Solved papers for CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2003

done CEE Kerala Engineering Solved Paper-2003

• question_answer1) If the velocity of light c, gravitational constant G and Plancks constant h are chosen as fundamental units, the dimensions 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) $[{{h}^{1/2}}{{c}^{-3/2}}{{G}^{1/2}}]$

E)

• question_answer2) A plate has a length$5\pm 0.1\text{ }cm$and breadth$2\pm 0.01\text{ }cm$. Then the area of the plate is:

A) $10\pm 0.1\text{ }c{{m}^{2}}$

B) $10\pm 0.01\text{ }c{{m}^{2}}$

C) $10\pm 0.001\text{ }c{{m}^{2}}$

D) $10\pm 1\text{ }c{{m}^{2}}$

E) $10c{{m}^{2}}$

• question_answer3) A ball hangs from a string inside a train moving along a horizontal straight track. The string is observed to incline towards the rear of the train making a constant small angle with the vertical. It shows that the train is:

A) moving with a uniform acceleration

B) moving with a uniform velocity

C) moving with a uniform retardation

D) moving with an acceleration which is increasing uniformly

E) at rest

• 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) $14m{{s}^{-1}},\text{ }-5m{{s}^{-2}}$

B) $19m{{s}^{-1}},-9m{{s}^{-2}}$

C) $-14m{{s}^{-1}},-5m{{s}^{-2}}$

D) $3m{{s}^{-1}},-5m{{s}^{-2}}$

E) $5m{{s}^{-1}},14m{{s}^{-2}}$

• question_answer5) An object travels north with a velocity of $10\text{ }m{{s}^{-1}}$and then speeds up to a velocity of $25\text{ }m{{s}^{-1}}$in 5 s. The acceleration of the object in these 5 s is:

A) $3\text{ }m{{s}^{-1}}$in north direction

B) $3\text{ }m{{s}^{-2}}$in north direction

C) $\text{15 }m{{s}^{-2}}$ in north direction

D) $\text{3 }m{{s}^{-2}}$in south direction

E) $\text{10 }m{{s}^{-2}}$ in north direction

• question_answer6) An automobile in 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

E) 139.6

• question_answer7) A rifle shoots a bullet with a muzzle velocity of 500 ms1 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 below the target

E) 5 cm above the target

• 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 from the centre

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

E) $vr$along the radius away from the centre

• 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. Then the mass of the nucleus is:

A) m

B) 2m

C) 3m

D) 1m

E) 5m

• question_answer10) While driving a car around a curve of 200 m radius, the driver notices that a simple pendulum hung to the roof of the car is making an angle of $15{}^\circ$to the horizontal. The speed of the car in km/h is:

A) 60.5

B) 72.5

C) 82.5

D) 92.5

E) 106.5

• question_answer11) A stationary body of mass m explodes into 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 $1.5\text{ }m{{s}^{-1}}$Then the velocity of the third body is:

A) $4.5\sqrt{2}m{{s}^{-1}}$

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

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

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

E) $1\,m{{s}^{-1}}$

• question_answer12) In a simple pendulum the breaking strength of the string is double the weight of the bob. The bob is released from rest when the string is horizontal. The string breaks when it makes an angle 6 with the vertical. Then:

A) $\theta =30{}^\circ$

B) $\theta =45{}^\circ$

C) $\theta =60{}^\circ$

D) $\theta ={{\cos }^{-1}}(1/3)$

E) $\theta ={{\cos }^{-1}}(2/3)$

• question_answer13) An object of mass m falls on to a spring of constant k from h. Then the spring undergoes compression by a length$x$. The maximum compression x is given by the equation:

A) $mgh=\frac{1}{2}k{{x}^{2}}$

B) $mgh(h+x)=\frac{1}{2}k{{x}^{2}}$

C) $mg(h+x)=-kx$

D) $mgh=-kx$

E) $mgh=-\frac{1}{2}k{{x}^{2}}$

• question_answer14) A rocket of initial mass 1000 kg ejects mass at a constant rate of 10 kg/s with constant relative speed of$11\text{ }m{{s}^{-1}}$. Neglecting gravity, the acceleration of the rocket 1 min after the blast is:

A) $11/40\,m{{s}^{-2}}$

B) $22/40\,m{{s}^{-2}}$

C) $1.1/40\,m{{s}^{-2}}$

D) $1\,m{{s}^{-2}}$

E) $11/60\,\,m{{s}^{-2}}$

• 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) $ev/g$

B) ${{e}^{2}}v/g$

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

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

E) ${{e}^{2}}\sqrt{\left( \frac{2h}{g} \right)}$

• question_answer16) An object of mass m is attached to light string which passess 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) $\frac{{{r}_{2}}}{{{r}_{1}}}$

E) 1

• 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

E) equal to the total angular momentum about a parallel axis

• question_answer18) A car is racing on a circular track of 180 m radius with a speed of$32\text{ }m{{s}^{-1}}$. What should be the banking angle of the road to avoid changes of skidding of the vehicle at this speed without taking into consideration the friction between the tyre and the road?

A) $45{}^\circ$

B) $60{}^\circ$

C) $30{}^\circ$

D) $15{}^\circ$

E) $25{}^\circ$

• question_answer19) When a ceiling fan is switched on it makes 10 rotations in the first 3s. The number of rotations it makes in the next 3 s, assuming uniform angular acceleration is:

A) 40

B) 30

C) 20

D) 10

E) 50

• question_answer20) A body is projected vertically upwards from the surface of a planet of radius r with a velocity equal to 1/3rd the escape velocity for that planet. The maximum height attained by the body is:

A) R/2

B) R/3

C) R/S

D) R/8

E) R/9

• question_answer21) A man weighs 80 kg on earth 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

E) 0.82 times r

• question_answer22) An adulterated sample of milk has a density of $1032\text{ }kg{{m}^{-3}},$while pure milk has a density of$1080\text{ }kg{{m}^{-3}}$. Then the volume of pure milk in a sample of 10 L of adulterated milk is:

A) 0.5 L

B) 1.0 L

C) 2.0 L

D) 3.0 L

E) 4.0 L

• question_answer23) Typical silt (hard mud) particle of radius 20 um is on the top of lake water, its density is $2000\text{ }kg/{{m}^{3}}$and the viscosity of lake water is 1.0 mPa, 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 is ... mm/s.

A) 0.67

B) 0.77

C) 0.87

D) 0.97

E) 1.07

• 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 reach the ground at the same time

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

E) the hollow sphere will not roll down

• 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) $PV$

E) $\frac{V}{T}$

• 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) 200.0

E) 300.0

• question_answer27) During an adiabatic process, the volume of a gas is found to be inversely proportional to the root of its absolute temperature. The ratio ${{C}_{p}}/{{C}_{V}}$for the gas is:

A) 5/3

B) 4/3

C) 3/2

D) 5/4

E) 7/4

• question_answer28) 1 g of steam at$100{}^\circ C$and equal mass of ice at $0{}^\circ C$are mixed. The temperature of the mixture in steady state will be (latent heat of steam$=540\text{ }cal/g,$latent heat of ice = 80 $cal/g$):

A) $50{}^\circ C$

B) $100{}^\circ C$

C) $67{}^\circ C$

D) $33{}^\circ C$

E) $0{}^\circ C$

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

A) isothermally

C) isentropically

D) isobarically

E) isochorically

• question_answer30) A tuning fork of frequency 580 Hz is employed to produce transverse waves on a long rope. The distance between the nearest crusts is found to be 20 cm. The velocity of the wave is:

A) $58\text{ }m{{s}^{-1}}$

B) $580\text{ }m{{s}^{-1}}$

C) $20\text{ }m{{s}^{-1}}$

D) $\text{29 }m{{s}^{-1}}$

E) $116\,m{{s}^{-1}}$

• 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) $\sqrt{\left( \frac{10}{9} \right)}T$

E) $\frac{9}{100}T$

• question_answer32) The distance travelled by a sound wave when a tuning fork completes 25 vib in 16.5 m. If the frequency of the tuning fork is 500 Hz, find the velocity of sound.

A) $350\text{ }m{{s}^{-1}}$

B) $330\text{ }m{{s}^{-1}}$

C) $300\text{ }m{{s}^{-1}}$

D) $450\text{ }m{{s}^{-1}}$

E) $500\text{ }m{{s}^{-1}}$

• 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 2s. The initial frequency of vibration of each wire is:

A) 300 Hz

B) 500 Hz

C) 1000 Hz

D) 400 Hz

E) 600 Hz

• question_answer34) Three point charges 1C, 2C and 3C are placed at the corners of an equilateral triangle of side 1m. 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) $5.4\times {{10}^{10}}J$

E) zero

• 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) 2.5V, 7.5 V

B) 2V, 8V

C) 8V, 2V

D) 7.5V, 2.5V

E) 3V, 2V

• 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

E) 5kJ

• 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) $1:8$

E) $8:1$

• 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

E) iron, aluminium, copper

• question_answer39) In the Wheatstones 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

E) ${{R}_{2}}=1.5\,\,\Omega ,{{R}_{1}}=$any finite value

• 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) $10\,\mu F$

E) $2.5\,\mu F$

• 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) 7.42

B) 10.56

C) 14.38

D) 16.48

E) 18.29

• question_answer42) The resistances 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) $5\,\Omega$

E) $3\,\Omega$

• 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. Then the internal resistance of the cell is: A) $2.5\,\,\Omega$

B) $2.0\,\,\Omega$

C) $1.54\,\,\Omega$

D) $1.0\,\,\Omega$

E) $0.5\,\,\Omega$

• 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) $\frac{{{t}_{1}}-{{t}_{2}}}{2}$

E) $\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{1}}+{{t}_{2}}}$

• 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

E) II and IV

• question_answer46) The force on a conductor of length$l$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) $F=\frac{{{I}^{2}}l}{B}\sin \theta$

E) $F=\frac{{{I}^{2}}l}{B}\cos \theta$

• 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) $0{}^\circ$

B) $45{}^\circ$

C) $90{}^\circ$

D) $180{}^\circ$

E) any angle with which it is placed

• 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) $\frac{1}{CR}$

E) $\frac{1}{\sqrt{LCR}}$

• question_answer49) An AC is given by$i={{i}_{1}}\cos \omega t+{{i}_{2}}\sin \omega t$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) $\sqrt{\left( \frac{i_{1}^{2}-i_{2}^{2}}{2} \right)}$

E) $\frac{{{i}_{1}}{{i}_{2}}}{\sqrt{2}}$

• 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

E) 50V

• question_answer51) 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) $32:1$

E) $1:1000$

• question_answer52) 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

E) ultraviolet and X-ray spectrum

• question_answer53) Maxwell in his famous equation of electromagnetism introduced the concept:

A) AC current

B) DC current

C) displacement current

D) impedance

E) reactance

• question_answer54) Out of the following electromagnetic radiations, which has the shortest wavelength?

B) Infrared

C) Ultraviolet

D) Visible light

E) X-rays

• question_answer55) In Youngs double slit experiment, the width of one of the slits is slowly increased to make it twice the width of the other slit. Then in the interference pattern:

A) the intensity of maxima increase while that of minima decrease

B) the intensities of both maxima and minima decrease

C) the intensities of both maxima and minima remain the same

D) the intensity of maxima decrease while that of minima increase

E) the intensities of both maxima and minima increase

• question_answer56) Two coherent sources whose intensity ratio is $81:1$produce interference fringes. The ratio of minimum to maximum intensity, i.e., ${{I}_{\min }}:{{I}_{\max }}$is:

A) $16:25$

B) $9:1$

C) $1:9$

D) $25:16$

E) $5:4$

• question_answer57) An infinitely long rod lies along the axis of concave mirror of focal length$f$. The near end of the rod is at a distance$x>f$from the mirror. Then the length of the image of the rod is:

A) $\frac{{{f}^{2}}}{x+f}$

B) $\frac{{{f}^{2}}}{x}$

C) $\frac{xf}{x-f}$

D) $\frac{xf}{x+f}$

E) $\frac{{{f}^{2}}}{x-f}$

• question_answer58) A beaker containing a liquid appears to be half when it is actually two third full. The refractive index of liquid is:

A) 7/6

B) 6/5

C) 3/2

D) 5/4

E) 4/3

• question_answer59) If${{h}_{1}}$and${{h}_{2}}$are the heights of the images in conjugate position of a convex lens, then the height of the object is:

A) ${{h}_{1}}+{{h}_{2}}$

B) ${{h}_{1}}-{{h}_{2}}$

C) ${{h}_{1}}/{{h}_{2}}$

D) $\sqrt{{{h}_{1}}{{h}_{2}}}$

E) ${{h}_{1}}{{h}_{2}}$

• question_answer60) The power of the combination of a convex lens of focal length 50 cm and concave lens of focal length 40 cm is:

A) $+1\text{ }D$

B) $-1\,D$

C) zero

D) $+\,0.5D$

E) $-\,0.5D$

• question_answer61) Image formed by a convex lens is virtual and erect when the object is placed:

A) at F

B) between F and the lens

C) at 2F

D) beyond 2 F

E) at infinity

• question_answer62) The rest mass of photon is:

A) $\frac{hv}{c}$

B) $\frac{hv}{{{c}^{2}}}$

C) $\frac{hc}{\lambda }$

D) zero

E) $\frac{h}{\lambda }$

• question_answer63) A charged oil drop of mass $9.75\times {{10}^{-15}}kg$ and charge$30\times {{10}^{-16}}C$is suspended in a uniform electric field existing between two parallel plates. The field between the plates, taking $(g=10\text{ }m{{s}^{-2}})$is:

A) 3.25 V/m

B) 300 V/m

C) 325 V/m

D) 32.5 V/m

E) 3000 V/m

• question_answer64) If the wavelength of incident light changes from 400 nm to 300 nm, the stopping potential for photoelectrons emitted from a surface becomes approximately:

A) 1.0V greater

B) 1.0V smaller

C) 0.5V greater

D) 0.5V smaller

E) 0. IV greater

• question_answer65) Let the potential energy of hydrogen atom in the ground state be regarded as zero. Then its potential energy in the first excited state will be:

A) 20.4 eV

B) 13.6 eV

C) 3.4 eV

D) 6.8 eV

E) 10.2 eV

• question_answer66) Two radioactive nuclides$x$and y have half-lives 1 h and 2 h respectively. Initially the samples have equal number of nuclei. After 4 h the ratio of the numbers of$x$and y is:

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

B) 2

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

D) 1

E) $\frac{1}{16}$

• question_answer67) $_{92}{{U}^{238}}$decays successively to from$_{90}T{{h}^{234}},$$_{91}P{{a}^{234}}{{,}_{92}}{{U}^{234}}{{,}_{90}}T{{h}^{230}}{{,}_{88}}R{{a}^{226}}$during the reaction the number of$\alpha -$particles emitted is:

A) 4

B) 3

C) 5

D) 2

E) 1

• question_answer68) Let${{n}_{e}}$and${{n}_{h}}$represent the number density of electrons and holes in a semiconductor. Then:

A) ${{n}_{e}}>{{n}_{h}}$if the semiconductor is intrinsic

B) ${{n}_{e}}<{{n}_{h}}$if the semiconductor is intrinsic

C) ${{n}_{e}}\ne {{n}_{h}}$if the semiconductor is intrinsic

D) ${{n}_{e}}={{n}_{h}}$if the semiconductor is intrinsic

E) ${{n}_{e}}={{n}_{h}}$if the semiconductor is extrinsic

• question_answer69) In a n-p-n transistor amplifier, the collector current is 9 mA. If 90% of the electrons from the emitter reach the collector, then:

A) $\alpha =0.9,\beta =9.0$

B) the base current is 10 mA

C) the emitter current is 1 mA

D) $\alpha =9.0,\text{ }\beta =0.9$

E) $\alpha =0.99,\text{ }\beta =99.0$

• question_answer70) In a properly biased transistor:

A) both depletion layers are equally large

B) both depletion layers are equally small

C) emitter-base depletion layer is large but base-collector depletion layer is small

D) emitter-base depletion layer is small but base-collector depletion layer is large

E) both depletion layers vanish

• question_answer71) A dim star of magnitude$+14.5$explodes into a nova of magnitude$+2$. The factor by which the brightness of the star has increased is:

A) 12.5

B) ${{10}^{2}}$

C) ${{10}^{3}}$

D) ${{10}^{4}}$

E) ${{10}^{5}}$

• question_answer72) If the sun becomes twice as hot:

A) the output of radiated energy will be eight times larger

B) it will radiate predominantly in the infrared

C) it will radiate predominantly in the ultraviolet

D) the output of the radiated energy will be eight times smaller

E) the frequency spectrum of the radiated energy will not alter

• question_answer73) The standard adopted for the determination of atomic weight of elements is based on:

A) ${{H}^{1}}$

B) ${{C}^{12}}$

C) ${{O}^{16}}$

D) ${{S}^{32}}$

E) $C{{l}^{35}}$

• question_answer74) 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) $BeO$ and$BeC{{l}_{2}}$

E) ${{N}_{2}}O$and $NO$

• question_answer75) Paramagnetism of oxygen is explained on the basis of its electronic configuration of:

A) ${{({{\pi }^{*}}2{{p}_{x}})}^{1}}{{(\pi 2{{p}_{y}})}^{1}}$

B) ${{({{\pi }^{*}}2{{p}_{y}})}^{1}}{{({{\pi }^{*}}2{{p}_{z}})}^{1}}$

C) ${{({{\sigma }^{*}}2s)}^{1}}{{(\pi 2{{p}_{y}})}^{1}}$

D) ${{({{\sigma }^{*}}2s)}^{1}}{{(\pi 2{{p}_{y}})}^{1}}$

E) ${{(\pi 2{{p}_{x}})}^{1}}{{(\pi 2{{p}_{y}})}^{1}}$

• question_answer76) 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 interactions present in the molecule

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

E) The parameter is a correction factor to the volume of the container

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

E) for a definite mass of gas at constant temperature the volume is inversely proportional to its pressure

• question_answer78) The observation that the ground state of nitrogen atom has 3 unpaired electrons in its electronic configuration and not otherwise is associated with:

A) Paulis exclusion principle

B) Hunds rule of maximum multiplicity

C) Heisenbergs uncertainty relation

D) Ritz combination principle

E) Valence bond method

• question_answer79) Which of the following overlaps leads to bonding?

A) B) C) D) E) • question_answer80) 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

E) decreases down the group and remains constant across the period

• question_answer81) 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

E) All carbon to carbon bonds are$\sigma -$bonds

• question_answer82) An example of a polar covalent compound is:

A) $KCl$

B) $NaCl$

C) $CC{{l}_{4}}$

D) $HCl$

E) $C{{H}_{4}}$

• question_answer83) If$117g\text{ }NaCl$is dissolved in 1000 got water the concentration of the solution is said to be:

A) 2 molar

B) 2 molal

C) 1 normal

D) 1 molal

E) 2 normal

• question_answer84) A solution of 4.5 g of a pure non-electrolyte in 100 g of water was found to freeze at$0.465{}^\circ C$. The molecular weight of the solute is closest to: $({{k}_{f}}=1.86)$

A) 135.0

B) 172.0

C) 90.0

D) 86.2

E) 180.0

• question_answer85) The enthalpy of vaporization of substance is $840\text{ }J\text{ m}o{{l}^{-1}}$and its boiling point is$-173{}^\circ C$. Its entropy of vaporization is:

A) $42\text{ }J\text{ }mo{{l}^{-1}}{{K}^{-1}}$

B) $21\text{ }J\text{ }mo{{l}^{-1}}{{K}^{-1}}$

C) $84\text{ }J\text{ m}o{{l}^{-1}}{{K}^{-1}}$

D) $8.4\text{ }J\text{ mo}{{l}^{-1}}{{K}^{-1}}$

E) $0.028\text{ }J\text{ }mo{{l}^{-1}}{{K}^{-1}}$

• question_answer86) 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) 60, 000 cal

E) 62, 300 cal

• question_answer87) 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) $3.2\times {{10}^{-11}}$

E) $8\times {{10}^{-10}}$

• question_answer88) 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) ${{K}_{c}}={{K}_{p}}(RT)$

E) ${{K}_{c}}={{K}_{p}}{{(RT)}^{-1}}$

• question_answer89) Which of the following$1:1$mixture will act as buffer solution?

A) $HCl$and $NaOH$

B) $KOH$ and $C{{H}_{3}}COOH$

C) $C{{H}_{3}}COOH$ and $NaCl$

D) $C{{H}_{3}}COONa$ and $N{{H}_{4}}OH$

E) $C{{H}_{3}}COOH$ and$C{{H}_{3}}COONa$

• question_answer90) 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) $E{}^\circ$

B) $E{}^\circ +0.059$

C) $E{}^\circ +\frac{0.059}{2}$

D) $E{}^\circ -0.059$

E) $E{}^\circ -2\times 0.59$

• question_answer91) 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) $N{{O}_{3}}+3F{{e}^{2+}}+4{{H}^{+}}\xrightarrow[{}]{{}}NO$$+3F{{e}^{3+}}+2{{H}_{2}}O$

E) $2HN{{O}_{3}}+{{P}_{2}}{{O}_{5}}\xrightarrow{{}}2HP{{O}_{3}}+{{N}_{2}}{{O}_{5}}$

• question_answer92) 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 expends on the units of the concentration terms used

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

E) The value of${{t}_{1/2}}$for a first order reaction is independent of initial concentration

• question_answer93) Radioactive decay series of uranium is denoted as:

A) $4n+1$

B) $4n+2$

C) $4n$

D) $4n+3$

E) $4n+4$

• question_answer94) The number of isomeric hexanes is:

A) 5

B) 2

C) 3

D) 4

E) 6

• question_answer95) 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) $A{{l}^{3+}}>B{{a}^{2+}}>N{{a}^{+}}$

E) $N{{a}^{+}}>B{{a}^{2+}}>PO_{4}^{3-}$

• question_answer96) The two optical isomers given below, namely: A) enantiomers

B) geometrical isomers

C) diastereomers

D) structural isomers

E) conformational isomers

• question_answer97) Which of the following statement is wrong?

A) Using Lassaignes test nitrogen and sulphur present in organic compound can be tested

B) Using Beilsteins test the presence of halogen in a compound can be tested

C) In Lassaignes filtrate the nitrogen present in a organic compound is converted into$NaCN$

D) Lassaignes test fail to identify nitrogen in diazo compound

E) In the estimation of carbon, an organic compound is heated with$CaO$in a combustion tube

• question_answer98) Cist-trans isomers generally:

A) contain an asymmetric carbon atom

B) rotate the plane of polarized light

C) are enantiomorphs

D) contain a triple bond

E) contain double bonded carbon atoms

• question_answer99) Wurtzs reaction involves the reduction of alkyl halide with:

A) $Zn/HCl$

B) $HI$

C) $Zn/Cu$couple

D) Na in ether

E) $Zn$in an inert solvent

• question_answer100) The reaction ${{C}_{12}}{{H}_{26}}\xrightarrow[{}]{{}}{{C}_{6}}{{H}_{12}}+{{C}_{6}}{{H}_{14}}$represent:

A) substitution

B) synthesis

C) cracking

D) polymerization

• question_answer101) The compound that does not answer iodoform test is:

A) ethanol

B) ethanol

C) methanol

D) propanone

E) acetophenone

• question_answer102) Which one of the following compound reacts with chlorobenzene to produce DDT?

A) Acetaldehyde

B) Nitrobenzene

C) m-chloroacetaldehyde

D) Trichloroacetaldehyde

E) Benzene

• question_answer103) Conversion of benzaldehyde to 3-phenylprop-2-en-l-oic acid is:

A) Perkin condensation

B) Claisen condensation

D) Aldol condensation

E) none of the above

• question_answer104) Which of the following compounds forms an addition compound with$C{{H}_{3}}MgBr,$which on hydrolysis produce a secondary alcohol?

A) $HCHO$

B) $C{{H}_{3}}CHO$ $RCHO+Grignard\text{ }reagent\xrightarrow{{}}$ secondary alcohol

C) $C{{H}_{3}}OC{{H}_{3}}$

D) $C{{H}_{3}}COC{{H}_{3}}$

E) $C{{H}_{3}}COOC{{H}_{3}}$

• question_answer105) 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
Select the correct answer using the codes given below:

A) 2, 3 and 4

B) 1, 2, 3 and 4

C) 1, 2 and 4

D) 1, 2 and 3

E) 1, 3 and 4

• question_answer106) 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) Phenyl isocyanide

E) Aniline

• question_answer107) 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

E) hydration and oxidation

• question_answer108) A certain metal will liberate hydrogen from dilute acids. It 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

E) sodium

• question_answer109) 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

E) $5\alpha$particles and$2\beta$particles

• question_answer110) 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

E) produces hydrogen

• question_answer111) The equilibrium molecular structure of hydrogen peroxide is:

A) Planar as given below B) linear

C) tetrahedral

D) non planar

E) planar as given below • question_answer112) 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

E) 1 only

• question_answer113) Alkali metals have high oxidation potential and hence, they behave as:

A) oxidizing agents

B) Lewis bases

C) reducing agents

D) electrolytes

E) Bronsted bases

• question_answer114) Water is oxidized to oxygen by:

A) $Cl{{O}_{2}}$

B) $KMn{{O}_{4}}$

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

D) fluorine

E) ozone

• question_answer115) 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 1-carbocation has planar carbons and is very reactive

E) Zirconium and Hafnium are strikingly similar because of their almost same ionic radii

• question_answer116) The magnetic momenta, 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) $\mu =n/(n+2)$

D) $\mu =n/\sqrt{(n+2)}$

E) $\mu =\sqrt{n+(n+2)}$

• question_answer117) 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

E) $p{{K}_{a}}$of trichloroacetic acid is less than that of acetic acid

• question_answer118) Which of the following is not a thermoplastic?

A) Polystyrene

B) Teflon

C) Polyvinyl chloride

D) Nylon 6, 6

E) Novalac

• question_answer119) Which set is the correct pairing set (or contains complementary pairs) responsible for the structure of DNA? (A-adenine, G-guanine, C-cytosine, T-thymine, U-uracil)

A) A-T, G-C

B) A-C, G-T

C) A-G, C-T

D) A-U, G-C

E) T-U, G-C

• question_answer120) Barbituric acid and its derivatives are well known as:

A) tranquilizers

B) antiseptics

C) analgesics

D) antipyretics

E) antibiotic

• question_answer121) If$f(x)={{\log }_{x}}({{\log }_{e}}x),$then$f(x)$at$x=e$is equal to:

A) 1

B) 2

C) 0

D) $e$

E) $1/e$

• question_answer122) The number of terms in the expansion of ${{(a+b+c)}^{10}}$is:

A) 11

B) 21

C) 55

D) 66

E) 44

• question_answer123) For what value of$\lambda ,$the system of equations $x+y+z=6,\text{ }x+2y+3z=10,$$x+2y+\lambda z=10$is consistent?

A) 1

B) 2

C) $-1$

D) 3

E) $-3$

• question_answer124) 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

E) 0

• question_answer125) 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) $2x+y=4$

E) none of these

• question_answer126) 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

E) 1.95

• question_answer127) 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) $(a,a)$

E) $(-a,a)$

• question_answer128) If two circles of the same radius r and centres at (2,3) and (5,6) respectively cut orthogonally, then the value of r is:

A) 3

B) 2

C) 1

D) 5

E) 6

• question_answer129) The equation to the sides of a triangle are $x-3y=0,\text{ }4x+3y=5$and$3x+y=0$. The line $3x-4y=0$passes through:

A) the incentre

B) the centroid

C) the orthocentre

D) the circumcentre

E) none of these

• question_answer130) 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) $x{{y}^{2}}$

E) $\frac{x-1}{{{y}^{2}}}$

• question_answer131) 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) $2x+3y=21$

E) $x-3y=21$

• question_answer132) 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) 4

E) 3

• question_answer133) If$y=lo{{g}^{n}}x,$where$lo{{g}^{n}}$means$log\text{ }log\text{ }log\text{ }...$(repeated n times), then $x\text{ }log\text{ }x\text{ }lo{{g}^{2}}x\text{ }lo{{g}^{3}}x\text{ }...\text{ }lo{{g}^{n-1}}\text{ }x\text{ }lo{{g}^{n}}x\frac{dy}{dx}$ is equal to:

A) $\log x$

B) $x$

C) $\frac{1}{\log x}$

D) $1$

E) ${{\log }^{n}}x$

• question_answer134) 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)

E) (1, 5/4)

• question_answer135) 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) ${{x}^{2}}=8y$

E) ${{x}^{2}}=-8y$

• question_answer136) The point on the curve$x{{y}^{2}}=1$that is nearest to the origin, is:

A) (1, 1)

B) (4, 1/2)

C) (1/4, 2)

D) $({{2}^{1/6}},{{(1/2)}^{1/12}})$

E) $({{(1/2)}^{1/3}},{{2}^{1/6}})$

• question_answer137) The distance of the point A (2, 3, 4) from$x-$axis is:

A) 5

B) $\sqrt{13}$

C) $2\sqrt{5}$

D) $5\sqrt{2}$

E) none of these

• question_answer138) The radius of the circle ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2y-4z-11=0$and $x+2y+2z-15=0$is:

A) $\sqrt{3}$

B) $\sqrt{5}$

C) $\sqrt{7}$

D) $3$

E) $\sqrt{2}$

• question_answer139) $\int{{{x}^{2}}{{(ax+b)}^{-2}}dx}$is equal to:

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

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

E) $\frac{2}{{{a}^{2}}}\left( x-\frac{b}{a}\log (ax+b) \right)+\frac{{{x}^{2}}}{a(ax+b)}+c$

• question_answer140) If the co-ordinate 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) $45{}^\circ$

B) $60{}^\circ$

C) $90{}^\circ$

D) $30{}^\circ$

E) $135{}^\circ$

• question_answer141) If$\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}|\overrightarrow{a}|=3,|\overrightarrow{b}|=5$and$|\overrightarrow{c}|=7,$then the angle between$\overrightarrow{a}$and$\overrightarrow{b}$is:

A) 0

B) $30{}^\circ$

C) $45{}^\circ$

D) $60{}^\circ$

E) $90{}^\circ$

• question_answer142) If$f(t)$is an odd function, the$\int_{0}^{x}{f(t)}\,dt$is:

A) an odd function

B) an even function

C) neither even nor odd

D) 0

E) 1

• question_answer143) The projection of$\hat{i}+3\text{ }\hat{j}+\hat{k}$on$2\hat{i}-3\text{ }\hat{j}+6\hat{k}$is:

A) 1/7

B) $-1/7$

C) 7

D) $-7$

E) 1

• question_answer144) If$\overrightarrow{a}\times \overrightarrow{b}=0$and$\overrightarrow{a}.\overrightarrow{b}=0$then:

A) $\overrightarrow{a}\bot \overrightarrow{b}$

B) $\overrightarrow{a}|\,|\overrightarrow{b}$

C) $\overrightarrow{a}=0$and$\overrightarrow{b}=\overrightarrow{0}$

D) $\overrightarrow{a}=\overrightarrow{0}$and$\overrightarrow{b}=\overrightarrow{0}$

E) cannot be determined

• question_answer145) 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) 1/2

B) 1/3

C) 2/9

D) 9/2

E) 9

• question_answer146) 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

E) non-collinear and non-coplanar

• question_answer147) ${{(\overrightarrow{a}\times \overrightarrow{b})}^{2}}$is equal to:

A) $\overset{{{\to }^{2}}}{\mathop{a}}\,+\overset{{{\to }^{2}}}{\mathop{b}}\,-(\overrightarrow{a}.\overrightarrow{b})$

B) $\overset{{{\to }^{2}}}{\mathop{a}}\,+\overset{{{\to }^{2}}}{\mathop{b}}\,-{{(\overrightarrow{a}.\overrightarrow{b})}^{2}}$

C) $\overset{{{\to }^{2}}}{\mathop{a}}\,+\overset{{{\to }^{2}}}{\mathop{b}}\,-2\,\,\overrightarrow{a}\,\,.\,\,\overrightarrow{b}$

D) $\overset{{{\to }^{2}}}{\mathop{a}}\,+\overset{{{\to }^{2}}}{\mathop{b}}\,-2\,\,\overrightarrow{a}\,\,.\,\,\overrightarrow{b}$

E) none of the above

• question_answer148) 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) $\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0$

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

• question_answer149) The value of $\left( \cos \frac{\pi }{2}+i\sin \frac{\pi }{2} \right)\left[ \cos \left( \frac{\pi }{{{2}^{2}}} \right)+i\sin \left( \frac{\pi }{{{2}^{2}}} \right) \right]$ $\left[ \cos \left( \frac{\pi }{{{2}^{3}}} \right)+i\sin \left( \frac{\pi }{{{2}^{3}}} \right) \right].....\infty$is:

A) $-1$

B) $1$

C) $0$

D) $\sqrt{2}$

E) $-\sqrt{2}$

• question_answer150) 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) $2\sin 3(\beta +\alpha )$

E) $\sin 3(\beta -\alpha )$

• question_answer151) 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) $\sqrt{x}+\sqrt{y}=\sqrt{a}$

E) ${{x}^{2}}-{{y}^{2}}={{a}^{2}}$

• question_answer152) 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

E) 3/7

• question_answer153) If $\underset{x\to a}{\mathop{\lim }}\,\frac{{{a}^{x}}-{{x}^{a}}}{{{x}^{x}}-{{a}^{a}}}=-1,$then a equals to:

A) 1

B) 0

C) e

D) $(1/e)$

E) $\infty$

• question_answer154) $\underset{x\to 0}{\mathop{\lim }}\,\frac{\tan x-\sin x}{{{x}^{3}}}$is equal to:

A) 0

B) 1

C) 1/2

D) $-1/2$

E) $\infty$

• question_answer155) $\underset{x\to a}{\mathop{\lim }}\,\frac{\log (x-a)}{\log ({{e}^{x}}-{{e}^{a}})}$is equal to:

A) 0

B) 1

C) a

D) does not exist

E) $-a$

• question_answer156) If$f(x)=|x{{|}^{3}},$ then$f(0)$ equals:

A) 0

B) 1/2

C) $-1$

D) $-1/2$

E) none of these

• question_answer157) $\int{{{e}^{-\log x}}}dx$is equal to:

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

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

C) ${{e}^{\log x}}+c$

D) $\log x+c$

E) $\log |x|+c$

• question_answer158) The area cut off by the latus rectum from the parabola${{y}^{2}}=4ax$is:

A) $(8/3)\text{ }a\text{ }sq\text{ }unit$

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

C) $(3/8)\text{ }{{a}^{2}}\text{ }sq\text{ }unit$

D) $(8/3)\text{ }{{a}^{3}}sq\text{ }unit$

E) $(8/3)\text{ }{{a}^{2}}\text{ }sq\text{ }unit$

• question_answer159) 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) $x-y=k{{e}^{x+y}}$

E) $x+y=k{{e}^{x-y}}$

• question_answer160) In how many ways can 8 students be arranged in a row?

A) $8!$

B) $7!$

C) 8

D) 7

E) $2\times 7!$

• question_answer161) 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) ${{P}^{4}}$

E) ${{P}^{5}}$

• question_answer162) The sum to 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) $\frac{{{3}^{n}}-1}{2}$

E) $\frac{{{3}^{n}}-n}{2({{3}^{n}})}$

• question_answer163) 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) ${{({{a}^{4}}c)}^{1/3}}+{{(a{{c}^{4}})}^{1/3}}+b=0$

E) ${{({{a}^{3}}c)}^{1/4}}-{{(a{{c}^{3}})}^{1/4}}+b=0$

• question_answer164) $^{20}{{C}_{4}}+{{2.}^{20}}{{C}_{3}}{{+}^{20}}{{C}_{2}}{{-}^{22}}{{C}_{18}}$is equal to:

A) 0

B) 1242

C) 7315

D) 6345

E) 3340

• question_answer165) If x=\frac{\left[ \begin{align} & 729+6(2)(243)+15(4)(81)+20(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

E) 25

• question_answer166) 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

E) 50

• question_answer167) 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) ${{2}^{n}}+{{3}^{n}}+{{5}^{n}}$

E) none of these

• question_answer168) The matrix $\left| \begin{matrix} 5 & 10 & 3 \\ -2 & -4 & 6 \\ -1 & -2 & b \\ \end{matrix} \right|$is a singular matrix, if b is equal to:

A) $-3$

B) 3

C) 0

D) for any value of b

E) for no value of b

• question_answer169) 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) 29

C) 90

D) 900

E) 81

• question_answer170) 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) ${{C}^{-1}}B{{A}^{-1}}$

E) ${{C}^{-1}}BA$

• question_answer171) The points$(1,1),(-5,5)$and$(13,\lambda )$lie on the same straight line, if$\lambda$is equal to:

A) 7

B) $-7$

C) $\pm 7$

D) 0

E) 14

• question_answer172) If$n=1,\text{ }2,\text{ }3,\text{ }....$then$\cos \alpha \cos 2\alpha \cos 4\alpha .....\cos {{2}^{n-1}}\alpha$ is equal to:

A) $\frac{\sin 2n\alpha }{2n\sin \alpha }$

B) $\frac{\sin {{2}^{n}}\alpha }{{{2}^{n}}\sin {{2}^{n-1}}\alpha }$

C) $\frac{\sin {{4}^{n-1}}\alpha }{{{4}^{n-1}}\sin \alpha }$

D) $\frac{\sin {{2}^{n}}\alpha }{{{2}^{n}}\sin \alpha }$

E) none of these

• question_answer173) If the lines $3x+4y+1=0,\text{ }5x+\lambda y+3=0$ and $2x+y-1=0$are concurrent, then $\lambda$ is equal to:

A) $-8$

B) 8

C) 4

D) $-4$

E) none of these

• question_answer174) If the equation$k{{x}^{2}}-2xy-{{y}^{2}}-2x+2y=0$represents a pair of lines, then k is equal to:

A) 2

B) $-2$

C) $-5$

D) 5

E) 3

• question_answer175) Let $A=\left[ \begin{matrix} {{\cos }^{2}}\theta & \sin \theta \cos \theta \\ \cos \theta \sin \theta & {{\sin }^{2}}\theta \\ \end{matrix} \right]$and$B=\left[ \begin{matrix} {{\cos }^{2}}\phi & \sin \phi \cos \phi \\ \cos \phi \sin \phi & {{\sin }^{2}}\phi \\ \end{matrix} \right]$then$AB=0$if:

A) $\theta =n\phi ,n=0,1,2,....$

B) $\theta +\phi =n\pi ,n=0,1,2,....$

C) $\theta =\phi +(2n+1)\frac{\pi }{2},n=0,1,2,....$

D) $\theta =\phi +n\frac{\pi }{2},n=0,1,2,....$

E) $\theta =\phi +3n\frac{\pi }{2},n=0,1,2,....$

• question_answer176) If the area of the circle $4{{x}^{2}}+4{{y}^{2}}-8x+16y+k=0$is$9\pi$sq unit, then the value of k is:

A) 4 sq unit

B) 16 sq unit

C) $-16$sq unit

D) $\pm 16$ sq unit

E) none of these

• question_answer177) If a focal chord of the parabola${{y}^{2}}=ax$is $2x-y-8=0,$then the equation of the directrix is:

A) $x+4=0$

B) $x-4=0$

C) $y-4=0$

D) $y+4=0$

E) none of these

• question_answer178) Let$X=\left[ \begin{matrix} {{x}_{1}} \\ {{x}_{2}} \\ {{x}_{3}} \\ \end{matrix} \right],A=\left[ \begin{matrix} 1 & -1 & 2 \\ 2 & 0 & 1 \\ 3 & 2 & 1 \\ \end{matrix} \right]$and$B=\left[ \begin{matrix} 3 \\ 1 \\ 4 \\ \end{matrix} \right]$. If$AX=B,$then$X$is equal to:

A) $\left[ \begin{matrix} 1 \\ 2 \\ 3 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} -1 \\ -2 \\ 3 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} -1 \\ -2 \\ -3 \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} -1 \\ 2 \\ 3 \\ \end{matrix} \right]$

E) $\left[ \begin{matrix} 0 \\ 2 \\ 1 \\ \end{matrix} \right]$

• question_answer179) A line make angles of$45{}^\circ$and$60{}^\circ$with the $x-$axis and the z-axis respectively. The angle made by it with y-axis is:

A) $30{}^\circ \,or\text{ }150{}^\circ$

B) $60{}^\circ \,or\text{ }120{}^\circ$

C) $45{}^\circ \,or\text{ }135{}^\circ$

D) $90{}^\circ$

E) none of these

• question_answer180) If$a=\frac{\pi }{18}$rad then$\cos a+\cos 2a+...+\cos 18a$ is equal to:

A) 0

B) $-1$

C) 1

D) $\pm 1$

E) none of these

• question_answer181) If$\sec \theta +\tan \theta =k,\cos \theta$equals to:

A) $\frac{{{k}^{2}}+1}{2k}$

B) $\frac{2k}{{{k}^{2}}+1}$

C) $\frac{k}{{{k}^{2}}+1}$

D) $\frac{k}{{{k}^{2}}-1}$

E) none of these

• question_answer182) $\underset{x\to \frac{\pi }{6}}{\mathop{\lim }}\,\frac{2{{\sin }^{2}}x+\sin x-1}{2{{\sin }^{2}}x-3\sin x+1}$is equal to:

A) 3

B) $-3$

C) 6

D) 0

E) 9

• question_answer183) If the function$f(x)$is defined by $f(x)=a+bx$and${{f}^{r}}=fff\text{ }...$(repeated r times), then ${{f}^{r}}(x)$is equal to:

A) $a+{{b}^{r}}x$

B) $ar+{{b}^{r}}x$

C) $ar+b{{x}^{r}}$

D) $a({{b}^{r}}-1)+{{b}^{r}}x$

E) $a\left( \frac{{{b}^{r}}-1}{b-1} \right)+{{b}^{r}}x$

• question_answer184) If a particle is moving such that the velocity acquired is proportional to the square root of the distance covered, then its acceleration is:

A) a constant

B) $\propto {{s}^{2}}$

C) $\propto \frac{1}{{{s}^{2}}}$

D) $\propto s$

E) $\propto \frac{1}{s}$

• question_answer185) If $f(x)=\frac{1-x}{1+x}(x\ne -1),$then${{f}^{-1}}(x)$W equals to:

A) $f(x)$

B) $\frac{1}{f(x)}$

C) $-f(x)$

D) $-\frac{1}{f(x)}$

E) not defined

• question_answer186) Domain of the function$f(x)={{\sin }^{-1}}({{\log }_{2}}x)$in the set of real numbers is:

A) $\{x:1\le x\le 2\}$

B) $\{x:1\le x\le 3\}$

C) $\{x:-1\le x\le 2\}$

D) $\left\{ x:\frac{1}{2}\le x\le 2 \right\}$

E) $\left\{ x:-\frac{1}{2}\le x\le 2 \right\}$

• question_answer187) If $\omega$ is a complex cube root of unity, then $\frac{a+b\omega +c{{\omega }^{2}}}{c+a\omega +b{{\omega }^{2}}}+\frac{c+a\omega +b{{\omega }^{2}}}{a+b\omega +c{{\omega }^{2}}}+\frac{b+c\omega +a{{\omega }^{2}}}{b+c{{\omega }^{4}}+a{{\omega }^{5}}}$ is equal to:

A) $1$

B) $\omega$

C) ${{\omega }^{2}}$

D) $-1$

E) 0

• question_answer188) If$\alpha ,\beta$and$\gamma$are angles such that$\tan \alpha +\tan \beta +\tan \gamma =\tan \alpha .\tan \beta .\tan \gamma$and$x=\cos \alpha +i\sin \alpha ,y=\cos \beta +i\sin \beta$and$z=\cos \gamma +i\sin \gamma ,$then$xyz$is equal to:

A) 1, but not$-1$

B) $-1$, but not 1

C) $1$or$-1$

D) 0

E) $i$

• question_answer189) If$\alpha$and$\beta$are complex cube roots of unity and $x=a\alpha +b\beta ,\text{ }y=a+b,\text{ }z=\alpha \beta +b\alpha ,$then$xyz$ is equal to:

A) $a+b$

B) $a-b$

C) ${{a}^{2}}+{{c}^{2}}$

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

E) ${{a}^{3}}+{{b}^{3}}$

• question_answer190) If a, b and c are distinct positive real numbers in AP, then the roots of the equation $a{{x}^{2}}+2bx+c=0$are:

A) imaginary

B) rational and equal

C) rational and distinct

D) irrational

E) real, may be rational or irrational

• question_answer191) If a, b and c are in AP, then which one of the following is not true?

A) $\frac{k}{a},\frac{k}{b}$and$\frac{k}{c}$are in HP

B) $a+k,\text{ }b+k$ and$c+k$ are in AP

C) $ka,kb$ and$kc$are in AP

D) ${{a}^{2}},\text{ }{{b}^{2}}$and${{c}^{2}}$are in AP

E) $a+b,\text{ }c+a$and$b+c$are in AP

• question_answer192) If${{z}_{1}},{{z}_{2}}$and${{z}_{3}}$are any three complex numbers, then the fourth vertex of the parallelogram whose three vertices are${{z}_{1}},{{z}_{2}}$and${{z}_{3}}$taken in order, is:

A) ${{z}_{1}}-{{z}_{2}}+{{z}_{3}}$

B) ${{z}_{1}}+{{z}_{2}}+{{z}_{3}}$

C) $\frac{1}{3}({{z}_{1}}-{{z}_{2}}+{{z}_{3}})$

D) $\frac{1}{3}({{z}_{1}}+{{z}_{2}}-{{z}_{3}})$

E) $\frac{1}{3}({{z}_{1}}-{{z}_{2}}-{{z}_{3}})$

• question_answer193) $\sqrt{4},\sqrt{4},\sqrt{4},\sqrt{4},....$to$\infty$are roots of the equation:

A) ${{x}^{2}}-4=0$

B) ${{x}^{2}}-4x+6=0$

C) ${{x}^{2}}-5x+4=0$

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

E) ${{x}^{2}}-x=0$

• question_answer194) If${{a}_{1}},{{a}_{2}},{{a}_{3}},.....,{{a}_{n}}$are the n arithmetic means between a and b, then$2\sum\limits_{i=1}^{n}{{{a}_{i}}}$equals:

A) $ab$

B) $n(a+b)$

C) $nab$

D) $\frac{(a+b)}{n}$

E) $\frac{n(a+b)}{ab}$

• question_answer195) Let a, b be the solutions of${{x}^{2}}+px+1=0$and c, d be the solutions of${{x}^{2}}+qx+1=0$. If $(a-c)(b-c)$and$(a+d)(b+d)$are the solutions of${{x}^{2}}+ax+\beta =0,$then $\beta$ equals:

A) $p+q$

B) $p-q$

C) ${{p}^{2}}+{{q}^{2}}$

D) ${{p}^{2}}-{{q}^{2}}$

E) ${{q}^{2}}-{{p}^{2}}$

• question_answer196) The $x-$co-ordinate of the incentre of the triangle where the mid points of the sides are (0, 1), (1,1) and (1, 0), is:

A) $2+\sqrt{2}$

B) $1+\sqrt{2}$

C) $2-\sqrt{2}$

D) $1-\sqrt{2}$

E) $3-\sqrt{2}$

• question_answer197) Which one of the following is true?

A) $\sin ({{\cos }^{-1}}x)=\cos ({{\sin }^{-1}}x)$

B) $\sec ({{\tan }^{-1}}x)=\tan ({{\sec }^{-1}}x)$

C) $\cos ({{\tan }^{-1}}x)=\tan ({{\cos }^{-1}}x)$

D) $\tan ({{\sin }^{-1}}x)=\sin ({{\tan }^{-1}}x)$

E) all of these

• question_answer198) If${{\tan }^{-1}}a+{{\tan }^{-1}}b={{\sin }^{-1}}1-{{\tan }^{-1}}c,$then:

A) $a+b+c=abc$

B) $ab+bc+ca=abc$

C) $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}-\frac{1}{abc}=0$

D) $ab+bc+ca=a+b+c$

E) none of the above

• question_answer199) Two consecutive sides of a parallelogram are $4x+5y=0$ and$7x+2y=0$. One diagonal of the parallelogram is$11x+7y=9$. If the other diagonal is$ax+by+c=0,$then:

A) $a=-1,b=-1,c=2$

B) $a=1,b=-1,c=0$

C) $a=-1,b=-1,c=0$

D) $a=1,b=1,c=0$

E) $a=-1,b=-1,c=1$

• question_answer200) The number of values of $\theta$ in the interval$[-\pi ,\pi ]$satisfying the equation$cos\theta +sin2\theta =0$is:

A) 1

B) 2

C) 3

D) 4

E) many

• question_answer201) From a set of 100 cards numbered 1 to 100, one card is drawn at random. The probability that the number obtained on the card is divisible by 6 or 8 but not by 24, is:

A) $\frac{6}{25}$

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

C) $\frac{1}{6}$

D) $\frac{2}{5}$

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

• question_answer202) If the line$x+y-1=0$is a tangent to the parabola${{y}^{2}}-y+x=0,$then the point of contact is:

A) (0, 1)

B) $(1,0)$

C) $(0,-1)$

D) $(-1,0)$

E) $(0,-1)$

• question_answer203) If$f(x)=\left\{ \begin{matrix} \frac{2x-1}{\sqrt{1+x}-1}, & -1\le x<\infty ,x\ne 0 \\ k, & x=0 \\ \end{matrix} \right.$ is continuous everywhere, then k is equal to :

A) $\frac{1}{2}\log 2$

B) $\log 4$

C) $\log 8$

D) $\log 2$

E) none of these

• question_answer204) If$\sec \left( \frac{{{x}^{2}}-{{y}^{2}}}{{{x}^{2}}+{{y}^{2}}} \right)={{e}^{a}},$then$\frac{dy}{dx}$is equal to:

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

B) $\frac{y}{x}$

C) $\frac{x}{y}$

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

E) $0$

• question_answer205) The curve represented by the equation $4{{x}^{2}}+16{{y}^{2}}-24x-32y-12=0$is:

A) a parabola

B) a pair of straight lines

C) an ellipse with eccentricity 1/2

D) an ellipse with eccentricity$\sqrt{3}/2$

E) a hyperbola with eccentricity 3/2

• question_answer206) It${{\sin }^{-1}}x+{{\sin }^{-1}}y=\frac{\pi }{2},$then$\frac{dy}{dx}$is equal to:

A) $\frac{x}{y}$

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

C) $\frac{y}{x}$

D) $-\frac{y}{x}$

E) none of these

• question_answer207) The maximum value of$\frac{\log x}{x}$is equal to:

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

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

C) $e$

D) $1$

E) $\frac{e}{2}$

• question_answer208) $ax+by-{{a}^{2}}=0,$where a, b are non-zero, is the equation to the straight line perpendicular to a line $l$and passing through the point where (crosses the$x-$axis. Then equation to the line$l$is:

A) $\frac{x}{b}-\frac{y}{a}=1$

B) $\frac{x}{a}-\frac{y}{b}=1$

C) $\frac{x}{b}+\frac{y}{a}=ab$

D) $\frac{x}{a}-\frac{y}{b}=ab$

E) $\frac{x}{a}+\frac{y}{b}=ab$

• question_answer209) $\int{\frac{{{a}^{x/2}}}{\sqrt{{{a}^{-x}}-{{a}^{x}}}}}dx$is equal to:

A) $\frac{1}{\log a}{{\sin }^{-1}}({{a}^{x}})+c$

B) $\frac{1}{\log a}{{\tan }^{-1}}({{a}^{x}})+c$

C) $2\sqrt{{{a}^{-x}}-{{a}^{x}}}+c$

D) $\log ({{a}^{x}}-1)+c$

E) ${{\sin }^{-1}}({{a}^{x}})+c$

• question_answer210) If$g(x)=\frac{f(x)-f(-x)}{2}$defined over$[-3,\text{ }3]$ and$f(x)=2{{x}^{2}}-4x+1,$then$\int_{-3}^{3}{g(x)}dx$is equal to:

A) 0

B) 4

C) $-4$

D) 8

E) none of these

• question_answer211) Let ABCD be the parallelogram whose sides AB and AD are represented by the vectors $2\hat{i}+4\hat{j}-5\hat{k}$and$\hat{i}+2\hat{j}+3\hat{k}$ respectively. Then, if a is a unit vector parallel to AC then a equals:

A) $\frac{1}{3}(3\hat{i}-6\hat{j}-2\hat{k})$

B) $\frac{1}{3}(3\hat{i}+6\hat{j}+2\hat{k})$

C) $\frac{1}{3}(3\hat{i}-6\hat{j}-3\hat{k})$

D) $\frac{1}{7}(3\hat{i}+6\hat{j}-2\hat{k})$

E) $\frac{1}{7}(3\hat{i}+5\hat{j}-3\hat{k})$

• question_answer212) The solution of$\frac{dy}{dx}+1=\cos ec(x+y)$is:

A) $\cos (x+y)+x=c$

B) $\cos (x+y)=c$

C) $\sin (x+y)+x=c$

D) $\sin (x+y)+\sin (x+y)=c$

E) $x-\cos (x+y)=c$

• question_answer213) Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in the power set of the second set. Then the values of m and n are:

A) $7,6$

B) $6,3$

C) $6,4$

D) $7,4$

E) $3,7$

• question_answer214) Let$\overrightarrow{a}$and$\overrightarrow{b}$be two unit vectors such that angle between them is$60{}^\circ$. Then$|\overrightarrow{a}-\overrightarrow{b}|$is equal to:

A) $\sqrt{5}$

B) $\sqrt{3}$

C) $0$

D) $1$

E) $\sqrt{2}$

• question_answer215) Two numbers within the brackets denote the ranks of 10 students of a class in two subjects$(1,10),(2,9),(3,8),(4,7),(5,6),(6,5)(7,4),(8,3)$$(9,2),(10,1),$then rank correlation coefficient is:

A) $0$

B) $-1$

C) $1$

D) $0.5$

E) $-0.5$

• question_answer216) $\int{\frac{\sin x}{\sin (x-a)}}dx$is equal to:

A) $x\cos a-\sin a.\log (x-a)+c$

B) $x\sin a+c$

C) $x\sin a+\sin a.\log \sin (x-a)+c$

D) $x\cos a+\sin a.\log \sin (x-a)+c$

E) $x\cos a+\cos a.\log \sin (x-a)+c$

• question_answer217) If$a=\hat{i}+2\hat{j}+3\hat{k},$and $\overrightarrow{b}=\hat{i}\times (\overrightarrow{a}\times \hat{i})+\hat{j}\times (\overrightarrow{a}\times \hat{j})+\overrightarrow{k}\times (\overrightarrow{a}\times \hat{k}),$ then length of $\vec{b}$ is equal to

A) $\sqrt{12}$

B) $2\sqrt{12}$

C) $3\sqrt{14}$

D) $3\sqrt{12}$

E) $2\sqrt{14}$

• question_answer218) $\int{\frac{f(x)}{f(x)\log [f(x)]}}dx$is equal to:

A) $\frac{f(x)}{\log f(x)}+c$

B) $f(x).\log f(x)+c$

C) $\log [\log f(x)]+c$

D) $\frac{1}{\log [\log f(x)]}+c$

E) $\frac{\log f(x)}{f(x)}+c$

• question_answer219) $\int{\frac{{{e}^{x}}}{(2+{{e}^{x}})({{e}^{x}}+1)}}dx$is equal to:

A) $\log \left( \frac{{{e}^{x}}+1}{{{e}^{x}}+2} \right)+c$

B) $\log \left( \frac{{{e}^{x}}+2}{{{e}^{x}}+1} \right)+c$

C) $\left( \frac{{{e}^{x}}+1}{{{e}^{x}}+2} \right)+c$

D) $\left( \frac{{{e}^{x}}+2}{{{e}^{x}}+1} \right)+c$

E) $\frac{1}{2}\log \left( \frac{{{e}^{x}}+1}{{{e}^{x}}+2} \right)+c$

• question_answer220) For any angle$\theta ,$the expression$\frac{2\cos 8\theta +1}{2\cos \theta +1}$is equal to:

A) $(2\cos \theta +1)(2\cos 2\theta +1)(2\cos 4\theta +1)$

B) $(\cos \theta -1)(\cos 2\theta -1)(\cos 4\theta -1)$

C) $(2\cos \theta -1)(2\cos 2\theta -1)(2\cos 4\theta -1)$

D) $(2\cos \theta +1)(2\cos 2\theta +1)(2\cos 4\theta +1)$

E) $(2\cos \theta -1)(2\cos 2\theta -1)(2\cos 4\theta +1)$

• question_answer221) If${{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}\theta d\theta ,}$then${{I}_{8}}+{{I}_{6}}$is equal to:

A) $\frac{1}{7}$

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

C) $\frac{1}{5}$

D) $\frac{1}{6}$

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

• question_answer222) The order of the differential equation ${{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}={{\left( 1+\frac{dy}{dx} \right)}^{1/2}}$is:

A) 2

B) 3

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

D) 4

E) 6

• question_answer223) If$m\tan (\theta -30{}^\circ )=n\tan (\theta +120{}^\circ ),$then$\cos 2\theta$equals:

A) $\frac{m+n}{m-n}$

B) $\frac{m-n}{m+n}$

C) $\frac{m-n}{2(m+n)}$

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

E) $\frac{2(m+n)}{m-n}$

• question_answer224) The integrating factor of the differential equation$\cos x\left( \frac{dy}{dx} \right)+y\sin x=1$is:

A) $cos\text{ }x$

B) $tan\text{ }x$

C) $sin\text{ }x$

D) $cot\text{ }x$

E) $sec\text{ }x$

• question_answer225) Solution of the differential equation $\tan y.{{\sec }^{2}}xdx+\tan x.{{\sec }^{2}}ydy=0$ is:

A) $tan\text{ }x+tan\text{ }y=k$

B) $tan\text{ }x-tan\text{ }y=k$

C) $(tan\text{ }x/tan\text{ }y)=k$

D) $tan\text{ }x.tan\text{ }y=k$

E) None of the above

• question_answer226) ${{\tan }^{-1}}\left( \frac{m}{2} \right)-{{\tan }^{-1}}\left( \frac{m-n}{m+n} \right)$ is equal to:

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

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

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

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

E) $\frac{2\pi }{3}$

• question_answer227) A class has 175 students. The following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?

A) 35

B) 48

C) 60

D) 22

E) 30

• question_answer228) Let S be the set of all real numbers. Then the relation$R=\{(a,b):1+ab>0\}$on S is:

A) reflexive and symmetric but not transitive

B) reflexive and transitive but not symmetric

C) symmetric and transitive but not reflexive

D) reflexive, transitive and symmetric

E) none of the above is true

• question_answer229) For the principal value branch of the graph of the function$y={{\sin }^{-1}}x,-1\le x\le 1,$which among the following is a true statement?

A) graph is symmetric about the$x-$axis

B) graph is symmetric about the y-axis

C) graph is not continuous

D) the line$x=1$is a tangent

E) the line y = 1 is a tangent

• question_answer230) Let$f\left( x+\frac{1}{x} \right)={{x}^{2}}+\frac{1}{{{x}^{2}}},x\ne 0,$then$f(x)$ equals to:

A) ${{x}^{2}}$

B) ${{x}^{2}}-1$

C) ${{x}^{2}}-2$

D) ${{x}^{2}}+1$

E) ${{x}^{2}}+2$

• question_answer231) A point P which represents a complex number z moves such that$|z-{{z}_{1}}|=|z-{{z}_{2}}|,$then its locus is:

A) a circle with centre${{z}_{1}}$

B) a circle with centre${{z}_{2}}$

C) a circle with centre$z$

D) an ellipse

E) perpendicular bisector of line joining${{z}_{1}}$ and${{z}_{2}}$

• question_answer232) The probability that in a family of 5 members, exactly 2 members have birthday on Sunday, is:

A) $\frac{12\times {{5}^{3}}}{{{7}^{5}}}$

B) $\frac{10\times {{6}^{2}}}{{{7}^{5}}}$

C) $\frac{2}{5}$

D) $\frac{10\times {{6}^{3}}}{{{7}^{5}}}$

E) $1$

• question_answer233) $\frac{{{(\cos \theta +i\sin \theta )}^{4}}}{{{(\sin \theta +i\cos \theta )}^{5}}}$is equal to:

A) $\cos \theta -i\sin \theta$

B) $\sin \theta -i\cos \theta$

C) $\cos 9\theta -i\sin 9\theta$

D) $\sin 9\theta -i\cos 9\theta$

E) $\cos \theta +i\sin \theta$

• question_answer234) The quadratic equation whose roots are twice the roots of$2{{x}^{2}}-5x+2=0$is:

A) $8{{x}^{2}}-10x+2=0$

B) ${{x}^{2}}-5x+4=0$

C) $2{{x}^{2}}-5x+2=0$

D) ${{x}^{2}}-10x+6=0$

E) none of the above

• question_answer235) Standard deviation of the first$2n+1$natural numbers is equal to:

A) $\sqrt{\frac{n(n+1)}{2}}$

B) $\sqrt{\frac{n(n+1)(2n+1)}{3}}$

C) $\sqrt{\frac{n(n+1)}{3}}$

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

E) $2n+1$

• question_answer236) If$\alpha +\beta =4$and${{\alpha }^{3}}+{{\beta }^{3}}=44,$then$\alpha ,\beta$are the roots of the equation.

A) $2{{x}^{2}}-7x+6=0$

B) $3{{x}^{2}}+9x+11=0$

C) $9{{x}^{2}}-27x+20=0$

D) $4{{x}^{2}}+22x+15=0$

E) $3{{x}^{2}}-12x-5=0$

• question_answer237) The coefficient of$x$in${{x}^{2}}+px+q=0$was taken as 17 in place of 13 and its roots were found to be$-2$and$-15$The roots of the original equation are:

A) 3, 7

B) $-3,7$

C) $-3,-7$

D) $3,10$

E) $-3,-10$

• question_answer238) If$g(x)=\min (x,{{x}^{2}})$where$x$is a real number, then:

A) $g(x)$is an increasing function

B) $g(x)$is a decreasing function

C) $g(x)$ is a constant function

D) $g(x)$is a continuous function except at$x=0$

E) $g(x)$is a continuous function except at $x=0$and$x=1$

• question_answer239) If$^{n}{{C}_{3}}=220,$then n equals to:

A) 10

B) 11

C) 12

D) 9

E) 8

• question_answer240) A polygon has 54 diagonals. Number of sides of this polygon is:

A) 12

B) 15

C) 16

D) 9

E) 14

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