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 done clear
B) At a distance of 2/73 from 2q done clear
C) At a distance of r/16 from 2q done clear
D) None of the above done clear
View Answer play_arrowquestion_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) \[{{k}_{1}}\] done clear
B) \[{{k}_{2}}\] done clear
C) \[CaC{{l}_{2}}\] done clear
D) \[C{{s}^{+}}\] done clear
View Answer play_arrowquestion_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 done clear
B) -0.54eV done clear
C) -8.5eV done clear
D) -2.72eV done clear
View Answer play_arrowquestion_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) \[{{N}_{2}}{{O}_{4}}(g)2N{{O}_{2}}(g)\] done clear
B) \[{{N}_{2}}{{O}_{4}}\] done clear
C) \[{{N}_{2}}{{O}_{4}}=92\] done clear
D) \[{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{p}}\] done clear
View Answer play_arrowquestion_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 done clear
B) 3 done clear
C) 2 done clear
D) 3/2 done clear
View Answer play_arrowquestion_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) \[Cl_{2}^{-},Cl{{O}_{2}}\] done clear
B) \[IF_{2}^{+},l_{3}^{-}\] done clear
C) \[ClO_{2}^{-},ClF_{2}^{+}\] done clear
D) \[C{{s}^{+}}\] done clear
View Answer play_arrowquestion_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 done clear
B) 450 nm done clear
C) 630 nm done clear
D) 1260nm done clear
View Answer play_arrowquestion_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) \[N{{a}^{+}}\] done clear
B) \[{{K}^{+}}\] done clear
C) \[{{C}_{2}}{{H}_{4}}B{{r}_{2}}\xrightarrow[{}]{Alc.KOH}{{C}_{2}}{{H}_{2}}\] done clear
D) \[{{I}_{2}}\] done clear
View Answer play_arrowquestion_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) \[{{(1.0002)}^{3000}}\] done clear
B) \[(a.\hat{i})(a\times \hat{i})+(a.\hat{j})(a\times \hat{j})+(a.\hat{k})(a\times \hat{k})\] done clear
C) \[A=\{(x,y):{{x}^{2}}+{{y}^{2}}=25\}\] done clear
D) \[B=\{(x,y):{{x}^{2}}+{{y}^{2}}=144\};\] done clear
View Answer play_arrowquestion_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 done clear
B) 15,20, 15 done clear
C) 5,15, 20 done clear
D) 5,10, 20 done clear
View Answer play_arrowquestion_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 \[n(n+1)d\] done clear
B) 8\[\frac{n(n+1)d}{2n+1}\] done clear
C) 57\[\frac{n(n+1)d}{2n}\] done clear
D) 2\[\frac{n(n-1)d}{2n+1}\] done clear
View Answer play_arrowquestion_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 done clear
B) 15m done clear
C) 22.5m done clear
D) 20.25m done clear
View Answer play_arrowquestion_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) \[\left[ 1\frac{1}{2},1 \right]\] done clear
B) \[\left[ -\frac{1}{2},1 \right]\] done clear
C) \[\omega \] done clear
D) \[(1+\omega )(1+{{\omega }^{2}}(1+{{\omega }^{3}})(1+{{\omega }^{4}})\] done clear
View Answer play_arrowquestion_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 done clear
B) 80 V done clear
C) 100 V done clear
D) 60 V done clear
View Answer play_arrowquestion_answer15) The following configuration of gate is equivalent to
A) NAND done clear
B) XOR done clear
C) OR done clear
D) None of these done clear
View Answer play_arrowquestion_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) \[\left( x+\frac{1}{{{x}^{2}}} \right),\] done clear
B) \[{{\sin }^{-1}}\left\{ \cos \left( {{\sin }^{-1}}\sqrt{\frac{2-\sqrt{3}}{4}} \right. \right.\] done clear
C) \[\left. \left. +{{\cos }^{-1}}\frac{\sqrt{12}}{4}+{{\sec }^{-1}}\sqrt{2} \right) \right\}\] done clear
D) \[\frac{\pi }{4}\] done clear
View Answer play_arrowquestion_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) \[9{{x}^{2}}-12xy\cos 6+4{{y}^{2}}\] done clear
B) \[-36{{\sin }^{2}}\theta \] done clear
C) \[36{{\sin }^{2}}\theta \] done clear
D) \[36{{\cos }^{2}}\theta \] done clear
View Answer play_arrowquestion_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) \[\pm \frac{3}{\sqrt{5}}\] done clear
B) \[\pm \frac{\sqrt{5}}{3}\] done clear
C) \[\pm \sqrt{\frac{3}{5}}\] done clear
D) \[y=(2x-1){{e}^{2(1-x)}}\] done clear
View Answer play_arrowquestion_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) \[y-1=0\] done clear
B) \[x-1=0\] done clear
C) \[x+y-1=0\] done clear
D) \[x-y+1=0\] done clear
View Answer play_arrowquestion_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) \[(p\to \tilde{\ }p\wedge )(\tilde{\ }p\to p)\] done clear
B) \[\frac{6!}{3!}\] done clear
C) \[\underset{x\to -1}{\mathop{\lim }}\,\left( \frac{{{x}^{4}}+{{x}^{2}}=x+1}{{{x}^{2}}-x+1} \right)\frac{1-\cos (x+1)}{{{(x+1)}^{2}}}\] done clear
D) \[\sqrt{\frac{2}{3}}\] done clear
View Answer play_arrowquestion_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) \[\sqrt{\frac{3}{2}}\] done clear
B) \[{{e}^{1/2}}\] done clear
C) \[{{\left( x-\frac{1}{x} \right)}^{4}}{{\left( x+\frac{1}{x} \right)}^{3}}.\] done clear
D) \[{{A}^{2}}=A\] done clear
View Answer play_arrowquestion_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 done clear
B) 2.65 J done clear
C) 0.2355 J done clear
D) 3.95 J done clear
View Answer play_arrowquestion_answer23) The time constant of L-R circuit is
A) LR done clear
B) \[{{(1+A)}^{n}}=I+\lambda A,\] done clear
C) \[\lambda \] done clear
D) \[2n-1\] done clear
View Answer play_arrowquestion_answer24) In wave mechanics, the angular momentum of an electron is given by
A) \[{{2}^{n}}-1\] done clear
B) \[u={{e}^{x}}\sin x\] done clear
C) \[v={{e}^{x}}\cos x\] done clear
D) \[v\frac{du}{dx}-u\frac{dv}{dx}={{u}^{2}}+{{v}^{2}}\] done clear
View Answer play_arrowquestion_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) \[\frac{{{d}^{2}}u}{d{{x}^{2}}}=-2u\] done clear
B) \[{{\tan }^{-1}}\left( \frac{\sqrt{1+{{x}^{2}}}-1}{x} \right)\] done clear
C) \[{{\tan }^{-1}}\left( \frac{2x\sqrt{1-{{x}^{2}}}}{1-2{{x}^{2}}} \right)\] done clear
D) zero done clear
View Answer play_arrowquestion_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. done clear
B) less serious as compared to the damage caused by the a-radiation done clear
C) equally serious as the damage caused by the \[\frac{1}{2}\]radiation done clear
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. done clear
View Answer play_arrowquestion_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 done clear
B) 22 done clear
C) 24 done clear
D) 26 done clear
View Answer play_arrowquestion_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) \[\frac{5}{4}\] done clear
B) \[y=x,x=e,y=\frac{1}{x}\] done clear
C) \[\frac{1}{2}\] done clear
D) \[\frac{3}{2}\] done clear
View Answer play_arrowquestion_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 done clear
B) 20.4eV done clear
C) 12.1eV done clear
D) 16.8eV done clear
View Answer play_arrowquestion_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) \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left\{ \frac{a_{1}^{1/x}+a_{2}^{1/x}+...+a_{n}^{1/x}}{n} \right\}}^{nx}},\] done clear
B) \[{{a}_{1}}+{{a}_{2}}+...+{{a}_{n}}\] done clear
C) \[{{e}^{{{a}_{1}}+{{a}_{2}}+...+{{a}_{n}}}}\] done clear
D) \[\frac{{{a}_{1}}+{{a}_{2}}+...+{{a}_{n}}}{n}\] done clear
View Answer play_arrowquestion_answer31) Order of magnitude of density of uranium nucleus is \[{{a}_{1}}{{a}_{2}}...{{a}_{n}}\]
A) \[\int_{{}}^{{}}{\frac{{{\sec }^{2}}x}{{{(\sec x+\tan x)}^{9/2}}}dx}\] done clear
B) \[-\frac{1}{{{(\sec x+\tan x)}^{11/2}}}\left\{ \frac{1}{11}-\frac{1}{7}{{(\sec x+\tan x)}^{2}} \right\}+K\] done clear
C) \[\frac{1}{{{(\sec x+\tan x)}^{11/2}}}\left\{ \frac{1}{11}-\frac{1}{7}{{(\sec x+\tan x)}^{2}} \right\}+K\] done clear
D) \[-\frac{1}{{{(\sec x+\tan x)}^{11/2}}}\left\{ \frac{1}{11}+\frac{1}{7}(\sec x+\tan x) \right\}+K\] done clear
View Answer play_arrowquestion_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) \[\left( \frac{1}{2},\frac{1}{2} \right)\] done clear
B) \[\left( \frac{1}{2},\pm \sqrt{2} \right)\] done clear
C) \[{{y}^{2}}-kx+8=0,\] done clear
D) \[\frac{1}{8}\] done clear
View Answer play_arrowquestion_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) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_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) \[x=1+xy\frac{dy}{dx}+\frac{{{(xy)}^{2}}}{2!}+{{\left( \frac{xy}{dx} \right)}^{2}}+\frac{{{(xy)}^{3}}}{3!}{{\left( \frac{dy}{dx} \right)}^{3}}\] done clear
B) \[y={{\log }_{e}}(x)+C\] done clear
C) \[y={{({{\log }_{e}}x)}^{2}}+C\] done clear
D) \[y=\pm \sqrt{{{\log }_{e}}x{{)}^{2}}+2C}\] done clear
View Answer play_arrowquestion_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) \[xy={{x}^{y}}+C\] done clear
B) \[\frac{4}{{{100}^{3}}}\] done clear
C) \[\frac{3}{{{50}^{3}}}\] done clear
D) \[\frac{3!}{{{100}^{3}}}\] done clear
View Answer play_arrowquestion_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 done clear
B) 5.55 J done clear
C) 4,44 J done clear
D) -10 J done clear
View Answer play_arrowquestion_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 done clear
B) 1/2 s done clear
C) 2/3 s done clear
D) 1/3 s done clear
View Answer play_arrowquestion_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 done clear
B) 7.29m done clear
C) 6.06 m done clear
D) 8.55 m done clear
View Answer play_arrowquestion_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) \[x=\frac{\pi }{2},\] done clear
B) \[-\frac{1}{6}\] done clear
C) \[-\frac{1}{24}\] done clear
D) \[-\frac{1}{48}\] done clear
View Answer play_arrowquestion_answer40) In the circuit diagram, the current through the Zener diode is
A) 10 mA done clear
B) 3.33 mA done clear
C) 6.67 mA done clear
D) 0 mA done clear
View Answer play_arrowquestion_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 done clear
B) 16/9 done clear
C) 15/12 done clear
D) 32/27 done clear
View Answer play_arrowquestion_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) \[x=\frac{1}{2}\] done clear
B) \[x=\frac{1}{2}\] done clear
C) \[\underset{x\to {{(1/2)}^{+}}}{\mathop{\lim }}\,f(x)=2\] done clear
D) \[\underset{x\to {{(1/2)}^{-}}}{\mathop{\lim }}\,f(x)=1\] done clear
View Answer play_arrowquestion_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 done clear
B) 5/6 done clear
C) 3/4 done clear
D) 6/7 done clear
View Answer play_arrowquestion_answer44) Out of a photon and an electron, the equation E =Pc, is valid for
A) both done clear
B) neither done clear
C) photon only done clear
D) electron only done clear
View Answer play_arrowquestion_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 done clear
B) 0.4 s done clear
C) 1.2s done clear
D) 1 s done clear
View Answer play_arrowquestion_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) \[{{2}^{x-y}}\left( \frac{{{2}^{y}}-1}{1-{{2}^{x}}} \right)\] done clear
B) \[\frac{{{2}^{x-y}}-{{2}^{x}}}{{{2}^{y}}}\] done clear
C) \[x-3y=0\] done clear
D) \[x+3y=0\] done clear
View Answer play_arrowquestion_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 done clear
B) 4.2 N downwards done clear
C) 8.3 N downwards done clear
D) 6.2 N upwards done clear
View Answer play_arrowquestion_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) \[\sin A+\cos A=m\] done clear
B) \[{{\sin }^{3}}A+{{\cos }^{3}}A=n,\] done clear
C) \[~{{m}^{3}}-3m+n=0\] done clear
D) \[{{n}^{3}}-3n+2m=0\] done clear
View Answer play_arrowquestion_answer49) When a copper sphere is heated, percentage change is
A) maximum in radius done clear
B) maximum in volume done clear
C) maximum in density done clear
D) equal in radius, volume and density done clear
View Answer play_arrowquestion_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 done clear
B) 600 done clear
C) 700 done clear
D) 400 done clear
View Answer play_arrowquestion_answer51) How many moles of \[{{c}^{2}}-3c-7=0\] would be in 50 g of the substance?
A) 0.0843 mol done clear
B) 0.952 mol done clear
C) 0,481 mol done clear
D) 0.140 mol done clear
View Answer play_arrowquestion_answer52) The ionisation energy of hydrogen atom is 13.6 eV. What will be the ionisation energy of He+?
A) 13.6eV done clear
B) 54.4eV done clear
C) 122.4eV done clear
D) Zero done clear
View Answer play_arrowquestion_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) done clear
B) \[{{c}^{2}}-3c+7=0\](increasing electron gain enthalpy, with negative sign) done clear
C) \[{{c}^{2}}+3c-7=0\] (increasing first ionization enthalpy) done clear
D) \[\frac{3}{{{1}^{2}}}+\frac{5}{{{1}^{2}}+{{2}^{2}}}+\frac{7}{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}+...,\] (increasing ionic size) done clear
View Answer play_arrowquestion_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) done clear
B) molecular orbital theory done clear
C) presence of hydrogen bond done clear
D) electro negativity difference between hydrogen and oxygen atoms done clear
View Answer play_arrowquestion_answer55) Under which of the following condition, vander Waals' gas approaches ideal behaviour?
A) Extremely lower pressure done clear
B) Low temperature done clear
C) High pressure done clear
D) Low product of pV done clear
View Answer play_arrowquestion_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 done clear
B) 676.5 kJ done clear
C) -676,5 kJ done clear
D) -110.5kJ done clear
View Answer play_arrowquestion_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 done clear
B) 16 done clear
C) 0.25 done clear
D) 4 done clear
View Answer play_arrowquestion_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 done clear
B) Two OH. bond lie in the same plane done clear
C) Pale blue liquid done clear
D) Can be oxidised by ozone done clear
View Answer play_arrowquestion_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 done clear
B) absorb moisture done clear
C) absorb \[\frac{1}{6}\ln \frac{3}{2}\] done clear
D) produce ozone done clear
View Answer play_arrowquestion_answer60) The relative Lewis acid character of boron trihalides is the order
A) \[\int_{1}^{4}{{{\log }_{e}}[x]dx}\] done clear
B) \[{{\log }_{e}}2\] done clear
C) \[{{\log }_{e}}3\] done clear
D) \[{{\log }_{e}}6\] done clear
View Answer play_arrowquestion_answer61) The IUPAC name of
A) 2-methyl-3-bromo hex anal done clear
B) 3-bromo-2-methyi but anal done clear
C) 2-bromo-3-bromo but anal done clear
D) 3-bromo-2-methyi pent anal done clear
View Answer play_arrowquestion_answer62) Which of the following would react most readily with nucleophiles?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer63) Ethyl acetpacetate shows, Which type of isomerism?
A) Chain done clear
B) Optical done clear
C) Mesmerism done clear
D) Tautomerism done clear
View Answer play_arrowquestion_answer64) \[9{{x}^{2}}+16{{y}^{2}}=144\] Here the compound C is
A) 3-bromo -2,4,5,6-trichloro toluene done clear
B) o-bromo toluene done clear
C) p-bromo toluene done clear
D) m-bromo toluene done clear
View Answer play_arrowquestion_answer65) An important product in the ozone deplation by chlorofluoro carbons is
A) \[\sqrt{12}\] done clear
B) \[\frac{7}{2}\] done clear
C) \[f(x)=\frac{\sin ({{e}^{x-2}}-1)}{\log (x-1)},\] done clear
D) \[\underset{x\to 2}{\mathop{\lim }}\,f(x)\] done clear
View Answer play_arrowquestion_answer66) The crystalline structure of NaCl is
A) hexagonal close packing done clear
B) face centred cubic done clear
C) square planar done clear
D) body centred cubic done clear
View Answer play_arrowquestion_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 done clear
B) 48g done clear
C) 38 g done clear
D) 380 g done clear
View Answer play_arrowquestion_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 done clear
B) + 0.35V done clear
C) +1.17V done clear
D) -1.17V done clear
View Answer play_arrowquestion_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 done clear
B) -28 kcal done clear
C) +28kcal done clear
D) +72kcal done clear
View Answer play_arrowquestion_answer70) The coagulating power of an electrolyte for arsenious sulphide decrease in order
A) \[\frac{{{a}^{2}}}{{{(a+b)}^{2}}}\] done clear
B) \[\frac{{{a}^{2}}}{{{b}^{2}}+{{(1-a)}^{2}}}\] done clear
C) \[\Delta ABC,\] done clear
D) \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=ac+\sqrt{3}ab,\] done clear
View Answer play_arrowquestion_answer71) \[(a\times b)\times c=\frac{1}{3}|b|\,\,|c|\] The element Y is
A) \[\theta \] done clear
B) \[\theta \] done clear
C) \[\frac{2\sqrt{2}}{3}\] done clear
D) \[\frac{\sqrt{2}}{3}\] done clear
View Answer play_arrowquestion_answer72) Hydrolysis of \[\frac{2}{3}\]gives \[\frac{1}{3}\] and X. Which of the following is -X?
A) \[2x-3y-4=0\] done clear
B) \[x+y=1,\] done clear
C) \[\sqrt{2}\] done clear
D) \[5\sqrt{2}\] done clear
View Answer play_arrowquestion_answer73) In the reaction,\[\frac{1}{\sqrt{2}}\]\[\frac{1}{2}\]identify the metal M,
A) Copper done clear
B) Iron done clear
C) Silver done clear
D) Zinc \[\lambda \]\[2n-1\] This process is called cynide process. It is used in the extraction of silver from argentite \[{{2}^{n}}-1\] done clear
View Answer play_arrowquestion_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) \[\frac{\pi }{4}\] done clear
B) \[f(x)=x{{e}^{-x}}\] done clear
C) \[[0,\infty ),\] done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer75) In the reaction sequence,\[\frac{1}{e}\]what is the molecular formula of V?
A) \[{{C}_{3}}{{H}_{6}}{{O}_{2}}\] done clear
B) \[{{C}_{3}}{{H}_{5}}N\] done clear
C) \[{{C}_{2}}{{H}_{4}}{{O}_{2}}\] done clear
D) \[{{C}_{2}}{{H}_{6}}O\] done clear
View Answer play_arrowquestion_answer76)
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer77) The product P in the reaction is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_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) \[\frac{\pi }{6}\] done clear
B) \[\frac{\pi }{4}\] done clear
C) \[\frac{\pi }{3}\] done clear
D) \[\frac{\pi }{2}\] done clear
View Answer play_arrowquestion_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) \[r=(\hat{i}+\hat{j})+\lambda (\hat{i}+2\hat{j}-\hat{k})\] done clear
B) \[r=(\hat{i}+\hat{j})+\mu (-\hat{i}+\hat{j}-2\hat{k}),\] done clear
C) \[r.(2\hat{i}+\hat{j}-3\hat{k})=-4\] done clear
D) \[r\times (-\hat{i}+\hat{j}+\hat{k})=0\] done clear
View Answer play_arrowquestion_answer80) Coupling of diazonium salts of the following takes place in the order
A) \[r.(-\hat{i}+\hat{j}+\hat{k})=0\] done clear
B) \[\frac{x-1}{2}=\frac{y-3}{4}=\frac{z-2}{3}\] done clear
C) \[3x+2y-2z+15=0,\] done clear
D) \[{{u}_{1}}\] done clear
View Answer play_arrowquestion_answer81) Which of the following pairs give positive Tollen's test?
A) Glucose, sucrose done clear
B) Glucose, fractose done clear
C) Hexanal, ace. to phenone done clear
D) Fractose, sucrose done clear
View Answer play_arrowquestion_answer82) Which one is chain growth polymer?
A) Teflon done clear
B) Nylon-6 done clear
C) Nylon-66 done clear
D) Bakelite done clear
View Answer play_arrowquestion_answer83) Sodium alkyl benzene sulphonate is used as
A) soap done clear
B) fertilizer done clear
C) detergent done clear
D) pesticide done clear
View Answer play_arrowquestion_answer84) Brown ring is made for
A) \[{{u}_{2}}\] done clear
B) \[{{u}_{1}}\] done clear
C) \[{{u}_{2}}\] done clear
D) \[{{u}_{2}}\] done clear
View Answer play_arrowquestion_answer85) The purest zinc is made by
A) electrolytic refining done clear
B) zone refining done clear
C) The van-Arkel method done clear
D) Mond process done clear
View Answer play_arrowquestion_answer86) Which of the following is the strongest oxidising agent?
A) \[{{u}_{1}}\] done clear
B) \[{{u}_{1}}\] done clear
C) \[{{u}_{2}}\] done clear
D) \[{{u}_{2}}\] done clear
View Answer play_arrowquestion_answer87) In aerosol, the dispersion medium is
A) solid done clear
B) liquid done clear
C) gas done clear
D) Any of these done clear
View Answer play_arrowquestion_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 done clear
B) 1000 K done clear
C) 800 K done clear
D) 1500 K done clear
E) 500K done clear
View Answer play_arrowquestion_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 done clear
B) 8.3 h done clear
C) 11h done clear
D) 16h done clear
View Answer play_arrowquestion_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 done clear
B) 3.86 done clear
C) 4.68 done clear
D) 2.86 done clear
View Answer play_arrowquestion_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 done clear
B) 6,8 done clear
C) 8,8 done clear
D) 8,6 done clear
View Answer play_arrowquestion_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 done clear
B) 0.4 done clear
C) 0.3 done clear
D) 0.2 done clear
View Answer play_arrowquestion_answer93) Enthalpy is equal to
A) \[\int_{{}}^{{}}{\frac{1}{\sin \left( x-\frac{\pi }{3} \right)\cos x}dx}\] done clear
B) \[2\log \left| \sin x+\sin \left( x-\frac{\pi }{3} \right) \right|+C\] done clear
C) \[2\log \left| \sin x.\sin \left( x-\frac{\pi }{3} \right) \right|+C\] done clear
D) \[2\log \left| \sin x-\sin \left( x-\frac{\pi }{3} \right) \right|+C\] done clear
View Answer play_arrowquestion_answer94) The isoelectronic pair is
A) \[{{x}^{2}}+\text{ }{{y}^{2}}=2{{a}^{2}}\] done clear
B) \[{{y}^{2}}=\text{ }8ax\] done clear
C) \[lF_{2}^{+},l_{3}^{-}\] done clear
D) \[y=\pm (x+2a)\] done clear
View Answer play_arrowquestion_answer95) Which of the following has largest ionic radius?
A) \[x=\pm (y+a)\] done clear
B) \[y=\pm (x+a)\] done clear
C) \[x+y+z=1\] done clear
D) \[2x+3y-z+4=0\] done clear
View Answer play_arrowquestion_answer96) The ground state term symbol for an electronic state is governed by
A) Heisenberg principle done clear
B) Hund's rule done clear
C) Aufbau principle done clear
D) Pauli exclusion principle done clear
View Answer play_arrowquestion_answer97) 2. 76 g of silver carbonate on being strongly heated yeild a residue weighing
A) 2.16g done clear
B) 2.48 g done clear
C) 2,64 g done clear
D) 2.32g done clear
View Answer play_arrowquestion_answer98) The following reaction is an example of ...... reaction.\[y-3z+6=0\]
A) addition done clear
B) dehydrobromination done clear
C) substitution done clear
D) bromination done clear
View Answer play_arrowquestion_answer99) \[3y-2+6=0\]dissolve in KI solution due to formation of
A) \[y+3z+6=0\] and \[3y-2z+6=0\] done clear
B) \[a=2\hat{i}=2\hat{j}-2\hat{k}\]and \[b=\hat{i}+\hat{j}\] done clear
C) \[a.c=\left| c \right|,\left| c-a \right|=2\sqrt{2}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer100) The product is
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer101) The approximate value of\[a\times b\] is
A) 1.2 done clear
B) 1.4 done clear
C) 1.6 done clear
D) 1.8 done clear
View Answer play_arrowquestion_answer102) \[\left| (a\times b)\times c \right|\]is equal to
A) 3a done clear
B) a done clear
C) 0 done clear
D) None of these done clear
View Answer play_arrowquestion_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 done clear
B) three points done clear
C) two points done clear
D) four points done clear
View Answer play_arrowquestion_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 done clear
B) \[\frac{x}{2}-\frac{y}{3}=1\] done clear
C) \[\frac{x}{-2}+\frac{y}{1}=1\] done clear
D) \[\frac{x}{2}-\frac{y}{3}=-1\] done clear
View Answer play_arrowquestion_answer105) The mean deviation from the mean of the series a, a.+ d, a + 2d,..., a + 2nd, is
A) \[\frac{x}{-2}+\frac{y}{1}=-1\] done clear
B) \[\frac{x}{2}+\frac{y}{3}=1\] done clear
C) \[\frac{x}{2}+\frac{y}{1}=1\] done clear
D) \[({{a}^{2}},-{{b}^{2}})\] done clear
View Answer play_arrowquestion_answer106) If \[{{x}^{2}}+9<{{(x+3)}^{2}}<8x+25,\]then f(x) is
A) increasing on \[\frac{x+y}{x-y}=\frac{5}{2},\] done clear
B) decreasing on R done clear
C) increasing on R done clear
D) decreasing on \[\frac{x}{y}\] done clear
View Answer play_arrowquestion_answer107) If \[\frac{3}{8}\] is an imaginary cube root of unity, then the value of\[\frac{8}{3}\]\[\frac{5}{3}\]is
A) \[\frac{3}{5}\] done clear
B) \[6\frac{2}{3}%\] done clear
C) \[U=k\left[ \frac{2q(8d)}{r}-\frac{(2q)(q)}{x}-\frac{(8q)(q)}{r-x} \right]\] done clear
D) None of these done clear
View Answer play_arrowquestion_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 done clear
B) 10,14 done clear
C) 12, 7 done clear
D) 14,12 done clear
View Answer play_arrowquestion_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. done clear
B) n - 2r is even done clear
C) n - 2r is odd done clear
D) None of the above done clear
View Answer play_arrowquestion_answer110) The value of \[\frac{2}{x}+\frac{8}{r-x}=y\]\[\frac{dy}{dx}=0\]is
A) \[-\frac{2}{{{x}^{2}}}+\frac{8}{{{(r-x)}^{2}}}=0\] done clear
B) \[\Rightarrow \] done clear
C) 0 done clear
D) \[\frac{x}{r-x}=\sqrt{\frac{2}{8}}=\frac{1}{2}\Rightarrow x=\frac{r}{3}\] done clear
View Answer play_arrowquestion_answer111) If \[x=\frac{r}{3},\frac{{{d}^{2}}y}{d{{x}^{2}}}=\]then \[x=\frac{r}{3},y\]is equal to
A) 36 done clear
B) \[\frac{{{N}_{2}}}{{{N}_{1}}}\] done clear
C) \[\frac{{{N}_{2}}}{{{N}_{1}}}=\exp \left( -\frac{{{E}_{2}}-{{E}_{1}}}{kT} \right)\] done clear
D) \[\lambda =550nm\] done clear
View Answer play_arrowquestion_answer112) \[\Rightarrow \]then x is equal to
A) \[{{E}_{2}}-{{E}_{1}}=\frac{hc}{\lambda }=3.16\times {{10}^{-19}}J\] done clear
B) \[\Rightarrow \] done clear
C) \[\frac{{{N}_{2}}}{{{N}_{1}}}=\exp \left( \frac{-3.16\times {{10}^{-19}}J}{(1.38\times {{10}^{-23}}1/k).(300k)} \right)\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer113) The aquation of the tangent to the curve \[\Rightarrow \] at the point of its maximum, is
A) \[\frac{{{N}_{2}}}{{{N}_{1}}}=1.1577\times {{10}^{-38}}\] done clear
B) \[{{E}_{n}}=\frac{-13.6}{({{n}^{2}})}eV\] done clear
C) \[\therefore \] done clear
D) \[E=\frac{-13.6}{{{(5)}^{2}}}eV=-0.54eV\] done clear
View Answer play_arrowquestion_answer114) The proposition \[iG=(i-{{i}_{0}})S\]is
A) a tautology done clear
B) a contradiction done clear
C) neither tautology nor contradiction done clear
D) both tautology and contradiction done clear
View Answer play_arrowquestion_answer115) The number of ways in which four letters can be selected from the word 'DEGREE', is
A) 7 done clear
B) 6 done clear
C) \[{{i}_{0}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_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 done clear
B) 270 done clear
C) 282 done clear
D) 342 done clear
View Answer play_arrowquestion_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 done clear
B) \[S=2.5\Omega ,G=25\Omega ,\] done clear
C) \[\frac{i}{{{i}_{0}}}=\frac{1}{11}\] done clear
D) \[\because \] done clear
View Answer play_arrowquestion_answer118) The term independent of x in the expansion of \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\] is
A) -3 done clear
B) 0 done clear
C) 1 done clear
D) 3 done clear
View Answer play_arrowquestion_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) \[\frac{{{C}_{p}}}{{{C}_{v}}}\] done clear
B) \[{{C}_{v}}=\frac{{{n}_{1}}{{C}_{{{v}_{1}}}}+{{n}_{2}}{{C}_{{{v}_{2}}}}}{{{n}_{1}}+{{n}_{2}}}\] done clear
C) 2n + 1 done clear
D) None of these done clear
View Answer play_arrowquestion_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) \[\gamma =\frac{{{C}_{p}}}{{{C}_{v}}}=\frac{{{n}_{1}}{{C}_{{{p}_{1}}}}+{{n}_{2}}{{C}_{{{p}_{2}}}}}{{{n}_{1}}{{C}_{{{v}_{1}}}}+{{n}_{2}}{{C}_{{{v}_{2}}}}}\] done clear
B) \[\therefore \] done clear
C) \[\frac{3}{2}=\frac{2\left( \frac{5}{2}R \right)+n\left( \frac{7}{2}R \right)}{2\left( \frac{3}{2}R \right)+n\left( \frac{5}{2}R \right)}\] done clear
D) All of these done clear
View Answer play_arrowquestion_answer121) The derivative of \[\Rightarrow \] with respect to \[\frac{3}{2}=\frac{10+7n}{6+5n}\]at x = 0, is
A) \[\Rightarrow \] done clear
B) \[I=\frac{E}{R'}\] done clear
C) \[E=-\frac{nd\phi }{dt},\] done clear
D) 1 done clear
View Answer play_arrowquestion_answer122) \[I=-\frac{n}{R'},\frac{d\phi }{dt}\]is equal to
A) \[{{E}_{2}}-{{E}_{1}},\] done clear
B) \[1.1577\times {{10}^{-38}}\] done clear
C) \[2.9\times {{10}^{-35}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer123) In a \[2.168\times {{10}^{-36}}\] a =0, then \[1.96\times {{10}^{-20}}\]is equal to
A) \[\Omega \] done clear
B) \[\Omega \] done clear
C) \[\frac{i}{{{i}_{0}}}=\frac{4}{11}\] done clear
D) 2 done clear
View Answer play_arrowquestion_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 done clear
B) 1 sq unit done clear
C) \[\frac{i}{{{i}_{0}}}=\frac{1}{11}\] sq units done clear
D) \[\sqrt{2}\] sq units done clear
View Answer play_arrowquestion_answer125) The value of \[4R\Omega .\]is
A) \[{{w}_{1}}\] done clear
B) \[{{w}_{2}}\] done clear
C) \[\frac{-({{w}_{2}}-{{w}_{1}})}{5Rt}\] done clear
D) \[\frac{-n({{w}_{2}}-{{w}_{1}})}{5Rt}\] done clear
View Answer play_arrowquestion_answer126) \[\frac{-n({{w}_{2}}-{{w}_{1}})}{Rnt}\]equals
A) \[\frac{-n({{w}_{2}}-{{w}_{1}})}{Rt}\] done clear
B) \[({{\mu }_{s}}=1.4)\] done clear
C) \[\frac{2}{\sqrt{3}}\left( \frac{\tau }{Bi} \right)\] done clear
D) None of the above done clear
View Answer play_arrowquestion_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) \[\frac{2}{\sqrt{3}}{{\left( \frac{\tau }{Bi} \right)}^{1/2}}\] done clear
B) \[\frac{1}{\sqrt{3}}\frac{\tau }{Bi}\] done clear
C) \[{{m}_{1}}\] done clear
D) \[{{m}_{2}}\] done clear
View Answer play_arrowquestion_answer128) If the line x -1 = 0 is the directrix of the parabola \[{{m}_{1}}\] then one of the value of k is
A) \[{{m}_{2}}\] done clear
B) 8 done clear
C) 4 done clear
D) \[{{m}_{1}}\] done clear
View Answer play_arrowquestion_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 done clear
B) 6 done clear
C) 9 done clear
D) 12 done clear
View Answer play_arrowquestion_answer130) Solution of the differential equation \[d\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}}\]+?is
A) \[d\sqrt{\frac{2{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}}\] done clear
B) \[d\sqrt{\frac{2{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}}}\] done clear
C) \[=20m{{s}^{-1}}\] done clear
D) \[(\text{take}\,g=10\text{ }m{{s}^{-}}^{2})\] done clear
View Answer play_arrowquestion_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) \[I={{I}_{0}}\sin \omega t,\] done clear
B) \[{{I}_{0}}=10\] done clear
C) \[\omega =100\pi \,\text{rad/s}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer132) If \[\pi \] is a continuous at \[\pi \]then k is equal to
A) 0 done clear
B) \[\pi \] done clear
C) \[\pi \] done clear
D) \[^{\text{235}}\text{U}\] done clear
View Answer play_arrowquestion_answer133) If [ ] denotes the greatest integer function, then\[36.5\times {{10}^{3}}kg\]
A) is continuous at \[36\times {{10}^{2}}kg\] done clear
B) is discontinuous at \[39.5\times {{10}^{3}}kg\] done clear
C) \[38.2\times {{10}^{3}}kg\] done clear
D) \[10\mu F\] done clear
View Answer play_arrowquestion_answer134) If\[200\mu F\] then
A) f(x) is not everywhere continuous done clear
B) f(x) is continuous and differentiable everywhere done clear
C) f(x) is not differentiable at two points done clear
D) (x) is not differentiable at one point done clear
View Answer play_arrowquestion_answer135) If \[{{E}_{2}}\]then \[{{r}_{1}}\]is equal to
A) 1 done clear
B) ? 1 done clear
C) i done clear
D) -i done clear
View Answer play_arrowquestion_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 done clear
B) 840 done clear
C) 1080 done clear
D) 480 done clear
View Answer play_arrowquestion_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 done clear
B) 2 done clear
C) 3 done clear
D) 4 done clear
View Answer play_arrowquestion_answer138) lf \[{{E}_{1}}{{r}_{2}}<{{E}_{2}}({{r}_{1}}+R)\] then\[{{E}_{2}}{{r}_{2}}<E(R+{{r}_{2}})\] is equal to
A) \[{{E}_{1}}{{r}_{1}}>{{E}_{2}}({{r}_{1}}+R)\] done clear
B) \[{{n}_{1}}\] done clear
C) \[{{n}_{1}}({{n}_{1}}>{{n}_{2}}).\] done clear
D) \[{{\alpha }_{\max }}\] done clear
View Answer play_arrowquestion_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) \[{{\sin }^{-1}}\left[ \frac{{{n}_{1}}}{{{n}_{2}}}\cos \left( {{\sin }^{-1}}\left( \frac{{{n}_{2}}}{{{n}_{1}}} \right) \right) \right]\] done clear
B) \[\frac{150}{2}=\frac{150\sqrt{3}}{2}-10t\] done clear
C) \[\Rightarrow \] done clear
D) \[10t=\frac{150(\sqrt{3}-1)}{2}\] done clear
View Answer play_arrowquestion_answer140) If \[\Rightarrow \]and \[\Rightarrow \]then
A) \[\Rightarrow \] done clear
B) \[t=7.5(\sqrt{3}-1)s\] done clear
C) \[I<II<III<IV\] done clear
D) \[NO_{3}^{-}\] done clear
View Answer play_arrowquestion_answer141) In \[C{{l}^{-}}\] if \[{{l}^{-}}\]Then, c is the root of the equation
A) \[B{{r}^{-}}\] done clear
B) \[HOCl\] done clear
C) \[HCl{{O}_{2}}\] done clear
D) \[HCl{{O}_{3}}\] done clear
View Answer play_arrowquestion_answer142) The sum to n terms of the series \[HCl{{O}_{4}}\]is
A) \[A\xrightarrow[{}]{{}}B;{{k}_{1}}={{10}^{10}}{{e}^{-20,000/T}}\] done clear
B) \[C\xrightarrow[{}]{{}}D;{{k}_{2}}={{10}^{12}}{{e}^{-24,606/T}}\] done clear
C) \[{{k}_{1}}\] done clear
D) \[{{k}_{2}}\] done clear
View Answer play_arrowquestion_answer143) The value of \[CaC{{l}_{2}}\]is
A) \[C{{s}^{+}}\] done clear
B) \[C{{l}^{-}}\] done clear
C) \[9.2g{{N}_{2}}{{O}_{4}}\] done clear
D) \[{{N}_{2}}{{O}_{4}}(g)2N{{O}_{2}}(g)\] done clear
View Answer play_arrowquestion_answer144) \[{{N}_{2}}{{O}_{4}}\]equals
A) \[{{N}_{2}}{{O}_{4}}=92\] done clear
B) \[{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{p}}\] done clear
C) \[-{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{p}}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_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 done clear
B) 3 done clear
C) \[-{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{v}}\] done clear
D) \[C{{l}_{2}}O,IC{{l}^{-}}_{2}\] done clear
View Answer play_arrowquestion_answer146) If \[Cl_{2}^{-},Cl{{O}_{2}}\] then \[IF_{2}^{+},l_{3}^{-}\]is-given by
A) -2 done clear
B) -1 done clear
C) 0 done clear
D) 1 done clear
View Answer play_arrowquestion_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) \[L{{i}^{+}}\] done clear
B) \[N{{a}^{+}}\] done clear
C) \[{{K}^{+}}\] done clear
D) \[{{C}_{2}}{{H}_{4}}B{{r}_{2}}\xrightarrow[{}]{Alc.KOH}{{C}_{2}}{{H}_{2}}\] done clear
View Answer play_arrowquestion_answer148) In a \[{{I}_{2}}\] if \[K{{l}_{2}}\]then the triangle is
A) equilateral done clear
B) right angled and isosceles done clear
C) right angled and not isosceles done clear
D) None of the above done clear
View Answer play_arrowquestion_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) \[l_{3}^{-}\] done clear
B) \[{{(1.0002)}^{3000}}\] done clear
C) \[(a.\hat{i})(a\times \hat{i})+(a.\hat{j})(a\times \hat{j})+(a.\hat{k})(a\times \hat{k})\] done clear
D) \[A=\{(x,y):{{x}^{2}}+{{y}^{2}}=25\}\] done clear
View Answer play_arrowquestion_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) \[f(x)=\sqrt{{{x}^{2}}-4,}a=2\] done clear
B) \[\sqrt{5}\] done clear
C) \[\sqrt{3}\] done clear
D) \[\sqrt{3}+1\] done clear
View Answer play_arrowquestion_answer151) The two tangents to the curve \[n(n+1)d\]at the points, where it crosses X-axis, are
A) parallel done clear
B) perpendicular done clear
C) inclined at an angle\[\frac{n(n+1)d}{2n+1}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer152) The greatest value of the function \[\frac{n(n+1)d}{2n}\]in\[\frac{n(n-1)d}{2n+1}\] is
A) \[f(x)=x{{e}^{x}}^{(1-x)},\] done clear
B) \[\left[ 1\frac{1}{2},1 \right]\] done clear
C) ?e done clear
D) e done clear
View Answer play_arrowquestion_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) \[\omega \] done clear
B) \[(1+\omega )(1+{{\omega }^{2}}(1+{{\omega }^{3}})(1+{{\omega }^{4}})\] done clear
C) \[(1+{{\omega }^{5}})...(1+{{\omega }^{3n}})\] done clear
D) \[{{2}^{3n}}\] done clear
View Answer play_arrowquestion_answer154) The range of the function \[{{2}^{2n}}\]is
A) [0,5] done clear
B) [0,2) done clear
C) (0,2) done clear
D) None of these done clear
View Answer play_arrowquestion_answer155) The image of the point P (1,3, 4) in the plane \[{{2}^{n}}\]is
A) (3, 5,-2) done clear
B) (-3,5,2) done clear
C) (3,-5,2) done clear
D) (3,5,2) done clear
View Answer play_arrowquestion_answer156) Equation of the plane that contains the lines\[{{x}^{2r}}\]and\[\left( x+\frac{1}{{{x}^{2}}} \right),\]is
A) \[{{\sin }^{-1}}\left\{ \cos \left( {{\sin }^{-1}}\sqrt{\frac{2-\sqrt{3}}{4}} \right. \right.\] done clear
B) \[\left. \left. +{{\cos }^{-1}}\frac{\sqrt{12}}{4}+{{\sec }^{-1}}\sqrt{2} \right) \right\}\] done clear
C) \[\frac{\pi }{4}\] done clear
D) None of these done clear
View Answer play_arrowquestion_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 done clear
B) 3 done clear
C) 6 done clear
D) 7 done clear
View Answer play_arrowquestion_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) \[y-1=0\] done clear
B) \[x-1=0\] done clear
C) \[x+y-1=0\] done clear
D) \[x-y+1=0\] done clear
View Answer play_arrowquestion_answer159) Let \[(p\to \tilde{\ }p\wedge )(\tilde{\ }p\to p)\] then the value of \[\frac{6!}{3!}\] is
A) 0 done clear
B) a + b + c done clear
C) ab + 6c + ca done clear
D) None of these done clear
View Answer play_arrowquestion_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) \[\sqrt{\frac{2}{3}}\] done clear
B) \[\sqrt{\frac{3}{2}}\] done clear
C) \[{{e}^{1/2}}\] done clear
D) None of these done clear
View Answer play_arrowquestion_answer161) The value of \[{{\left( x-\frac{1}{x} \right)}^{4}}{{\left( x+\frac{1}{x} \right)}^{3}}.\]is
A) \[{{A}^{2}}=A\] done clear
B) \[{{(1+A)}^{n}}=I+\lambda A,\] done clear
C) \[\lambda \] done clear
D) None of the above done clear
View Answer play_arrowquestion_answer162) Two common tangents to the circle \[2n-1\]and parabola \[{{2}^{n}}-1\]are
A) \[u={{e}^{x}}\sin x\] done clear
B) \[v={{e}^{x}}\cos x\] done clear
C) \[v\frac{du}{dx}-u\frac{dv}{dx}={{u}^{2}}+{{v}^{2}}\] done clear
D) \[\frac{{{d}^{2}}u}{d{{x}^{2}}}=2v\] done clear
View Answer play_arrowquestion_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) \[{{\tan }^{-1}}\left( \frac{2x\sqrt{1-{{x}^{2}}}}{1-2{{x}^{2}}} \right)\] done clear
B) \[\frac{1}{8}\] done clear
C) \[\frac{1}{4}\] done clear
D) \[\frac{1}{2}\] done clear
View Answer play_arrowquestion_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) \[{{\sin }^{2}}A+{{\sin }^{2}}B\text{ }+{{\sin }^{2}}C\] done clear
B) \[\frac{3\sqrt{3}}{2}\] done clear
C) 2 done clear
D) 3 done clear
View Answer play_arrowquestion_answer165) Order and degree of a differential equation \[\frac{9}{4}\]are
A) 4 and 2 done clear
B) 1 and 2 done clear
C) 1 and 4 done clear
D) 2 and 4 done clear
View Answer play_arrowquestion_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 done clear
B) 0.001 cm/s done clear
C) 2 mm/s done clear
D) 0.002 cm/s done clear
View Answer play_arrowquestion_answer167) The sum to infinity of the series \[\frac{5}{4}\]is
A) 2 done clear
B) 3 done clear
C) 4 done clear
D) 6 done clear
View Answer play_arrowquestion_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 \[\frac{1}{2}\] done clear
B) \[\frac{3}{2}\]and \[\frac{5}{2}\] done clear
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\[{{a}_{1}}+{{a}_{2}}+...+{{a}_{n}}\] done clear
D) None of the above done clear
View Answer play_arrowquestion_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 done clear
B) a + b = 2 done clear
C) a = 1+ 6 done clear
D) a = 1 ? 6 done clear
View Answer play_arrowquestion_answer170) The number of positive integral solutions of \[\frac{{{a}_{1}}+{{a}_{2}}+...+{{a}_{n}}}{n}\]is
A) 2 done clear
B) 3 done clear
C) 4 done clear
D) 5 done clear
View Answer play_arrow
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