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Solved papers for CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2008

done CEE Kerala Engineering Solved Paper-2008

  • question_answer1) If the ratio of amounts of scattering of two light waves is 1: 4, the ratio of their wavelengths is

    A) \[1:2\]

    B) \[\sqrt{2}:1\]

    C) \[1:\sqrt{2}\]

    D) \[1:1\]

    E) \[2:1\]

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  • question_answer2) In Youngs experiment, the third bright band for light of wavelength coincides with the fourth bright band for another source of light in the same arrangement. Then the wavelength of second source is

    A) \[3600\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    B) \[4000\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    C) \[5000\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    D) \[4500\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    E) \[5500\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

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  • question_answer3) If the angle of minimum deviation is of\[{{60}^{o}}\]for an equilateral prism, then the refractive index of the material of the prism is

    A) 1.41

    B) 1.5

    C) 1.6

    D) 1.33

    E) 1.73

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  • question_answer4) The wavelength of red light from He-Ne laser is 633 nm in air but 474 nm in the aqueous humor inside the eye ball. Then the speed of red light through the aqueous humor is

    A) \[3\times {{10}^{8}}m/s\]

    B) \[1.34\times {{10}^{8}}m/s\]

    C) \[2.25\times {{10}^{8}}m/s\]

    D) \[2.5\times {{10}^{8}}m/s\]

    E) \[2.75\times {{10}^{8}}m/s\]

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  • question_answer5) The radius of curvature of the convex face of a planoconvex lens is 15 cm and the refractive index of the material is 1.4. Then the power of the lens in dioptre is

    A) 1.6

    B) 1.66

    C) 2.6

    D) 2.66

    E) 1.4

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  • question_answer6) The threshold wavelength for photoelectric emission from a material is \[4800\overset{\text{o}}{\mathop{\text{A}}}\,\] . Photoelectrons will be emitted from the material, when it is illuminated with light from a

    A)  40 W blue lamp

    B)  40 W green lamp

    C)  100 W red lamp

    D)  100 W yellow lamp

    E)  1000 W green lamp

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  • question_answer7) The energy released in the fission of 1 kg of \[_{92}{{U}^{235}}\] is (energy per fission = 200 MeV)

    A) \[5.1\times {{10}^{26}}eV\]

    B) \[5.1\times {{10}^{26}}J\]

    C) \[8.2\times {{10}^{13}}J\]

    D) \[8.2\times {{10}^{13}}MeV\]

    E) \[5.1\times {{10}^{23}}MeV\]

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  • question_answer8) The nuclear radius of a certain nucleus is 7.2 fm and it has charge of\[1.28\times {{10}^{-17}}C\]. The number of neutrons inside the nucleus is

    A) 136

    B) 142

    C) 140

    D) 132

    E) 126

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  • question_answer9) Which one of the following statement is true, if half-life of a radioactive substance is 1 month?

    A) \[7/{{8}^{th}}\]part of the substance will disintegrate in 3 months

    B) \[1/{{8}^{th}}\]part of the substance will remain undecayed at the end of 4 months

    C) The substance will disintegrate completely in 4 months

    D) \[1/{{16}^{th}}\] part of the substance will remain undecayed at the end of 3 months

    E) The substance will disintegrate completely in 2 months

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  • question_answer10) A common emitter amplifier gives an output of 3 V for an input of 0.01 V. If\[\beta \]of the transistor is 100 and the input resistance is \[1\text{ }k\Omega ,\]then the collector resistance is

    A) \[\text{1 }k\Omega \]

    B) \[\text{3 }k\Omega \]

    C) \[\text{30 }k\Omega \]

    D) \[\text{30 }k\Omega \]

    E) \[\text{6 }k\Omega \]

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  • question_answer11) The current\[I\]through\[10\,\Omega \]resistor in the circuit given below is

    A) 50mA

    B) 20mA

    C) 40mA

    D) 80mA

    E) 35mA

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  • question_answer12) The combination of the following gates produces

    A) AND gate

    B) NAND gate

    C) NOR gate

    D) OR gate

    E) NOT gate

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  • question_answer13) The resonance frequency of the tank circuit of an oscillator when\[L=\frac{10}{{{\pi }^{2}}}mH\] and\[C=0.04\text{ }\mu F\]are connected in parallel is

    A) 250 kHz

    B) 25 kHz

    C) 2.5 kHz

    D) 25 MHz

    E) 2.5MHz

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  • question_answer14) In satellite communication

    1. the frequency used lies between 5 MHz and 10 MHz.
    2. the uplink and downlink frequencies are different.
    3. the orbit of geostationary satellite lies in the equatorial plane at an inclination of\[0{}^\circ \]
    In the above statements

    A) only 2 and 3 are true

    B) all are true

    C) only 2 is true

    D) only 1 and 2 are true

    E) only 1 is true

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  • question_answer15) The principle used in the transmission of signals through an optical fibre is

    A) total internal reflection

    B) reflection

    C) refraction

    D) dispersion

    E) interference

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  • question_answer16) Which of the following statement is wrong?

    A) Ground wave propagation can be sustained at frequencies 500 kHz to 1,500 kHz

    B) Statellite communication is useful for the frequencies above 30 MHz

    C) Sky wave propagation is useful in the range of 30 to 40 MHz

    D) Sky wave propagation takes place through tropospheric space

    E) The phenomenon involved in sky wave propagation is total internal reflection.

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  • question_answer17) A signal wave of frequency 12 kHZ is modulated with a carrier wave of frequency 2.51 MHz. The upper and lower side band frequencies are respectively

    A) 2512 kHz and 2508 kHz

    B) 2522 kHz and 2488 kHz

    C) 2502 kHz and 2498 kHz

    D) 2522 kHz and 2498 kHz

    E) 2512 kHz and 2488 kHz

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  • question_answer18) Millikans oil-drop experiment established that

    A) electric charge depends on velocity

    B) specific charge of electron is\[1.76\times {{10}^{11}}\] \[Ck{{g}^{-1}}\]

    C) electron has wave nature

    D) electric charge is quantized

    E) electron has particle nature

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  • question_answer19) If C is the capacitance and V is the potential, the dimensional formula for\[C{{V}^{2}}\]is

    A) \[[M{{L}^{2}}{{T}^{-1}}]\]

    B) \[[M{{L}^{-2}}{{T}^{-3}}]\]

    C) \[[M{{L}^{2}}{{T}^{-2}}]\]

    D) \[[M{{L}^{-2}}{{T}^{-2}}]\]

    E) \[[M{{L}^{-1}}{{T}^{-1}}]\]

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  • question_answer20) An object is dropped from rest. Its v-t graph is

    A)

    B)

    C)

    D)

    E)

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  • question_answer21) A particle starts from rest at\[t=0\]and moves in a straight line with an acceleration as shown in figure. The velocity of the particle at \[t=3\text{ }s\] is

    A) \[2m{{s}^{-1}}\]

    B) \[4m{{s}^{-1}}\]

    C) \[6m{{s}^{-1}}\]

    D) \[8\,m{{s}^{-1}}\]

    E) \[1\text{ }m{{s}^{-1}}\]

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  • question_answer22) Two cars A and B are moving with same speed of 45 km/h along same direction. If a third car C coming from the opposite direction with a speed of 36 km/h meets two cars in an interval of 5 min, the distance of separation of two cars A and B should be (in km)

    A) 6.75

    B) 7.25

    C) 5.55

    D) 8.35

    E) 4.75

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  • question_answer23) Two particles A and B are projected with same speed so that the ratio of their maximum heights reached is 3:1. If the speed of A is doubled without altering other parameters, the ratio of the horizontal ranges attained by A and B is

    A) \[1:1\]

    B) \[2:1\]

    C) \[4:1\]

    D) \[3:2\]

    E) \[4:3\]

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  • question_answer24) An object of mass 5 kg is attached to the hook of a spring balance and the balance is suspended vertically from the roof of a lift. The reading on the spring balance when the lift is going up with an acceleration of 0.25 \[m{{s}^{-2}}\]is \[(g=10\text{ }m{{s}^{-2}})\]

    A) 51.25 N

    B) 48.75 N

    C) 52.75 N

    D) 47.25 N

    E) 55 N

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  • question_answer25) A particle acted upon by constant forces \[4\hat{i}+\hat{j}-3\hat{k}\] and\[3\hat{i}+\hat{j}-\hat{k}\]is displaced from the point\[\hat{i}+2\hat{j}+3\hat{k}\]to the, point\[5\hat{i}+4\hat{j}+\hat{k}\]. The total work done by the forces in SI unit is

    A) 20

    B) 40

    C) 50

    D) 30

    E) 35

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  • question_answer26) Two bodies A and B have masses 20 kg and 5 kg respectively. Each one is acted upon by a force of 4 kg-wt. If they acquire the same kinetic energy in times\[{{t}_{A}}\]and\[{{t}_{B}},\]then the ratio\[\frac{{{t}_{A}}}{{{t}_{B}}}\]is

    A) \[\frac{1}{2}\]

    B) \[2\]

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

    D) \[\frac{5}{6}\]

    E) \[\frac{1}{5}\]

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  • question_answer27) A bullet of mass 0.05 kg moving with a speed of\[80\text{ }m{{s}^{-1}}\]enters a wooden block and is stopped after a distance of 0.40 m. The average resistive force exerted by the block on the bellow is

    A) 300 N

    B) 20 N

    C) 400 N

    D) 40 N

    E) 200 N

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  • question_answer28) A particle of mass 2 kg is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below. The velocity of the particle after 10 s is

    A) \[20\text{ }m{{s}^{-1}}\]

    B) \[10\text{ }m{{s}^{-1}}\]

    C) \[75\text{ }m{{s}^{-1}}\]

    D) \[26\text{ }m{{s}^{-1}}\]

    E) \[50\text{ }m{{s}^{-1}}\]

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  • question_answer29) The height of the dam, in a hydroelectric power station is 10 m. In order to generate 1 MW of electric power, the mass of water (in kg) that must fall per second on the blades of the turbines is

    A) \[{{10}^{6}}\]

    B) \[{{10}^{5}}\]

    C) \[{{10}^{3}}\]

    D) \[{{10}^{4}}\]

    E) \[{{10}^{2}}\]

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  • question_answer30) A spring gun of spring constant 90 N/cm is compressed 12 cm by a ball of mass 16 g. If the trigger is pulled, the velocity of the ball is

    A) \[50\text{ }m{{s}^{-1}}\]

    B) \[9\text{ }m{{s}^{-1}}\]

    C) \[40\text{ }m{{s}^{-1}}\]

    D) \[\text{26 }m{{s}^{-1}}\]

    E) \[90\text{ }m{{s}^{-1}}\]

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  • question_answer31) A particle is moving under the influence of a force given by\[F=kx,\]where k is a constant and\[x\]is the distance moved. The energy (in joules) gained by the particle in moving from \[x=0\]to\[x=3\]is

    A) 2k

    B) 3.5 k

    C) 4.5 k

    D) 9k

    E) 9.5 k

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  • question_answer32) A thin circular ring of mass M and radius R rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity cd. Four small spheres each of mass m (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be

    A) \[4\omega \]

    B) \[\frac{M}{4m}\omega \]

    C) \[\left( \frac{M+4m}{M} \right)\omega \]

    D) \[\left( \frac{M}{M-4m} \right)\omega \]

    E) \[\left( \frac{M}{M+4m} \right)\omega \]

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  • question_answer33) The angular velocity of a wheel increases from 100 rps to 300 rps in 10 s. The number of revolutions made during that time is

    A) 600

    B) 1500

    C) 1000

    D) 3000

    E) 2000

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  • question_answer34) Three identical spheres, each of mass 3 kg are placed touching each other with their centres lying on a straight line. The centres of the sphere are marked at P, Q and R respectively. The distance of centre of mass of system from P is

    A) \[\frac{PQ+QR+PR}{3}\]

    B) \[\frac{PQ+PR}{3}\]

    C) \[\frac{PQ+QR+PR}{9}\]

    D) \[\frac{PQ+PR}{9}\]

    E) \[\frac{PQ+QR}{3}\]

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  • question_answer35) Infinite number of masses, each 1 kg, are placed along the x-axis at\[x=\pm \text{ }1\text{ }m,\pm 2m,\pm \text{ }4\] \[m,\pm \text{ }8\text{ }m,\pm \text{ }16m....\]The magnitude of the resultant gravitational potential in terms of gravitational constant G at the origin\[(x=0)\]is

    A) \[G/2\]

    B) \[G\]

    C) \[2G\]

    D) \[4G\]

    E) \[8G\]

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  • question_answer36) Three identical bodies of mass M are located at the vertices of an equilateral triangle of side L. They revolve under the effect of mutual gravitational force in a circular orbit, circumscribing the triangle while preserving the equilateral triangle. Their orbital velocity is

    A) \[\sqrt{\frac{GM}{L}}\]

    B) \[\sqrt{\frac{3GM}{2L}}\]

    C) \[\sqrt{\frac{3GM}{L}}\]

    D) \[\sqrt{\frac{2GM}{3L}}\]

    E) \[\sqrt{\frac{GM}{3L}}\]

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  • question_answer37) A satellite is revolving around the earth with a kinetic energy E. The minimum addition of kinetic energy needed to make it escape from its orbit is

    A) \[2E\]

    B) \[\sqrt{E}\]

    C) \[E/2\]

    D) \[\sqrt{E/2}\]

    E) \[E\]

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  • question_answer38) Eight drops of a liquid of density p and each of radius a are falling through air with a constant velocity\[3.75\,cm{{s}^{-1}}\]. When the eight drops coalesce to form a single drop the terminal velocity of the new drop will be

    A) \[1.5\times {{10}^{-2}}m{{s}^{-1}}\]

    B) \[2.4\times {{10}^{-2}}m{{s}^{-1}}\]

    C) \[0.75\times {{10}^{-2}}m{{s}^{-1}}\]

    D) \[25\times {{10}^{-2}}m{{s}^{-1}}\]

    E) \[15\times {{10}^{-2}}m{{s}^{-1}}\]

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  • question_answer39) If the volume of a block of aluminium is decreased by 1%, the pressure (stress) on its surface is increased by (Bulk modulus of \[Al=7.5\times {{10}^{10}}N{{m}^{-2}})\]

    A) \[7.5\times {{10}^{10}}N{{m}^{-2}}\]

    B) \[7.5\times {{10}^{8}}\text{ }N{{m}^{-2}}\]

    C) \[7.5\times {{10}^{6}}N{{m}^{-2}}\]

    D) \[7.5\times {{10}^{4}}N{{m}^{-2}}\]

    E) \[7.5\times {{10}^{2}}N{{m}^{-2}}\]

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  • question_answer40) The excess pressure inside one soap bubble is three times that inside a second soap bubble, then the ratio of their surface areas is

    A) \[1:9\]

    B) \[1:3\]

    C) \[3:1\]

    D) \[1:27\]

    E) \[9:1\]

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  • question_answer41) The area of cross-section of one limb of an U-tube is twice that of other. Both the limbs contain mercury at the same level. Water is poured in the wider tube so that mercury level in it goes down by 1 cm. The height of water column is (density of water\[={{10}^{3}}\,kg\,{{m}^{-3}},\]density of mercury \[=13.6\times {{10}^{3}}\] \[kg{{m}^{-3}}\])

    A) 13.6m

    B) 40.8m

    C) 27.2m

    D) 54.4m

    E) 6.8m

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  • question_answer42) A bubble of 8 mole of helium is submerged at a certain depth in water. The temperature of water increases by\[{{30}^{o}}C\]. How much heat is added approximately to helium during expansion?

    A) 4000 J

    B) 3000 J

    C) 3500 J

    D) 4500 J

    E) 5000J

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  • question_answer43) The plots of intensity of radiation versus wavelength of three black bodies at temperatures\[{{T}_{1}},{{T}_{2}}\]and\[{{T}_{3}}\]are shown. Then,

    A) \[{{T}_{3}}>{{T}_{2}}>{{T}_{1}}\]

    B) \[{{T}_{1}}>{{T}_{2}}>{{T}_{3}}\]

    C) \[{{T}_{2}}>{{T}_{3}}>{{T}_{1}}\]

    D) \[{{T}_{3}}>{{T}_{1}}>{{T}_{2}}\]

    E) \[{{T}_{3}}>{{T}_{1}}>{{T}_{2}}\]

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  • question_answer44) Three rods made of same material and having same cross-section are joined as shown in the figure. Each rod is of same length. The temperature at the junction of the three rods is

    A) \[{{45}^{o}}C\]

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

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

    D) \[{{20}^{o}}C\]

    E) \[{{60}^{o}}C\]

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  • question_answer45) The p-V diagram of a gas undergoing a cyclic process (ABCDA) is shown in the graph where P is in units of\[N{{m}^{-2}}\]and V in\[c{{m}^{3}}\]. Identify the incorrect statement.

    A) 0.4 J of work is done by the gas from A to B.

    B) 0.2 J of work is done on the gas from C and D.

    C) No work is done by the gas from B to C.

    D) Net work done by the gas in one cycle is 0.2 J.

    E) Work is done by the gas in going from B to C and on the gas from D to A.

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  • question_answer46) The period of a simple pendulum inside a stationary lift is T. The lift accelerates upwards with an acceleration of g/3. The time period of pendulum will be

    A) \[\sqrt{2}T\]

    B) \[\frac{T}{\sqrt{2}}\]

    C) \[\frac{\sqrt{3}}{2}T\]

    D) \[\frac{T}{3}\]

    E) \[\frac{2}{3}T\]

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  • question_answer47) The amplitude of SHM \[y=2(\sin 5\pi t+\sqrt{2}\cos \pi t)\]is

    A) 2

    B) \[2\sqrt{2}\]

    C) 4

    D) \[2\sqrt{3}\]

    E) \[4\sqrt{2}\]

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  • question_answer48) The total energy of a simple harmonic oscillator is proportional to

    A) square root of displacement

    B) velocity

    C) frequency

    D) amplitude

    E) square of the amplitude

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  • question_answer49) A sonometer wire 100 cm long has a fundamental frequency of 330 Hz. The velocity of propagation of transverse waves on the wire is

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

    B) \[660\text{ }m{{s}^{-1}}\]

    C) \[990\,m{{s}^{-1}}\]

    D) \[115\,m{{s}^{-1}}\]

    E) \[550\text{ }m{{s}^{-1}}\]

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  • question_answer50) A glass tube of length 1.0 m is completely filled with water. A vibrating tuning fork of frequency 500 Hz is kept over the mouth of the tube and the water is drained out slowly at the bottom of the tube. If velocity of sound in air is \[330\,m{{s}^{-1}},\] then the total number of resonances that occur will be

    A) 2

    B) 3

    C) 1

    D) 5

    E) 4

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  • question_answer51) A bus is moving with a velocity of 5 ms towards a huge wall. The driver sounds a horn of frequency 165 Hz. If the speed of sound in air is\[335\text{ }m{{s}^{-1}},\] the number of beats heard per second by a passenger inside the bus will be

    A) 3

    B) 4

    C) 5

    D) 6

    E) 7

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  • question_answer52) Two identical conducting spheres carrying different charges attract each other with a force F when placed in air medium at a distance d apart. The spheres are brought into contact and then taken to their original positions. Now the two spheres repel each other with a force whose magnitude is equal to that of the initial attractive force-The ratio between initial charges on the spheres is

    A) \[-(3+\sqrt{8})\]only

    B) \[-3+\sqrt{8}\]only

    C) \[-(3+\sqrt{8})\,or\ (-3+\sqrt{8})\]

    D) \[+\sqrt{3}\]

    E) \[-\sqrt{8}\]

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  • question_answer53) Small drops of the same size are charged to V volt each. If n such drops coalesce to form a single large drop, its potential will be

    A) \[Vn\]

    B) \[V/n\]

    C) \[V{{n}^{1/3}}\]

    D) \[V{{n}^{2/3}}\]

    E) \[V{{n}^{1/2}}\]

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  • question_answer54) A capacitor of capacitance value\[1\,\mu F\]is charged to 30 V and the battery is then disconnected. If the remaining circuit is connected across a\[2\,\mu F\]capacitor, the energy lost by the system is

    A) \[300\,\mu J\]

    B) \[450\,\mu J\]

    C) \[225\,\mu J\]

    D) \[245.0\,J\]

    E) \[100\,\mu J\]

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  • question_answer55) An electric dipole of length 1 cm is placed with the axis making an angle of\[{{30}^{o}}\]to an electric field of strength\[{{10}^{4}}N{{C}^{-1}}\]. If it experiences a torque of\[10\sqrt{2}Nm,\]the potential energy of the dipole is

    A) \[0.245\text{ }J\]

    B) \[2.45\times {{10}^{-4}}J\]

    C) \[0.0245\text{ }J\]

    D) \[245.0\text{ }J\]

    E) \[24.5\times {{10}^{-4}}J\]

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  • question_answer56) Three charges\[{{Q}_{0}},-q\]and\[-q\]are placed at the vertices of an isosceles right angle triangle as in the figure. The net electrostatic potential energy is zero if\[{{Q}_{0}}\]is equal to

    A) \[\frac{q}{4}\]

    B) \[\frac{2q}{\sqrt{32}}\]

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

    D) \[+q\]

    E) \[\frac{q}{\sqrt{2}}\]

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  • question_answer57) In the figure shown below, the terminal voltage across\[{{E}_{2}}\]is

    A) 12V

    B) 12.66V

    C) 11.34V

    D) 11.66V

    E) 12.33V

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  • question_answer58) The drift velocity of the electrons in a copper wire of length 2 m under the application of a potential difference of 220 V is\[0.5\text{ }m{{s}^{-1}}\]. Their mobility (in\[{{m}^{2}}{{V}^{-1}}{{s}^{-1}}\])

    A) \[2.5\times {{10}^{-3}}\]

    B) \[2.5\times {{10}^{-2}}\]

    C) \[5\times {{10}^{2}}\]

    D) \[5\times {{10}^{-3}}\]

    E) \[5\times {{10}^{-2}}\]

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  • question_answer59) When two resistances \[{{R}_{1}}\] and \[{{R}_{2}}\] are connected in series, they consume 12 W power. When they are connected in parallel, they consume 50 W power. What the ratio of the powers of\[{{R}_{1}}\]and\[{{R}_{2}}\]?

    A) 1/4

    B) 4

    C) 3/2

    D) 3

    E) 1

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  • question_answer60) In the circuit shown, if the resistance\[5\,\Omega \]develops a heat of 42 J per second, heat developed in 20 must be about (in\[J{{s}^{-1}}\])

    A) 25

    B) 20

    C) 30

    D) 35

    E) 40

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  • question_answer61) When a Daniel cell is connected in the secondary circuit of a potentiometer, the balancing length is found to be 540 cm. If the balancing length becomes 500 cm when the cell is short circuited with \[1\,\Omega ,\] the internal of the cell is

    A) \[0.08\,\Omega \]

    B) \[0.04\,\Omega \]

    C) \[1.0\,\Omega \]

    D) \[1.0\,8\,\Omega \]

    E) \[1.45\,\Omega \]

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  • question_answer62) Two particles of equal charges after being accelerated through the same potential difference enter a uniform transverse magnetic field and describe circular path of radii\[{{R}_{1}}\]and\[{{R}_{2}}\]respectively. Then the ratio of their masses\[({{M}_{1}}/{{M}_{2}})\]is

    A) \[\frac{{{R}_{1}}}{{{R}_{2}}}\]

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

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

    D) \[{{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{2}}\]

    E) \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{1/2}}\]

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  • question_answer63) Electromagnets are made of soft iron because soft iron has

    A) low susceptibility and low retentivity

    B) low susceptibility and high retentivity

    C) high permeability and low retentivity

    D) high permeability and high coercivity

    E) low permeability and low retentivity

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  • question_answer64) Which one of the following characteristics is not associated with a ferromagnetic material?

    A) It is strongly attracted by a magnet

    B) It tends to move from a region of strong magnetic field to a region of low magnetic field

    C) Its origin is the spin of electrons

    D) Above the Curie temperature, it exhibits paramagnetic properties

    E) Its magnetic susceptibility is large and positive

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  • question_answer65) The oscillating frequency of a cyclotron is 10 MHz. If the radius of its dees is 0.5 m, the kinetic energy of a proton, which is accelerated by the cyclotron is

    A) 10.2 MeV

    B) 2.55 MeV

    C) 20.4 MeV

    D) 5.1 MeV

    E) 1.5 MeV

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  • question_answer66) In a certain place, die horizontal component of magnetic field is\[\frac{1}{\sqrt{3}}\]times to vertical component. The angle of dip at this place is

    A) zero

    B) \[\pi /3\]

    C) \[\pi /2\]

    D) \[\pi /6\]

    E) \[\pi /4\]

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  • question_answer67) An alternating voltage\[e=200\text{ }sin\text{ }100t\]is applied to a series combination\[R=30\,\Omega \]and an inductor of 400 mH. The power factor of the circuit is

    A) 0.01

    B) 0.2

    C) 0.05

    D) 0.042

    E) 0.6

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  • question_answer68) The flux linked with a circuit is given by \[\phi ={{t}^{3}}+3t-7\]. The graph between time (\[x-\]axis) and induced emf (y-axis) will be a

    A) straight line through the origin

    B) straight line with positive intercept

    C) straight line with negative intercept

    D) parabola through the origin

    E) parabola not through the origin

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  • question_answer69) If the self-inductance of 500 turn coil is 125 mH, then the self-inductance of similar coil of 800 turns is

    A) 48.8 mH

    B) 200 mH

    C) 187.5 mH

    D) 320 mH

    E) 78.1 mH

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  • question_answer70) A resistor \[30\,\Omega ,\] inductor of reactance \[10\,\Omega \] and capacitor of reactance \[10\,\Omega \] are connected in series to an AC voltage source\[e=300\sqrt{2}\,sin(\omega t)\]. The current in the circuit is

    A) \[10\sqrt{2}A\]

    B) \[10\text{ }A\]

    C) \[30\sqrt{11}A\]

    D) \[30\sqrt{11}\text{ }A\]

    E) 5 A

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  • question_answer71) A plane electromagnetic wave travelling along the\[X-\]direction has a wavelength of 3 mm. The variation in the electric field occurs in the \[Y-\]direction with an amplitude\[66\,V{{m}^{-1}}\]. The equations for the electric and magnetic fields as a function of\[x\]and t are respectively.

    A) \[{{E}_{y}}=33\,\cos \pi \times {{10}^{11}}\left( t-\frac{x}{c} \right),\] \[{{B}_{z}}=1.1\times {{10}^{-7}}\cos \pi \times {{10}^{11}}\left( t-\frac{x}{c} \right)\]

    B) \[{{E}_{y}}=11\,\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right),\] \[{{B}_{y}}=11\times {{10}^{-7}}\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right)\]

    C) \[{{E}_{x}}=33\,\cos \pi \times {{10}^{11}}\left( t-\frac{x}{c} \right),\] \[{{B}_{x}}=11\times {{10}^{-7}}\cos \pi \times {{10}^{11}}\left( t-\frac{x}{c} \right)\]

    D) \[{{E}_{y}}=66\,\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right),\] \[{{B}_{z}}=2.2\times {{10}^{-7}}\cos 2\pi \times {{10}^{11}}\left( t-\frac{x}{c} \right)\]

    E) \[{{E}_{y}}=66\,\cos \pi \times {{10}^{11}}\left( t-\frac{x}{c} \right),\] \[{{B}_{y}}=2.2\times {{10}^{-7}}\,\cos \pi \times {{10}^{11}}\left( t-\frac{x}{c} \right)\]

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  • question_answer72) A plane electromagnetic wave travels in free space along \[x-\]axis. At a particular point in space, the electric field along y-axis is\[9.3\text{ }V{{m}^{-1}}\]. The magnetic induction is

    A) \[3.1\times {{10}^{-8}}T\]

    B) \[3\times {{10}^{-5}}T\]

    C) \[3\times {{10}^{-6}}T\]

    D) \[9.3\times {{10}^{-6}}T\]

    E) \[3.1\times {{10}^{-7}}T\]

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  • question_answer73) The reaction of\[CHC{{l}_{3}}\]and alcoholic\[KOH\]with p-toluidine gives

    A)

    B)

    C)

    D)

    E)

    View Answer play_arrow
  • question_answer74) The dihalogen derivative X of a hydrocarbon with three carbon atoms reacts with alcoholic KOH and produces another hydrocarbon which forms a red precipitate with ammoniacal\[C{{u}_{2}}C{{l}_{2}}\]. X gives an aldehyde on reaction with aqueous KOH. The compound Jf is

    A) 1, 3-dichloropropane

    B) 1, 2-dichloropropane

    C) 2, 2-dichloropropane

    D) 1, 1-dichloropropane

    E) 1, 3-dichloropropene

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  • question_answer75) An organic compound X with molecular formula,\[{{C}_{7}}{{H}_{8}}O\]is insoluble in aqueous \[NaHC{{O}_{3}}\]but dissolves in NaOH. When treated with bromine water X rapidly gives\[Y,{{C}_{7}}{{H}_{5}}OB{{r}_{3}}\]. The compounds X and V respectively, are

    A) benzyl alcohol and 2, 4, 6-tribromo-3- methoxy benzene

    B) benzyl alcohol and 2, 4, 6-tribromo-3-methyl phenol

    C) o-cresol and 3, 4, 5-tribromo-2-methyl phenol

    D) methoxybenzene and 2, 4, 6-tribromo-3- methoxy benzene

    E) m-cresol and 2, 4, 6-tribromo-3-methyl phenol

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  • question_answer76) The products obtained when benzyl phenyl ether is heated with HI in the mole ratio\[1:1\]are

    1. phenol
    2. benzyl alcohol
    3. benzyl iodide
    4. iodobenzene

    A) 1 and 3 only

    B) 3 and 4 only

    C) 1 and 4 only

    D) 2 and 4 only

    E) 2 and 3 only

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  • question_answer77) The product P in the reaction is

    A)

    B)

    C)

    D)

    E)

    View Answer play_arrow
  • question_answer78) The correct order of increasing basic nature of the following bases is

    1.
    2.
    3.
    4.
    5.

    A) \[2<5<1<3<4\]

    B) \[5<2<1<3<4\]

    C) \[2<5<1<4<3\]

    D) \[5<2<1<4<3\]

    E) \[2<5<4<3<1\]

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  • question_answer79) Which one of the following is a non-steroidal hormone?

    A) Estradiol

    B) Prostaglandin

    C) Progesterone

    D) Estrone

    E) Testosterone

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  • question_answer80) Which set of terms correctly identifies the carbohydrate shown?

    1. Pentose
    2. Hexose
    3. Aldose
    4. Ketose
    5. Pyranose
    6. Furanose

    A) 1, 3 and 6

    B) 1, 3, and 5

    C) 2, 3 and 5

    D) 2, 3 and 6

    E) 1, 4 and 6

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  • question_answer81) Which of the following is used as an oxidiser in rocket propellants?

    A) Alcohol

    B) Acrylic rubber

    C) Hydrazine

    D) Polyurethane

    E) Ammonium perchlorate

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  • question_answer82) Which among the following is not an antibiotic?

    A) Penicillin

    B) Oxytocin

    C) Erythromycin

    D) Tetracycline

    E) Ofloxacin

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  • question_answer83) \[MnO_{4}^{-}\] ions are reduced in acidic condition to \[M{{n}^{2+}}\]ions whereas they are reduced in neutral condition to\[Mn{{O}_{2}}\]. The oxidation of 25 mL of a solution X containing \[F{{e}^{2+}}\]ions required in acidic condition 20 mL of a solution Y containing\[Mn{{O}_{4}}\]ions. What volume of solution Y would be required to oxidise 25 mL of a solution X containing \[F{{e}^{2+}}\] ions in neutral condition?

    A) 11.4mL

    B) 12.0 mL

    C) 33.3 mL

    D) 35.0 mL

    E) 25.0 mL

    View Answer play_arrow
  • question_answer84) The percentage of an element M is 53 in its oxide of molecular formula \[{{M}_{2}}{{O}_{3}}\]. Its atomic mass is about

    A) 45

    B) 9

    C) 18

    D) 36

    E) 27

    View Answer play_arrow
  • question_answer85) The electronic configuration of the element with maximum electron affinity is

    A) \[1{{s}^{2}},\text{ }2{{s}^{2}},\text{ }2{{p}^{3}}\]

    B) \[1{{s}^{2}},\text{ }2{{s}^{2}},\text{ }2{{p}^{5}}\]

    C) \[1{{s}^{2}},\text{ }2{{s}^{2}},\text{ }2{{p}^{6}},\text{ }3{{s}^{2}},\text{ }3{{p}^{5}}\]

    D) \[1{{s}^{2}},\text{ }2{{s}^{2}},\text{ }2{{p}^{6}},\text{ }3{{s}^{2}},\text{ }3{{p}^{3}}\]

    E) \[1{{s}^{2}},\text{ }2{{s}^{2}},\text{ }2{{p}^{6}},\text{ }3{{s}^{1}}\]

    View Answer play_arrow
  • question_answer86) The incorrect statement/s among the following is/are

    I.\[NC{{l}_{5}}\]does not exist while\[PC{{l}_{5}}\]does
    II. Lead prefers to form tetravalent compounds
    III. The three\[CO\]bonds are not equal in the carbonate ion
    IV. Both\[O_{2}^{+}\]and\[NO\]are paramagnetic

    A) I, III and IV

    B) I and IV

    C) II and III

    D) I and III

    E) IV only

    View Answer play_arrow
  • question_answer87) A solid compound contains X, Y and Z atoms in a cubic lattice with X atom occupying the comers. Y atoms in the body centred positions and Z atoms at the centres of faces of the unit cell. What is the empirical formula of the compound?

    A) \[X{{Y}_{2}}{{Z}_{3}}\]

    B) \[XY{{Z}_{3}}\]

    C) \[{{X}_{2}}{{Y}_{2}}{{Z}_{3}}\]

    D) \[{{X}_{8}}Y{{Z}_{6}}\]

    E) \[XYZ\]

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  • question_answer88) \[KCl\]crystallises in the same type of lattice as does\[NaCl\]. Given that\[{{r}_{Na}}+/{{r}_{C{{l}^{-}}}}=0.55\]and\[{{r}_{{{K}^{+}}}}/{{r}_{C{{l}^{-}}}}=0.74\]. Calculate the ratio of the side of the unit cell for\[KCl\]to that of\[NaCl\].

    A) 1.123

    B) 0.0891

    C) 1.414

    D) 0.414

    E) 1.732

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  • question_answer89) The first ionisation energy of oxygen is less than that of nitrogen. Which of the following is the correct reason for this observation?

    A) Lesser effective nuclear charge of oxygen than nitrogen

    B) Lesser atomic size of oxygen than nitrogen

    C) Greater interelectron repulsion between two electrons in the same p-orbital counter balances the increase in effective nuclear charge on moving from nitrogen to oxygen

    D) Greater effective nuclear charge of oxygen than nitrogen

    E) Higher electronegativity of oxygen than Nitrogen

    View Answer play_arrow
  • question_answer90)

    Column - I Column - II
    (A) \[He\] (i) High electron affinity
    (B) \[Cl\] (ii) Most electropositive element
    (C) \[Ca\] (iii) Strongest reducing agent
    (D) \[Li\] (iv) Hishest lonisation energy
    The correct match of contents in Column I with those in Column II is

    A) A-iii, B-i, C-ii, D-iv

    B) A-iv, B-iii, C-ii, D-i

    C) A-ii, B-iv, C-i, D-iii

    D) A-i, B-ii, C-iii, D-iv

    E) A-iv, B-i, C-ii, D-iii

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  • question_answer91) Which pair of the following chlorides do not impart colour to the flame?

    A) \[BeC{{l}_{2}}\]and\[SrC{{l}_{2}}\]

    B) \[BeC{{l}_{2}}\]and \[MgC{{l}_{2}}\]

    C) \[CaC{{l}_{2}}\]and\[BaC{{l}_{2}}\]

    D) \[BaC{{l}_{2}}\]and \[SrC{{l}_{2}}\]

    E) \[MgC{{l}_{2}}\]and \[CaC{{l}_{2}}\]

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  • question_answer92) Sodium peroxide which is a yellow solid, when exposed to air becomes white due to the formation of

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

    B) \[N{{a}_{2}}O\]

    C) \[N{{a}_{2}}O\]and\[{{O}_{3}}\]

    D) \[NaOH\]and\[N{{a}_{2}}C{{O}_{3}}\]

    E) \[NaOH\]and\[{{H}_{2}}{{O}_{2}}\]

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  • question_answer93) Which one of the following reactions involves disproportionation?

    A) \[2{{H}_{2}}S{{O}_{4}}+Cu\xrightarrow{{}}CuS{{O}_{4}}+2{{H}_{2}}O+S{{O}_{2}}\]

    B) \[A{{s}_{2}}{{O}_{3}}+3{{H}_{2}}S\xrightarrow{{}}A{{s}_{2}}{{S}_{3}}+3{{H}_{2}}O\]

    C) \[2KOH+C{{l}_{2}}\xrightarrow{{}}KCl+KOCl+{{H}_{2}}O\]

    D) \[C{{a}_{3}}{{P}_{2}}+6{{H}_{2}}O\xrightarrow{{}}3Ca{{(OH)}_{2}}+2P{{H}_{3}}\]

    E) \[4N{{H}_{3}}+3{{O}_{2}}\xrightarrow{{}}2{{N}_{2}}+6{{H}_{2}}O\]

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  • question_answer94) The element evolving two different gases on reaction with cone sulphuric acid is

    A) \[P\]

    B) \[C\]

    C) \[Hg\]

    D) \[S\]

    E) \[Sn\]

    View Answer play_arrow
  • question_answer95) Which one of the following reactions will occur on heating \[AgN{{O}_{3}}\] above its melting point?

    A) \[2AgN{{O}_{3}}\xrightarrow[{}]{{}}2Ag+2N{{O}_{2}}+{{O}_{2}}\]

    B) \[2AgN{{O}_{3}}\xrightarrow[{}]{{}}2Ag+{{N}_{2}}+3{{O}_{2}}\]

    C) \[2AgN{{O}_{3}}\xrightarrow[{}]{{}}2AgN{{O}_{2}}+{{O}_{2}}\]

    D) \[2AgN{{O}_{3}}\xrightarrow[{}]{{}}2Ag+2NO+2{{O}_{2}}\]

    E) \[2AgN{{O}_{3}}\xrightarrow[{}]{{}}A{{g}_{2}}O+{{N}_{2}}{{O}_{3}}+{{O}_{2}}\]

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  • question_answer96) Pick out the correct statements from the following

    1. Cobalt (III) is more stable in octahedral complexes
    2. Zinc forms coloured ions or complexes
    3. Most of the d-block elements and their compounds are ferromagnetic
    4. Osmium shows (VIII) oxidation state
    5. Cobalt (II) is more stable in octahedral complexes

    A) 1 and 2

    B) 1 and 3

    C) 2 and 4

    D) 1 and 4

    E) 2 and 5

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  • question_answer97) Identify the nuclear reaction that differs from the rest.

    A) Positron emission

    B) \[K-\]capture

    C) \[\beta -\]decay

    D) \[\alpha -\]decay

    E) \[\gamma -\]decay

    View Answer play_arrow
  • question_answer98) Two radioactive elements X and Fhave half-lives of 6 min and 15 min respectively. An experiment starts with 8 times as many atoms of X as Y. How long it takes for the number of atoms of X left equals the number of atoms of Y left?

    A) 6 min

    B) 12 min

    C) 48 min

    D) 30 min

    E) 24 min

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  • question_answer99) Using the following thermochemical equations (i) \[S(rh)+3/2{{O}_{2}}(g)\xrightarrow[{}]{{}}S{{O}_{3}}(g)\] \[\Delta H=-2x\,kJ\,mo{{l}^{-1}}\] (ii) \[S{{O}_{2}}(g)+1/2{{O}_{2}}(g)\xrightarrow{{}}S{{O}_{3}}(g)\] \[\Delta H=-y\,kJ\,mo{{l}^{-1}}\] Find out the heat of formation of\[S{{O}_{2}}(g)\]in kJ\[mo{{l}^{-1}}\].

    A) \[(2x+y)\]

    B) \[(x+y)\]

    C) \[(2x/y)\]

    D) \[(y-2x)\]

    E) \[(2x-y)\]

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  • question_answer100) The lattice enthalpy and hydration enthalpy of four compounds are given below

    Compound Lattice enthalpy (in kJ \[mo{{l}^{-1}}\]) Hydration enthalpy (in kJ \[mo{{l}^{-1}}\])
    P +780 -920
    Q +1012 -812
    R +828 -878
    S +632 -600
    The pair of compounds which is soluble in water is

    A) P and Q

    B) Q and R

    C) R and S

    D) Q and S

    E) P and R

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  • question_answer101) 1.6 moles of\[PC{{l}_{5}}(g)\]is placed in\[4\text{ }d{{m}^{3}}\]closed vessel. When the temperature is raised to 500 K, it decomposes and at equilibrium 1.2 moles of\[PC{{l}_{5}}(g)\]remains. What is the\[{{K}_{c}}\]value for the decomposition of\[PC{{l}_{5}}(g)\]to\[PC{{l}_{3}}(g)\]and\[C{{l}_{2}}(g)\]at 500 K?

    A) 0.013

    B) 0.050

    C) 0.033

    D) 0.067

    E) 0.045

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  • question_answer102) For a concentrated solution of a weak electrolyte\[{{A}_{x}}{{B}_{y}}\]By of concentration C, the degree of dissociation\[\alpha \]is given as

    A) \[\alpha =\sqrt{{{K}_{eq}}/C(x+y)}\]

    B) \[\alpha =\sqrt{{{K}_{eq}}C/(xy)}\]

    C) \[\alpha ={{({{K}_{eq}}/{{C}^{x+y-1}}{{x}^{x}}{{y}^{y}})}^{1/(x+y)}}\]

    D) \[\alpha =({{K}_{eq}}/Cxy)\]

    E) \[\alpha =({{K}_{eq}}/{{C}^{xy}})\]

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  • question_answer103) The relative lowering of vapour pressure of an aqueous solution containing non-volatile solute is 0.0125. The molality of the solution is

    A) 0.70

    B) 0.50

    C) 0.60

    D) 0.80

    E) 0.40

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  • question_answer104) Two liquids X and Y form an ideal solution. The mixture has a vapour pressure of 400 mm at 300 K when mixed in the molar ratio of\[1:1\]and a vapour pressure of 350 mm when mixed in the molar ratio of\[1:2\]at the same temperature. The vapour pressures of the two pure liquids X and Y respectively are

    A) 250 mm, 550 mm

    B) 350 mm, 450 mm

    C) 350 mm, 700 mm

    D) 500 mm, 500 mm

    E) 550 mm, 250 mm

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  • question_answer105) In which of the following the oxidation number of oxygen has been arranged in increasing order?

    A) \[O{{F}_{2}}<K{{O}_{2}}<Ba{{O}_{2}}<{{O}_{3}}\]

    B) \[Ba{{O}_{2}}<K{{O}_{2}}<{{O}_{3}}<O{{F}_{2}}\]

    C) \[Ba{{O}_{2}}<{{O}_{3}}<O{{F}_{2}}<K{{O}_{2}}\]

    D) \[K{{O}_{2}}<O{{F}_{2}}<{{O}_{3}}<Ba{{O}_{2}}\]

    E) \[O{{F}_{2}}<{{O}_{3}}<K{{O}_{2}}<Ba{{O}_{2}}\]

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  • question_answer106) The pH of a solution obtained by mixing 50 mL of\[1\text{ }N\text{ }HCl\]and 30 mL of\[1\text{ }N\text{ }NaOH\]is [log 2.5 = 0.3979]

    A) 3.979

    B) 0.6021

    C) 12.042

    D) 1.2042

    E) 0.3979

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  • question_answer107) For a zero order reaction, the plot of concentration of reactant vs time is (intercept refers to concentration axis)

    A) linear with +ve slope and zero intercept

    B) linear with -ve slope and zero intercept

    C) linear with -ve slope and non-zero intercept

    D) linear with +ve slope and non-zero intercept

    E) a curve asymptotic to concentration axis

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  • question_answer108) For the two gaseous reactions, following data are given \[A\xrightarrow{{}}B;{{k}_{1}}={{10}^{10}}{{e}^{-20,000/T}}\] \[C\xrightarrow{{}}D;{{k}_{2}}={{10}^{12}}{{e}^{-24,606/T}}\] the temperature at which\[{{k}_{1}}\]becomes equal to \[{{k}_{2}}\]is

    A) 400 K

    B) 1000 K

    C) 800 K

    D) 1500 K

    E) 500 K

    View Answer play_arrow
  • question_answer109) Plot of\[log\text{ }x/m\]against log p is a straight line inclined at an angle of\[45{}^\circ \]. When the pressure is 0.5 arm and Freundlich parameter. \[k\]is 10, the amount of solute adsorbed per gram of adsorbent will be\[(log\text{ }5=0.6990)\]

    A) 1 g

    B) 2 g

    C) 3 g

    D) 5 g

    E) 2.5 g

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  • question_answer110) The number of moles of lead nitrate needed to coagulate 2 moles of colloidal\[[AgI]{{I}^{-}}\]is

    A) 2

    B) 1

    C) 1/2

    D) 2/3

    E) 5/2

    View Answer play_arrow
  • question_answer111) The primary and secondary valencies of chromium in the complex ion, dichlorodioxalatochromium (III), are respectively

    A) 3, 4

    B) 4, 3

    C) 3,6

    D) 6, 3

    E) 4, 4

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  • question_answer112) The two isomers X and Y with the formula \[Cr{{({{H}_{2}}O)}_{5}}ClB{{r}_{2}}\]were taken for experiment on depression in freezing point. It was found that one mole of X gave depression corresponding to 2 moles of particles and one mole of Y gave depression due to 3 moles of particles. The structural formulae of X and Y respectively are

    A) \[[Cr{{({{H}_{2}}O)}_{5}}Cl]B{{r}_{2}};[Cr{{({{H}_{2}}O)}_{4}}B{{r}_{2}}]Cl.{{H}_{2}}O\]

    B) \[[Cr{{({{H}_{2}}O)}_{5}}Cl]B{{r}_{2}};[Cr{{({{H}_{2}}O)}_{3}}ClB{{r}_{2}}.2{{H}_{2}}O]\]

    C) \[[Cr{{({{H}_{2}}O)}_{5}}Br]BrCl;[Cr{{({{H}_{2}}O)}_{4}}ClBr]Br.{{H}_{2}}O\]

    D) \[[Cr{{({{H}_{2}}O)}_{5}}Cl]B{{r}_{2}};[Cr{{({{H}_{2}}O)}_{4}}ClBr]Br.{{H}_{2}}O\]

    E) \[[Cr{{({{H}_{2}}O)}_{4}}B{{r}_{2}}]Cl.{{H}_{2}}O;[Cr{{({{H}_{2}}O)}_{5}}Cl]B{{r}_{2}}\]

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  • question_answer113) Which of the following process is suitable for the purification of aniline?

    A) Simple distillation

    B) Fractional distillation

    C) Fractional crystallisation

    D) Steam distillation

    E) Azeotropic distillation

    View Answer play_arrow
  • question_answer114) 0.1 mole of a carbohydrate with empirical formula \[C{{H}_{2}}O\] contains 1 g of hydrogen. What is its molecular formula?

    A) \[{{C}_{5}}{{H}_{10}}{{O}_{5}}\]

    B) \[{{C}_{6}}{{H}_{12}}{{O}_{6}}\]

    C) \[{{C}_{4}}{{H}_{8}}{{O}_{4}}\]

    D) \[{{C}_{3}}{{H}_{6}}{{O}_{3}}\]

    E) \[{{C}_{2}}{{H}_{4}}{{O}_{2}}\]

    View Answer play_arrow
  • question_answer115) Of the isomeric hexanes, the isomers that give the minimum and maximum number of monochloro derivatives are respectively

    A) 3-methylpentane and 2,3-dimethylbutane

    B) 2, 3-dimethylbutane and n-hexane

    C) 2, 2-dimethylbutane and 2-methylpentane

    D) 2, 3-dimethylbutane and 2-methylpentane

    E) (d) 2-methylpentane and 2, 2-dimethylbutane

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  • question_answer116) The reaction of with HBr gives predominantly

    A)

    B)

    C)

    D)

    E)

    View Answer play_arrow
  • question_answer117) Which one of the following carbanions is the least stable?

    A) \[C{{H}_{3}}CH_{2}^{-}\]

    B) \[HC\equiv {{C}^{-}}\]

    C) \[{{({{C}_{6}}{{H}_{5}})}_{3}}{{C}^{-}}\]

    D) \[CH_{3}^{-}\]

    E) \[{{(C{{H}_{3}})}_{3}}{{C}^{-}}\]

    View Answer play_arrow
  • question_answer118) An organic compound with molecular formula \[{{C}_{6}}{{H}_{12}}\]upon ozonolysis give only acetone as the product. The compound is

    A) 2, 3-dimethyl-1-butene

    B) 3-hexane

    C) 2-hexene

    D) 2, 3-dimethyl-2-butene

    E) 3-methyl-1-pentene

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  • question_answer119) Which one of the following compounds is capable of existing in a meso form?

    A) 3, 3-dibromopentane

    B) 4-bromo-2-pentanol

    C) 3-bromo-2-pentanol

    D) 2, 3-dibromopentane

    E) 2, 4-dibromopentane

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  • question_answer120) Acyclic stereoisomer having the molecular formula\[{{C}_{4}}{{H}_{7}}Cl\]are classified and tabulated. Find out the correct set of numbers.

    A)

    Geometrical Optical
    6 2

    B)

    Geometrical Optical
    4 2

    C)

    Geometrical Optical
    6 0

    D)

    Geometrical Optical
    4 0

    E)

    Geometrical Optical
    5 2

    View Answer play_arrow
  • question_answer121) Let n be the natural number. Then the range of the function\[f(n){{=}^{8-n}}{{p}_{n-4}},4\le n\le 6,\]is

    A) {1, 2, 3, 4}

    B) {1, 2, 3, 4, 5, 6}

    C) {1, 2, 3}

    D) {1, 2, 3, 4, 5}

    E) \[\phi \]

    View Answer play_arrow
  • question_answer122) If\[f(x)=ax+b\]and\[g(x)=cx+d,\]then\[f[g(x)]-g[f(x)]\]is equivalent to

    A) \[f(a)-g(c)\]

    B) \[f(c)+g(a)\]

    C) \[f(d)+g(b)\]

    D) \[f(b)-g(b)\]

    E) \[f(d)-g(b)\]

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  • question_answer123) Which one of the following functions is one-to-one?

    A) \[f(x)=\sin x,x\in [-\pi ,\pi ]\]

    B) \[f(x)=\sin x,x\in \left[ -\frac{3\pi }{2},-\frac{\pi }{4} \right]\]

    C) \[f(x)=\cos x,x\in \left[ -\frac{\pi }{2},\frac{\pi }{2} \right]\]

    D) \[f(x)=\cos x,x\in [\pi ,2\pi )\]

    E) \[f(x)=\cos x,x\in \left[ -\frac{\pi }{4},\frac{\pi }{4} \right]\]

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  • question_answer124) In a certain town 25% families own a cell phone, 15% families own a scooter and 65% families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is

    A) 10000

    B) 20000

    C) 30000

    D) 40000

    E) 50000

    View Answer play_arrow
  • question_answer125) If\[f(x)=\log \left( \frac{1+x}{1-x} \right),-1<x<1,\]then \[f\left( \frac{3x+{{x}^{3}}}{1+3{{x}^{2}}} \right)-f\left( \frac{2x}{1+{{x}^{2}}} \right)\]is

    A) \[{{[f(x)]}^{3}}\]

    B) \[{{[f(x)]}^{2}}\]

    C) \[-f(x)\]

    D) \[f(x)\]

    E) \[3f(x)\]

    View Answer play_arrow
  • question_answer126) Let\[{{a}_{n}}={{i}^{{{(n+1)}^{2}}}},\]where\[i=\sqrt{-1}\]and\[n=1,2,3.....\]. Then the value of\[{{a}_{1}}+{{a}_{3}}+{{a}_{5}}+...+{{a}_{25}}\]is

    A) 13

    B) \[13+i\]

    C) \[13-i\]

    D) 12

    E) \[12-i\]

    View Answer play_arrow
  • question_answer127) If\[\frac{5{{z}_{2}}}{11{{z}_{1}}}\]is purely imaginary, then the value of\[\left[ \frac{2{{z}_{1}}+3{{z}_{2}}}{2{{z}_{1}}-3{{z}_{2}}} \right]\]is

    A) \[\frac{37}{33}\]

    B) \[2\]

    C) 1

    D) \[3\]

    E) \[\frac{33}{37}\]

    View Answer play_arrow
  • question_answer128) If\[2\alpha =-1-i\sqrt{3}\]and\[2\beta =-1-i\sqrt{3},\]then\[5{{\alpha }^{4}}+5{{\beta }^{4}}+7{{\alpha }^{-1}}{{\beta }^{-1}}\]is equal to

    A) \[-1\]

    B) \[-2\]

    C) 0

    D) 1

    E) 2

    View Answer play_arrow
  • question_answer129) If\[\sqrt{x+iy}=\pm (a+ib),\]then\[\sqrt{-x-iy}\]is equal to

    A) \[\pm (b+ia)\]

    B) \[\pm (a-ib)\]

    C) \[(ai+b)\]

    D) \[\pm (b-ia)\]

    E) None of these

    View Answer play_arrow
  • question_answer130) If\[{{(\sqrt{5}+\sqrt{3}i)}^{33}}={{2}^{49}}z,\]then modulus of the complex number z is equal to

    A) 1

    B) \[\sqrt{2}\]

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

    D) 4

    E) 8

    View Answer play_arrow
  • question_answer131) If a is positive and if A and G are the arithmetic mean and the geometric mean of the roots of\[{{x}^{2}}-2ax+{{a}^{2}}=0\]respectively, then

    A) \[A=G\]

    B) \[A=2G\]

    C) \[2A=G\]

    D) \[{{A}^{2}}=G\]

    E) \[A={{G}^{2}}\]

    View Answer play_arrow
  • question_answer132) Suppose that two persons A and B solve the equation\[{{x}^{2}}+ax+b=0\]. While solving A commits a mistake in the coefficient of\[x\]was taken as 15 in place of-9 and finds the roots as \[-7\]and\[-2\]. Then, the equation is

    A) \[{{x}^{2}}+9x+14=0\]

    B) \[{{x}^{2}}-9x+14=0\]

    C) \[{{x}^{2}}+9x-14=0\]

    D) \[{{x}^{2}}-9x-14=0\]

    E) None of the above

    View Answer play_arrow
  • question_answer133) If\[{{x}^{2}}+2x+n>10\]for all real number\[x,\]then which of the following conditions is true?

    A) \[n<11\]

    B) \[n=10\]

    C) \[n=11\]

    D) \[n>11\]

    E) \[n<-11\]

    View Answer play_arrow
  • question_answer134) If\[\alpha ,\beta \]are the roots of the equation\[{{x}^{2}}+x+1=0,\]then the equation whose roots are\[{{\alpha }^{22}}\]and\[{{\beta }^{19}}\]is

    A) \[{{x}^{2}}-x+1=0\]

    B) \[{{x}^{2}}+x+1=0\]

    C) \[{{x}^{2}}+x-1=0\]

    D) \[{{x}^{2}}-x-1=0\]

    E) \[2{{x}^{2}}+x+1=0\]

    View Answer play_arrow
  • question_answer135) If\[\sec \theta \]and\[\tan \theta \]are the roots of \[a{{x}^{2}}+bx+c=0;\]\[(a,b\ne 0)\]then the value of\[\sec \theta -\tan \theta \]is

    A) \[-\frac{a}{b}\]

    B) \[\frac{\sqrt{{{b}^{2}}-4ac}}{a}\]

    C) \[1-\frac{a}{b}\]

    D) \[1+\frac{{{a}^{2}}}{{{b}^{2}}}\]

    E) \[\frac{a}{b}\]

    View Answer play_arrow
  • question_answer136) If the sum of 12th and 22nd terms of an AP is 100, then the sum of the first 33 terms of the AP is

    A) 1700

    B) 1650

    C) 3300

    D) 3400

    E) 3500

    View Answer play_arrow
  • question_answer137) The coefficient of x in the expansion of\[(14+x)(1+2x)(1+3x)....(1+100x)\]is

    A) 5050

    B) 10100

    C) 5151

    D) 4950

    E) 1100

    View Answer play_arrow
  • question_answer138) Let a, b, c be in AP. If \[0<a,b,c<1,x=\sum\limits_{n=0}^{\infty }{{{a}^{n}}},\] \[y=\sum\limits_{n=0}^{\infty }{{{b}^{n}}}\]and\[z=\sum\limits_{n=0}^{\infty }{{{c}^{n}}},\]then

    A) \[2y=x+z\]

    B) \[2x=y+z\]

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

    D) \[2xz=xy+yz\]

    E) \[z=\frac{2xy}{x+y}\]

    View Answer play_arrow
  • question_answer139) The sum of the first n terms of the series \[\frac{1}{\sqrt{2}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{11}}+.....\]is

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

    B) \[\sqrt{3n+2}-\sqrt{2}\]

    C) \[\sqrt{3n+2}+\sqrt{2}\]

    D) \[\frac{1}{3}(\sqrt{2}-\sqrt{3m+2})\]

    E) \[\frac{1}{3}(\sqrt{3n+2}+\sqrt{2})\]

    View Answer play_arrow
  • question_answer140) The HM of two numbers is 4. Their AM is A and GM is G. If\[2A+{{G}^{2}}=27,\]then A is equal to

    A) 9

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

    C) 18

    D) 27

    E) 15

    View Answer play_arrow
  • question_answer141) The coefficient of\[{{x}^{101}}\]in\[1+\frac{(a-bx)}{1!}+\frac{{{(q-bx)}^{2}}}{2!}+....\]is equal to

    A) \[\frac{{{e}^{a}}{{b}^{101}}}{101!}\]

    B) \[\frac{-{{e}^{a}}{{b}^{100}}}{100!}\]

    C) \[\frac{{{e}^{a}}b}{101!}\]

    D) \[\frac{-{{e}^{a}}{{b}^{101}}}{101!}\]

    E) \[\frac{{{e}^{a}}{{b}^{100}}}{101!}\]

    View Answer play_arrow
  • question_answer142) The value of \[lo{{g}^{2}}20\text{ }lo{{g}^{2}}80-lo{{g}^{2}}5\text{ }lo{{g}^{2}}320\]is equal to

    A) 5

    B) 6

    C) 7

    D) 8

    E) 10

    View Answer play_arrow
  • question_answer143) The sum of the series\[lo{{g}_{9}}3+lo{{g}_{27}}3-lo{{g}_{81}}3+lo{{g}_{243}}3-.....\]is

    A) \[1-lo{{g}_{e}}2\]

    B) \[1+lo{{g}_{e}}2\]

    C) \[lo{{g}_{e}}2\]

    D) \[lo{{g}_{e}}3\]

    E) \[1+lo{{g}_{e}}3\]

    View Answer play_arrow
  • question_answer144) The number of ways in which 5 ladies and 7 gentlemen can be seated in a round table so that no two ladies sit together, is

    A) \[\frac{7}{2}{{(720)}^{2}}\]

    B) \[7{{(360)}^{2}}\]

    C) \[7{{(720)}^{2}}\]

    D) \[720\]

    E) \[360\]

    View Answer play_arrow
  • question_answer145) The number of four-letter words that can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R, is

    A) \[\frac{11!}{2!2!2!}\]

    B) \[59\]

    C) \[56\]

    D) \[\frac{11!}{3!2!2!}\]

    E) \[\frac{11!}{3!3!2!}\]

    View Answer play_arrow
  • question_answer146) All the words that can be formed using alphabets A, H, L, U, R are written as in a dictionary (no alphabet is repeated). Then, the rank of the word RAHUL is

    A) 70

    B) 71

    C) 72

    D) 73

    E) 74

    View Answer play_arrow
  • question_answer147) The coefficient of\[{{a}^{5}}{{b}^{6}}{{c}^{7}}\]in the expansion of\[{{(be+ca+ab)}^{9}}\]is

    A) 100

    B) 120

    C) 720

    D) 1260

    E) 1440

    View Answer play_arrow
  • question_answer148) The value\[{{(}^{7}}{{C}_{0}}{{+}^{7}}{{C}_{1}})+{{(}^{7}}{{C}_{1}}{{+}^{7}}{{C}_{2}})+....\]\[+{{(}^{7}}{{C}_{6}}{{+}^{7}}{{C}_{7}})\]is

    A) \[{{2}^{8}}-1\]

    B) \[{{2}^{8}}+1\]

    C) \[28\]

    D) \[1-{{2}^{8}}\]

    E) \[{{2}^{8}}-2\]

    View Answer play_arrow
  • question_answer149) If the expansion of\[{{\left( \frac{3\sqrt{x}}{7}-\frac{5}{2x\sqrt{x}} \right)}^{13n}}\]contains a term independent of\[x\]in the 14th term, then n should be

    A) 10

    B) 5

    C) 6

    D) 4

    E) 11

    View Answer play_arrow
  • question_answer150) If the matrix M, is given by \[{{M}_{r}}=\left[ \begin{matrix} r & r-1 \\ r-1 & r \\ \end{matrix} \right],r=1,2,3,....,\]then the value of\[\det ({{M}_{1}})+\det ({{M}_{2}})+....+\det ({{M}_{2008}})\] is

    A) 2007

    B) 2008

    C) \[{{(2008)}^{2}}\]

    D) \[{{(2007)}^{2}}\]

    E) \[2009\]

    View Answer play_arrow
  • question_answer151) Let\[A=\left[ \begin{matrix} {{\alpha }^{2}} & 5 \\ 5 & -\alpha \\ \end{matrix} \right]\]and\[|{{A}^{10}}\text{ }\!\!|\!\!\text{ }=1024,\]then a is equal to

    A) 2

    B) \[-2\]

    C) 3

    D) \[-3\]

    E) \[-5\]

    View Answer play_arrow
  • question_answer152) If \[\omega \ne 1\]is a cube root of unity, then the value of \[\left| \begin{matrix}    1+2{{\omega }^{100}}+{{\omega }^{200}}  \\    1  \\    \omega   \\ \end{matrix}\begin{matrix}    {{\omega }^{2}}  \\    1+{{\omega }^{100}}+2{{\omega }^{200}}  \\    {{\omega }^{2}}  \\ \end{matrix}\begin{matrix}    1  \\    \omega   \\    1+{{\omega }^{100}}+2{{\omega }^{200}}  \\ \end{matrix} \right|\] is equal to

    A) \[0\]                                    

    B) \[1\]                    

    C) \[\omega \]                      

    D) \[{{\omega }^{2}}\]

    E) \[1+\omega \]

    View Answer play_arrow
  • question_answer153) If\[\alpha \]is a cube root of unity, then the value of \[\left| \begin{matrix} \alpha & {{\alpha }^{3}} & {{\alpha }^{5}} \\ {{\alpha }^{3}} & {{\alpha }^{5}} & \alpha \\ {{\alpha }^{5}} & \alpha & {{\alpha }^{3}} \\ \end{matrix} \right|\]is equal to

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

    B) \[3({{\alpha }^{3}}+{{\alpha }^{6}}+{{\alpha }^{9}})\]

    C) \[3(\alpha +{{\alpha }^{2}}+{{\alpha }^{3}})\]

    D) \[3{{\alpha }^{4}}\]

    E) \[0\]

    View Answer play_arrow
  • question_answer154) If\[f(\alpha )=\left| \begin{matrix} 1 & \alpha & {{\alpha }^{2}} \\ \alpha & {{\alpha }^{2}} & 1 \\ {{\alpha }^{2}} & 1 & \alpha \\ \end{matrix} \right|,\]then\[f(\sqrt[3]{3})\]is equal to

    A) 1

    B) \[-4\]

    C) 4

    D) 2

    E) \[-2\]

    View Answer play_arrow
  • question_answer155) If\[A=\left| \begin{matrix} 3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3 \\ \end{matrix} \right|,\]then\[{{A}^{4}}\]is equal to

    A) 27 A

    B) 81 A

    C) 243 A

    D) 729 A

    E) 3 A

    View Answer play_arrow
  • question_answer156) Suppose a, b and c are real numbers such that\[\frac{a}{b}>1\]and\[\frac{a}{c}<0\]. Which one of the following is true?

    A) \[a+b-c>0\]

    B) \[a>b\]

    C) \[(a-c)(b-c)>0\]

    D) \[a+b+c>0\]

    E) \[abc>0\]

    View Answer play_arrow
  • question_answer157) The set of admissible values of\[x\]such that\[\frac{2x+3}{2x-9}<0\]is

    A) \[\left( -\infty ,-\frac{3}{2} \right)\cup \left( \frac{9}{2},\infty \right)\]

    B) \[(-\infty ,0)\cup \left( \frac{9}{2},\infty \right)\]

    C) \[\left( -\frac{3}{2},0 \right)\]

    D) \[\left( 0,\frac{9}{2} \right)\]

    E) \[\left( -\frac{3}{2},\frac{9}{2} \right)\]

    View Answer play_arrow
  • question_answer158) Let p be the statement Ravi races and let q be the statement Ravi wins. Then, the verbal translation of\[\tilde{\ }(p\vee (\tilde{\ }q))\]is

    A) Ravi does not race and Ravi does not win

    B) It is not true that Ravi races and that Ravi does not win

    C) Ravi does not race of Ravi wins

    D) It is not true that Ravi races or that Ravi does not win

    E) It is not true that Ravi does not race and Ravi does not win

    View Answer play_arrow
  • question_answer159) Let B be a boolean algebra. If\[a,b\in B,\]then\[(x.y)\]equal to

    A) \[a.b\]

    B) \[x.y\]

    C) \[x.y\]

    D) \[(x-y)\]

    E) \[x+y\]

    View Answer play_arrow
  • question_answer160) The output of the circuit is

    A) \[{{x}_{3}}.(x_{1}^{}+{{x}_{2}})\]

    B) \[(x_{3}^{}+{{x}_{2}}).{{x}_{1}}\]

    C) \[x_{3}^{}({{x}_{1}}+{{x}_{2}})\]

    D) \[({{x}_{1}}+{{x}_{2}}).{{x}_{3}}\]

    E) \[(x_{1}^{}\,+x_{2}^{}).{{x}_{3}}\]

    View Answer play_arrow
  • question_answer161) If\[\sin \theta =\sin 15{}^\circ +\sin 45{}^\circ ,\]where\[0{}^\circ <\theta <90{}^\circ ,\] then\[\theta \]is equal to

    A) \[45{}^\circ \]

    B) \[54{}^\circ \]

    C) \[60{}^\circ \]

    D) \[72{}^\circ \]

    E) \[75{}^\circ \]

    View Answer play_arrow
  • question_answer162) If \[{{({{\tan }^{-1}}x)}^{2}}+{{({{\cot }^{-1}}x)}^{2}}=\frac{5{{\pi }^{2}}}{8},\]then\[x\]is equal to

    A) 0

    B) 2

    C) 1

    D) \[-1\]

    E) \[2\sqrt{2}\]

    View Answer play_arrow
  • question_answer163) If O is at the origin, OA is along the negative\[x-\]axis and\[(-40,9)\]is point on OB, then the value of \[\sin \,\angle AOB\] is

    A) 5/16

    B) 9/40

    C) 9/41

    D) 19/41

    E) None of these

    View Answer play_arrow
  • question_answer164) If\[x=h+a\text{ }sec\theta \]and\[y=k+b\text{ }cosec\theta \]. Then

    A) \[\frac{{{a}^{2}}}{{{(x+h)}^{2}}}-\frac{{{b}^{2}}}{{{(y+k)}^{2}}}=1\]

    B) \[\frac{{{a}^{2}}}{{{(x-h)}^{2}}}+\frac{{{b}^{2}}}{{{(y-k)}^{2}}}=1\]

    C) \[\frac{{{(x-h)}^{2}}}{{{a}^{2}}}+\frac{{{(y-k)}^{2}}}{{{b}^{2}}}=1\]

    D) \[\frac{{{(x-h)}^{2}}}{{{a}^{2}}}-\frac{{{(y-k)}^{2}}}{{{b}^{2}}}=1\]

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

    View Answer play_arrow
  • question_answer165) \[5{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)+7{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)\]\[-4{{\tan }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)-{{\tan }^{-1}}x=5\pi ,\]then\[x\]is equal to

    A) 3

    B) \[-\sqrt{3}\]

    C) \[\sqrt{2}\]

    D) \[2\]

    E) \[\sqrt{3}\]

    View Answer play_arrow
  • question_answer166) If\[cos\alpha +cos\beta =0=sin\alpha +sin\beta ,\]then\[cos2\alpha +\] \[cos2\beta \]is equal to

    A) \[-2\sin (\alpha +\beta )\]

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

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

    D) \[-2\cos (\alpha +\beta )\]

    E) \[-2\cos (\alpha -\beta )\]

    View Answer play_arrow
  • question_answer167) In an equilateral triangle of side\[2\sqrt{3},\]the circumradius is

    A) 1 cm

    B) \[\sqrt{3}cm\]

    C) 2 cm

    D) \[2\sqrt{3}cm\]

    E) 4cm

    View Answer play_arrow
  • question_answer168) The area of the triangle whose sides are 6, 5, \[\sqrt{13}\](in square units) is

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

    B) 9

    C) \[6\sqrt{2}\]

    D) 11

    E) \[13\]

    View Answer play_arrow
  • question_answer169) In a triangle ABC,\[\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}.\]If\[a=\frac{1}{\sqrt{6}},\]then the area of the triangle (in square units) is

    A) 1/24

    B) \[\sqrt{3}/24\]

    C) 1/8

    D) \[1/\sqrt{3}\]

    E) \[5/12\sqrt{3}\]

    View Answer play_arrow
  • question_answer170) In\[\Delta ABC,a=13cm,b=12cm\]and\[c=5cm\]Then the distance of A from BC is

    A) \[\frac{\sqrt{3}+1}{3\sqrt{3}}cm\]

    B) \[\frac{60}{13}cm\]

    C) \[\frac{65}{12}cm\]

    D) \[\frac{144}{13}cm\]

    E) \[\frac{65}{13}cm\]

    View Answer play_arrow
  • question_answer171) In any triangle\[ABC,\text{ }{{c}^{2}}sin\text{ }2B+{{b}^{2}}sin\text{ }2C\]is equal to

    A) \[\frac{\Delta }{2}\]

    B) \[\Delta \]

    C) \[2\Delta \]

    D) \[3\Delta \]

    E) \[4\Delta \]

    View Answer play_arrow
  • question_answer172) A flagpole stands on a building of height 450 ft and an observer on a level ground is 300 ft from the base of the building. The angle of elevation of the bottom of the flagpole is\[30{}^\circ \]and the height of the flagpole is 50 ft. If\[\theta \]is the angle of elevation of the top of the flagpole, then\[\tan \theta \]is equal to

    A) \[\frac{4}{3\sqrt{3}}\]

    B) \[\frac{\sqrt{3}}{2}\]

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

    D) \[\frac{\sqrt{3}}{5}\]

    E) \[\frac{4\sqrt{3}+1}{6}\]

    View Answer play_arrow
  • question_answer173) If A (0, 0), B (12, 0), C (12, 2), D (6, 7) and E (0, 5) are the vertices of the pentagon ABCDE, then its area in square units, is

    A) 58

    B) 60

    C) 61

    D) 62

    E) 63

    View Answer play_arrow
  • question_answer174) If the line segment joining the points P (a, b) and Q (c, d) subtends an angle \[\theta \] at the origin, then the value of\[\cos \theta \]is

    A) \[\frac{ab+cd}{\sqrt{{{a}^{2}}+{{b}^{2}}}\sqrt{{{c}^{2}}+{{d}^{2}}}}\]

    B) \[\frac{ab}{\sqrt{{{a}^{2}}+{{b}^{2}}}}+\frac{bd}{\sqrt{{{c}^{2}}+{{d}^{2}}}}\]

    C) \[\frac{ac+bd}{\sqrt{{{a}^{2}}+{{b}^{2}}}\sqrt{{{c}^{2}}+{{d}^{2}}}}\]

    D) \[\frac{ab-cd}{\sqrt{{{a}^{2}}+{{b}^{2}}}\sqrt{{{c}^{2}}+{{d}^{2}}}}\]

    E) \[\frac{ab-cd}{\sqrt{{{a}^{2}}+{{b}^{2}}}\sqrt{{{c}^{2}}+{{d}^{2}}}}\]

    View Answer play_arrow
  • question_answer175) The equation of a line through the point (1, 2) whose distance from the point (3, 1) has the greatest value, is

    A) \[y=2x\]

    B) \[y=x+1\]

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

    D) \[y=3x-1\]

    E) \[y=x+7\]

    View Answer play_arrow
  • question_answer176) If a line with y-intercept 2, is perpendicular to the line\[3x-2y=6,\]then its\[x-\]intercept is

    A) 1

    B) 2

    C) \[-4\]

    D) 4

    E) 3

    View Answer play_arrow
  • question_answer177) If the lines \[ax+ky+10=0,\text{ }bx+(k+1)y+10=0\]and \[cx+(k+2)y+10=0\]are concurrent, then

    A) a, b, c are in GP

    B) a, b, care in HP

    C) a, b, c are in AP

    D) \[{{(a+b)}^{2}}=c\]

    E) \[a+b=c\]

    View Answer play_arrow
  • question_answer178) The lines\[(a+2b)x+(a-3b)y=a-b\]for different values of a and b pass through the fixed point whose coordinates are

    A) \[\left( \frac{2}{5},\frac{2}{5} \right)\]

    B) \[\left( \frac{3}{5},\frac{3}{5} \right)\]

    C) \[\left( \frac{1}{5},\frac{1}{5} \right)\]

    D) \[\left( \frac{3}{5},\frac{2}{5} \right)\]

    E) \[\left( \frac{2}{5},\frac{3}{5} \right)\]

    View Answer play_arrow
  • question_answer179) A line passes through the point of intersection of the lines\[100x+50y-1=0\]and\[75x+25y+\] \[3=0\]and makes equal intercepts on the axes. Its equation is

    A) \[25x+25y-1=0\]

    B) \[5x-5y+3=0\]

    C) \[25x+25y-4=0\]

    D) \[25x-25y+6=0\]

    E) \[5x-5y+7=0\]

    View Answer play_arrow
  • question_answer180) The circumcentre of the triangle with vertices (0, 30), (4, 0) and (30, 0) is

    A) (10, 10)

    B) (10, 12)

    C) (12, 12)

    D) (15, 15)

    E) (17, 17)

    View Answer play_arrow
  • question_answer181) The image of the centre of the circle\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]with respect to the mirror \[x+y=1\]is

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

    B) \[(\sqrt{2},\sqrt{2})\]

    C) \[(\sqrt{2},2\sqrt{2})\]

    D) \[(-\sqrt{2},2)\]

    E) None of these

    View Answer play_arrow
  • question_answer182) If\[(3,-2)\]is the centre of a circle and\[4x+3y+19=0\]is a tangent to the circle, then the equation of the circle is

    A) \[{{x}^{2}}+{{y}^{2}}-6x+4y+25=0\]

    B) \[{{x}^{2}}+{{y}^{2}}-6x+4y+12=0\]

    C) \[{{x}^{2}}+{{y}^{2}}-6x+4y-12=0\]

    D) \[{{x}^{2}}+{{y}^{2}}-6x+4y+13=0\]

    E) \[{{x}^{2}}+{{y}^{2}}-6x+4y+9=0\]

    View Answer play_arrow
  • question_answer183) The circles\[{{x}^{2}}+{{y}^{2}}-4x-6y-12=0\]and \[{{x}^{2}}+{{y}^{2}}+4x+6y+4=0\]

    A) touch externally

    B) do not intersect

    C) touch internally

    D) intersect at two points

    E) are concentric

    View Answer play_arrow
  • question_answer184) A conic section is defined by the equations\[x=-1+\sec t,\text{ }y=2+3\text{ }tan\text{ }t\]. The coordinates of the foci are

    A) \[(-1-\sqrt{10},2)\]and \[(-1+\sqrt{10},2)\]

    B) \[(-1-\sqrt{8},2)\]and \[(-1+\sqrt{8},2)\]

    C) \[(-1,2-\sqrt{8})\]and \[(-1,2+\sqrt{8})\]

    D) \[(-1,2-\sqrt{10})\]and \[(-1,2+\sqrt{10})\]

    E) \[(\sqrt{10},0)\]and \[(-\sqrt{10},0)\]

    View Answer play_arrow
  • question_answer185) If the foci of the ellipse\[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{16}=1\]are\[(0,\sqrt{7})\]and\[(0,-\sqrt{7}),\]then the foci of the ellipse\[\frac{{{x}^{2}}}{9+{{t}^{2}}}+\frac{{{y}^{2}}}{16+{{t}^{2}}}=1\,t\in R,\]

    A) \[(0,\sqrt{7}),(0,-\sqrt{7})\]

    B) \[(0,7),(0,7)\]

    C) \[(0,\,2\sqrt{7}),\,(0,\,-2\sqrt{7})\]

    D) \[(\sqrt{7},0),(-\sqrt{7},0)\]

    E) \[(\sqrt{7},2\sqrt{7}),(\sqrt{7},-2\sqrt{7})\]

    View Answer play_arrow
  • question_answer186) If the lines joining the foci of the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}\,+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\] where\[a>b,\]and an extremly of its minor axis are inclined at an angle\[60{}^\circ ,\]then the eccentricity of the ellipse is

    A) \[-\frac{\sqrt{3}}{2}\]

    B) \[\frac{1}{2}\]

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

    D) \[\frac{\sqrt{7}}{3}\]

    E) \[\sqrt{3}\]

    View Answer play_arrow
  • question_answer187) Equation of the directrix of the conic \[{{x}^{2}}+4y+4=0\]is

    A) \[y=1\]

    B) \[y=-1\]

    C) \[y=0\]

    D) \[x=0\]

    E) \[x=1\]

    View Answer play_arrow
  • question_answer188) If\[\overrightarrow{a},\overrightarrow{b}\]and\[\overrightarrow{c}\]are position vectors of the vertices of the triangle ABC, then\[\frac{\left| \left( \overrightarrow{a}-\overrightarrow{c} \right)\times \left( \overrightarrow{b}-\overrightarrow{a} \right) \right|}{\left( \overrightarrow{c}-\overrightarrow{a} \right).\left( \overrightarrow{b}-\overrightarrow{a} \right)}\]is equal to

    A) \[cot\text{ }A\]

    B) \[cot\,C\]

    C) \[-tanC\]

    D) \[tan\,C\]

    E) \[tan\text{ }A\]

    View Answer play_arrow
  • question_answer189) If\[\overrightarrow{a}\]is a vector of magnitude 50, collinear with the vector\[\overrightarrow{b}=6\hat{i}-8\hat{j}-\frac{15}{2}\hat{k}\]and makes an acute angle with the positive direction of\[z-\]axis, then a is equal to

    A) \[-24\hat{i}+32\hat{j}+30\hat{k}\]

    B) \[24\hat{i}-32\hat{j}-30\hat{k}\]

    C) \[12\hat{i}-16\hat{j}-15\hat{k}\]

    D) \[-12\hat{i}+16\hat{j}-15\hat{k}\]

    E) None of the above

    View Answer play_arrow
  • question_answer190) If the volume of a parallelepiped with \[\overrightarrow{a}\times \overrightarrow{b},\text{ }\overrightarrow{b}\times \overrightarrow{c},\text{ }\overrightarrow{c}\times \overrightarrow{a}\] as cotermmus edges is\[9\text{ }cu\]units, then the volume of the parallelepiped with \[(a\times b)\times (b\times c),(b\times c)\times (c\times a),\] \[(c\times a)\times (a\times b)\]as coterminus edges is

    A) 9 cu unit

    B) 729 cu unit

    C) 81 cu unit

    D) 27 cu unit

    E) 243 cu unit

    View Answer play_arrow
  • question_answer191) If the constant forces\[2\hat{i}-5\hat{j}+6\hat{k}\]and \[-\hat{i}+2\hat{j}-\hat{k}\]act on a particle due to which it is displaced from a point\[A(4,-3,-2)\]to a point B \[(6,1,-3),\]then the work done by the forces is

    A) 10 unit

    B) \[-10\]unit

    C) 9 unit

    D) \[-9\]unit

    E) None of the above

    View Answer play_arrow
  • question_answer192) If\[\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{c}\times \overrightarrow{d}\]and\[\overrightarrow{a}\times \overrightarrow{c}=\overrightarrow{b}\times \overrightarrow{d},\]then

    A) \[(\overrightarrow{a}-\overrightarrow{d})=\lambda (\overrightarrow{b}-\overrightarrow{c})\]

    B) \[(\overrightarrow{a}+\overrightarrow{d})=\lambda (\overrightarrow{b}+\overrightarrow{c})\]

    C) \[(\overrightarrow{a}-\overrightarrow{d})=\lambda (\overrightarrow{c}+\overrightarrow{d})\]

    D) \[(\overrightarrow{a}+\overrightarrow{d})=\lambda (\overrightarrow{c}-\overrightarrow{d})\]

    E) None of the above

    View Answer play_arrow
  • question_answer193) A unit vector in\[xy-\]plane makes an angle of \[45{}^\circ \]with the vector\[\hat{i}+\hat{j}\]and an angle of\[60{}^\circ \]with the vector\[3\hat{i}-4\hat{j},\]is

    A) \[\hat{i}\]

    B) \[\frac{\hat{i}+\hat{j}}{\sqrt{2}}\]

    C) \[\frac{\hat{i}-\hat{j}}{\sqrt{2}}\]

    D) \[\frac{2\hat{i}-\hat{j}}{\sqrt{2}}\]

    E) None of these

    View Answer play_arrow
  • question_answer194) Let a, b, c be distinct non-negative numbers. If the vector\[a\hat{i}+a\hat{j}+c\hat{k},\text{ }\hat{i}+\hat{k}\]and\[c\hat{i}+c\hat{j}+b\hat{k}\] lies in a plane, then c is

    A) the GM of a and b

    B) the AM of a and b

    C) the HM of a and b

    D) equal to zero

    E) None of the above

    View Answer play_arrow
  • question_answer195) The equation of the plane perpendicular to the line\[\frac{x-1}{1}=\frac{y-2}{-1}=\frac{z+1}{2}\]and passing through the point (2, 3, 1) is

    A) \[\overrightarrow{r}.(\hat{i}+\hat{j}+2\hat{k})=1\]

    B) \[\overrightarrow{r}.(\hat{i}-\hat{j}+2\hat{k})=1\]

    C) \[\overrightarrow{r}.(\hat{i}-\hat{j}+2\hat{k})=7\]

    D) \[\overrightarrow{r}.(\hat{i}+\hat{j}-2\hat{k})=10\]

    E) None of the above

    View Answer play_arrow
  • question_answer196) The coordinates of the foot of the perpendicular drawn from the point A (1, 0, 3) to the join of the points B (4, 7, 1) and C (3, 5, 3) are

    A) \[\left( \frac{5}{3},\frac{7}{3},\frac{17}{3} \right)\]

    B) \[(5,7,17)\]

    C) \[\left( \frac{5}{7},-\frac{7}{3},\frac{17}{3} \right)\]

    D) \[\left( -\frac{5}{3},\frac{7}{3},-\frac{17}{3} \right)\]

    E) None of these

    View Answer play_arrow
  • question_answer197) If a line makes angles\[\alpha ,\beta ,\gamma \]and \[\delta \] with four diagonals of a cube, then the value of \[si{{n}^{2}}\alpha +si{{n}^{2}}\beta +si{{n}^{2}}\gamma +si{{n}^{2}}\delta \]is

    A) \[\frac{4}{3}\]

    B) \[\frac{8}{3}\]

    C) \[\frac{7}{3}\]

    D) \[1\]

    E) None of these

    View Answer play_arrow
  • question_answer198) If the planes\[\overrightarrow{r}.(2\hat{i}-\lambda \hat{j}+3\hat{k})=0\]and\[\overrightarrow{r}.(\lambda \hat{i}+5\hat{j}-\hat{k})=0\]are perpendicular to each other, then the value of\[{{\lambda }^{2}}+\lambda \]is

    A) 0

    B) 2

    C) 1

    D) 3

    E) 4

    View Answer play_arrow
  • question_answer199) The Cartesian form of the plane\[\overrightarrow{r}=(s-2t)\hat{i}+(3-t)\hat{j}+(2s+t)\hat{k}\]is

    A) \[2x-5y-z-15=0\]

    B) \[2x-5y+z-15=0\]

    C) \[2x-5y-z+15=0\]

    D) \[2x+5y-z+15=0\]

    E) \[2x+5y+z+15=0\]

    View Answer play_arrow
  • question_answer200) Let\[P(-7,1,-5)\]be a point on a plane and let\[O\]be the origin. If OP is normal to the plane, then the equation of the plane is

    A) \[7x-y+5z+75=0\]

    B) \[7x+y-5z+73=0\]

    C) \[7x+y+5z+73=0\]

    D) \[7x-y-5z+75=0\]

    E) \[7x-y-5z+73=0\]

    View Answer play_arrow
  • question_answer201) The shortest distance from the plane \[12x+4y+3z=327\]to the sphere\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\]\[+4x-2y-6z=155\]is

    A) 26

    B) \[11\frac{4}{13}\]

    C) 13

    D) 39

    E) None of these

    View Answer play_arrow
  • question_answer202) The point in the\[xy-\]plane which is equidistant from the point (2, 0, 3), (0, 3, 2) and (0, 0, 1)is

    A) \[(1,2,3)\]

    B) \[(-3,2,0)\]

    C) \[(3,-2,0)\]

    D) \[(3,2,0)\]

    E) \[(3,2,1)\]

    View Answer play_arrow
  • question_answer203) The average of the four-digit numbers that can be formed using each of the digits 3, 5, 7 and 9 exactly once in each number is

    A) 4444

    B) 5555

    C) 6666

    D) 7777

    E) 8888

    View Answer play_arrow
  • question_answer204) If A and B are any two events, then\[P(A\cap B)\]is equal to

    A) \[P(A)+P(B)\]

    B) \[P(A)P(B)\]

    C) \[P(B)-P(A\cap B)\]

    D) \[P(A)-P(A\cap B)\]

    E) \[1-P(A\cap B)\]

    View Answer play_arrow
  • question_answer205) A die has four blank faces and two faces marked 3. The chance of getting a total of 12 in 5 throws is

    A) \[^{5}{{C}_{4}}{{\left( \frac{1}{3} \right)}^{4}}\left( \frac{2}{3} \right)\]

    B) \[^{5}{{C}_{4}}\left( \frac{1}{3} \right){{\left( \frac{2}{3} \right)}^{4}}\]

    C) \[^{5}{{C}_{4}}{{\left( \frac{1}{6} \right)}^{5}}\]

    D) \[^{5}{{C}_{4}}{{\left( \frac{1}{6} \right)}^{4}}\left( \frac{5}{6} \right)\]

    E) \[^{5}{{C}_{4}}{{\left( \frac{5}{6} \right)}^{4}}\left( \frac{1}{6} \right)\]

    View Answer play_arrow
  • question_answer206) The standard deviation for the scores 1, 2, 3, 4, 5, 6 and 7 is 2. Then, the standard deviation of 12, 23, 34, 45, 56, 67 and 78 is

    A) 2

    B) 4

    C) 22

    D) 11

    E) 44

    View Answer play_arrow
  • question_answer207) \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{2x-1}{\sqrt{{{x}^{2}}+2x+1}}\]is equal to

    A) 2

    B) \[-2\]

    C) 1

    D) \[-1\]

    E) 0

    View Answer play_arrow
  • question_answer208) If\[f(x)=\left\{ \begin{matrix} \frac{x-1}{2{{x}^{2}}-7x+5}, & for\,x\ne 1 \\ -\frac{1}{3}, & for\,x=1 \\ \end{matrix} \right.\], then\[f(1)\]is equal to

    A) \[-\frac{1}{9}\]

    B) \[-\frac{2}{9}\]

    C) \[-13\]

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

    E) None of these

    View Answer play_arrow
  • question_answer209) If\[f(x)=\left\{ \begin{matrix} \frac{1-\cos x}{x}, & x\ne 0 \\ k, & x=0 \\ \end{matrix} \right.\]is continuous at\[x=0,\]then the value of\[k\]is

    A) \[0\]

    B) \[1/2\]

    C) \[\frac{1}{4}\]

    D) \[-\frac{1}{2}\]

    E) None of these

    View Answer play_arrow
  • question_answer210) If\[f(1)=1,f(1)=2,\]then\[\underset{x\to 1}{\mathop{\lim }}\,\frac{\sqrt{f(x)}-1}{\sqrt{x}-1}\]is

    A) 2

    B) 4

    C) 1

    D) 1/2

    E) 3

    View Answer play_arrow
  • question_answer211) Let\[f(x)=\sin x,g(x)={{x}^{2}}\]and\[h(x)={{\log }_{e}}x\]. If\[f(x)=(hogof)(x),\]then\[f(x)\]is equal to

    A) \[a\cos e{{c}^{3}}x\]

    B) \[a\cot {{x}^{2}}-4{{x}^{2}}\cos e{{c}^{2}}{{x}^{2}}\]

    C) \[2x\cot {{x}^{2}}\]

    D) \[-2\cos e{{c}^{2}}x\]

    E) \[4\cos e{{c}^{2}}x\]

    View Answer play_arrow
  • question_answer212) If\[y={{\tan }^{-1}}\left( \frac{4x}{1+5{{x}^{2}}} \right)+{{\tan }^{-1}}\left( \frac{2+3x}{3-2x} \right),\]then\[\frac{dy}{dx}\]is equal to

    A) \[\frac{5}{1+25{{x}^{2}}}\]

    B) \[\frac{1}{1+25{{x}^{2}}}\]

    C) \[0\]

    D) \[\frac{5}{1-25{{x}^{2}}}\]

    E) None of these

    View Answer play_arrow
  • question_answer213) If\[y={{\log }_{a}}x+{{\log }_{x}}+a+{{\log }_{x}}x+{{\log }_{a}}a,\]then \[\frac{dy}{dx}\]is equal to

    A) \[\frac{1}{x}+x\log a\]

    B) \[\frac{\log a}{x}+\frac{x}{\log a}\]

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

    D) \[x\log a\]

    E) None of the above

    View Answer play_arrow
  • question_answer214) If \[y={{\sin }^{-1}}(3x-4{{x}^{3}})+{{\cos }^{-1}}(4{{x}^{3}}-3x)\] \[+{{\tan }^{-1}}(E),\]then\[\frac{dy}{dx}\]is equal to

    A) \[5\]

    B) \[0\]

    C) \[\frac{2}{\sqrt{1+{{x}^{2}}}}\]

    D) \[\frac{2}{\sqrt{1-{{x}^{2}}}}\]

    E) \[\frac{2}{\sqrt{1-{{x}^{2}}}}\]

    View Answer play_arrow
  • question_answer215) If\[f(x)=\frac{x-1}{4}+\frac{{{(x-1)}^{3}}}{12}+\frac{{{(x-1)}^{5}}}{20}\]\[+\frac{{{(x-1)}^{7}}}{28}+....,\]where\[0<x<2,\]then\[f(x)\]is equal to

    A) \[\frac{1}{4x(2-x)}\]

    B) \[\frac{1}{4{{(x-2)}^{2}}}\]

    C) \[\frac{1}{2-x}\]

    D) \[\frac{1}{2+x}\]

    E) \[\frac{1}{{{(x-4)}^{2}}}\]

    View Answer play_arrow
  • question_answer216) If\[f(x)=\sin x,\]the derivative of\[f(\log x)\]w.r.t. \[x\]is

    A) \[\cos x\]

    B) \[f(\log x)\]

    C) \[\cos (\log x)\]

    D) \[\frac{\cos (\log x)}{x}\]

    E) \[\frac{\cos (\log x)}{2x}\]

    View Answer play_arrow
  • question_answer217) If\[f(x+y)=2f(x)f(y),f(5)=1024(\log 2)\]and\[f(2)=8,\]then the value of\[f(3)\]is

    A) \[64(log\text{ }2)\]

    B) \[128\text{ }(log\text{ }2)\]

    C) 256

    D) \[256\text{ }(log\text{ }2)\]

    E) \[1024(log\text{ }2)\]

    View Answer play_arrow
  • question_answer218) Gas is being pumped into a spherical balloon at the rate of\[30\text{ }f{{t}^{3}}/min\]. Then, the rate at which the radius increases when it reaches the value 15ft is

    A) \[\frac{1}{15\pi }ft/\min \]

    B) \[\frac{1}{30\pi }ft/\min \]

    C) \[\frac{1}{20}ft/\min \]

    D) \[\frac{1}{25}ft/\min \]

    E) None of these

    View Answer play_arrow
  • question_answer219) The area of the triangle formed by the coordinate axes and the normal to the curve \[y={{e}^{2x}}+{{x}^{2}}\]at the point

    A) (0, 1) is \[0\]

    B) \[1\,sq\,unit\]

    C) \[\frac{1}{2}\,sq\,unit\]

    D) \[2\,sq\,unit\]

    E) \[4\,sq\,unit\]

    View Answer play_arrow
  • question_answer220) A point on curve\[x{{y}^{2}}=1\]which is at minimum distance from the origin is

    A) (1, 1)

    B) (1/4, 2)

    C) \[({{2}^{1/6}},{{2}^{-1/3}})\]

    D) \[({{2}^{-1/3}},{{2}^{1/6}})\]

    E) None of the above

    View Answer play_arrow
  • question_answer221) A spherical iron ball of radius 10 cm, coated with a layer of ice of uniform thickness, melts at a rate of\[100\,\pi \,c{{m}^{3}}/min\]. The rate at which the thickness of decreases when the thickness of ice is 5 cm, is

    A) 1 cm/min

    B) 2 cm/min

    C) \[\frac{1}{376}cm/min\]

    D) 5 cm/min

    E) 3 cm/min

    View Answer play_arrow
  • question_answer222) If\[a{{x}^{2}}+bx+4\]attains its minimum value\[-1\]at \[x=1,\]then the values of a and b are respectively

    A) \[5,-10\]

    B) \[5,-5\]

    C) 5, 5

    D) \[10,-5\]

    E) 10, 10

    View Answer play_arrow
  • question_answer223) The function\[f(x={{(9-{{x}^{2}})}^{2}}\]increases in

    A) \[(-3,0)\cup (3,\infty )\]

    B) \[(-\infty ,-3)\cup (3,\infty )\]

    C) \[(-\infty ,-3)\cup (0,3)\]

    D) \[(-3,3)\]

    E) \[(3,\infty )\]

    View Answer play_arrow
  • question_answer224) Let\[g(x)=\left\{ \begin{matrix} 2e, & if\,x\le 1 \\ \log (x-1), & if\,x>1 \\ \end{matrix} \right..\]The equation of the normal to\[y=g(x)\]at the point ( 3, log 2), is

    A) \[y-2x=6+log\text{ }2\]

    B) \[y+2x=6+log2\]

    C) \[y+2x=6-log\text{ }2\]

    D) \[y+2x=-6+log\text{ }2\]

    E) \[y-2x=-6+log\text{ }2\]

    View Answer play_arrow
  • question_answer225) \[\int{\frac{\sec x\cos ecx}{2\cot x-\sec x\cos ecx}}dx\]is equal to

    A) \[\log |\sec x+\tan x|+c\]

    B) \[\log |\sec x+\cos ecx|+c\]

    C) \[\frac{1}{2}\log |\sec 2x+\tan 2x|+c\]

    D) \[\log |\sec 2x+\cos ec2x|+c\]

    E) \[\log |\sec 2x\,\cos ec2x|+c\]

    View Answer play_arrow
  • question_answer226) If\[\int_{0}^{a}{f(2a-x)dx}=\mu \]and\[\int_{0}^{a}{f(x)dx}=\lambda ,\]then \[\int_{0}^{2a}{f(2a-x)dx}\]equals

    A) \[2\lambda -\mu \]

    B) \[\lambda +\mu \]

    C) \[\mu -\lambda \]

    D) \[\lambda -2\mu \]

    E) None of the above

    View Answer play_arrow
  • question_answer227) \[\int{\tan ({{\sin }^{-1}}x)}dx\]is equal to

    A) \[\frac{1}{\sqrt{1-{{x}^{2}}}}+c\]

    B) \[\sqrt{1-{{x}^{2}}}+c\]

    C) \[\frac{-x}{\sqrt{1-{{x}^{2}}}}+c\]

    D) \[\frac{x}{\sqrt{1-{{x}^{2}}}}+c\]

    E) \[-\sqrt{1-{{x}^{2}}}+c\]

    View Answer play_arrow
  • question_answer228) \[{{\int{(\sin x-\cos x)}}^{4}}(\sin x+\cos x)dx\]is equal to

    A) \[\frac{\sin x-\cos x}{5}+c\]

    B) \[\frac{{{(\sin x-\cos x)}^{5}}}{5}+c\]

    C) \[\frac{{{(\sin x-\cos x)}^{4}}}{4}+c\]

    D) \[\frac{{{(\sin x+\cos x)}^{5}}}{5}+c\]

    E) None of the above

    View Answer play_arrow
  • question_answer229) \[\int{{{e}^{\sin \theta }}[\log \sin \theta +\cos e{{c}^{2}}\theta ]}\cos \theta d\theta \] is equal to

    A) \[\int{{{e}^{\sin \theta }}[\log \sin \theta +\cos e{{c}^{2}}\theta ]}+c\]

    B) \[{{e}^{\sin \theta }}[\log \sin \theta +\cos ec\theta ]+c\]

    C) \[{{e}^{\sin \theta }}[\log \sin \theta -\cos ec\theta ]+c\]

    D) \[{{e}^{\sin \theta }}[\log \sin \theta -\cos e{{c}^{2}}\theta ]+c\]

    E) \[{{e}^{\sin \theta }}[\log \sin \theta +{{\cos }^{2}}\theta ]+c\]

    View Answer play_arrow
  • question_answer230) \[\int{{{e}^{3\log x}}{{({{x}^{4}}+1)}^{-1}}}dx\]is equal to

    A) \[{{e}^{3\log x}}+c\]

    B) \[\frac{1}{4}\log ({{x}^{4}}+1)+c\]

    C) \[\log ({{x}^{4}}+1)+c\]

    D) \[\frac{1}{2}\log ({{x}^{4}}+1)+c\]

    E) \[\frac{{{x}^{4}}}{{{x}^{4}}+1}+c\]

    View Answer play_arrow
  • question_answer231) If\[\int_{0}^{\lambda }{xf(\sin x)}dx=A\int_{0}^{\pi /2}{f(\sin x)}dx,\]then A is equal to

    A) \[0\]

    B) \[\pi \]

    C) \[\frac{\pi }{4}\]

    D) \[2\pi \]

    E) \[3\pi \]

    View Answer play_arrow
  • question_answer232) \[\int_{-2}^{2}{|[x]|}dx\]is equal to

    A) 1

    B) 2

    C) 3

    D) 4

    E) 5

    View Answer play_arrow
  • question_answer233) If\[\int{\frac{\sin x}{\sin (x-\alpha )}}dx=Ax+B\log \sin (x-\alpha )+C,\] then the value of\[A-B\]at\[\alpha =\frac{\pi }{2}\]is

    A) \[-1\]

    B) 1

    C) 2

    D) 0

    E) \[-2\]

    View Answer play_arrow
  • question_answer234) The area bounded by\[y={{\sin }^{-1}}x,x=\frac{1}{\sqrt{2}}\]and \[x-\]axis is

    A) \[\left( \frac{1}{\sqrt{2}}+1 \right)sq\,unit\]

    B) \[\left( 1-\frac{1}{\sqrt{2}} \right)sq\,unit\]

    C) \[\frac{\pi }{4\sqrt{2}}sq\,unit\]

    D) \[\left( \frac{\pi }{4\sqrt{2}}+\frac{1}{\sqrt{2}}-1 \right)sq\text{ }unit\]

    E) None of the above

    View Answer play_arrow
  • question_answer235) If\[x\text{ }dy=y(dx+y\text{ }dy),y(1)=1\]and\[y(x)>0,\]then\[y(-3)\]is equal to

    A) 3

    B) 2

    C) 1

    D) 0

    E) \[-1\]

    View Answer play_arrow
  • question_answer236) If\[\int_{a}^{b}{{{x}^{3}}}dx=0\]and\[\int_{a}^{b}{{{x}^{2}}}dx=\frac{2}{3},\]then the values of a and b are respectively

    A) \[1,-1\]

    B) \[-1,1\]

    C) \[1,1\]

    D) \[-1,-1\]

    E) \[1,0\]

    View Answer play_arrow
  • question_answer237) The differential equation representing the family of curves\[{{y}^{2}}=2c(x+{{c}^{3}}),\]where c is a positive parameter, is of

    A) order 1, degree 1

    B) order 1, degree 2

    C) order 1, degree 3

    D) order 1, degree 4

    E) order 2, degree 1

    View Answer play_arrow
  • question_answer238) The differential equation representing the family of curves\[y=x{{e}^{cx}}\](c is a constant) is

    A) \[\frac{dy}{dx}=\frac{y}{x}\left( 1-\log \frac{y}{x} \right)\]

    B) \[\frac{dy}{dx}=\frac{y}{x}\log \left( \frac{y}{x} \right)+1\]

    C) \[\frac{dy}{dx}=\frac{y}{x}\left( 1+\log \frac{y}{x} \right)\]

    D) \[\frac{dy}{dx}+1=\frac{y}{x}\log \left( \frac{y}{x} \right)\]

    E) \[\frac{dy}{dx}=\frac{x}{y}\left( 1+\log \frac{y}{x} \right)\]

    View Answer play_arrow
  • question_answer239) The solution of \[\frac{dy}{dx}=1+y+{{y}^{2}}+x+xy+x{{y}^{2}}\]is

    A) \[{{\tan }^{-1}}\left( \frac{2y+1}{\sqrt{3}} \right)=x+{{x}^{2}}+c\]

    B) \[4{{\tan }^{-1}}\left( \frac{2y+1}{\sqrt{3}} \right)=x+{{x}^{2}}+c\]

    C) \[\sqrt{3}{{\tan }^{-1}}\left( \frac{3y+1}{3} \right)=4(1+x+{{x}^{2}})+c\]

    D) \[{{\tan }^{-1}}\left( \frac{2y+1}{3} \right)=4(2x+{{x}^{2}})+c\]

    E) \[4{{\tan }^{-1}}\left( \frac{2y+1}{\sqrt{3}} \right)=\sqrt{3}(2x+{{x}^{2}})+c\]

    View Answer play_arrow
  • question_answer240) The integrating factor of the differential equation \[\frac{dy}{dx}+\frac{y}{(1-x)\sqrt{x}}=1-\sqrt{x}\]is

    A) \[\frac{1-\sqrt{x}}{1+\sqrt{x}}\]

    B) \[\frac{1+\sqrt{x}}{1-\sqrt{x}}\]

    C) \[\frac{1-x}{1+x}\]

    D) \[\frac{\sqrt{x}}{1-\sqrt{x}}\]

    E) \[\frac{\sqrt{x}}{1+\sqrt{x}}\]

    View Answer play_arrow

   



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