Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2005

done JCECE Engineering Solved Paper-2005

  • 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) \[[{{h}^{1}}{{c}^{1}}{{G}^{-1}}]\]

    B) \[[{{h}^{1/2}}{{c}^{1/2}}{{G}^{-1/2}}]\]

    C) \[[{{h}^{1}}{{c}^{-3}}{{G}^{1}}]\]

    D) \[[{{h}^{1/2}}{{c}^{-3/2}}{{G}^{1/2}}]\]

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  • question_answer2) The radius of sphere is measured to be\[(2.1\pm 0.5)\,\,cm\]. Calculate its surface area with error limits:

    A) \[(55.4\pm 26.4)c{{m}^{2}}\]

    B) \[(55.4\pm 0.02)c{{m}^{2}}\]

    C) \[(55.4\pm 2.64)c{{m}^{2}}\]

    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 \[\Delta S=2\left( \frac{\Delta r}{r} \right)(S)\] \[=\frac{2\times 0.5\times 55.4}{2.1}=26.38=26.4\,\,c{{m}^{2}}\] \[\therefore \] \[S=(55.4\pm 26.4)c{{m}^{2}}\]

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  • question_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) \[11.9\,\,N\]

    B) \[25\,\,N\]

    C) \[50\,\,N\]

    D) \[22.9\,\,N\]

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  • question_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) \[14m{{s}^{-1}},\,\,5\,\,m{{s}^{-2}}\]

    B) \[19m{{s}^{-1}},\,\,-9m{{s}^{-2}}\]

    C) \[-14m{{s}^{-1}},\,\,-5m{{s}^{-2}}\]

    D) \[5m{{s}^{-1}},\,\,14\,\,m{{s}^{-2}}\]

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  • question_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

    B) \[3\,\,m{{s}^{-2}}\] in north direction

    C) \[15\,\,m{{s}^{-2}}\]in north direction

    D) \[3\,\,m{{s}^{-2}}\]in south direction

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  • question_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) \[72\]

    B) \[92.5\]

    C) \[102.6\]

    D) \[129.6\]

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  • question_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

    B) \[10\,\,cm\] below the target

    C) \[10\,\,cm\] above the target

    D) \[5\,\,cm\] above the target

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  • question_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

    B) \[{{v}^{2}}/r\] along the radius, away from the centre

    C) \[m{{v}^{2}}/r\] along the radius, away the centre

    D) \[m{{v}^{2}}/r\]along the radius, towards the centre

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  • question_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) \[m\]

    B) \[2\,\,m\]

    C) \[3\,\,m\]

    D) \[\frac{3}{2}m\]

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  • question_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) \[1000:1\]

    B) \[100:1\]

    C) \[1:32\]

    D) \[32:1\]

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  • question_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) \[4.5\sqrt{2}m{{s}^{-1}}\]

    B) \[5\,\,m{{s}^{-1}}\]

    C) \[5\sqrt{32}m{{s}^{-1}}\]

    D) \[1.5\,\,m{{s}^{-1}}\]

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  • question_answer12) In the electromagnetic spectrum, the visible spectrum lies between:

    A) radio waves and microwaves-

    B) infrared and ultraviolet rays

    C) microwaves and infrared spectrum

    D) \[X-\]ray and gamma ray spectrum

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  • question_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) \[m\,\,g\,\,h=\frac{1}{2}k{{x}^{2}}\]

    B) \[m\,\,g(h+x)=\frac{1}{2}k{{x}^{2}}\]

    C) \[m\,\,g(h+x)=-kx\]

    D) \[m\,\,g\,\,h=-kx\]

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  • question_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) \[137.5\,\,kg/s\]

    B) \[185.5\,\,kg/s\]

    C) \[127.5\,\,kg/s\]

    D) \[187.5\,\,kg/s\]

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  • question_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) \[\frac{ev}{g}\]

    B) \[\frac{{{e}^{2}}v}{g}\]

    C) \[{{e}^{2}}\sqrt{\left( \frac{8h}{g} \right)}\]

    D) \[{{e}^{2}}\sqrt{\left( \frac{h}{g} \right)}\]

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  • question_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) \[{{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}\]

    B) \[{{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\]

    C) \[\frac{{{r}_{1}}}{{{r}_{2}}}\]

    D) \[\frac{{{r}_{2}}}{{{r}_{1}}}\]

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  • question_answer17) Total angular momentum of a rotating body remains constant, if the net torque acting on the body is:

    A) zero

    B) maximum

    C) minimum

    D) unity

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  • question_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) \[{{45}^{o}}\]

    B) \[{{60}^{o}}\]

    C) \[{{30}^{o}}\]

    D) \[{{15}^{o}}\]

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  • question_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) \[40\]

    B) \[30\]

    C) \[20\]

    D) \[10\]

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  • question_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) \[R/2\]

    B) \[R/3\]

    C) \[R/5\]

    D) \[R/9\]

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  • question_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 \[r\]

    B) \[0.41\] times \[r\]

    C) \[0.51\] times \[r\]

    D) \[0.61\] times \[r\]

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  • question_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) \[0.5\,\,L\]

    B) \[1.0\,\,L\]

    C) \[2.0\,\,L\]

    D) \[4.0\,\,L\]

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  • question_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) \[0.67\]

    B) \[0.77\]

    C) \[0.87\]

    D) \[0.97\]

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  • question_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

    B) hollow sphere reaches the ground first

    C) both spheres reaches the ground at the same time

    D) the time at which the spheres reach the ground cannot be specified by the given data

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  • question_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) \[\frac{PV}{RT}\]

    B) \[\frac{PV}{kT}\]

    C) \[\frac{PR}{T}\]

    D) \[PV\]

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  • question_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) \[33.3\]

    B) \[50.0\]

    C) \[100.0\]

    D) \[300.0\]

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  • question_answer27) Maxwell in his famous equation of electromagnetism introduced the concept:

    A) \[AC\] current

    B) \[DC\] current

    C) displacement current

    D) impedance

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  • question_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) \[{{50}^{o}}C\]

    B) \[{{100}^{o}}C\]

    C) \[{{67}^{o}}C\]

    D) \[{{33}^{o}}C\]

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  • question_answer29) The work done by a gas is maximum when it expands:

    A) isothermally

    B) adiabatically

    C) isochorically

    D) isobarically

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  • question_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) \[58\,\,m{{s}^{-1}}\]

    B) \[580\,\,m{{s}^{-1}}\]

    C) \[20\,\,m{{s}^{-1}}\]

    D) \[116\,\,m{{s}^{-1}}\]

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  • question_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) \[T\]

    B) \[\frac{10}{9}T\]

    C) \[\sqrt{\left( \frac{9}{10} \right)T}\]

    D) \[\sqrt{\left( \frac{10}{9} \right)T}\]

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  • question_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) \[350\,\,m{{s}^{-1}}\]

    B) \[330\,\,m{{s}^{-1}}\]

    C) \[300\,\,m{{s}^{-1}}\]

    D) \[450\,\,m{{s}^{-1}}\]

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  • question_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) \[300\,\,Hz\]

    B) \[500\,\,Hz\]

    C) \[1000\,\,Hz\]

    D) \[400\,\,Hz\]

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  • question_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) \[2.7\times {{10}^{10}}J\]

    B) \[9.9\times {{10}^{10}}J\]

    C) \[10.8\times {{10}^{10}}J\]

    D) \[5.4\times {{10}^{10}}J\]

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  • question_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) \[2.5\,\,V,\,\,7.5\,\,V\]

    B) \[2\,\,V,\,\,8\,\,V\]

    C) \[8\,\,V,\,\,2\,\,V\]

    D) \[7.5\,\,V,\,\,2.5\,\,V\]

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  • question_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) \[30\,\,kJ\]

    B) \[20\,\,kJ\]

    C) \[15\,\,kJ\]

    D) \[10\,\,kJ\]

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  • question_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) \[1:1\]

    B) \[1:2\]

    C) \[2:1\]

    D) \[8:1\]

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  • question_answer38) The examples of diamagnetic, paramagnetic and ferromagnetic materials are respectively:

    A) copper, aluminium, iron

    B) aluminium, copper, iron

    C) copper, iron, aluminium

    D) aluminium, iron, copper

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  • question_answer39) In the Wheatstone's bridge shown below, in order to balance the bridge we must have:

    A) \[{{R}_{1}}=3\Omega ,\,\,{{R}_{2}}=3\Omega \]

    B) \[{{R}_{1}}=6\Omega ,\,\,{{R}_{2}}=1.5\Omega \]

    C) \[{{R}_{1}}=1.5\Omega ,\,{{R}_{2}}=\]any finite value

    D) \[{{R}_{1}}=3\Omega ,\,\,{{R}_{2}}=\]any finite value

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  • question_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) \[40\,\,\mu F\]

    B) \[20\,\,\mu F\]

    C) \[13.3\,\,\mu F\]

    D) \[10\,\,\mu F\]

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  • question_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) \[7.43\]

    B) \[10.56\]

    C) \[14.38\]

    D) \[16.48\]

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  • question_answer42) The resistors are connected as shown in the figure below. Find the equivalent resistance between the points \[A\] and \[B\].

    A) \[205\Omega \]

    B) \[10\Omega \]

    C) \[3.5\Omega \]

    D) \[5\Omega \]

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  • question_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) \[2.5\Omega \]

    B) \[2.0\Omega \]

    C) \[1.54\Omega \]

    D) \[1.0\Omega \]

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  • question_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) \[{{t}_{1}}+{{t}_{2}}\]

    B) \[{{t}_{1}}{{t}_{2}}\]

    C) \[\frac{{{t}_{1}}+{{t}_{2}}}{2}\]

    D) \[\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{1}}+{{t}_{2}}}\]

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  • question_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 \[II\]

    B) \[I\] and \[III\]

    C) \[I\] and \[IV\]

    D) \[II\] and\[III\]

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  • question_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) \[F=i\,\,l\,\,B\,\,\sin \,\,\theta \]

    B) \[F={{i}^{2}}l\,\,{{B}^{2}}\sin \theta \]

    C) \[F=i\,\,l\,\,B\,\,\cos \theta \]

    D) \[F=\frac{{{i}^{2}}l}{B}\sin \theta \]

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  • question_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) \[{{0}^{o}}\]

    B) \[{{45}^{o}}\]

    C) \[{{90}^{o}}\]

    D) \[{{180}^{o}}\]

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  • question_answer48) The resonant frequency of an \[LCR\] circuit occurs at a frequency equal to:

    A) \[\frac{1}{LC}\]

    B) \[\frac{1}{\sqrt{LC}}\]

    C) \[\frac{1}{LCR}\]

    D) \[\frac{1}{CR}\]

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  • question_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) \[\frac{{{i}_{1}}+{{i}_{2}}}{\sqrt{2}}\]

    B) \[\frac{{{i}_{1}}-{{i}_{2}}}{\sqrt{2}}\]

    C) \[\sqrt{\left( \frac{i_{1}^{2}+i_{2}^{2}}{2} \right)}\]

    D) \[\sqrt{\left( \frac{i_{1}^{2}-i_{2}^{2}}{2} \right)}\]

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  • question_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) \[1\,\,V\]

    B) \[10\,\,V\]

    C) \[5\,\,V\]

    D) \[100\,\,V\]

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  • question_answer51) The standard adopted for the determination of atomic weight of elements is based on:

    A) \[{{H}^{1}}\]

    B) \[{{C}^{12}}\]

    C) \[{{O}^{16}}\]

    D) \[{{S}^{32}}\]

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  • question_answer52) Law of multiple proportions is illustrated by one of the following pairs:

    A) \[{{H}_{2}}S\]and\[S{{O}_{2}}\]

    B) \[N{{H}_{3}}\]and\[N{{O}_{2}}\]

    C) \[N{{a}_{2}}S\]and\[N{{a}_{2}}O\]

    D) \[{{N}_{2}}O\]and\[NO\]

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  • question_answer53) Par magnetism of oxygen is explained on the basis of its electronic configuration of:

    A) \[(2\pi _{x}^{*}){{(2{{\pi }_{y}})}^{1}}\]

    B) \[{{({{\pi }^{*}}2{{p}_{y}})}^{1}}({{\pi }^{*}}2p_{z}^{1})\]

    C) \[{{(2\sigma _{s}^{*})}^{1}}{{(2{{\pi }_{y}})}^{1}}\]

    D) \[{{(2{{\sigma }_{s}}^{*})}^{1}}{{(2{{\pi }_{y}})}^{1}}\]

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  • question_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

    B) The parameter a accounts for the shape of gas phase molecules

    C) The parameter \[a\] accounts for intermolecular interaction?s present in the molecule

    D) The parameter \[a\] has no physical significance and van der Waals? introduced it as a numerical correction factor only

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  • question_answer55) Avogadro's hypothesis states that:

    A) the ideal gas consists of a large number of small particles called molecules

    B) under the same conditions of temperature and pressure equal volumes of gases contain the same number of molecules

    C) volume of a definite quantity of gas at constant pressure is directly proportional to absolute temperature

    D) a given mass of gas at constant pressure is , directly proportional to absolute temperature

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  • question_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

    B) Hund's rule of maximum multiplicity

    C) Heisenberg's uncertainty principle

    D) Ritz combination principle.

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  • question_answer57) Which of the following overlaps leads to bonding?

    A)

    B)

    C)

    D)

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  • question_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

    B) increases down the group and decreases across the period

    C) increases across the period and also down the group

    D) decreases across the period and also down the group

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  • question_answer59) Which of the following statements is correct?

    A) All carbon to carbon bonds contain a sigma bond and one or more pi bonds

    B) All carbon to hydrogen bonds are pi bonds

    C) All oxygen to hydrogen bonds are hydrogen bonds

    D) All carbon to hydrogen bonds are sigma bonds

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  • question_answer60) An example of a polar covalent compound is:

    A) \[KCl\]

    B) \[NaCl\]

    C) \[CC{{l}_{4}}\]

    D) \[HCl\]

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  • question_answer61) If \[117\,\,g\,\,NaCl\] is dissolved in \[1000\,\,g\] of water the concentration of the solution is said to be:

    A) \[2\,\,molar\]

    B) \[2\,\,molal\]

    C) \[1\,\,normal\]

    D) \[1\,\,molal\]

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  • question_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) \[135.0\]

    B) \[172.0\]

    C) \[90.0\]

    D) \[180.0\]

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  • question_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) \[42\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}\]

    B) \[21\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}\]

    C) \[84\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}\]

    D) \[8.4\,\,J\,\,mo{{l}^{-1}}{{K}^{-1}}\]

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  • question_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) \[105,700\,\,cal\]

    B) \[61,000\,\,cal\]

    C) \[105,000\,\,cal\]

    D) \[62,300\,\,cal\]

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  • question_answer65) A saturated solution of\[Ca{{F}_{2}}\]is\[2\times {{10}^{-4}}mol/L\]. Its solubility product constant is:

    A) \[2.6\times {{10}^{-9}}\]

    B) \[4\times {{10}^{-8}}\]

    C) \[8\times {{10}^{-12}}\]

    D) \[3.2\times {{10}^{-11}}\]

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  • question_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) \[{{K}_{p}}={{K}_{c}}{{(RT)}^{2}}\]

    B) \[{{K}_{p}}={{K}_{c}}{{(RT)}^{-2}}\]

    C) \[{{K}_{p}}={{K}_{c}}\]

    D) \[{{K}_{c}}={{K}_{p}}(RT)\]

    View Answer play_arrow
  • question_answer67) Which of the following \[1:1\] mixture will act as buffer solution?

    A) \[HCl\]and\[NaOH\]

    B) \[KOH\]and\[C{{H}_{3}}COOH\]

    C) \[C{{H}_{3}}COOH\]\[NaCl\]

    D) \[C{{H}_{3}}COOH\]and\[C{{H}_{3}}COONa\]

    View Answer play_arrow
  • question_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) \[{{E}_{0}}\]

    B) \[{{E}_{0}}+0.059\]

    C) \[{{E}_{0}}+\frac{0.059}{2}\]

    D) \[{{E}_{0}}=\frac{0.059}{2}\]

    View Answer play_arrow
  • question_answer69) In one of the following reactions \[HN{{O}_{3}}\]does not behave as an oxidizing agent. Identify it:

    A) \[{{I}_{2}}+10HN{{O}_{3}}\xrightarrow[{}]{{}}2HI{{O}_{3}}+10N{{O}_{2}}+4{{H}_{2}}O\]

    B) \[3Cu+8HN{{O}_{3}}\xrightarrow{{}}3Cu{{(N{{O}_{3}})}_{2}}\]\[+2NO+4{{H}_{2}}O\]

    C) \[4Zn+10HN{{O}_{3}}\xrightarrow{{}}4Zn{{(N{{O}_{3}})}_{2}}\]\[+N{{H}_{4}}N{{O}_{3}}+3{{H}_{2}}O\]

    D) \[2HN{{O}_{3}}+{{P}_{2}}{{O}_{3}}\xrightarrow{{}}2HP{{O}_{3}}+{{N}_{2}}{{O}_{5}}\]

    View Answer play_arrow
  • question_answer70) Which of the following statement is not correct?

    A) In zero order reaction the rate of the reaction remains constant throughout

    B) A second order reaction would become a pseudo first order reaction when one of the reactants is taken in large excess

    C) The value of first order rate constant depends on the units of the concentration terms used

    D) In a first order reaction the plot of \[\log (a-x)vs\] time gives a straight line

    View Answer play_arrow
  • question_answer71) Radioactive decay series of uranium is denoted as:

    A) \[4n+1\]

    B) \[4n+2\]

    C) \[4n\]

    D) \[4n+3\]

    View Answer play_arrow
  • question_answer72) The number of isomeric hexanes is:

    A) \[5\]

    B) \[2\]

    C) \[3\]

    D) \[4\]

    View Answer play_arrow
  • question_answer73) The coagulating power of an electrolyte for arsenious sulphide decreases in the order:

    A) \[N{{a}^{+}}<A{{l}^{3+}}<B{{a}^{2+}}\]

    B) \[PO_{4}^{3-}<SO_{4}^{2-}<C{{l}^{-}}\]

    C) \[Cl<SO_{4}^{2-}<PO_{4}^{3-}\]

    D) \[A{{l}^{3+}}<B{{a}^{2+}}<N{{a}^{+}}\]

    View Answer play_arrow
  • question_answer74) The two optical isomers given below, namely, \[(a)\]:

    A) enantiomers

    B) geometrical isomers

    C) diastereomers

    D) structural isomers

    View Answer play_arrow
  • question_answer75) Which of the following statement is wrong?

    A) Using Lassaigne's test nitrogen and sulphur present in organic compound can be tested

    B) Using Beilstein's test the presence of halogen in a compound can be tested

    C) In Lassaigne's filtrate the nitrogen present in organic compound is converted into \[NaCN\]

    D) In the estimation of carbon, an organic compound is heated with \[CaO\] in a combustion tube

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  • question_answer76) \[Cis-trans\] isomers generally:

    A) contain an asymmetric carbon atom

    B) rotate the .plane of polarized light

    C) are enantiomorphism

    D) contain double bonded carbon atoms

    View Answer play_arrow
  • question_answer77) Wurtz's reaction involves the reduction of alkyl halide with:

    A) \[Zn/HCl\]

    B) \[HI\]

    C) \[Zn/Cu\]couple

    D) \[Na\]is ether

    View Answer play_arrow
  • question_answer78) The reaction \[{{C}_{12}}{{H}_{26}}\xrightarrow[{}]{{}}{{C}_{6}}{{H}_{12}}+{{C}_{6}}{{H}_{14}}\]represent:

    A) substitution

    B) synthesis

    C) cracking

    D) polymerization

    View Answer play_arrow
  • question_answer79) The compound that does not answer iodoform test is:

    A) ethanol

    B) ethanol

    C) methanol

    D) propanone

    View Answer play_arrow
  • question_answer80) Which one of the following compound reacts with chlorobenzene to produce\[DDT?\]

    A) Acetaldehyde

    B) Nitrobenzene

    C) \[m-\]chloroacetaldehyde

    D) Trichloroacetaldehyde

    View Answer play_arrow
  • question_answer81) Conversion of benzaldehyde to 3-phenyl-prop-2-en-1-oic acid is:

    A) Perkin condensation

    B) Claisen condensation

    C) Oxidative addition

    D) Aldol condensation

    View Answer play_arrow
  • question_answer82) Which of the following compounds forms an addition compound with \[C{{H}_{3}}MgBr\], which on hydrolysis produce a secondary alcohol?

    A) \[HCHO\]

    B) \[C{{H}_{3}}CHO\]

    C) \[C{{H}_{3}}OC{{H}_{3}}\]

    D) \[C{{H}_{3}}COC{{H}_{3}}\]

    View Answer play_arrow
  • question_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

    B) 1, 2, 3 and 4

    C) 1, 2 and

    D) 1, 3 and 4

    View Answer play_arrow
  • question_answer84) Which of the following compounds on treatment first with \[NaN{{O}_{2}}/HCl\] and then coupled with phenol produces p-hydroxyazobenzene?

    A) Nitrobenzene

    B) Azobenzene

    C) Phenol

    D) Aniline

    View Answer play_arrow
  • question_answer85) Initial setting of cement is mainly due to:

    A) hydration and gel formation

    B) dehydration and gel formation

    C) hydration and hydrolysis

    D) dehydration and dehydrolysis

    View Answer play_arrow
  • question_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

    B) potassium

    C) copper

    D) mercury

    View Answer play_arrow
  • question_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

    B) \[5\] alpha particles and \[0\] beta particles

    C) \[8\] alpha and \[6\] beta particles

    D) \[10\] alpha particles and \[10\] beta particles

    View Answer play_arrow
  • question_answer88) Hydrogen peroxide when added to a solution of potassium permanganate acidified with sulphuric acid:

    A) forms water only

    B) acts as an oxidizing agent

    C) acts as a reducing agent

    D) reduces sulphuric acid

    View Answer play_arrow
  • question_answer89) The equilibrium molecular structure of hydrogen peroxide is:

    A) planar as given below

    B) linear

    C) tetrahedral

    D) non planar

    View Answer play_arrow
  • question_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 \[3\]

    B) \[2\] and \[3\]

    C) \[1\] and \[2\]

    D) \[1,\,\,2\] and \[3\]

    View Answer play_arrow
  • question_answer91) Alkali metals have high oxidation potential and hence, they behave as:

    A) oxidizing agents

    B) Lewis bases

    C) reducing agents

    D) electrolytes

    View Answer play_arrow
  • question_answer92) Water is oxidized to oxygen by:

    A) \[Cl{{O}_{2}}\]

    B) \[KMn{{O}_{4}}\]

    C) \[{{H}_{2}}{{O}_{2}}\]

    D) fluorine

    View Answer play_arrow
  • question_answer93) Identify the incorrect statement:

    A) The molarity of a solution is independent of temperature

    B) The tendency for catenation is much higher for carbon than for silicon

    C) Nitriles and iso nitriles constitute metamers

    D) \[t-\]butyl carbocation has planar carbons and is very reactive

    View Answer play_arrow
  • question_answer94) The magnetic moment p, of transition metals is related to the number of unpaired electrons, \[n\] as:

    A) \[\mu =n{{(n+2)}^{2}}\]

    B) \[\mu ={{n}^{2}}(n+2)\]

    C) \[\mu =\frac{n}{(n+2)}\]

    D) \[\mu =\frac{n}{\sqrt{n+2}}\]

    View Answer play_arrow
  • question_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

    B) Dibenzol peroxide is a catalyst in the polymerization of\[PVC\]

    C) Borosilicate glass is heat resistant

    D) Concentrated \[HN{{O}_{3}}\] can be safely transported in aluminium containers

    View Answer play_arrow
  • question_answer96) Which of the following is not a thermoplastic?

    A) Polystyrene

    B) Teflon

    C) Polyvinyl chloride

    D) Nylon\[-6,\,\,6\]

    View Answer play_arrow
  • question_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) \[A-T,\,\,G-C\]

    B) \[A-C,\,\,G-T\]

    C) \[A-G,\,\,C-T\]

    D) \[A-U,\,\,G-C\]

    View Answer play_arrow
  • question_answer98) Barbituric acid and its derivatives are well known as:

    A) tranquilizers

    B) antiseptics

    C) analgesics

    D) antipyretics

    View Answer play_arrow
  • question_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) \[112\]

    B) \[512\]

    C) \[400\]

    D) \[614\]

    View Answer play_arrow
  • question_answer100) The first artificial disintegration of an atomic nucleus was achieved by:

    A) Geiger

    B) Wilson

    C) Madam Curie

    D) Rutherford

    View Answer play_arrow
  • question_answer101) If \[f(x)={{\log }_{x}}({{\log }_{e}}x)\], then \[f'(x)\] at \[x=e\] is equal to:

    A) \[1\]

    B) \[2\]

    C) \[0\]

    D) \[1/e\]

    View Answer play_arrow
  • question_answer102) The number of terms in the expansion of \[{{(a+b+c)}^{10}}\]is:

    A) \[11\]

    B) \[21\]

    C) \[55\]

    D) \[66\]

    View Answer play_arrow
  • question_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) \[1\]

    B) \[2\]

    C) \[-1\]

    D) \[3\]

    View Answer play_arrow
  • question_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) \[3\]

    B) \[10\]

    C) \[13\]

    D) \[5\]

    View Answer play_arrow
  • question_answer105) A straight line through \[P(1,\,\,2)\] is such that its intercept between the axes is bisected at P. Its equation is:

    A) \[x+y=-1\]

    B) \[x+y=3\]

    C) \[x+2y=5\]

    D) \[2x+y=4\]

    View Answer play_arrow
  • question_answer106) The radius of any circle touching the lines \[3x-4y+5=0\] and \[6x-8y-9=0\] is:

    A) \[1.9\]

    B) \[0.95\]

    C) \[2.9\]

    D) \[1.45\]

    View Answer play_arrow
  • question_answer107) The point on the curve \[\sqrt{x}+\sqrt{y}=\sqrt{a}\], the normal at which is parallel to the \[x-\]axis, is:

    A) \[(0,\,\,0)\]

    B) \[(0,\,\,a)\]

    C) \[(a,\,\,0)\]

    D) \[(a,\,\,a)\]

    View Answer play_arrow
  • question_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) \[3\]

    B) \[2\]

    C) \[1\]

    D) \[5\]

    View Answer play_arrow
  • question_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

    B) centroid

    C) orthocentre

    D) circumcentre

    View Answer play_arrow
  • question_answer110) For\[|x|\,\,<1\], let\[y=1+x+{{x}^{2}}+...\]to\[\infty \], then\[\frac{dy}{dx}=-y\]is equal to:

    A) \[\frac{x}{y}\]

    B) \[\frac{{{x}^{2}}}{{{y}^{2}}}\]

    C) \[\frac{x}{{{y}^{2}}}\]

    D) \[x{{y}^{2}}\]

    View Answer play_arrow
  • question_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) \[x+3y=21\]

    B) \[2x-3y=7\]

    C) \[x+7y=31\]

    D) \[2x+3y=21\]

    View Answer play_arrow
  • question_answer112) The number of common tangents to two circles \[{{x}^{2}}+{{y}^{2}}=4\] and \[{{x}^{2}}+{{y}^{2}}-8x+12=0\]is:

    A) \[1\]

    B) \[2\]

    C) \[5\]

    D) \[3\]

    View Answer play_arrow
  • question_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) \[\log x\]

    B) \[x\]

    C) \[\frac{1}{\log x}\]

    D) \[{{\log }^{n}}x\]

    View Answer play_arrow
  • question_answer114) The focus of the parabola \[{{y}^{2}}-x-2y+2=0\] is:

    A) \[(1/4,\,\,0)\]

    B) \[(1,\,\,2)\]

    C) \[(5/4,\,\,1)\]

    D) \[(3/4,\,\,5/2)\]

    View Answer play_arrow
  • question_answer115) The equation of the parabola with vertex at the origin and directrix \[y=2\] is:

    A) \[{{y}^{2}}=8x\]

    B) \[{{y}^{2}}=-8x\]

    C) \[{{y}^{2}}=\sqrt{8}x\]

    D) \[{{x}^{2}}=-8y\]

    View Answer play_arrow
  • question_answer116) The point on the curve \[x{{y}^{2}}=1\] that is nearest to the origin, is:

    A) \[(1,\,\,1)\]

    B) \[(4,\,\,1/2)\]

    C) \[(5/4,\,\,1)\]

    D) \[(3/4,\,\,5/2)\]

    View Answer play_arrow
  • question_answer117) The distance of. the point \[A(2,\,\,3,\,\,4)\] from \[x-\]axis is:

    A) \[5\]

    B) \[\sqrt{13}\]

    C) \[2\sqrt{5}\]

    D) \[5\sqrt{2}\]

    View Answer play_arrow
  • question_answer118) The radius of the circle\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2y-4z-11=0\],\[x+2y+2z-15=0\]is:

    A) \[\sqrt{3}\]

    B) \[\sqrt{5}\]

    C) \[\sqrt{7}\]

    D) \[3\]

    View Answer play_arrow
  • question_answer119) \[\int{{{x}^{2}}{{(ax+b)}^{-2}}dx}\]is equal to:

    A) \[\frac{2}{{{a}^{2}}}\left( x-\frac{b}{a}x\log (ax+b) \right)+c\]

    B) \[\frac{2}{{{a}^{2}}}\left( x-\frac{b}{a}\log (ax+b) \right)-\frac{{{x}^{2}}}{a(ax+b)}+c\]

    C) \[\frac{2}{{{a}^{2}}}\left( x+\frac{b}{a}\log (ax+b) \right)+\frac{{{x}^{2}}}{a(ax+b)}+c\]

    D) \[\frac{2}{{{a}^{2}}}\left( x+\frac{b}{a}\log (ax+b) \right)-\frac{{{x}^{2}}}{a(ax+b)}+c\]

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  • question_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) \[{{45}^{o}}\]

    B) \[{{60}^{o}}\]

    C) \[{{90}^{o}}\]

    D) \[{{30}^{o}}\]

    View Answer play_arrow
  • question_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) \[{{0}^{o}}\]

    B) \[{{30}^{o}}\]

    C) \[{{90}^{o}}\]

    D) \[{{30}^{o}}\]

    View Answer play_arrow
  • question_answer122) If\[f(t)\]is an odd function, then\[\int_{0}^{x}{f(t)}\,dt\]is:

    A) an odd function

    B) an even function

    C) neither even nor odd

    D) \[0\]

    View Answer play_arrow
  • question_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) \[1/7\]

    B) \[-1/7\]

    C) \[7\]

    D) \[-7\]

    View Answer play_arrow
  • question_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) \[\overset{\to }{\mathop{\mathbf{a}}}\,\bot \overset{\to }{\mathop{\mathbf{b}}}\,\]

    B) \[\overset{\to }{\mathop{\mathbf{a}}}\,||\overset{\to }{\mathop{\mathbf{b}}}\,\]

    C) \[\overset{\to }{\mathop{\mathbf{a}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]and\[\overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]

    D) \[\overset{\to }{\mathop{\mathbf{a}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]and\[\overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{0}}}\,\]

    View Answer play_arrow
  • question_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) \[\frac{1}{2}\]

    B) \[\frac{1}{3}\]

    C) \[\frac{2}{9}\]

    D) \[\frac{9}{2}\]

    View Answer play_arrow
  • question_answer126) The points\[A(4,\,\,5,\,\,1),\] \[B(0,\,\,-1,\,\,1),\] \[C(3,\,\,9,\,\,4)\]and\[D(-4,\,\,4,\,\,4)\] are:

    A) collinear

    B) coplanar

    C) non-coplanar

    D) non-collinear

    View Answer play_arrow
  • question_answer127) \[{{(\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,)}^{2}}\] is equal to:

    A) \[\overset{\to }{\mathop{{{\mathbf{a}}^{\mathbf{2}}}}}\,+\overset{\to }{\mathop{{{\mathbf{b}}^{\mathbf{2}}}}}\,-(\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,)\]

    B) \[\overset{\to }{\mathop{{{\mathbf{a}}^{\mathbf{2}}}}}\,\overset{\to }{\mathop{{{\mathbf{b}}^{\mathbf{2}}}}}\,-{{(\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,)}^{2}}\]

    C) \[\overset{\to }{\mathop{{{\mathbf{a}}^{\mathbf{2}}}}}\,+\overset{\to }{\mathop{{{\mathbf{b}}^{\mathbf{2}}}}}\,-2\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,\]

    D) \[\overset{\to }{\mathop{{{\mathbf{a}}^{\mathbf{2}}}}}\,+\overset{\to }{\mathop{{{\mathbf{b}}^{\mathbf{2}}}}}\,-2\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,\]

    View Answer play_arrow
  • question_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) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\]

    B) \[xy\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\]

    C) \[xy\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\]

    D) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\]

    View Answer play_arrow
  • question_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) \[-1\]

    B) \[1\]

    C) \[0\]

    D) \[\sqrt{2}\]

    View Answer play_arrow
  • question_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) \[2\cos 3(\beta -\alpha )\]

    B) \[2\cos 3(\beta +\alpha )\]

    C) \[2\sin 3(\beta -\alpha )\]

    D) \[2\sin 3(\beta +\alpha )\]

    View Answer play_arrow
  • question_answer131) Solution of the equation\[x{{\left( \frac{dy}{dx} \right)}^{2}}+2\sqrt{xy}\frac{dy}{dx}+y=0\]is:

    A) \[x+y=a\]

    B) \[\sqrt{x}-\sqrt{y}=\sqrt{a}\]

    C) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]

    D) \[\sqrt{x}+\sqrt{y}=\sqrt{a}\]

    View Answer play_arrow
  • question_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) \[1/196\]

    B) \[2/7\]

    C) \[1/7\]

    D) \[13/56\]

    View Answer play_arrow
  • question_answer133) If\[\underset{x\to a}{\mathop{\lim }}\,\frac{{{a}^{x}}-{{x}^{a}}}{{{x}^{x}}-{{a}^{a}}}=-1\],then\[a\]equals:

    A) \[1\]

    B) \[0\]

    C) \[e\]

    D) \[(1/e)\]

    View Answer play_arrow
  • question_answer134) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\tan x-\sin x}{{{x}^{3}}}\]is equal to:

    A) \[0\]

    B) \[1\]

    C) \[1/2\]

    D) \[-1/2\]

    View Answer play_arrow
  • question_answer135) \[\underset{x\to a}{\mathop{\lim }}\,\frac{\log (x-a)}{\log ({{e}^{x}}-{{e}^{a}})}\]is equal to:

    A) \[0\]

    B) \[1\]

    C) \[a\]

    D) does not exist

    View Answer play_arrow
  • question_answer136) If\[f(x)=|x{{|}^{3}}\], then\[f'(0)\]equals:

    A) \[0\]

    B) \[1/2\]

    C) \[-1\]

    D) \[-1/2\]

    View Answer play_arrow
  • question_answer137) \[\int{{{e}^{-\log x}}}dx\]is equal to:

    A) \[{{e}^{-\log x}}+c\]

    B) \[-x{{e}^{-\log x}}+c\]

    C) \[{{e}^{\log x}}+c\]

    D) \[\log |x|+c\]

    View Answer play_arrow
  • question_answer138) The area cut off by the latus rectum from the parabola \[{{y}^{2}}=4ax\] is:

    A) \[(8/3)a\,\,sq\,\,unit\]

    B) \[(8/3)\sqrt{a}\,\,sq\,\,unit\]

    C) \[(3/8)\sqrt{a}\,\,sq\,\,unit\]

    D) \[(8/3){{a}^{2}}\,\,sq\,\,unit\]

    View Answer play_arrow
  • question_answer139) The solution of differential equation\[(x+y)(dx-dy)=dx+dy\]is:

    A) \[x-y=k{{e}^{x-y}}\]

    B) \[x+y=k{{e}^{x+y}}\]

    C) \[x+y=k(x-y)\]

    D) \[x+y=k{{e}^{x-y}}\]

    View Answer play_arrow
  • question_answer140) In how many ways can 8 students be arranged in a row?

    A) \[8!\]

    B) \[7!\]

    C) \[8\]

    D) \[7\]

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  • question_answer141) If the third term of a \[GP\] is \[p\]. Then the product of the first \[5\] terms of the \[GP\] is:

    A) \[{{p}^{3}}\]

    B) \[{{p}^{2}}\]

    C) \[{{p}^{10}}\]

    D) \[{{p}^{5}}\]

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  • question_answer142) The sum of n terms of the series\[\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+...\]is:

    A) \[\frac{{{3}^{n}}(2n+1)+1}{2({{3}^{n}})}\]

    B) \[\frac{{{3}^{n}}(2n+1)-1}{2({{3}^{n}})}\]

    C) \[\frac{{{3}^{n}}n-1}{2({{3}^{n}})}\]

    D) \[\frac{{{3}^{n}}-1}{2}\]

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  • question_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) \[{{(ac)}^{1/3}}+{{(ab)}^{1/3}}+c=0\]

    B) \[{{({{a}^{3}}b)}^{1/4}}+{{(a{{b}^{3}})}^{1/4}}+c=0\]

    C) \[{{({{a}^{3}}c)}^{1/4}}+{{(a{{c}^{3}})}^{1/4}}+b=0\]

    D) \[{{({{a}^{4}}c)}^{1/3}}+{{(a{{c}^{4}})}^{1/3}}+b=0\]

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  • question_answer144) \[^{20}{{C}_{4}}+2{{\cdot }^{20}}{{C}_{3}}{{+}^{20}}{{C}_{2}}{{-}^{22}}{{C}_{18}}\]is equal to :

    A) \[0\]

    B) \[1242\]

    C) \[7315\]

    D) \[6345\]

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  • question_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) \[0.2\]

    B) \[4.8\]

    C) \[1.02\]

    D) \[5.2\]

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  • question_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) \[20\]

    B) \[25\]

    C) \[12\]

    D) \[24\]

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  • question_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) \[{{(30)}^{n}}\]

    B) \[{{(10)}^{n}}\]

    C) \[0\]

    D) \[{{2}^{n}}+{{3}^{n}}+{{5}^{n}}\]

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  • question_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) \[-3\]

    B) \[3\]

    C) \[0\]

    D) for any value of\[b\]

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  • question_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

    B) \[{{2}^{9}}\]

    C) \[90\]

    D) \[900\]

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  • question_answer150) For non-singular square matrices \[A,\,\,\,B\] and \[C\] of the same order, \[{{(A{{B}^{-1}}C)}^{-1}}\]is equal to:

    A) \[{{A}^{-1}}B{{C}^{-1}}\]

    B) \[{{C}^{-1}}{{B}^{-1}}{{A}^{-1}}\]

    C) \[CB{{A}^{-1}}\]

    D) \[{{C}^{-1}}B{{A}^{-1}}\]

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