question_answer1) If the velocity of light \[c\], gravitational constant \[G\] and Planck's constant \[h\], are chosen as fundamental units, the dimensional formula of length L in the new system is:
A) \[[{{h}^{1}}{{c}^{1}}{{G}^{-1}}]\] done clear
B) \[[{{h}^{1/2}}{{c}^{1/2}}{{G}^{-1/2}}]\] done clear
C) \[[{{h}^{1}}{{c}^{-3}}{{G}^{1}}]\] done clear
D) \[[{{h}^{1/2}}{{c}^{-3/2}}{{G}^{1/2}}]\] done clear
View Answer play_arrowquestion_answer2) The radius of sphere is measured to be\[(2.1\pm 0.5)\,\,cm\]. Calculate its surface area with error limits:
A) \[(55.4\pm 26.4)c{{m}^{2}}\] done clear
B) \[(55.4\pm 0.02)c{{m}^{2}}\] done clear
C) \[(55.4\pm 2.64)c{{m}^{2}}\] done clear
D) \[(55.4\pm 0.26)c{{m}^{2}}\] Surface area, \[S=4\pi {{r}^{2}}=4\times \frac{22}{7}\times {{(2.1)}^{2}}=55.44=55.4\,\,c{{m}^{2}}\] Further, \[\frac{\Delta S}{S}=2\cdot \frac{\Delta r}{r}\] or \[\Delta S=2\left( \frac{\Delta r}{r} \right)(S)\] \[=\frac{2\times 0.5\times 55.4}{2.1}=26.38=26.4\,\,c{{m}^{2}}\] \[\therefore \] \[S=(55.4\pm 26.4)c{{m}^{2}}\] done clear
View Answer play_arrowquestion_answer3) A block of mass \[2\,\,kg\] rests on a plane inclined at an angle of \[{{30}^{o}}\] with the horizontal. The coefficient of friction between the block and surface is \[0.7\]. The frictional force acting on the block is:
A) \[11.9\,\,N\] done clear
B) \[25\,\,N\] done clear
C) \[50\,\,N\] done clear
D) \[22.9\,\,N\] done clear
View Answer play_arrowquestion_answer4) A particle moves along \[Y-\]axis in such a way that its \[y-\]coordinate varies with time \[t\] according to the relation \[y=3+5t+7{{t}^{2}}\]. The initial velocity and acceleration of the particle are respectively:
A) \[14m{{s}^{-1}},\,\,5\,\,m{{s}^{-2}}\] done clear
B) \[19m{{s}^{-1}},\,\,-9m{{s}^{-2}}\] done clear
C) \[-14m{{s}^{-1}},\,\,-5m{{s}^{-2}}\] done clear
D) \[5m{{s}^{-1}},\,\,14\,\,m{{s}^{-2}}\] done clear
View Answer play_arrowquestion_answer5) An object travels north with a velocity of \[10\,\,m{{s}^{-1}}\] and then speeds up to a velocity of \[25\,\,m{{s}^{-1}}\]in\[5\,s\]. The acceleration of the object in these \[5\,s\] is:
A) \[12\,\,m{{s}^{-2}}\] in north direction done clear
B) \[3\,\,m{{s}^{-2}}\] in north direction done clear
C) \[15\,\,m{{s}^{-2}}\]in north direction done clear
D) \[3\,\,m{{s}^{-2}}\]in south direction done clear
View Answer play_arrowquestion_answer6) An automobile travelling at \[50\,\,km/h\], can be stopped at a distance of \[40\,\,m\] by applying brakes. If the same automobile is travelling at \[90\,\,km/h\], all other conditions remaining same and assuming no skidding, the minimum stopping distance in metres is:
A) \[72\] done clear
B) \[92.5\] done clear
C) \[102.6\] done clear
D) \[129.6\] done clear
View Answer play_arrowquestion_answer7) A rifle shoots a bullet with a muzzle velocity of \[500\,\,m{{s}^{-1}}\] at a small target \[50\,\,m\] away. To hit the target the rifle must be aimed: (Take\[g=10\,\,m{{s}^{-2}})\]
A) exactly at the target done clear
B) \[10\,\,cm\] below the target done clear
C) \[10\,\,cm\] above the target done clear
D) \[5\,\,cm\] above the target done clear
View Answer play_arrowquestion_answer8) The centripetal acceleration of particle of mass \[m\] moving with a velocity \[v\] in a circular orbit of radius \[r\] is:
A) \[{{v}^{2}}/r\] along the radius, towards the centre done clear
B) \[{{v}^{2}}/r\] along the radius, away from the centre done clear
C) \[m{{v}^{2}}/r\] along the radius, away the centre done clear
D) \[m{{v}^{2}}/r\]along the radius, towards the centre done clear
View Answer play_arrowquestion_answer9) An \[\alpha -\]particle of mass m suffers one dimensional elastic collision with a nucleus of unknown mass. After the collision the \[\alpha -\]particle is scattered directly backwards losing \[75%\] of its kinetic energy. The mass of the unknown nucleus is:
A) \[m\] done clear
B) \[2\,\,m\] done clear
C) \[3\,\,m\] done clear
D) \[\frac{3}{2}m\] done clear
View Answer play_arrowquestion_answer10) If a transformer of an audio amplifier has output impedance \[8000\,\,\Omega \] and the speaker has input impedance of \[8\,\,\Omega \], the primary and secondary turns of this transformer connected between the output of amplifier and to loud speaker should have the ratio:
A) \[1000:1\] done clear
B) \[100:1\] done clear
C) \[1:32\] done clear
D) \[32:1\] done clear
View Answer play_arrowquestion_answer11) A stationary body of mass m explodes into the three parts having masses in the ratio\[1:3:3\]. The two fractions with equal masses move at right angles to each other with a velocity of\[1.5\,\,m{{s}^{-1}}\]. The velocity of the third part is:
A) \[4.5\sqrt{2}m{{s}^{-1}}\] done clear
B) \[5\,\,m{{s}^{-1}}\] done clear
C) \[5\sqrt{32}m{{s}^{-1}}\] done clear
D) \[1.5\,\,m{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer12) In the electromagnetic spectrum, the visible spectrum lies between:
A) radio waves and microwaves- done clear
B) infrared and ultraviolet rays done clear
C) microwaves and infrared spectrum done clear
D) \[X-\]ray and gamma ray spectrum done clear
View Answer play_arrowquestion_answer13) An object of mass \[m\] falls on to a spring of constant \[k\] from height \[h\]. The spring undergoes compression by a length \[x\]. The maximum compression \[x\] is given by the equation:
A) \[m\,\,g\,\,h=\frac{1}{2}k{{x}^{2}}\] done clear
B) \[m\,\,g(h+x)=\frac{1}{2}k{{x}^{2}}\] done clear
C) \[m\,\,g(h+x)=-kx\] done clear
D) \[m\,\,g\,\,h=-kx\] done clear
View Answer play_arrowquestion_answer14) A \[5000\,\,kg\] rocket is set for vertical, firing. The exhaust speed, is \[800\,\,m/s\]. To, give an initial upward acceleration of \[20\,\,m/{{s}^{2}}\], the amount of gas ejected per second to supply the needed thrust will be:
A) \[137.5\,\,kg/s\] done clear
B) \[185.5\,\,kg/s\] done clear
C) \[127.5\,\,kg/s\] done clear
D) \[187.5\,\,kg/s\] done clear
View Answer play_arrowquestion_answer15) An elastic ball is dropped from a height \[h\] and it rebounds many times from the floor. If the coefficient of restitution is \[e\], the time interval between the second and the third impact, is:
A) \[\frac{ev}{g}\] done clear
B) \[\frac{{{e}^{2}}v}{g}\] done clear
C) \[{{e}^{2}}\sqrt{\left( \frac{8h}{g} \right)}\] done clear
D) \[{{e}^{2}}\sqrt{\left( \frac{h}{g} \right)}\] done clear
View Answer play_arrowquestion_answer16) An object of mass \[m\] is attached to light string which passes through a hollow tube. The object is set into rotation in a horizontal circle of radius \[{{r}_{1}}\]. If the string is pulled shortening the radius to \[{{r}_{2}}\], the ratio of new kinetic energy to the original kinetic energy is:
A) \[{{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}\] done clear
B) \[{{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\] done clear
C) \[\frac{{{r}_{1}}}{{{r}_{2}}}\] done clear
D) \[\frac{{{r}_{2}}}{{{r}_{1}}}\] done clear
View Answer play_arrowquestion_answer17) Total angular momentum of a rotating body remains constant, if the net torque acting on the body is:
A) zero done clear
B) maximum done clear
C) minimum done clear
D) unity done clear
View Answer play_arrowquestion_answer18) A car is racing on a circular track of \[180\,\,m\] radius with a speed of \[32\,\,m{{s}^{-1}}\]. What should be the banking angle of the road to avoid chances of skidding of the vehicle at this speed without taking into consideration the friction between the tyre and the road?
A) \[{{45}^{o}}\] done clear
B) \[{{60}^{o}}\] done clear
C) \[{{30}^{o}}\] done clear
D) \[{{15}^{o}}\] done clear
View Answer play_arrowquestion_answer19) When a ceiling fan is switched on it makes \[10\] rotations in the first \[3\,\,s\]. The number of rotations it makes in the next \[3\,\,s\], assuming uniform angular acceleration is:
A) \[40\] done clear
B) \[30\] done clear
C) \[20\] done clear
D) \[10\] done clear
View Answer play_arrowquestion_answer20) A body is projected vertically upwards from the surface of a planet of radius r with a velocity equal to l/3rd the escape velocity for the planet. The maximum height attained by the body is:
A) \[R/2\] done clear
B) \[R/3\] done clear
C) \[R/5\] done clear
D) \[R/9\] done clear
View Answer play_arrowquestion_answer21) A man weighs \[80\,\,kg\] on earth's surface. The height above ground where he will weigh \[40\,\,kg\], is: (Radius of earth is\[6400\,\,km)\]
A) \[0.31\] times \[r\] done clear
B) \[0.41\] times \[r\] done clear
C) \[0.51\] times \[r\] done clear
D) \[0.61\] times \[r\] done clear
View Answer play_arrowquestion_answer22) An adulterated sample of milk has a density of\[1032\,\,kg\text{-}{{m}^{-3}}\], while pure milk has a density of\[1080\,\,kg\text{-}{{m}^{-3}}\]. The volume of pure milk in a sample of \[10\,\,L\] adulterated milk is:
A) \[0.5\,\,L\] done clear
B) \[1.0\,\,L\] done clear
C) \[2.0\,\,L\] done clear
D) \[4.0\,\,L\] done clear
View Answer play_arrowquestion_answer23) Typical silt (hard mud) particle of radius \[20\,\,\mu m\] is on the top of lake water, its density is \[2000\,\,kg/{{m}^{3}}\] and the viscosity of lake water is\[1.0\,\,m\,\,Pa\], density is \[1000\,\,kg/{{m}^{3}}\]. If the lake is still (has no internal fluid motion), the terminal speed with which the particle hits the bottom of the lake in \[mm/s\] is:
A) \[0.67\] done clear
B) \[0.77\] done clear
C) \[0.87\] done clear
D) \[0.97\] done clear
View Answer play_arrowquestion_answer24) A solid sphere and a hollow sphere, both of the same size and same mass roll down an inclined plane. Then:
A) solid sphere reaches the ground first done clear
B) hollow sphere reaches the ground first done clear
C) both spheres reaches the ground at the same time done clear
D) the time at which the spheres reach the ground cannot be specified by the given data done clear
View Answer play_arrowquestion_answer25) If \[P\] is the pressure, \[V\] the volume, \[R\] the gas constant, \[k\] the Boltzmann constant and \[T\] the absolute temperature, then the number of molecules in the given mass of the gas is given by:
A) \[\frac{PV}{RT}\] done clear
B) \[\frac{PV}{kT}\] done clear
C) \[\frac{PR}{T}\] done clear
D) \[PV\] done clear
View Answer play_arrowquestion_answer26) An air bubble is released from the bottom of a pond and is found to expand to thrice its original volume as it reached the surface. If the atmospheric pressure is \[100\,\,kPa\], the absolute pressure at the bottom of lake in \[kPa\] is ... (assume no temperature variation) :
A) \[33.3\] done clear
B) \[50.0\] done clear
C) \[100.0\] done clear
D) \[300.0\] done clear
View Answer play_arrowquestion_answer27) Maxwell in his famous equation of electromagnetism introduced the concept:
A) \[AC\] current done clear
B) \[DC\] current done clear
C) displacement current done clear
D) impedance done clear
View Answer play_arrowquestion_answer28) \[1\,\,g\] of steam at \[{{100}^{o}}C\] and equal mass of ice at \[{{0}^{o}}C\] are mixed. The temperature of .the mixture in steady state will be (latent heat of steam\[=540\,\,cal/g\], latent heat of ice \[=80\,\,cal/g)\]:
A) \[{{50}^{o}}C\] done clear
B) \[{{100}^{o}}C\] done clear
C) \[{{67}^{o}}C\] done clear
D) \[{{33}^{o}}C\] done clear
View Answer play_arrowquestion_answer29) The work done by a gas is maximum when it expands:
A) isothermally done clear
B) adiabatically done clear
C) isochorically done clear
D) isobarically done clear
View Answer play_arrowquestion_answer30) A tuning fork of frequency \[580\,\,Hz\] is employed to produce transverse waves on a long rope. The distance between the nearest crests is found to be \[20\,\,cm\]. The velocity of the wave is:
A) \[58\,\,m{{s}^{-1}}\] done clear
B) \[580\,\,m{{s}^{-1}}\] done clear
C) \[20\,\,m{{s}^{-1}}\] done clear
D) \[116\,\,m{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer31) A heavy brass sphere is hung from a weightless inelastic spring and as a simple pendulum its time period of oscillation is \[T\]. When the sphere is immersed in a non-viscous liquid of density \[1/10\] that of brass, it will act as a simple pendulum of period:
A) \[T\] done clear
B) \[\frac{10}{9}T\] done clear
C) \[\sqrt{\left( \frac{9}{10} \right)T}\] done clear
D) \[\sqrt{\left( \frac{10}{9} \right)T}\] done clear
View Answer play_arrowquestion_answer32) The distance travelled by a sound wave when a tuning fork completes \[25\] vibrations is\[16.5\,\,m\]. If the frequency of the tuning fork is \[500\,\,Hz\], find the velocity of sound.
A) \[350\,\,m{{s}^{-1}}\] done clear
B) \[330\,\,m{{s}^{-1}}\] done clear
C) \[300\,\,m{{s}^{-1}}\] done clear
D) \[450\,\,m{{s}^{-1}}\] done clear
View Answer play_arrowquestion_answer33) Two instruments having stretched strings are being played in unison. When the tension of one of, the instruments is increased by \[1%\], \[3\] beats are produced in \[2\,\,s\]. The initial frequency of vibration of each wire is:
A) \[300\,\,Hz\] done clear
B) \[500\,\,Hz\] done clear
C) \[1000\,\,Hz\] done clear
D) \[400\,\,Hz\] done clear
View Answer play_arrowquestion_answer34) Three point charges \[1C,\,\,\,2C\] and \[3C\] are placed at the comers of an equilateral triangle of side \[1\,\,m\]. The work done in bringing these charges to the vertices of a smaller similar triangle of side\[0.5\,\,m\]is:
A) \[2.7\times {{10}^{10}}J\] done clear
B) \[9.9\times {{10}^{10}}J\] done clear
C) \[10.8\times {{10}^{10}}J\] done clear
D) \[5.4\times {{10}^{10}}J\] done clear
View Answer play_arrowquestion_answer35) The capacitors \[A\] and \[B\] have identical geometry. A material with a dielectric constant \[3\] is present between the plates of \[B\]. The potential difference across \[A\] and \[B\] are respectively:
A) \[2.5\,\,V,\,\,7.5\,\,V\] done clear
B) \[2\,\,V,\,\,8\,\,V\] done clear
C) \[8\,\,V,\,\,2\,\,V\] done clear
D) \[7.5\,\,V,\,\,2.5\,\,V\] done clear
View Answer play_arrowquestion_answer36) An electric bulb is marked \[100\,\,W,\,\,230\,\,V\]. If the supply voltage drops to \[115\,\,V\], what is the total energy produced by the bulb in\[10\,\,\min ?\]
A) \[30\,\,kJ\] done clear
B) \[20\,\,kJ\] done clear
C) \[15\,\,kJ\] done clear
D) \[10\,\,kJ\] done clear
View Answer play_arrowquestion_answer37) A circular coil carrying a current has a radius\[R\]. The ratio of magnetic induction at the centre of the coil and at a distance equal to \[\sqrt{3}R\] from the centre of the coil on the axis is:
A) \[1:1\] done clear
B) \[1:2\] done clear
C) \[2:1\] done clear
D) \[8:1\] done clear
View Answer play_arrowquestion_answer38) The examples of diamagnetic, paramagnetic and ferromagnetic materials are respectively:
A) copper, aluminium, iron done clear
B) aluminium, copper, iron done clear
C) copper, iron, aluminium done clear
D) aluminium, iron, copper done clear
View Answer play_arrowquestion_answer39) In the Wheatstone's bridge shown below, in order to balance the bridge we must have:
A) \[{{R}_{1}}=3\Omega ,\,\,{{R}_{2}}=3\Omega \] done clear
B) \[{{R}_{1}}=6\Omega ,\,\,{{R}_{2}}=1.5\Omega \] done clear
C) \[{{R}_{1}}=1.5\Omega ,\,{{R}_{2}}=\]any finite value done clear
D) \[{{R}_{1}}=3\Omega ,\,\,{{R}_{2}}=\]any finite value done clear
View Answer play_arrowquestion_answer40) Four \[10\,\,\mu F\] capacitors are connected to a \[500\,\,V\] supply as shown in the figure. The equivalent capacitance of the network is :
A) \[40\,\,\mu F\] done clear
B) \[20\,\,\mu F\] done clear
C) \[13.3\,\,\mu F\] done clear
D) \[10\,\,\mu F\] done clear
View Answer play_arrowquestion_answer41) A resistor is constructed as hollow cylinder of dimensions \[{{r}_{a}}=0.5\,\,cm\] and \[{{r}_{b}}=1.0\,\,cm\] and\[\rho =3.5\times {{10}^{-5}}\Omega m\]. The resistance of the configuration for the length of \[5\,\,cm\] cylinder is \[...\times {{10}^{-3}}\Omega \]:
A) \[7.43\] done clear
B) \[10.56\] done clear
C) \[14.38\] done clear
D) \[16.48\] done clear
View Answer play_arrowquestion_answer42) The resistors are connected as shown in the figure below. Find the equivalent resistance between the points \[A\] and \[B\].
A) \[205\Omega \] done clear
B) \[10\Omega \] done clear
C) \[3.5\Omega \] done clear
D) \[5\Omega \] done clear
View Answer play_arrowquestion_answer43) The figure below shows a \[2.0\,\,V\] potentiometer used for the determination of internal resistance of a \[2.5\,\,V\] cell. The balance point of the cell in the open circuit is \[75\,\,cm\]. When a resistor of \[10\Omega \] is used in the external circuit of the cell, the balance point shifts to \[65\,\,cm\] length of potentiometer wire. The internal resistance of the cell is:
A) \[2.5\Omega \] done clear
B) \[2.0\Omega \] done clear
C) \[1.54\Omega \] done clear
D) \[1.0\Omega \] done clear
View Answer play_arrowquestion_answer44) An electric heater boils \[1\,\,kg\] of water in a time\[{{t}_{1}}\]. Another heater boils the same amount of water in a time \[{{t}_{2}}\] When the two heaters are connected in parallel, the time required by them together to boil the same amount of water is:
A) \[{{t}_{1}}+{{t}_{2}}\] done clear
B) \[{{t}_{1}}{{t}_{2}}\] done clear
C) \[\frac{{{t}_{1}}+{{t}_{2}}}{2}\] done clear
D) \[\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{1}}+{{t}_{2}}}\] done clear
View Answer play_arrowquestion_answer45) Two thin metallic strips, carrying current in the direction shown, cross each other perpendicularly without touching but being close to each other, as shown in the figure. The regions which contain some points of zero magnetic induction are:
A) \[I\] and \[II\] done clear
B) \[I\] and \[III\] done clear
C) \[I\] and \[IV\] done clear
D) \[II\] and\[III\] done clear
View Answer play_arrowquestion_answer46) The force on a conductor of length (placed in a magnetic field of magnitude B and carrying a current \[i\] is given by \[(\theta \] is the angle, the conductor makes with the direction of \[B)\]:
A) \[F=i\,\,l\,\,B\,\,\sin \,\,\theta \] done clear
B) \[F={{i}^{2}}l\,\,{{B}^{2}}\sin \theta \] done clear
C) \[F=i\,\,l\,\,B\,\,\cos \theta \] done clear
D) \[F=\frac{{{i}^{2}}l}{B}\sin \theta \] done clear
View Answer play_arrowquestion_answer47) A needle made of bismuth is suspended freely in a magnetic field. The angle which the needle makes with the magnetic field is:
A) \[{{0}^{o}}\] done clear
B) \[{{45}^{o}}\] done clear
C) \[{{90}^{o}}\] done clear
D) \[{{180}^{o}}\] done clear
View Answer play_arrowquestion_answer48) The resonant frequency of an \[LCR\] circuit occurs at a frequency equal to:
A) \[\frac{1}{LC}\] done clear
B) \[\frac{1}{\sqrt{LC}}\] done clear
C) \[\frac{1}{LCR}\] done clear
D) \[\frac{1}{CR}\] done clear
View Answer play_arrowquestion_answer49) An alternating current is given by\[i={{i}_{1}}\cos \theta t+{{i}_{2}}\sin \omega t\]. The rms current is given by:
A) \[\frac{{{i}_{1}}+{{i}_{2}}}{\sqrt{2}}\] done clear
B) \[\frac{{{i}_{1}}-{{i}_{2}}}{\sqrt{2}}\] done clear
C) \[\sqrt{\left( \frac{i_{1}^{2}+i_{2}^{2}}{2} \right)}\] done clear
D) \[\sqrt{\left( \frac{i_{1}^{2}-i_{2}^{2}}{2} \right)}\] done clear
View Answer play_arrowquestion_answer50) The coefficient of mutual inductance between the primary and secondary of the coil is \[5\,\,H\]. A current of \[10\,\,A\] is cut-off in \[0.5\,\,s\]. The induced emf is:
A) \[1\,\,V\] done clear
B) \[10\,\,V\] done clear
C) \[5\,\,V\] done clear
D) \[100\,\,V\] done clear
View Answer play_arrowquestion_answer51) The standard adopted for the determination of atomic weight of elements is based on:
A) \[{{H}^{1}}\] done clear
B) \[{{C}^{12}}\] done clear
C) \[{{O}^{16}}\] done clear
D) \[{{S}^{32}}\] done clear
View Answer play_arrowquestion_answer52) Law of multiple proportions is illustrated by one of the following pairs:
A) \[{{H}_{2}}S\]and\[S{{O}_{2}}\] done clear
B) \[N{{H}_{3}}\]and\[N{{O}_{2}}\] done clear
C) \[N{{a}_{2}}S\]and\[N{{a}_{2}}O\] done clear
D) \[{{N}_{2}}O\]and\[NO\] done clear
View Answer play_arrowquestion_answer53) Par magnetism of oxygen is explained on the basis of its electronic configuration of:
A) \[(2\pi _{x}^{*}){{(2{{\pi }_{y}})}^{1}}\] done clear
B) \[{{({{\pi }^{*}}2{{p}_{y}})}^{1}}({{\pi }^{*}}2p_{z}^{1})\] done clear
C) \[{{(2\sigma _{s}^{*})}^{1}}{{(2{{\pi }_{y}})}^{1}}\] done clear
D) \[{{(2{{\sigma }_{s}}^{*})}^{1}}{{(2{{\pi }_{y}})}^{1}}\] done clear
View Answer play_arrowquestion_answer54) The van der Waals' equation for a real gas is given by the formula \[\left( P+\frac{{{n}^{2}}a}{{{V}^{2}}} \right)(V-nb)=nRT\] where \[P,\,\,V,\,\,T\] and \[n\] are the pressure, volume, temperature and the number of moles of the gas. Which one is the correct interpretation for the parameter\[a?\]
A) The parameter a accounts for the finite size of the molecule, not included temperature in the ideal gas law done clear
B) The parameter a accounts for the shape of gas phase molecules done clear
C) The parameter \[a\] accounts for intermolecular interaction?s present in the molecule done clear
D) The parameter \[a\] has no physical significance and van der Waals? introduced it as a numerical correction factor only done clear
View Answer play_arrowquestion_answer55) Avogadro's hypothesis states that:
A) the ideal gas consists of a large number of small particles called molecules done clear
B) under the same conditions of temperature and pressure equal volumes of gases contain the same number of molecules done clear
C) volume of a definite quantity of gas at constant pressure is directly proportional to absolute temperature done clear
D) a given mass of gas at constant pressure is , directly proportional to absolute temperature done clear
View Answer play_arrowquestion_answer56) The observation that the ground state of nitrogen atom has \[3\] unpaired electrons in its electronic configuration and not otherwise is associated with:
A) Pauli's exclusion principle done clear
B) Hund's rule of maximum multiplicity done clear
C) Heisenberg's uncertainty principle done clear
D) Ritz combination principle. done clear
View Answer play_arrowquestion_answer57) Which of the following overlaps leads to bonding?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer58) In the periodic table metallic character of elements shows one of the following trend:
A) decreases down the group and increases across the period done clear
B) increases down the group and decreases across the period done clear
C) increases across the period and also down the group done clear
D) decreases across the period and also down the group done clear
View Answer play_arrowquestion_answer59) Which of the following statements is correct?
A) All carbon to carbon bonds contain a sigma bond and one or more pi bonds done clear
B) All carbon to hydrogen bonds are pi bonds done clear
C) All oxygen to hydrogen bonds are hydrogen bonds done clear
D) All carbon to hydrogen bonds are sigma bonds done clear
View Answer play_arrowquestion_answer60) An example of a polar covalent compound is:
A) \[KCl\] done clear
B) \[NaCl\] done clear
C) \[CC{{l}_{4}}\] done clear
D) \[HCl\] done clear
View Answer play_arrowquestion_answer61) If \[117\,\,g\,\,NaCl\] is dissolved in \[1000\,\,g\] of water the concentration of the solution is said to be:
A) \[2\,\,molar\] done clear
B) \[2\,\,molal\] done clear
C) \[1\,\,normal\] done clear
D) \[1\,\,molal\] done clear
View Answer play_arrowquestion_answer62) A solution \[\text{of}\]\[4.5\,\,g\] of a pure non-electrolyte in \[100\,\,g\] of water was found to freeze at\[{{0.465}^{o}}C\]. The molecular weight of the solute is closest to\[({{k}_{f}}=1.86)\]:
A) \[135.0\] done clear
B) \[172.0\] done clear
C) \[90.0\] done clear
D) \[180.0\] done clear
View Answer play_arrowquestion_answer63) The enthalpy of vaporization of substance is \[840\,\,J\text{-}mo{{l}^{-1}}\] and its boiling point is\[-{{173}^{o}}C\]. Its entropy of vaporization is:
A) \[42\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}\] done clear
B) \[21\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}\] done clear
C) \[84\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}\] done clear
D) \[8.4\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}\] done clear
View Answer play_arrowquestion_answer64) Given the following thermochemical equations: \[Zn+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}ZnO+84,000\,\,cal\] \[Hg+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}HgO+21,700\,\,cal\] Accordingly the heat of reaction for the following reaction \[Zn+HgO\xrightarrow{{}}Hg+\]heat is:
A) \[105,700\,\,cal\] done clear
B) \[61,000\,\,cal\] done clear
C) \[105,000\,\,cal\] done clear
D) \[62,300\,\,cal\] done clear
View Answer play_arrowquestion_answer65) A saturated solution of\[Ca{{F}_{2}}\]is\[2\times {{10}^{-4}}mol/L\]. Its solubility product constant is:
A) \[2.6\times {{10}^{-9}}\] done clear
B) \[4\times {{10}^{-8}}\] done clear
C) \[8\times {{10}^{-12}}\] done clear
D) \[3.2\times {{10}^{-11}}\] done clear
View Answer play_arrowquestion_answer66) For the reaction\[{{H}_{2}}(g)+{{I}_{2}}(g)2HI(g)\] the equilibrium constants expressed in terms of concentrations \[{{K}_{c}}\] and in terms of partial pressures\[{{K}_{p}},\]are related as:
A) \[{{K}_{p}}={{K}_{c}}{{(RT)}^{2}}\] done clear
B) \[{{K}_{p}}={{K}_{c}}{{(RT)}^{-2}}\] done clear
C) \[{{K}_{p}}={{K}_{c}}\] done clear
D) \[{{K}_{c}}={{K}_{p}}(RT)\] done clear
View Answer play_arrowquestion_answer67) Which of the following \[1:1\] mixture will act as buffer solution?
A) \[HCl\]and\[NaOH\] done clear
B) \[KOH\]and\[C{{H}_{3}}COOH\] done clear
C) \[C{{H}_{3}}COOH\]\[NaCl\] done clear
D) \[C{{H}_{3}}COOH\]and\[C{{H}_{3}}COONa\] done clear
View Answer play_arrowquestion_answer68) What is potential of platinum wire dipped into a solution of \[0.1\,\,M\]in\[S{{n}^{2+}}\] and \[0.01\,\,M\] in\[S{{n}^{4+}}\]?
A) \[{{E}_{0}}\] done clear
B) \[{{E}_{0}}+0.059\] done clear
C) \[{{E}_{0}}+\frac{0.059}{2}\] done clear
D) \[{{E}_{0}}=\frac{0.059}{2}\] done clear
View Answer play_arrowquestion_answer69) In one of the following reactions \[HN{{O}_{3}}\]does not behave as an oxidizing agent. Identify it:
A) \[{{I}_{2}}+10HN{{O}_{3}}\xrightarrow[{}]{{}}2HI{{O}_{3}}+10N{{O}_{2}}+4{{H}_{2}}O\] done clear
B) \[3Cu+8HN{{O}_{3}}\xrightarrow{{}}3Cu{{(N{{O}_{3}})}_{2}}\]\[+2NO+4{{H}_{2}}O\] done clear
C) \[4Zn+10HN{{O}_{3}}\xrightarrow{{}}4Zn{{(N{{O}_{3}})}_{2}}\]\[+N{{H}_{4}}N{{O}_{3}}+3{{H}_{2}}O\] done clear
D) \[2HN{{O}_{3}}+{{P}_{2}}{{O}_{3}}\xrightarrow{{}}2HP{{O}_{3}}+{{N}_{2}}{{O}_{5}}\] done clear
View Answer play_arrowquestion_answer70) Which of the following statement is not correct?
A) In zero order reaction the rate of the reaction remains constant throughout done clear
B) A second order reaction would become a pseudo first order reaction when one of the reactants is taken in large excess done clear
C) The value of first order rate constant depends on the units of the concentration terms used done clear
D) In a first order reaction the plot of \[\log (a-x)vs\] time gives a straight line done clear
View Answer play_arrowquestion_answer71) Radioactive decay series of uranium is denoted as:
A) \[4n+1\] done clear
B) \[4n+2\] done clear
C) \[4n\] done clear
D) \[4n+3\] done clear
View Answer play_arrowquestion_answer72) The number of isomeric hexanes is:
A) \[5\] done clear
B) \[2\] done clear
C) \[3\] done clear
D) \[4\] done clear
View Answer play_arrowquestion_answer73) The coagulating power of an electrolyte for arsenious sulphide decreases in the order:
A) \[N{{a}^{+}}<A{{l}^{3+}}<B{{a}^{2+}}\] done clear
B) \[PO_{4}^{3-}<SO_{4}^{2-}<C{{l}^{-}}\] done clear
C) \[Cl<SO_{4}^{2-}<PO_{4}^{3-}\] done clear
D) \[A{{l}^{3+}}<B{{a}^{2+}}<N{{a}^{+}}\] done clear
View Answer play_arrowquestion_answer74) The two optical isomers given below, namely, \[(a)\]:
A) enantiomers done clear
B) geometrical isomers done clear
C) diastereomers done clear
D) structural isomers done clear
View Answer play_arrowquestion_answer75) Which of the following statement is wrong?
A) Using Lassaigne's test nitrogen and sulphur present in organic compound can be tested done clear
B) Using Beilstein's test the presence of halogen in a compound can be tested done clear
C) In Lassaigne's filtrate the nitrogen present in organic compound is converted into \[NaCN\] done clear
D) In the estimation of carbon, an organic compound is heated with \[CaO\] in a combustion tube done clear
View Answer play_arrowquestion_answer76) \[Cis-trans\] isomers generally:
A) contain an asymmetric carbon atom done clear
B) rotate the .plane of polarized light done clear
C) are enantiomorphism done clear
D) contain double bonded carbon atoms done clear
View Answer play_arrowquestion_answer77) Wurtz's reaction involves the reduction of alkyl halide with:
A) \[Zn/HCl\] done clear
B) \[HI\] done clear
C) \[Zn/Cu\]couple done clear
D) \[Na\]is ether done clear
View Answer play_arrowquestion_answer78) The reaction \[{{C}_{12}}{{H}_{26}}\xrightarrow[{}]{{}}{{C}_{6}}{{H}_{12}}+{{C}_{6}}{{H}_{14}}\]represent:
A) substitution done clear
B) synthesis done clear
C) cracking done clear
D) polymerization done clear
View Answer play_arrowquestion_answer79) The compound that does not answer iodoform test is:
A) ethanol done clear
B) ethanol done clear
C) methanol done clear
D) propanone done clear
View Answer play_arrowquestion_answer80) Which one of the following compound reacts with chlorobenzene to produce\[DDT?\]
A) Acetaldehyde done clear
B) Nitrobenzene done clear
C) \[m-\]chloroacetaldehyde done clear
D) Trichloroacetaldehyde done clear
View Answer play_arrowquestion_answer81) Conversion of benzaldehyde to 3-phenyl-prop-2-en-1-oic acid is:
A) Perkin condensation done clear
B) Claisen condensation done clear
C) Oxidative addition done clear
D) Aldol condensation done clear
View Answer play_arrowquestion_answer82) Which of the following compounds forms an addition compound with \[C{{H}_{3}}MgBr\], which on hydrolysis produce a secondary alcohol?
A) \[HCHO\] done clear
B) \[C{{H}_{3}}CHO\] done clear
C) \[C{{H}_{3}}OC{{H}_{3}}\] done clear
D) \[C{{H}_{3}}COC{{H}_{3}}\] done clear
View Answer play_arrowquestion_answer83) Which of the following pairs are correctly matched?
1. Haber process | Manufacture of ammonia |
2. Leblanc process | Manufacture of sulphuric acid |
3. Birkeland-Eyde process | Manufacture of nitric acid |
4. Solvay process | Manufacture of sodium carbonate |
A) 2, 3 and 4 done clear
B) 1, 2, 3 and 4 done clear
C) 1, 2 and done clear
D) 1, 3 and 4 done clear
View Answer play_arrowquestion_answer84) Which of the following compounds on treatment first with \[NaN{{O}_{2}}/HCl\] and then coupled with phenol produces p-hydroxyazobenzene?
A) Nitrobenzene done clear
B) Azobenzene done clear
C) Phenol done clear
D) Aniline done clear
View Answer play_arrowquestion_answer85) Initial setting of cement is mainly due to:
A) hydration and gel formation done clear
B) dehydration and gel formation done clear
C) hydration and hydrolysis done clear
D) dehydration and dehydrolysis done clear
View Answer play_arrowquestion_answer86) A certain metal will liberate hydrogen from dilute acids. If will react with water to form hydrogen only when the metal is heated and the water is in the form of steam. The metal is probably:
A) iron done clear
B) potassium done clear
C) copper done clear
D) mercury done clear
View Answer play_arrowquestion_answer87) The number of alpha and beta particles emitted in the chain of reactions leading to the decay of\[_{92}^{238}U\]to\[_{82}^{206}Pb\]
A) \[8\] beta particles and \[6\] alpha particles done clear
B) \[5\] alpha particles and \[0\] beta particles done clear
C) \[8\] alpha and \[6\] beta particles done clear
D) \[10\] alpha particles and \[10\] beta particles done clear
View Answer play_arrowquestion_answer88) Hydrogen peroxide when added to a solution of potassium permanganate acidified with sulphuric acid:
A) forms water only done clear
B) acts as an oxidizing agent done clear
C) acts as a reducing agent done clear
D) reduces sulphuric acid done clear
View Answer play_arrowquestion_answer89) The equilibrium molecular structure of hydrogen peroxide is:
A) planar as given below done clear
B) linear done clear
C) tetrahedral done clear
D) non planar done clear
View Answer play_arrowquestion_answer90) Consider the following compounds. 1. Sulphur dioxide 2. Hydrogen peroxide 3. Ozone Among these compounds identify those that can act as bleaching agent:
A) \[1\] and \[3\] done clear
B) \[2\] and \[3\] done clear
C) \[1\] and \[2\] done clear
D) \[1,\,\,2\] and \[3\] done clear
View Answer play_arrowquestion_answer91) Alkali metals have high oxidation potential and hence, they behave as:
A) oxidizing agents done clear
B) Lewis bases done clear
C) reducing agents done clear
D) electrolytes done clear
View Answer play_arrowquestion_answer92) Water is oxidized to oxygen by:
A) \[Cl{{O}_{2}}\] done clear
B) \[KMn{{O}_{4}}\] done clear
C) \[{{H}_{2}}{{O}_{2}}\] done clear
D) fluorine done clear
View Answer play_arrowquestion_answer93) Identify the incorrect statement:
A) The molarity of a solution is independent of temperature done clear
B) The tendency for catenation is much higher for carbon than for silicon done clear
C) Nitriles and iso nitriles constitute metamers done clear
D) \[t-\]butyl carbocation has planar carbons and is very reactive done clear
View Answer play_arrowquestion_answer94) The magnetic moment p, of transition metals is related to the number of unpaired electrons, \[n\] as:
A) \[\mu =n{{(n+2)}^{2}}\] done clear
B) \[\mu ={{n}^{2}}(n+2)\] done clear
C) \[\mu =\frac{n}{(n+2)}\] done clear
D) \[\mu =\frac{n}{\sqrt{n+2}}\] done clear
View Answer play_arrowquestion_answer95) Which one of the following statement is wrong?
A) The \[IUPAC\] name of \[[Co{{(N{{H}_{3}})}_{6}}C{{l}_{3}}]\] is hexamine cobalt \[(III)\] chloride done clear
B) Dibenzol peroxide is a catalyst in the polymerization of\[PVC\] done clear
C) Borosilicate glass is heat resistant done clear
D) Concentrated \[HN{{O}_{3}}\] can be safely transported in aluminium containers done clear
View Answer play_arrowquestion_answer96) Which of the following is not a thermoplastic?
A) Polystyrene done clear
B) Teflon done clear
C) Polyvinyl chloride done clear
D) Nylon\[-6,\,\,6\] done clear
View Answer play_arrowquestion_answer97) Which set is the correct pairing set (or contains complementary pairs) responsible for the structure of\[DNA?\] (A-adenine, G-guanine, C-cystosine, T-thymine, U-uracil)
A) \[A-T,\,\,G-C\] done clear
B) \[A-C,\,\,G-T\] done clear
C) \[A-G,\,\,C-T\] done clear
D) \[A-U,\,\,G-C\] done clear
View Answer play_arrowquestion_answer98) Barbituric acid and its derivatives are well known as:
A) tranquilizers done clear
B) antiseptics done clear
C) analgesics done clear
D) antipyretics done clear
View Answer play_arrowquestion_answer99) The rate of a reaction is doubled for every \[{{10}^{o}}\] rise in temperature. The increase in reaction rate as a result of temperature rise from \[{{10}^{o}}\] to \[{{100}^{o}}\] is:
A) \[112\] done clear
B) \[512\] done clear
C) \[400\] done clear
D) \[614\] done clear
View Answer play_arrowquestion_answer100) The first artificial disintegration of an atomic nucleus was achieved by:
A) Geiger done clear
B) Wilson done clear
C) Madam Curie done clear
D) Rutherford done clear
View Answer play_arrowquestion_answer101) If \[f(x)={{\log }_{x}}({{\log }_{e}}x)\], then \[f'(x)\] at \[x=e\] is equal to:
A) \[1\] done clear
B) \[2\] done clear
C) \[0\] done clear
D) \[1/e\] done clear
View Answer play_arrowquestion_answer102) The number of terms in the expansion of \[{{(a+b+c)}^{10}}\]is:
A) \[11\] done clear
B) \[21\] done clear
C) \[55\] done clear
D) \[66\] done clear
View Answer play_arrowquestion_answer103) For what value of K, the system of equations\[x+y+z=6,\,\,x+2y+3z=10\],\[x+2y+\lambda z=10\]is consistent?
A) \[1\] done clear
B) \[2\] done clear
C) \[-1\] done clear
D) \[3\] done clear
View Answer play_arrowquestion_answer104) Let\[f(x)\]be twice differentiable such that\[f'\,\,'(x)=-f(x),\,\,f'(x)=g(x)\], where \[f'(x)\] and\[f'\,\,'(x)\] represent the first and second derivatives of \[f(x)\] respectively. Also if \[h(x)={{[f(x)]}^{2}}+{{[g(x)]}^{2}}\]and \[h(5)=5\], then \[h(10)\] is equal to :
A) \[3\] done clear
B) \[10\] done clear
C) \[13\] done clear
D) \[5\] done clear
View Answer play_arrowquestion_answer105) A straight line through \[P(1,\,\,2)\] is such that its intercept between the axes is bisected at P. Its equation is:
A) \[x+y=-1\] done clear
B) \[x+y=3\] done clear
C) \[x+2y=5\] done clear
D) \[2x+y=4\] done clear
View Answer play_arrowquestion_answer106) The radius of any circle touching the lines \[3x-4y+5=0\] and \[6x-8y-9=0\] is:
A) \[1.9\] done clear
B) \[0.95\] done clear
C) \[2.9\] done clear
D) \[1.45\] done clear
View Answer play_arrowquestion_answer107) The point on the curve \[\sqrt{x}+\sqrt{y}=\sqrt{a}\], the normal at which is parallel to the \[x-\]axis, is:
A) \[(0,\,\,0)\] done clear
B) \[(0,\,\,a)\] done clear
C) \[(a,\,\,0)\] done clear
D) \[(a,\,\,a)\] done clear
View Answer play_arrowquestion_answer108) If two circles of the same radius rand centres at \[(2,\,\,3)\] and \[(5,\,\,6)\] respectively cut orthogonally, then the value of \[r\] is:
A) \[3\] done clear
B) \[2\] done clear
C) \[1\] done clear
D) \[5\] done clear
View Answer play_arrowquestion_answer109) The equation to the sides of a triangle are \[x-3y=0,\]\[4x+3y=5\]and \[3x+y=0\]. The line \[3x-4y=0\] passes through the:
A) in centre done clear
B) centroid done clear
C) orthocentre done clear
D) circumcentre done clear
View Answer play_arrowquestion_answer110) For\[|x|\,\,<1\], let\[y=1+x+{{x}^{2}}+...\]to\[\infty \], then\[\frac{dy}{dx}=-y\]is equal to:
A) \[\frac{x}{y}\] done clear
B) \[\frac{{{x}^{2}}}{{{y}^{2}}}\] done clear
C) \[\frac{x}{{{y}^{2}}}\] done clear
D) \[x{{y}^{2}}\] done clear
View Answer play_arrowquestion_answer111) If\[(-4,\,\,5)\] is one vertex and \[7x-y+8=0\] is one diagonal of a square, then the equation of the second diagonal is:
A) \[x+3y=21\] done clear
B) \[2x-3y=7\] done clear
C) \[x+7y=31\] done clear
D) \[2x+3y=21\] done clear
View Answer play_arrowquestion_answer112) The number of common tangents to two circles \[{{x}^{2}}+{{y}^{2}}=4\] and \[{{x}^{2}}+{{y}^{2}}-8x+12=0\]is:
A) \[1\] done clear
B) \[2\] done clear
C) \[5\] done clear
D) \[3\] done clear
View Answer play_arrowquestion_answer113) If \[y={{\log }^{n}}x\], where\[{{\log }^{n}}\]means\[\log \log \log ...\](repeated \[n\] times), then\[x\log x{{\log }^{2}}x{{\log }^{3}}x...{{\log }^{n-1}}x{{\log }^{n}}x\frac{dy}{dx}\]is equal to:
A) \[\log x\] done clear
B) \[x\] done clear
C) \[\frac{1}{\log x}\] done clear
D) \[{{\log }^{n}}x\] done clear
View Answer play_arrowquestion_answer114) The focus of the parabola \[{{y}^{2}}-x-2y+2=0\] is:
A) \[(1/4,\,\,0)\] done clear
B) \[(1,\,\,2)\] done clear
C) \[(5/4,\,\,1)\] done clear
D) \[(3/4,\,\,5/2)\] done clear
View Answer play_arrowquestion_answer115) The equation of the parabola with vertex at the origin and directrix \[y=2\] is:
A) \[{{y}^{2}}=8x\] done clear
B) \[{{y}^{2}}=-8x\] done clear
C) \[{{y}^{2}}=\sqrt{8}x\] done clear
D) \[{{x}^{2}}=-8y\] done clear
View Answer play_arrowquestion_answer116) The point on the curve \[x{{y}^{2}}=1\] that is nearest to the origin, is:
A) \[(1,\,\,1)\] done clear
B) \[(4,\,\,1/2)\] done clear
C) \[(5/4,\,\,1)\] done clear
D) \[(3/4,\,\,5/2)\] done clear
View Answer play_arrowquestion_answer117) The distance of. the point \[A(2,\,\,3,\,\,4)\] from \[x-\]axis is:
A) \[5\] done clear
B) \[\sqrt{13}\] done clear
C) \[2\sqrt{5}\] done clear
D) \[5\sqrt{2}\] done clear
View Answer play_arrowquestion_answer118) The radius of the circle\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2y-4z-11=0\],\[x+2y+2z-15=0\]is:
A) \[\sqrt{3}\] done clear
B) \[\sqrt{5}\] done clear
C) \[\sqrt{7}\] done clear
D) \[3\] done clear
View Answer play_arrowquestion_answer119) \[\int{{{x}^{2}}{{(ax+b)}^{-2}}dx}\]is equal to:
A) \[\frac{2}{{{a}^{2}}}\left( x-\frac{b}{a}x\log (ax+b) \right)+c\] done clear
B) \[\frac{2}{{{a}^{2}}}\left( x-\frac{b}{a}\log (ax+b) \right)-\frac{{{x}^{2}}}{a(ax+b)}+c\] done clear
C) \[\frac{2}{{{a}^{2}}}\left( x+\frac{b}{a}\log (ax+b) \right)+\frac{{{x}^{2}}}{a(ax+b)}+c\] done clear
D) \[\frac{2}{{{a}^{2}}}\left( x+\frac{b}{a}\log (ax+b) \right)-\frac{{{x}^{2}}}{a(ax+b)}+c\] done clear
View Answer play_arrowquestion_answer120) If the coordinate of the vertices of a triangle\[ABC\]be\[A(-1,\,\,3,\,\,2),\]\[B(2,\,\,3,\,\,5)\]and\[C(3,\,\,5,\,\,-2)\] then \[\angle A\]is equal to:
A) \[{{45}^{o}}\] done clear
B) \[{{60}^{o}}\] done clear
C) \[{{90}^{o}}\] done clear
D) \[{{30}^{o}}\] done clear
View Answer play_arrowquestion_answer121) If\[\overset{\to }{\mathop{\mathbf{a}}}\,+\overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,=0\],\[|\overset{\to }{\mathop{\mathbf{a}}}\,|=3,\,\,|\overset{\to }{\mathop{\mathbf{b}}}\,|=5\]and\[|\overset{\to }{\mathop{\mathbf{c}}}\,|\,\,=7\], then the angle between \[\overset{\to }{\mathop{\mathbf{a}}}\,\] and \[\overset{\to }{\mathop{\mathbf{b}}}\,\] is:
A) \[{{0}^{o}}\] done clear
B) \[{{30}^{o}}\] done clear
C) \[{{90}^{o}}\] done clear
D) \[{{30}^{o}}\] done clear
View Answer play_arrowquestion_answer122) If\[f(t)\]is an odd function, then\[\int_{0}^{x}{f(t)}\,dt\]is:
A) an odd function done clear
B) an even function done clear
C) neither even nor odd done clear
D) \[0\] done clear
View Answer play_arrowquestion_answer123) The projection of\[\widehat{\mathbf{i}}+3\widehat{\mathbf{j}}+\widehat{\mathbf{k}}\]on\[2\widehat{\mathbf{i}}-3\widehat{\mathbf{j}}+6\widehat{\mathbf{k}}\]is:
A) \[1/7\] done clear
B) \[-1/7\] done clear
C) \[7\] done clear
D) \[-7\] done clear
View Answer play_arrowquestion_answer124) If\[\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,=0\]and\[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=0\], then:
A) \[\overset{\to }{\mathop{\mathbf{a}}}\,\bot \overset{\to }{\mathop{\mathbf{b}}}\,\] done clear
B) \[\overset{\to }{\mathop{\mathbf{a}}}\,||\overset{\to }{\mathop{\mathbf{b}}}\,\] done clear
C) \[\overset{\to }{\mathop{\mathbf{a}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]and\[\overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\] done clear
D) \[\overset{\to }{\mathop{\mathbf{a}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]and\[\overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\] done clear
View Answer play_arrowquestion_answer125) If the area bounded by the parabola \[y=2-{{x}^{2}}\] and the line \[x+y=0\] is \[A\] sq unit, then \[A\] equals:
A) \[\frac{1}{2}\] done clear
B) \[\frac{1}{3}\] done clear
C) \[\frac{2}{9}\] done clear
D) \[\frac{9}{2}\] done clear
View Answer play_arrowquestion_answer126) The points\[A(4,\,\,5,\,\,1),\] \[B(0,\,\,-1,\,\,1),\] \[C(3,\,\,9,\,\,4)\]and\[D(-4,\,\,4,\,\,4)\] are:
A) collinear done clear
B) coplanar done clear
C) non-coplanar done clear
D) non-collinear done clear
View Answer play_arrowquestion_answer127) \[{{(\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,)}^{2}}\] is equal to:
A) \[\overset{\to }{\mathop{{{\mathbf{a}}^{\mathbf{2}}}}}\,+\overset{\to }{\mathop{{{\mathbf{b}}^{\mathbf{2}}}}}\,-(\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,)\] done clear
B) \[\overset{\to }{\mathop{{{\mathbf{a}}^{\mathbf{2}}}}}\,\overset{\to }{\mathop{{{\mathbf{b}}^{\mathbf{2}}}}}\,-{{(\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,)}^{2}}\] done clear
C) \[\overset{\to }{\mathop{{{\mathbf{a}}^{\mathbf{2}}}}}\,+\overset{\to }{\mathop{{{\mathbf{b}}^{\mathbf{2}}}}}\,-2\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,\] done clear
D) \[\overset{\to }{\mathop{{{\mathbf{a}}^{\mathbf{2}}}}}\,+\overset{\to }{\mathop{{{\mathbf{b}}^{\mathbf{2}}}}}\,-2\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,\] done clear
View Answer play_arrowquestion_answer128) Let \[F\] denotes the family of ellipses whose centre is at the origin and major axis is the \[y-\]axis. Then equation of the family \[F\] is:
A) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\] done clear
B) \[xy\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\] done clear
C) \[xy\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\] done clear
D) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\] done clear
View Answer play_arrowquestion_answer129) The value of\[\left( \cos \frac{\pi }{2}+i\sin \frac{\pi }{2} \right)\left( \cos \left( \frac{\pi }{{{2}^{2}}} \right)+i\sin \left( \frac{\pi }{{{2}^{2}}} \right) \right)\]\[\times \left( \cos \left( \frac{\pi }{{{2}^{3}}} \right)+i\sin \left( \frac{\pi }{{{2}^{3}}} \right) \right)...\infty \]is:
A) \[-1\] done clear
B) \[1\] done clear
C) \[0\] done clear
D) \[\sqrt{2}\] done clear
View Answer play_arrowquestion_answer130) If\[x+\frac{1}{x}=2\sin \alpha ,\] \[y+\frac{1}{y}=2\cos \beta \], then\[{{x}^{3}}{{y}^{3}}+\frac{1}{{{x}^{3}}{{y}^{3}}}\]is:
A) \[2\cos 3(\beta -\alpha )\] done clear
B) \[2\cos 3(\beta +\alpha )\] done clear
C) \[2\sin 3(\beta -\alpha )\] done clear
D) \[2\sin 3(\beta +\alpha )\] done clear
View Answer play_arrowquestion_answer131) Solution of the equation\[x{{\left( \frac{dy}{dx} \right)}^{2}}+2\sqrt{xy}\frac{dy}{dx}+y=0\]is:
A) \[x+y=a\] done clear
B) \[\sqrt{x}-\sqrt{y}=\sqrt{a}\] done clear
C) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] done clear
D) \[\sqrt{x}+\sqrt{y}=\sqrt{a}\] done clear
View Answer play_arrowquestion_answer132) A bag contains \[5\] white and \[3\] black balls and \[4\] balls are successively drawn out and not replaced. The probability that they are alternately of different colours, is:
A) \[1/196\] done clear
B) \[2/7\] done clear
C) \[1/7\] done clear
D) \[13/56\] done clear
View Answer play_arrowquestion_answer133) If\[\underset{x\to a}{\mathop{\lim }}\,\frac{{{a}^{x}}-{{x}^{a}}}{{{x}^{x}}-{{a}^{a}}}=-1\],then\[a\]equals:
A) \[1\] done clear
B) \[0\] done clear
C) \[e\] done clear
D) \[(1/e)\] done clear
View Answer play_arrowquestion_answer134) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\tan x-\sin x}{{{x}^{3}}}\]is equal to:
A) \[0\] done clear
B) \[1\] done clear
C) \[1/2\] done clear
D) \[-1/2\] done clear
View Answer play_arrowquestion_answer135) \[\underset{x\to a}{\mathop{\lim }}\,\frac{\log (x-a)}{\log ({{e}^{x}}-{{e}^{a}})}\]is equal to:
A) \[0\] done clear
B) \[1\] done clear
C) \[a\] done clear
D) does not exist done clear
View Answer play_arrowquestion_answer136) If\[f(x)=|x{{|}^{3}}\], then\[f'(0)\]equals:
A) \[0\] done clear
B) \[1/2\] done clear
C) \[-1\] done clear
D) \[-1/2\] done clear
View Answer play_arrowquestion_answer137) \[\int{{{e}^{-\log x}}}dx\]is equal to:
A) \[{{e}^{-\log x}}+c\] done clear
B) \[-x{{e}^{-\log x}}+c\] done clear
C) \[{{e}^{\log x}}+c\] done clear
D) \[\log |x|+c\] done clear
View Answer play_arrowquestion_answer138) The area cut off by the latus rectum from the parabola \[{{y}^{2}}=4ax\] is:
A) \[(8/3)a\,\,sq\,\,unit\] done clear
B) \[(8/3)\sqrt{a}\,\,sq\,\,unit\] done clear
C) \[(3/8)\sqrt{a}\,\,sq\,\,unit\] done clear
D) \[(8/3){{a}^{2}}\,\,sq\,\,unit\] done clear
View Answer play_arrowquestion_answer139) The solution of differential equation\[(x+y)(dx-dy)=dx+dy\]is:
A) \[x-y=k{{e}^{x-y}}\] done clear
B) \[x+y=k{{e}^{x+y}}\] done clear
C) \[x+y=k(x-y)\] done clear
D) \[x+y=k{{e}^{x-y}}\] done clear
View Answer play_arrowquestion_answer140) In how many ways can 8 students be arranged in a row?
A) \[8!\] done clear
B) \[7!\] done clear
C) \[8\] done clear
D) \[7\] done clear
View Answer play_arrowquestion_answer141) If the third term of a \[GP\] is \[p\]. Then the product of the first \[5\] terms of the \[GP\] is:
A) \[{{p}^{3}}\] done clear
B) \[{{p}^{2}}\] done clear
C) \[{{p}^{10}}\] done clear
D) \[{{p}^{5}}\] done clear
View Answer play_arrowquestion_answer142) The sum of n terms of the series\[\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+...\]is:
A) \[\frac{{{3}^{n}}(2n+1)+1}{2({{3}^{n}})}\] done clear
B) \[\frac{{{3}^{n}}(2n+1)-1}{2({{3}^{n}})}\] done clear
C) \[\frac{{{3}^{n}}n-1}{2({{3}^{n}})}\] done clear
D) \[\frac{{{3}^{n}}-1}{2}\] done clear
View Answer play_arrowquestion_answer143) If \[\alpha \] and \[\beta \] are the solutions of the quadratic equation \[a{{x}^{2}}+bx+c=0\] such that \[\beta ={{\alpha }^{1/3}}\], then:
A) \[{{(ac)}^{1/3}}+{{(ab)}^{1/3}}+c=0\] done clear
B) \[{{({{a}^{3}}b)}^{1/4}}+{{(a{{b}^{3}})}^{1/4}}+c=0\] done clear
C) \[{{({{a}^{3}}c)}^{1/4}}+{{(a{{c}^{3}})}^{1/4}}+b=0\] done clear
D) \[{{({{a}^{4}}c)}^{1/3}}+{{(a{{c}^{4}})}^{1/3}}+b=0\] done clear
View Answer play_arrowquestion_answer144) \[^{20}{{C}_{4}}+2{{\cdot }^{20}}{{C}_{3}}{{+}^{20}}{{C}_{2}}{{-}^{22}}{{C}_{18}}\]is equal to :
A) \[0\] done clear
B) \[1242\] done clear
C) \[7315\] done clear
D) \[6345\] done clear
View Answer play_arrowquestion_answer145) If\[x=\frac{\left[ \begin{align} & 729+6(2)(243)+15(4)(81)+20 \\ & \times (8)(27)+15(16)(9)+6(32)3+64 \\ \end{align} \right]}{1+4(4)+6(16)+4(64)+256}\]then \[\sqrt{x}-\frac{1}{\sqrt{x}}\] is equal to:
A) \[0.2\] done clear
B) \[4.8\] done clear
C) \[1.02\] done clear
D) \[5.2\] done clear
View Answer play_arrowquestion_answer146) Along a road lie an odd number of stones placed at intervals of \[10\,\,m\]. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man started the job with one of the end stones by carrying them in succession. In carrying all the stones, the man covered a total distance of\[3\,\,km\]. Then the total number of stones is:
A) \[20\] done clear
B) \[25\] done clear
C) \[12\] done clear
D) \[24\] done clear
View Answer play_arrowquestion_answer147) If\[a=1+2+4+...\]to \[n\] terms,\[b=1+3+9+...\]to \[n\] terms and \[c=1+5+25+...\]to \[n\] terms, then\[\left| \begin{matrix} a & 2b & 4c \\ 2 & 2 & 2 \\ {{2}^{n}} & {{3}^{n}} & {{5}^{n}} \\ \end{matrix} \right|\]equals:
A) \[{{(30)}^{n}}\] done clear
B) \[{{(10)}^{n}}\] done clear
C) \[0\] done clear
D) \[{{2}^{n}}+{{3}^{n}}+{{5}^{n}}\] done clear
View Answer play_arrowquestion_answer148) The matrix \[\left[ \begin{matrix} 5 & 10 & 3 \\ -2 & -4 & 6 \\ -1 & -2 & b \\ \end{matrix} \right]\] is a singular matrix, if is equal to:
A) \[-3\] done clear
B) \[3\] done clear
C) \[0\] done clear
D) for any value of\[b\] done clear
View Answer play_arrowquestion_answer149) Let \[N\] be the number of quadratic equations with coefficients from \[\{0,\,\,1,\,\,2,\,\,....,\,\,9\}\] such that zero is a solution of each equation. Then the value of \[N\] is:
A) infinite done clear
B) \[{{2}^{9}}\] done clear
C) \[90\] done clear
D) \[900\] done clear
View Answer play_arrowquestion_answer150) For non-singular square matrices \[A,\,\,\,B\] and \[C\] of the same order, \[{{(A{{B}^{-1}}C)}^{-1}}\]is equal to:
A) \[{{A}^{-1}}B{{C}^{-1}}\] done clear
B) \[{{C}^{-1}}{{B}^{-1}}{{A}^{-1}}\] done clear
C) \[CB{{A}^{-1}}\] done clear
D) \[{{C}^{-1}}B{{A}^{-1}}\] done clear
View Answer play_arrow
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