\pi -2x)}^{3}}}, & x\ne \frac{\pi }{2} \\ k, & x=\frac{\pi }{2} \\ \end{matrix} \right.$A ray of light strikes the face AB as shown in figure. After refraction, it is incident on a spherical surface CD of radius of curvature 0.4 m and enters a medium of refractive index 1.514 to meet PQ at E. Find the distance OE up to two places of decimal. A) 7m

B) 7.29m

C) 6.06 m

D) 8.55 m

• question_answer39) The ratio of the energy required to raise a satellite upto a height h above the earth to the kinetic energy of the satellite into the orbit is

A) $x=\frac{\pi }{2},$

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

C) $-\frac{1}{24}$

D) $-\frac{1}{48}$

• question_answer40) In the circuit diagram, the current through the Zener diode is A) 10 mA

B) 3.33 mA

C) 6.67 mA

D) 0 mA

• question_answer41) The frequency of son meter wire is f, but when the weights producing the tensions are completely immersed in water, the frequency becomes f/2 and on immersing the weights in a certain liquid, the frequency becomes f/3. The specific gravity of the liquid is

A) 4/3

B) 16/9

C) 15/12

D) 32/27

• question_answer42) Find the frequency of light which ejects electron from a metal surface fully stopped by a retarding potential of 3V. The photoelectric effect begins in this metal at a frequency of $f(x)=[x]+\left[ x+\frac{1}{2} \right]$

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

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

C) $\underset{x\to {{(1/2)}^{+}}}{\mathop{\lim }}\,f(x)=2$

D) $\underset{x\to {{(1/2)}^{-}}}{\mathop{\lim }}\,f(x)=1$

• question_answer43) Equations of a stationary and a travelling waves are as follows, $f(x)=\min \{1,{{x}^{2}},{{x}^{3}}\},$and ${{x}_{n}}=\cos \frac{\pi }{{{3}^{n}}}+i\sin \frac{\pi }{{{3}^{n}}},$ The phase difference between two points ${{x}_{1}}.{{x}_{2}}.{{x}_{3}}...$and $9{{x}^{2}}-18\text{ }\!\!|\!\!\text{ x }\!\!|\!\!\text{ }+5=0$ are ${{\log }_{e}}$and ${{2}^{x}}+{{2}^{y}}={{2}^{x+y}}y,$ respectively for two waves. The ratio $\frac{dy}{dx}$is

A) 1

B) 5/6

C) 3/4

D) 6/7

• question_answer44) Out of a photon and an electron, the equation E =Pc, is valid for

A) both

B) neither

C) photon only

D) electron only

• question_answer45) A small block of wood of specific gravity 0.5 is submerged at a depth of 1.2 m in a vessel filled with the water. The vessel is accelerated upwards with an acceleration $\frac{{{2}^{x}}+{{2}^{y}}}{{{2}^{x}}-{{2}^{y}}}$ Time taken by the block to reach the surface, if it is released with zero initial velocity is

A) 0.6 s

B) 0.4 s

C) 1.2s

D) 1 s

• question_answer46) An electron beam accelerated from rest through a potential 'difference of 5000 V in vacuum is allowed to impinge on a surface normally. The incident current is $\frac{{{2}^{x}}+{{2}^{y}}}{1+{{2}^{x+y}}}$ and if the electron comes to rest on striking the surface, the force on it is

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

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

C) $x-3y=0$

D) $x+3y=0$

• question_answer47) A uniform rod of length 2 m, specific gravity 0.5 and mass 2 kg is hinged at one end to the bottom of a tank of water (specific gravity =1.0) filled upto a height of 1 m as shown in the figure. Taking the case $3x-y=0$the force exerted by the hinge on the rod is A) 10.2 N upwards

B) 4.2 N downwards

C) 8.3 N downwards

D) 6.2 N upwards

• question_answer48) A projectile is thrown in upward direction making an angle of 60? with the horizontal direction with a velocity of 150 $2x+y=0$ Then, the time after which its inclination with horizontal is 45?, is

A) $\sin A+\cos A=m$

B) ${{\sin }^{3}}A+{{\cos }^{3}}A=n,$

C) $~{{m}^{3}}-3m+n=0$

D) ${{n}^{3}}-3n+2m=0$

• question_answer49) When a copper sphere is heated, percentage change is

B) maximum in volume

C) maximum in density

D) equal in radius, volume and density

• question_answer50) In Young's double slit experiment, fringes of width ${{m}^{3}}-3m+2n=0$ are produced on the screen kept at a distance of 1m from the slit. When the screen is moved away by ${{m}^{3}}+3m+2n=0$fringe width changes by $\Delta ABC,$The separation between the slits is $a=4,b=3,\angle A=60{}^\circ .$ The wavelength of light used is..... .nm.

A) 500

B) 600

C) 700

D) 400

• question_answer51) How many moles of ${{c}^{2}}-3c-7=0$ would be in 50 g of the substance?

A) 0.0843 mol

B) 0.952 mol

C) 0,481 mol

D) 0.140 mol

• question_answer52) The ionisation energy of hydrogen atom is 13.6 eV. What will be the ionisation energy of He+?

A) 13.6eV

B) 54.4eV

C) 122.4eV

D) Zero

• question_answer53) In which of the following arrangement the order is not according to the property indicated against it?

A) ${{c}^{2}}+3c+7=0$ (increasing metallic radius)

B) ${{c}^{2}}-3c+7=0$(increasing electron gain enthalpy, with negative sign)

C) ${{c}^{2}}+3c-7=0$ (increasing first ionization enthalpy)

D) $\frac{3}{{{1}^{2}}}+\frac{5}{{{1}^{2}}+{{2}^{2}}}+\frac{7}{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}+...,$ (increasing ionic size)

• question_answer54) The bond angle in $\frac{6n}{n+1}$ is 104.5?. This fact can be explained with the help of

A) valence shell electron pair repulsion theory (VSEPR)

B) molecular orbital theory

C) presence of hydrogen bond

D) electro negativity difference between hydrogen and oxygen atoms

• question_answer55) Under which of the following condition, vander Waals' gas approaches ideal behaviour?

A) Extremely lower pressure

B) Low temperature

C) High pressure

D) Low product of pV

• question_answer56) The enthalpy of combustion of carbon and carbon monoxide are - 393.5 and 283 kJ/mol respectively. The enthalpy of formation of carbon monoxide per mole is

A) 110.5 kJ

B) 676.5 kJ

C) -676,5 kJ

D) -110.5kJ

• question_answer57) Equivalent amounts of $\frac{9n}{n+1}$ and $\frac{12n}{n+1}$are heated in a closed vessel till equilibrium is obtained. If 80% of the hydrogen can be converted to HI, the $\frac{3n}{n+1}$at this temperature is

A) 64

B) 16

C) 0.25

D) 4

• question_answer58) Which of the following is false about $\int_{\sqrt{\ln 2}}^{\sqrt{\ln 3}}{\frac{x\sin {{x}^{2}}}{\sin {{x}^{2}}+\sin (\ln 6-{{x}^{2}})}dx}$?

A) Act as both oxidising and reducing agent

B) Two OH. bond lie in the same plane

C) Pale blue liquid

D) Can be oxidised by ozone

• question_answer59) $\frac{1}{4}\ln \frac{3}{2}$ is used in space and submarines because it

A) absorb $\frac{1}{2}\ln \frac{3}{2}$ and increase $\ln \frac{3}{2}$ concentration

B) absorb moisture

C) absorb $\frac{1}{6}\ln \frac{3}{2}$

D) produce ozone

• question_answer60) The relative Lewis acid character of boron trihalides is the order

A) $\int_{1}^{4}{{{\log }_{e}}[x]dx}$

B) ${{\log }_{e}}2$

C) ${{\log }_{e}}3$

D) ${{\log }_{e}}6$

• question_answer61) The IUPAC name of A) 2-methyl-3-bromo hex anal

B) 3-bromo-2-methyi but anal

C) 2-bromo-3-bromo but anal

D) 3-bromo-2-methyi pent anal

• question_answer62) Which of the following would react most readily with nucleophiles?

A) B) C) D) • question_answer63) Ethyl acetpacetate shows, Which type of isomerism?

A) Chain

B) Optical

C) Mesmerism

D) Tautomerism

• question_answer64) $9{{x}^{2}}+16{{y}^{2}}=144$ Here the compound C is

A) 3-bromo -2,4,5,6-trichloro toluene

B) o-bromo toluene

C) p-bromo toluene

D) m-bromo toluene

• question_answer65) An important product in the ozone deplation by chlorofluoro carbons is

A) $\sqrt{12}$

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

C) $f(x)=\frac{\sin ({{e}^{x-2}}-1)}{\log (x-1)},$

D) $\underset{x\to 2}{\mathop{\lim }}\,f(x)$

• question_answer66) The crystalline structure of NaCl is

A) hexagonal close packing

B) face centred cubic

C) square planar

D) body centred cubic

• question_answer67) 40% by weight solution will contain how much mass of the solute in 1L solution, density of the solution is 1.2 g/mL?

A) 480g

B) 48g

C) 38 g

D) 380 g

• question_answer68) The standard reduction potential E? for half reactions are, ${{x}^{2}}-ax+b=0,$ ${{\sin }^{2}}(A+B)$ The emf of the cell reaction; $\frac{{{a}^{2}}}{{{a}^{2}}+{{(1-b)}^{2}}}$is

A) -0.35V

B) + 0.35V

C) +1.17V

D) -1.17V

• question_answer69) $\frac{{{a}^{2}}}{{{a}^{2}}+{{b}^{2}}}$ The activation energy for the forward reaction is 50 kcal. What is the activation energy for the back word reaction?

A) -72 kcal

B) -28 kcal

C) +28kcal

D) +72kcal

• question_answer70) The coagulating power of an electrolyte for arsenious sulphide decrease in order

A) $\frac{{{a}^{2}}}{{{(a+b)}^{2}}}$

B) $\frac{{{a}^{2}}}{{{b}^{2}}+{{(1-a)}^{2}}}$

C) $\Delta ABC,$

D) ${{a}^{2}}+{{b}^{2}}+{{c}^{2}}=ac+\sqrt{3}ab,$

• question_answer71) $(a\times b)\times c=\frac{1}{3}|b|\,\,|c|$ The element Y is

A) $\theta$

B) $\theta$

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

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

• question_answer72) Hydrolysis of $\frac{2}{3}$gives $\frac{1}{3}$ and X. Which of the following is -X?

A) $2x-3y-4=0$

B) $x+y=1,$

C) $\sqrt{2}$

D) $5\sqrt{2}$

• question_answer73) In the reaction,$\frac{1}{\sqrt{2}}$$\frac{1}{2}$identify the metal M,

A) Copper

B) Iron

C) Silver

D) Zinc $\lambda$$2n-1$ This process is called cynide process. It is used in the extraction of silver from argentite ${{2}^{n}}-1$

• question_answer74) In which of the following complex ion, the central matal ion is in a state of $a{{x}^{2}}+2hxy+b{{y}^{2}}=1,a>0$hybridisation?

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

B) $f(x)=x{{e}^{-x}}$

C) $[0,\infty ),$

D) $0$

• question_answer75) In the reaction sequence,$\frac{1}{e}$what is the molecular formula of V?

A) ${{C}_{3}}{{H}_{6}}{{O}_{2}}$

B) ${{C}_{3}}{{H}_{5}}N$

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

D) ${{C}_{2}}{{H}_{6}}O$

• question_answer76) A) B) C) D) • question_answer77) The product P in the reaction is A) B) C) D) • question_answer78) An organic compound of molecular formula $\theta$did not give a silver mirror with Tollen's reagent, but gave an oxime with hydroxylamine, it may be

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

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

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

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

• question_answer79) Given the following sequence of reactions, $f(x)={{\log }_{5}}(25-{{x}^{2}})$ $2x-y+z+3=0,$The major product C is

A) $r=(\hat{i}+\hat{j})+\lambda (\hat{i}+2\hat{j}-\hat{k})$

B) $r=(\hat{i}+\hat{j})+\mu (-\hat{i}+\hat{j}-2\hat{k}),$

C) $r.(2\hat{i}+\hat{j}-3\hat{k})=-4$

D) $r\times (-\hat{i}+\hat{j}+\hat{k})=0$

• question_answer80) Coupling of diazonium salts of the following takes place in the order A) $r.(-\hat{i}+\hat{j}+\hat{k})=0$

B) $\frac{x-1}{2}=\frac{y-3}{4}=\frac{z-2}{3}$

C) $3x+2y-2z+15=0,$

D) ${{u}_{1}}$

• question_answer81) Which of the following pairs give positive Tollen's test?

A) Glucose, sucrose

B) Glucose, fractose

C) Hexanal, ace. to phenone

D) Fractose, sucrose

• question_answer82) Which one is chain growth polymer?

A) Teflon

B) Nylon-6

C) Nylon-66

D) Bakelite

• question_answer83) Sodium alkyl benzene sulphonate is used as

A) soap

B) fertilizer

C) detergent

D) pesticide

A) ${{u}_{2}}$

B) ${{u}_{1}}$

C) ${{u}_{2}}$

D) ${{u}_{2}}$

A) electrolytic refining

B) zone refining

C) The van-Arkel method

D) Mond process

• question_answer86) Which of the following is the strongest oxidising agent?

A) ${{u}_{1}}$

B) ${{u}_{1}}$

C) ${{u}_{2}}$

D) ${{u}_{2}}$

• question_answer87) In aerosol, the dispersion medium is

A) solid

B) liquid

C) gas

D) Any of these

• question_answer88) For the two gaseous reactions, following data ${{u}_{2}}$ $\frac{13}{30}$the temperature at which $\frac{23}{30}$ becomes equal to $\frac{19}{30}$is

A) 400K

B) 1000 K

C) 800 K

D) 1500 K

E) 500K

• question_answer89) How long (in hours] must a current of 5.0 A be maintained to electroplate 60g of calcium from molten $\frac{11}{30}$?

A) 27 h

B) 8.3 h

C) 11h

D) 16h

• question_answer90) Calculate the molal depression constant of a solvent which has freezing point 16.6? C and latent heat of fusion 180.75 J/g.

A) 2.68

B) 3.86

C) 4.68

D) 2.86

• question_answer91) In CsCI type structure, the coordination number of ${{D}_{k}}=\left| \begin{matrix} a & {{2}^{k}} & {{2}^{16}}-1 \\ b & 3({{4}^{k}}) & 2({{4}^{16}}-1) \\ c & 7({{8}^{k}}) & 4({{8}^{16}}-1) \\ \end{matrix} \right|,$ and $\sum\limits_{k=1}^{16}{{{D}_{k}}}$respectively are

A) 6, 6

B) 6,8

C) 8,8

D) 8,6

• question_answer92) ${{x}^{2}}-4x+4{{y}^{2}}=12$is heated in 1L vessel till equilibrium state is established.$\frac{\sqrt{3}}{2}$ In equilibrium state, 50% $\frac{2}{\sqrt{3}}$ was dissociated, equilibrium constant will be (molecular wt. of $\sqrt{3}$)

A) 0.1

B) 0.4

C) 0.3

D) 0.2

• question_answer93) Enthalpy is equal to

A) $\int_{{}}^{{}}{\frac{1}{\sin \left( x-\frac{\pi }{3} \right)\cos x}dx}$

B) $2\log \left| \sin x+\sin \left( x-\frac{\pi }{3} \right) \right|+C$

C) $2\log \left| \sin x.\sin \left( x-\frac{\pi }{3} \right) \right|+C$

D) $2\log \left| \sin x-\sin \left( x-\frac{\pi }{3} \right) \right|+C$

• question_answer94) The isoelectronic pair is

A) ${{x}^{2}}+\text{ }{{y}^{2}}=2{{a}^{2}}$

B) ${{y}^{2}}=\text{ }8ax$

C) $lF_{2}^{+},l_{3}^{-}$

D) $y=\pm (x+2a)$

A) $x=\pm (y+a)$

B) $y=\pm (x+a)$

C) $x+y+z=1$

D) $2x+3y-z+4=0$

• question_answer96) The ground state term symbol for an electronic state is governed by

A) Heisenberg principle

B) Hund's rule

C) Aufbau principle

D) Pauli exclusion principle

• question_answer97) 2. 76 g of silver carbonate on being strongly heated yeild a residue weighing

A) 2.16g

B) 2.48 g

C) 2,64 g

D) 2.32g

• question_answer98) The following reaction is an example of ...... reaction.$y-3z+6=0$

B) dehydrobromination

C) substitution

D) bromination

• question_answer99) $3y-2+6=0$dissolve in KI solution due to formation of

A) $y+3z+6=0$ and $3y-2z+6=0$

B) $a=2\hat{i}=2\hat{j}-2\hat{k}$and $b=\hat{i}+\hat{j}$

C) $a.c=\left| c \right|,\left| c-a \right|=2\sqrt{2}$

D) None of the above

• question_answer100) The product is

A) B) C) D) • question_answer101) The approximate value of$a\times b$ is

A) 1.2

B) 1.4

C) 1.6

D) 1.8

• question_answer102) $\left| (a\times b)\times c \right|$is equal to

A) 3a

B) a

C) 0

D) None of these

• question_answer103) If $\frac{2}{3}$ and $\frac{3}{2}$ then $\frac{{{d}^{2}}y}{d{{x}^{2}}}={{\left\{ y+{{\left( \frac{dy}{dx} \right)}^{2}} \right\}}^{1/4}}$contains

A) one point

B) three points

C) two points

D) four points

• question_answer104) The value of c prescribed by Lagrange's mean value theorem, when $1+\frac{2}{3}+\frac{6}{{{3}^{2}}}+\frac{10}{{{3}^{3}}}+\frac{14}{{{3}^{4}}}+...$ and b = 3, is

A) 2.5

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

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

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

• question_answer105) The mean deviation from the mean of the series a, a.+ d, a + 2d,..., a + 2nd, is

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

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

C) $\frac{x}{2}+\frac{y}{1}=1$

D) $({{a}^{2}},-{{b}^{2}})$

• question_answer106) If ${{x}^{2}}+9<{{(x+3)}^{2}}<8x+25,$then f(x) is

A) increasing on $\frac{x+y}{x-y}=\frac{5}{2},$

B) decreasing on R

C) increasing on R

D) decreasing on $\frac{x}{y}$

• question_answer107) If $\frac{3}{8}$ is an imaginary cube root of unity, then the value of$\frac{8}{3}$$\frac{5}{3}$is

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

B) $6\frac{2}{3}%$

C) $U=k\left[ \frac{2q(8d)}{r}-\frac{(2q)(q)}{x}-\frac{(8q)(q)}{r-x} \right]$

D) None of these

• question_answer108) Let X denotes the number of times heads occur in n tosses of a fair coin. If P (X = 4), P (X = 5) and P (X = 6} are in AP, then the value of n is

A) 7,14

B) 10,14

C) 12, 7

D) 14,12

• question_answer109) If there is a term containing $k=\frac{1}{4\pi {{\varepsilon }_{0}}}$ in$\frac{2}{x}+\frac{8}{r-x}$then

A) n - 2f is a positive integral multiple of 3.

B) n - 2r is even

C) n - 2r is odd

D) None of the above

• question_answer110) The value of $\frac{2}{x}+\frac{8}{r-x}=y$$\frac{dy}{dx}=0$is

A) $-\frac{2}{{{x}^{2}}}+\frac{8}{{{(r-x)}^{2}}}=0$

B) $\Rightarrow$

C) 0

D) $\frac{x}{r-x}=\sqrt{\frac{2}{8}}=\frac{1}{2}\Rightarrow x=\frac{r}{3}$

• question_answer111) If $x=\frac{r}{3},\frac{{{d}^{2}}y}{d{{x}^{2}}}=$then $x=\frac{r}{3},y$is equal to

A) 36

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

C) $\frac{{{N}_{2}}}{{{N}_{1}}}=\exp \left( -\frac{{{E}_{2}}-{{E}_{1}}}{kT} \right)$

D) $\lambda =550nm$

• question_answer112) $\Rightarrow$then x is equal to

A) ${{E}_{2}}-{{E}_{1}}=\frac{hc}{\lambda }=3.16\times {{10}^{-19}}J$

B) $\Rightarrow$

C) $\frac{{{N}_{2}}}{{{N}_{1}}}=\exp \left( \frac{-3.16\times {{10}^{-19}}J}{(1.38\times {{10}^{-23}}1/k).(300k)} \right)$

D) None of these

• question_answer113) The aquation of the tangent to the curve $\Rightarrow$ at the point of its maximum, is

A) $\frac{{{N}_{2}}}{{{N}_{1}}}=1.1577\times {{10}^{-38}}$

B) ${{E}_{n}}=\frac{-13.6}{({{n}^{2}})}eV$

C) $\therefore$

D) $E=\frac{-13.6}{{{(5)}^{2}}}eV=-0.54eV$

• question_answer114) The proposition $iG=(i-{{i}_{0}})S$is

A) a tautology

• question_answer115) The number of ways in which four letters can be selected from the word 'DEGREE', is

A) 7

B) 6

C) ${{i}_{0}}$

D) None of these

• question_answer116) If PQRS is a convex quadrilateral with 3, 4, 5 and 6 points marked on sides PQ, QR, RS and PS respectively. Then, the number of triangles with vertices on different sides is

A) 220

B) 270

C) 282

D) 342

• question_answer117) $\underset{x\to -1}{\mathop{\lim }}\,{{\left( \frac{{{x}^{4}}+{{x}^{2}}+x+1}{{{x}^{2}}-x-1} \right)}^{\frac{1-\cos (x+1)}{{{(x+1)}^{2}}}}}$is equal to

A) 1

B) $S=2.5\Omega ,G=25\Omega ,$

C) $\frac{i}{{{i}_{0}}}=\frac{1}{11}$

D) $\because$

• question_answer118) The term independent of x in the expansion of ${{v}_{rms}}=\sqrt{\frac{3RT}{M}}$ is

A) -3

B) 0

C) 1

D) 3

• question_answer119) If A is a square matrix such that ${{v}_{sound}}=\sqrt{\frac{\gamma RT}{M}},$and ${{v}_{rms}}=2{{v}_{sound}}$ then $\gamma =\frac{3}{2}=$ is equal to

A) $\frac{{{C}_{p}}}{{{C}_{v}}}$

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

C) 2n + 1

D) None of these

• question_answer120) The functions ${{C}_{p}}=\frac{{{n}_{1}}{{C}_{{{p}_{1}}}}+{{n}_{2}}{{C}_{{{p}_{2}}}}}{{{n}_{1}}+{{n}_{2}}}$ and $\therefore$satisfy the equation

A) $\gamma =\frac{{{C}_{p}}}{{{C}_{v}}}=\frac{{{n}_{1}}{{C}_{{{p}_{1}}}}+{{n}_{2}}{{C}_{{{p}_{2}}}}}{{{n}_{1}}{{C}_{{{v}_{1}}}}+{{n}_{2}}{{C}_{{{v}_{2}}}}}$

B) $\therefore$

C) $\frac{3}{2}=\frac{2\left( \frac{5}{2}R \right)+n\left( \frac{7}{2}R \right)}{2\left( \frac{3}{2}R \right)+n\left( \frac{5}{2}R \right)}$

D) All of these

• question_answer121) The derivative of $\Rightarrow$ with respect to $\frac{3}{2}=\frac{10+7n}{6+5n}$at x = 0, is

A) $\Rightarrow$

B) $I=\frac{E}{R'}$

C) $E=-\frac{nd\phi }{dt},$

D) 1

• question_answer122) $I=-\frac{n}{R'},\frac{d\phi }{dt}$is equal to

A) ${{E}_{2}}-{{E}_{1}},$

B) $1.1577\times {{10}^{-38}}$

C) $2.9\times {{10}^{-35}}$

D) None of these

• question_answer123) In a $2.168\times {{10}^{-36}}$ a =0, then $1.96\times {{10}^{-20}}$is equal to

A) $\Omega$

B) $\Omega$

C) $\frac{i}{{{i}_{0}}}=\frac{4}{11}$

D) 2

• question_answer124) The area of the region enclosed by the curves $\frac{i}{{{i}_{0}}}=\frac{3}{11}$and the positive X-axis, is

A) $\frac{i}{{{i}_{0}}}=\frac{2}{10}$ sq unit

B) 1 sq unit

C) $\frac{i}{{{i}_{0}}}=\frac{1}{11}$ sq units

D) $\sqrt{2}$ sq units

• question_answer125) The value of $4R\Omega .$is

A) ${{w}_{1}}$

B) ${{w}_{2}}$

C) $\frac{-({{w}_{2}}-{{w}_{1}})}{5Rt}$

D) $\frac{-n({{w}_{2}}-{{w}_{1}})}{5Rt}$

• question_answer126) $\frac{-n({{w}_{2}}-{{w}_{1}})}{Rnt}$equals

A) $\frac{-n({{w}_{2}}-{{w}_{1}})}{Rt}$

B) $({{\mu }_{s}}=1.4)$

C) $\frac{2}{\sqrt{3}}\left( \frac{\tau }{Bi} \right)$

D) None of the above

• question_answer127) The centre of the circle passing through (0,0) and (1,0) and touching the circle $2{{\left( \frac{\tau }{\sqrt{3}Bi} \right)}^{1/2}}$is

A) $\frac{2}{\sqrt{3}}{{\left( \frac{\tau }{Bi} \right)}^{1/2}}$

B) $\frac{1}{\sqrt{3}}\frac{\tau }{Bi}$

C) ${{m}_{1}}$

D) ${{m}_{2}}$

• question_answer128) If the line x -1 = 0 is the directrix of the parabola ${{m}_{1}}$ then one of the value of k is

A) ${{m}_{2}}$

B) 8

C) 4

D) ${{m}_{1}}$

• question_answer129) The area of the region bounded by the parabola $d\sqrt{\frac{{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}}}$ the tangent to the parabola at the point (2,3J and the X-axis, is

A) 3

B) 6

C) 9

D) 12

• question_answer130) Solution of the differential equation $d\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}}$+?is

A) $d\sqrt{\frac{2{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}}$

B) $d\sqrt{\frac{2{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}}}$

C) $=20m{{s}^{-1}}$

D) $(\text{take}\,g=10\text{ }m{{s}^{-}}^{2})$

• question_answer131) Numbers 1,2,3,...,100 are written down on each of the cards A, B and C. One number is selected at random from each of the cards. The probability that the numbers so selected can be the measures (in cm) of three sides of a right angled triangle, is

A) $I={{I}_{0}}\sin \omega t,$

B) ${{I}_{0}}=10$

C) $\omega =100\pi \,\text{rad/s}$

D) None of these

• question_answer132) If $\pi$ is a continuous at $\pi$then k is equal to

A) 0

B) $\pi$

C) $\pi$

D) $^{\text{235}}\text{U}$

• question_answer133) If [ ] denotes the greatest integer function, then$36.5\times {{10}^{3}}kg$

A) is continuous at $36\times {{10}^{2}}kg$

B) is discontinuous at $39.5\times {{10}^{3}}kg$

C) $38.2\times {{10}^{3}}kg$

D) $10\mu F$

• question_answer134) If$200\mu F$ then

A) f(x) is not everywhere continuous

B) f(x) is continuous and differentiable everywhere

C) f(x) is not differentiable at two points

D) (x) is not differentiable at one point

• question_answer135) If ${{E}_{2}}$then ${{r}_{1}}$is equal to

A) 1

B) ? 1

C) i

D) -i

• question_answer136) The total number of natural numbers of 6 digits that can be made with digits 1, 2, 3, 4, if all digits are to appear in the same number at least once, is

A) 1560

B) 840

C) 1080

D) 480

• question_answer137) The number of solutions of the equation ${{r}_{2}}$belonging to the domain of definition of ${{E}_{2}}{{r}_{1}}>{{E}_{1}}(R+{{r}_{2}})$ {(x + 1) (x + 2)}, is

A) 1

B) 2

C) 3

D) 4

• question_answer138) lf ${{E}_{1}}{{r}_{2}}<{{E}_{2}}({{r}_{1}}+R)$ then${{E}_{2}}{{r}_{2}}<E(R+{{r}_{2}})$ is equal to

A) ${{E}_{1}}{{r}_{1}}>{{E}_{2}}({{r}_{1}}+R)$

B) ${{n}_{1}}$

C) ${{n}_{1}}({{n}_{1}}>{{n}_{2}}).$

D) ${{\alpha }_{\max }}$

• question_answer139) If 3x + y = 0 is a tangent to the circle with centre at the point (2, - 1), then the equation of the other tangent to the circle from the origin, is

A) ${{\sin }^{-1}}\left[ \frac{{{n}_{1}}}{{{n}_{2}}}\cos \left( {{\sin }^{-1}}\left( \frac{{{n}_{2}}}{{{n}_{1}}} \right) \right) \right]$

B) $\frac{150}{2}=\frac{150\sqrt{3}}{2}-10t$

C) $\Rightarrow$

D) $10t=\frac{150(\sqrt{3}-1)}{2}$

• question_answer140) If $\Rightarrow$and $\Rightarrow$then

A) $\Rightarrow$

B) $t=7.5(\sqrt{3}-1)s$

C) $I<II<III<IV$

D) $NO_{3}^{-}$

• question_answer141) In $C{{l}^{-}}$ if ${{l}^{-}}$Then, c is the root of the equation

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

B) $HOCl$

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

D) $HCl{{O}_{3}}$

• question_answer142) The sum to n terms of the series $HCl{{O}_{4}}$is

A) $A\xrightarrow[{}]{{}}B;{{k}_{1}}={{10}^{10}}{{e}^{-20,000/T}}$

B) $C\xrightarrow[{}]{{}}D;{{k}_{2}}={{10}^{12}}{{e}^{-24,606/T}}$

C) ${{k}_{1}}$

D) ${{k}_{2}}$

• question_answer143) The value of $CaC{{l}_{2}}$is

A) $C{{s}^{+}}$

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

C) $9.2g{{N}_{2}}{{O}_{4}}$

D) ${{N}_{2}}{{O}_{4}}(g)2N{{O}_{2}}(g)$

• question_answer144) ${{N}_{2}}{{O}_{4}}$equals

A) ${{N}_{2}}{{O}_{4}}=92$

B) ${{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{p}}$

C) $-{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{p}}$

D) None of the above

• question_answer145) The radius of the circle passing through the foci of the ellipse ${{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{v}}$ and having its centre at (0,3), is

A) 4

B) 3

C) $-{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{v}}$

D) $C{{l}_{2}}O,IC{{l}^{-}}_{2}$

• question_answer146) If $Cl_{2}^{-},Cl{{O}_{2}}$ then $IF_{2}^{+},l_{3}^{-}$is-given by

A) -2

B) -1

C) 0

D) 1

• question_answer147) If tan A and tan B are the roots of the equation $ClO_{2}^{-},ClF_{2}^{+}$then the value of $C{{s}^{+}}$is

A) $L{{i}^{+}}$

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

C) ${{K}^{+}}$

D) ${{C}_{2}}{{H}_{4}}B{{r}_{2}}\xrightarrow[{}]{Alc.KOH}{{C}_{2}}{{H}_{2}}$

• question_answer148) In a ${{I}_{2}}$ if $K{{l}_{2}}$then the triangle is

A) equilateral

B) right angled and isosceles

C) right angled and not isosceles

D) None of the above

• question_answer149) Let a.b and c be non-zero vectors such that no two are collinear and ${{l}^{-}}$a. If ${{K}^{+}};{{l}^{-}}$ is the acute angle between the vectors b and c, then sin ${{l}_{2}}$ equals

A) $l_{3}^{-}$

B) ${{(1.0002)}^{3000}}$

C) $(a.\hat{i})(a\times \hat{i})+(a.\hat{j})(a\times \hat{j})+(a.\hat{k})(a\times \hat{k})$

D) $A=\{(x,y):{{x}^{2}}+{{y}^{2}}=25\}$

• question_answer150) The distance of the point [1,1) from the line $B=\{(x,y):{{x}^{2}}+{{y}^{2}}=144\};$in the direction of the line $A\cap B$is

A) $f(x)=\sqrt{{{x}^{2}}-4,}a=2$

B) $\sqrt{5}$

C) $\sqrt{3}$

D) $\sqrt{3}+1$

• question_answer151) The two tangents to the curve $n(n+1)d$at the points, where it crosses X-axis, are

A) parallel

B) perpendicular

C) inclined at an angle$\frac{n(n+1)d}{2n+1}$

D) None of these

• question_answer152) The greatest value of the function $\frac{n(n+1)d}{2n}$in$\frac{n(n-1)d}{2n+1}$ is

A) $f(x)=x{{e}^{x}}^{(1-x)},$

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

C) ?e

D) e

• question_answer153) If an isosceles triangle of vertical angle 29 is inscribed in a circle of radius a. Then, area of the triangle is maximum, when $\left[ -\frac{1}{2},1 \right]$ is equal to

A) $\omega$

B) $(1+\omega )(1+{{\omega }^{2}}(1+{{\omega }^{3}})(1+{{\omega }^{4}})$

C) $(1+{{\omega }^{5}})...(1+{{\omega }^{3n}})$

D) ${{2}^{3n}}$

• question_answer154) The range of the function ${{2}^{2n}}$is

A) [0,5]

B) [0,2)

C) (0,2)

D) None of these

• question_answer155) The image of the point P (1,3, 4) in the plane ${{2}^{n}}$is

A) (3, 5,-2)

B) (-3,5,2)

C) (3,-5,2)

D) (3,5,2)

• question_answer156) Equation of the plane that contains the lines${{x}^{2r}}$and$\left( x+\frac{1}{{{x}^{2}}} \right),$is

A) ${{\sin }^{-1}}\left\{ \cos \left( {{\sin }^{-1}}\sqrt{\frac{2-\sqrt{3}}{4}} \right. \right.$

B) $\left. \left. +{{\cos }^{-1}}\frac{\sqrt{12}}{4}+{{\sec }^{-1}}\sqrt{2} \right) \right\}$

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

D) None of these

• question_answer157) The distance of the point (3,8,2) from the line $\frac{\pi }{6}$measured parallel to the plane $\frac{\pi }{2}$ is

A) 2

B) 3

C) 6

D) 7

• question_answer158) Let.${{\cos }^{-1}}\frac{x}{2}+{{\cos }^{-1}}\frac{y}{3}=\theta ,$ and $9{{x}^{2}}-12xy\cos 6+4{{y}^{2}}$be two urns such that $-36{{\sin }^{2}}\theta$contains 3 white, 2 red balls and $36{{\sin }^{2}}\theta$ contains only 1 white ball. A fair coin is tossed. If head appears, then 1 ball is drawn at random from urn $36{{\cos }^{2}}\theta$ and put into $\tan \left( {{\sec }^{-1}}x \right)=\sin \left( {{\cos }^{-1}}\frac{1}{\sqrt{5}} \right),$. However, if tail appears, then 2 balls are drawn at random from $\pm \frac{3}{\sqrt{5}}$ and put into $\pm \frac{\sqrt{5}}{3}$. Now, 1 ball is drawn at random from $\pm \sqrt{\frac{3}{5}}$. Then, probability of the drawn ball from $y=(2x-1){{e}^{2(1-x)}}$ being white is

A) $y-1=0$

B) $x-1=0$

C) $x+y-1=0$

D) $x-y+1=0$

• question_answer159) Let $(p\to \tilde{\ }p\wedge )(\tilde{\ }p\to p)$ then the value of $\frac{6!}{3!}$ is

A) 0

B) a + b + c

C) ab + 6c + ca

D) None of these

• question_answer160) The eccentricity of the conic $\underset{x\to -1}{\mathop{\lim }}\,\left( \frac{{{x}^{4}}+{{x}^{2}}=x+1}{{{x}^{2}}-x+1} \right)\frac{1-\cos (x+1)}{{{(x+1)}^{2}}}$is

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

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

C) ${{e}^{1/2}}$

D) None of these

• question_answer161) The value of ${{\left( x-\frac{1}{x} \right)}^{4}}{{\left( x+\frac{1}{x} \right)}^{3}}.$is

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

B) ${{(1+A)}^{n}}=I+\lambda A,$

C) $\lambda$

D) None of the above

• question_answer162) Two common tangents to the circle $2n-1$and parabola ${{2}^{n}}-1$are

A) $u={{e}^{x}}\sin x$

B) $v={{e}^{x}}\cos x$

C) $v\frac{du}{dx}-u\frac{dv}{dx}={{u}^{2}}+{{v}^{2}}$

D) $\frac{{{d}^{2}}u}{d{{x}^{2}}}=2v$

• question_answer163) The equation of the plane through the intersection of the planes $\frac{{{d}^{2}}u}{d{{x}^{2}}}=-2u$and ${{\tan }^{-1}}\left( \frac{\sqrt{1+{{x}^{2}}}-1}{x} \right)$and parallel to -Y-axis, is

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

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

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

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

• question_answer164) Let $\int_{{}}^{{}}{\frac{1-{{x}^{2}}}{(1+{{x}^{2}})\sqrt{1+{{x}^{4}}}}dx}$and $\sqrt{2}{{\sin }^{-1}}\left\{ \frac{\sqrt{2}x}{{{x}^{2}}+1} \right\}+C$vector such that $\frac{1}{\sqrt{2}}{{\sin }^{-1}}\left\{ \frac{\sqrt{2}x}{{{x}^{2}}+1} \right\}+C$and the angle between $\frac{1}{2}{{\sin }^{-1}}\left\{ \frac{\sqrt{2}x}{{{x}^{2}}+1} \right\}+C$ and c is 30?. Then, $\Delta ABC,\left| \begin{matrix} 1 & a & b \\ 1 & c & a \\ 1 & b & c \\ \end{matrix} \right|=0,$is equal to

A) ${{\sin }^{2}}A+{{\sin }^{2}}B\text{ }+{{\sin }^{2}}C$

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

C) 2

D) 3

• question_answer165) Order and degree of a differential equation $\frac{9}{4}$are

A) 4 and 2

B) 1 and 2

C) 1 and 4

D) 2 and 4

• question_answer166) A cone whose height is always equal to its diameter, is increasing in volume at the rate of 40cm3/s. At what rate is the radius increasing when its circular base area is 1m2?

A) 1 mm/s

B) 0.001 cm/s

C) 2 mm/s

D) 0.002 cm/s

• question_answer167) The sum to infinity of the series $\frac{5}{4}$is

A) 2

B) 3

C) 4

D) 6

• question_answer168) The equations of the straight lines passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is -1, is

A) $y=x,x=e,y=\frac{1}{x}$ and $\frac{1}{2}$

B) $\frac{3}{2}$and $\frac{5}{2}$

C) $\underset{x\to \infty }{\mathop{\lim }}\,{{\left\{ \frac{a_{1}^{1/x}+a_{2}^{1/x}+...+a_{n}^{1/x}}{n} \right\}}^{nx}},$and${{a}_{1}}+{{a}_{2}}+...+{{a}_{n}}$

D) None of the above

• question_answer169) One possible condition for the three points (a,b), (b, a) and ${{e}^{{{a}_{1}}+{{a}_{2}}+...+{{a}_{n}}}}$ to be collinear, is

A) a - 6 = 2

B) a + b = 2

C) a = 1+ 6

D) a = 1 ? 6

• question_answer170) The number of positive integral solutions of $\frac{{{a}_{1}}+{{a}_{2}}+...+{{a}_{n}}}{n}$is

A) 2

B) 3

C) 4

D) 5

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