question_answer1) Which of the following is a true statement?
A) The total entropy of thermally interacting systems is conserved
B) Carnot engine has 100% efficiency
C) Total entropy does not change in a reversible process
D) Total entropy in an irreversible process can either increase or decrease
View Answer play_arrowquestion_answer2) Which of the following is not related to the Bernoulli's principle?
A) Rise of a liquid column inside a capillary
B) Operation of a venturimeter
C) Lift provided to an aeroplane by the air
D) Propelling force provided to an aeroplane by its propellers
View Answer play_arrowquestion_answer3) A steel wire can support a maximum load of w before reaching its elastic limit. How much load can another wire, made out of identical steel, but with a radius one half the radius of the first wire, support before reaching its elastic limit?
A) \[w\]
B) \[\frac{w}{2}\]
C) \[\frac{w}{4}\]
D) \[4\,w\]
View Answer play_arrowquestion_answer4) Which of the following laws of thermodynamics forms the basis for the definition of temperature?
A) First law
B) Zeroth law
C) Second law
D) Third law
View Answer play_arrowquestion_answer5) The air pressure inside a soap bubble of radius R exceeds the outside air pressure by\[10\text{ }Pa\]. By how much will the pressure inside a bubble of radius 2R exceed the outside air pressure?
A) \[20\text{ }Pa\]
B) \[40\text{ }Pa\]
C) \[2.5\text{ }Pa\]
D) \[5\text{ }Pa\]
View Answer play_arrowquestion_answer6) Taking the radius of the earth to be \[6400\text{ }km,\] by what percentage will the acceleration due to gravity at a height of \[100\text{ }km\]from the surface of the earth differ from that on the surface of the earth?
A) About 1.5%
B) About 5%
C) About 8%
D) About 3%
View Answer play_arrowquestion_answer7) Which of the following statements is true for the three types of magnetism - para, dia and ferro?
A) Paramagnetism is associated with negative susceptibility and dia and ferromagnetism with positive susceptibility
B) Diamagnetism is generally weakest of the Three and is associated with negative susceptibility
C) Ferromagnetism is the strongest of the three and is associated with negative susceptibility
D) All three are associated with positive susceptibility, diamagnetism is the weakest form of magnetism and ferromagnetism is the strongest form
View Answer play_arrowquestion_answer8) The molecules in an ideal gas at \[{{27}^{o}}C\]have a certain mean velocity. At what approximate temperature, will the mean velocity be doubled?
A) \[{{54}^{o}}C\]
B) \[{{327}^{o}}C\]
C) \[{{1200}^{o}}C\]
D) \[{{927}^{o}}C\]
View Answer play_arrowquestion_answer9) Which of the two
(i) Compressing a gas isothermally until its volume is reduced by half |
(ii) Compressing the same gas adiabatically until its volume is reduced by half, require more work to be done? |
A) (i)
B) (ii)
C) Both will require the same amount of work
D) It will depend upon the nature of the gas
View Answer play_arrowquestion_answer10) Three coplanar, parallel, long straight wires are equally spaced, that is, the distance between each pair of successive wires is the same. The first and the third wire carry currents of 1 A each, in the same direction. What must be the current in the second wire (wire in the middle), so that the other two wires do not feel any net force?
A) \[0.25\text{ }A\]in opposite direction to those in the first and the third
B) \[0.5\text{ }A\]in the same direction as those in the first and the third
C) \[0.5\text{ }A\]in the opposite direction to those in the first and the third
D) \[0.25\text{ }A\]in the same direction as those in the first and the third
View Answer play_arrowquestion_answer11) A conducting rod of length L is moving in a uniform magnetic field with a velocity v without rotation. The velocity of the rod is perpendicular to the rod, and the motion of the rod is confined to a plane perpendicular to the magnetic field. What is the induced emf developed across the rod?
A) \[BLv\]
B) \[B{{v}^{2}}L\]
C) \[\frac{BL}{v}\]
D) \[B{{L}^{2}}v\]
View Answer play_arrowquestion_answer12) What is the resonance frequency of a driven L-C-R oscillator?
A) \[\frac{1}{LC}\]
B) \[\frac{1}{2\pi LC}\]
C) \[{{(LC)}^{-1/2}}\]
D) \[{{(2\pi LC)}^{-1/2}}\]
View Answer play_arrowquestion_answer13) A bar magnet is placed upright on a floor (so that the axis of the magnet is vertical). A copper ring is held above the magnet, with its plane horizontal and released. The copper ring falls in such a manner that its axis always coincides with that of the magnet. What will be the acceleration with which the ring will fall? Acceleration due to gravity is \[10m/{{s}^{2}}\].
A) \[10m/{{s}^{2}}\]
B) Less than \[10m/{{s}^{2}}\]
C) More than \[10m/{{s}^{2}}\]
D) the answer will depend upon which pole of the magnet is up
View Answer play_arrowquestion_answer14) A short solenoid of radius a, number of turns per unit length \[{{n}_{1}}\] and length L is kept coaxially inside a very long solenoid of radius b, number of turns per unit length\[{{n}_{2}}\]. What is the mutual inductance of the system?
A) \[{{\mu }_{0}}\pi {{b}^{2}}{{n}_{1}}{{n}_{2}}L\]
B) \[{{\mu }_{0}}\pi {{a}^{2}}{{n}_{1}}{{n}_{2}}{{L}^{2}}\]
C) \[{{\mu }_{0}}\pi {{a}^{2}}{{n}_{1}}{{n}_{2}}L\]
D) \[{{\mu }_{0}}\pi {{b}^{2}}{{n}_{1}}{{n}_{2}}{{L}^{2}}\]
View Answer play_arrowquestion_answer15) Which of the following is a semiconductor?
A) \[F{{e}_{2}}{{O}_{3}}\]
B) \[Si{{O}_{2}}\]
C) \[GaAs\]
D) \[CuO\]
View Answer play_arrowquestion_answer16) What is the order of the reverse saturation current before break down in a Zener diode?
A) Ampere
B) Milli-ampere
C) It depends on the applied voltage
D) Micro-ampere
View Answer play_arrowquestion_answer17) Which logic gate does the following truth table represent?
Input A | Input B | Output Q |
0 | 0 | 1 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 1 |
A) NAND
B) AND
C) OR
D) NOR
View Answer play_arrowquestion_answer18) What is the equivalent expression of the decimal number 212 in binary number system?
A) \[11000100\]
B) \[10010100\]
C) \[11010100\]
D) \[11010110\]
View Answer play_arrowquestion_answer19) Why do we need carrier wave of high frequency to transmit audio signal over long distances?
A) High frequency carrier wave can propagate with a faster speed
B) High frequency carrier waves offer availability of higher transmission bandwidth
C) High frequency carrier waves offer availability of lower transmission bandwidth
D) High frequency carrier waves is easy to produce
View Answer play_arrowquestion_answer20) What does the Pointing vector represent?
A) Power flowing across unit area in an electromagnetic field
B) Charge flowing across unit area per unit time in an electromagnetic field
C) Momentum flowing across unit area per unit time in an electromagnetic field
D) Angular momentum flowing across unit area per unit time in an electromagnetic field
View Answer play_arrowquestion_answer21) In television transmission what type of modulation is used?
A) Only amplitude modulation
B) Only frequency modulation
C) Both amplitude and frequency modulation
D) TV signal does not need any kind of modulation
View Answer play_arrowquestion_answer22) Which of the following is true for any collision?
A) Both linear momentum and kinetic energy are conserved
B) Neither linear momentum nor kinetic energy may be conserved
C) Linear momentum is always conserved, however, kinetic energy may or may not be conserved
D) Kinetic energy is always conserved, but linear momentum may or may not be conserved
View Answer play_arrowquestion_answer23) A uniform rod of length L and mass M is held vertical, with its bottom end pivoted to the floor. The rod falls under gravity, freely turning about the pivot. If acceleration due to gravity is g, what is the instantaneous angular speed of the rod when it makes an angle \[{{60}^{o}}\] with the vertical?
A) \[{{\left( \frac{g}{L} \right)}^{1/2}}\]
B) \[{{\left( \frac{3g}{4L} \right)}^{1/2}}\]
C) \[{{\left( \frac{3\sqrt{3}g}{2L} \right)}^{1/2}}\]
D) \[{{\left( \frac{3g}{2L} \right)}^{1/2}}\]
View Answer play_arrowquestion_answer24) A cheetah, weighing \[150\text{ }kg,\] chases a deer, weighing \[30\text{ }kg,\] in a straight path. The speed of the cheetah is \[20\text{ }m/s\]and that of the deer is\[25\text{ }m/s\]. The approximate speed of the centre of mass of the pair is
A) \[21\text{ }m/s\]
B) \[24\text{ }m/s\]
C) \[26\text{ }m/s\]
D) zero
View Answer play_arrowquestion_answer25) A tennis racket can be idealized as a uniform ring of mass M and radius R, attached to a uniform rod also of mass M and length L. The rod and the ring are coplanar and the line of the rod passes through the centre of the ring. The moment of inertia of the object (racket) about an axis through the centre of the ring and perpendicular to its plane is
A) \[\frac{1}{2}M(6{{R}^{2}}+{{L}^{2}})\]
B) \[\frac{1}{12}M(18{{R}^{2}}+{{L}^{2}})\]
C) \[\frac{1}{3}M(6{{R}^{2}}+{{L}^{2}}+3LR)\]
D) None of the above
View Answer play_arrowquestion_answer26) How long will a satellite, placed in a circular orbit of radius that is \[{{\left( \frac{1}{4} \right)}^{th}}\] the radius of a geostationary satellite, take to complete one revolution around the earth?
A) \[12\text{ }h\]
B) \[\text{6 }h\]
C) \[3\text{ }h\]
D) \[4\text{ }days\]
View Answer play_arrowquestion_answer27) A rocket is fired from inside a deep mine, so as to escape the earth's gravitational field. The minimum velocity to be rocket is
A) exactly the same as the escape velocity of fire from the earth's surface
B) a little more than the escape velocity of fire from the earth's surface
C) a little less than the escape velocity of fire from the earth's surface
D) infinity
View Answer play_arrowquestion_answer28) Which of the following is the correct Kirchhoff?s loop rule?
A) The algebraic sum of the currents meeting at a junction is zero
B) The algebraic sum of potential drops across all resistors in a circuit is zero
C) The algebraic sum of the currents across all the resistors in a circuit is zero
D) The algebraic sum of potential drops across all resistors plus those across sources in a circuit is zero
View Answer play_arrowquestion_answer29) What are the dimensions of electrical conductivity?
A) \[[M{{L}^{-3}}{{T}^{3}}{{I}^{2}}]\]
B) \[[{{M}^{-1}}{{L}^{3}}{{T}^{2}}{{I}^{3}}]\]
C) \[[{{M}^{-1}}{{L}^{-2}}{{T}^{3}}{{I}^{2}}]\]
D) \[[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}I]\]
View Answer play_arrowquestion_answer30) A coil has resistance\[25.00\,\Omega \]. and \[25.17\text{ }\Omega \]at \[{{20}^{o}}C\]and \[{{35}^{o}}C\]respectively. What is the temperature coefficient of resistance?
A) \[4.545\times {{10}^{-4}}{{/}^{o}}C\]
B) \[4.545\times {{10}^{-3}}{{/}^{o}}C\]
C) \[4.545\times {{10}^{-2}}{{/}^{o}}C\]
D) \[4.545\times {{10}^{-5}}{{/}^{o}}C\]
View Answer play_arrowquestion_answer31) An electron and a proton, both having the same kinetic energy, enter a region of uniform magnetic field, in a plane perpendicular to the field. If their masses are denoted by \[{{m}_{e}}\] and \[{{m}_{p}}\] respectively, then the ratio of the radii (electron to proton) of their circular orbits is
A) \[\sqrt{\frac{{{m}_{p}}}{{{m}_{e}}}}\]
B) \[\sqrt{\frac{{{m}_{e}}}{{{m}_{p}}}}\]
C) \[\frac{{{m}_{e}}}{{{m}_{p}}}\]
D) \[1\]
View Answer play_arrowquestion_answer32) In using Ampere's law to find the magnetic field of a straight, long solenoid, the loop (Amperian loop) that is taken is
A) a circular loop, coaxial with the solenoid
B) a rectangular loop in a plane perpendicular to the axis of the solenoid
C) a rectangular loop in a plane containing the axis of the solenoid, the loop being totally within the solenoid
D) a rectangular loop in a plane containing the axis of the solenoid, the loop being partly inside the solenoid and partly outside it
View Answer play_arrowquestion_answer33) A rectangular coil, of sides \[2\text{ }cm\]and \[3\text{ }cm\] respectively, has 10 turns in it. It carries a current of 1 A, and is placed in a uniform magnetic field of 0.2 T in such a manner that its plane makes an angle \[{{60}^{o}}\] with the field direction. The torque on the loop is
A) \[6.0\times {{10}^{-4}}\text{ }N-m\]
B) \[6.0\times {{10}^{-5}}\text{ }N-m\]
C) \[1.2\times {{10}^{-3}}\text{ }N-m\]
D) \[6.0\text{ }N-m\]
View Answer play_arrowquestion_answer34) Which of the following facts about the photoelectric effect can be understood without invoking the quantum concept of light propagation?
A) The rate of photoelectrons emission, when they are emitted, increases with the intensity of light used
B) There is a threshold frequency, below which no photoelectrons are emitted, no matter how long the light is thrown on the metallic surface
C) Once the frequency of light is more than the threshold frequency, photoelectrons are emitted almost instantaneously, no matter how weak the light intensity is
D) For each frequency of light, exceeding the threshold frequency, there is a maximum kinetic energy of the emitted electrons
View Answer play_arrowquestion_answer35) Consider the four gases-hydrogen, oxygen, nitrogen and helium, at the same temperature. Arrange them in the increasing order of the de-Broglie wavelengths of their molecules
A) hydrogen, helium, nitrogen, oxygen
B) oxygen, nitrogen, hydrogen, helium
C) oxygen, nitrogen, helium, hydrogen
D) nitrogen, oxygen, helium, hydrogen
View Answer play_arrowquestion_answer36) The half-life of \[^{60}Co\] is approximately \[5.25\] years. In a sample containing \[1\text{ }g\] of freshly prepared \[^{60}Co,\] how much of the isotope will be left after 21 years?
A) \[125\,\,mg\]
B) \[62.5\text{ }mg\]
C) Nothing will be left
D) \[31.25\text{ }mg\]
View Answer play_arrowquestion_answer37) Which, of the following is true of the Balmer series of the hydrogen spectrum?
A) The entire series falls in the ultraviolet region
B) The entire series falls in the infrared region
C) The series is partly in the visible region and partly in the ultraviolet region
D) The series is partly in the visible region and partly in the infrared region
View Answer play_arrowquestion_answer38) In a nuclear fusion reaction, two nuclei, A and B, fuse to produce a nucleus C, releasing an amount of energy \[\Delta E\] in the process. If the mass defects of the three nuclei are \[\Delta {{M}_{A}},\] \[\Delta {{M}_{B}}\] and am(; respectively, then which of the following relations holds? Here is the speed of light
A) \[\Delta {{M}_{A}}+\Delta {{M}_{B}}=\Delta {{M}_{C}}-\Delta E/{{c}^{2}}\]
B) \[\Delta {{M}_{A}}+\Delta {{M}_{B}}=\Delta {{M}_{C}}+\Delta E/{{c}^{2}}\]
C) \[\Delta {{M}_{A}}-\Delta {{M}_{B}}=\Delta {{M}_{C}}-\Delta E/{{c}^{2}}\]
D) \[\Delta {{M}_{A}}-\Delta {{M}_{B}}=\Delta {{M}_{C}}+\Delta E/{{c}^{2}}\]
View Answer play_arrowquestion_answer39) Which of the following postulates of the Bohr model led to the quantization of energy of the hydrogen atom?
A) The electron goes around the nucleus in circular orbits
B) The angular momentum of the electron can only be an integral multiple of \[h/2\pi \]
C) The magnitude of the linear momentum of the electron is quantized
D) Quantization of energy is itself a postulate of the Bohr model
View Answer play_arrowquestion_answer40) A certain vector in the x-y plane has an x-component of \[12\text{ }m\]and a y -component of 8 m. It is then rotated in the x-y plane so that its x-component is halved. Then ifs new y-component is approximately
A) \[14\,\,m\]
B) \[13.11\,\,m\]
C) \[10\text{ }m\]
D) \[2.0\text{ }m\]
View Answer play_arrowquestion_answer41) A block is placed on a plane inclined at \[{{12}^{o}}\] to the horizontal. What is the maximum value of coefficient of static friction for which the block slides down the plane?
A) \[\tan \,\,{{12}^{o}}\]
B) \[\cos \,\,{{12}^{o}}\]
C) \[sin\,\,{{12}^{o}}\]
D) None of these
View Answer play_arrowquestion_answer42) A brick of mass m, tied to a rope, is being whirled in a vertical circle, with a uniform speed. The tension in the rope is
A) the same throughout
B) largest when the brick is at the highest point of the circular path and smallest when it is at the lowest point
C) largest when the rope is horizontal and smallest when it is vertical
D) largest when the brick is at the lowest point and smallest when it is at the highest point
View Answer play_arrowquestion_answer43) Two blocks, of mass \[1\text{ }kg\]and \[2\text{ }kg\] respectively, are connected by a spring and kept on a frictionless table. The blocks are pulled apart, so that the spring is stretched, and released from rest. At a certain instant of time, the block of mass \[1\text{ }kg,\] is found to be moving at a speed\[2\text{ }m/s\]. What must be the speed of the other block at this instant?
A) \[1\text{ }m/s\]
B) \[0.5\text{ }m/s\]
C) \[4m/s\]
D) \[0.25\text{ }m/s\]
View Answer play_arrowquestion_answer44) A coin of mass \[10\text{ }g\]rolls along a horizontal table with a velocity of \[6\text{ }cm/s\]. Its total kinetic energy is
A) \[9\,\,\mu J\]
B) \[18\,\,\mu J\]
C) \[27\,\,\mu J\]
D) \[36\,\,\mu J\]
View Answer play_arrowquestion_answer45) A simple harmonic oscillator oscillates, with an amplitude A. At what point of its motion, is the power delivered to it by the restoring force maximum?
A) When it is at a displacement \[\pm \frac{A}{\sqrt{2}}\] from the equilibrium point and moving towards the equilibrium point
B) When it is at the maximum displacement
C) When it passes through the equilibrium point, either way
D) When' it is at a displacement \[\pm \frac{A}{\sqrt{2}}\] from the equilibrium point and moving away from the equilibrium point
View Answer play_arrowquestion_answer46) There is a point charge q located at the centre of a cube. What is the electric flux of this point charge, through a face of the cube?
A) \[\frac{q}{{{\varepsilon }_{0}}}\]
B) \[\frac{q}{6{{\varepsilon }_{0}}}\]
C) \[\frac{q}{3{{\varepsilon }_{0}}}\]
D) It will depend upon the size of the cube
View Answer play_arrowquestion_answer47) A point dipole is located at the origin in some orientation. The electric field, at the point \[(10\,cm,10\,cm)\]on the x-y plane is measured to have a magnitude \[1.0\times {{10}^{-3}}V/m\]. What will be the magnitude of the electric field at the point\[(20\,\,cm,\,\,20\,\,cm)\]?
A) \[5.0\times {{10}^{-4}}V/m\]
B) \[2.5\times {{10}^{-4}}V/m\]
C) It will depend on the orientation of the dipole
D) \[1.25\times {{10}^{-4}}V/m\]
View Answer play_arrowquestion_answer48) Which of the following statements is false for a perfect conductor?
A) The surface of the conductor is an equipotential surface
B) The electric, field just outside the surface of a conductor is perpendicular to the surface
C) The charge carried by a conductor is always uniformly distributed over the surface of the conductor
D) None of the above
View Answer play_arrowquestion_answer49) A parallel plate capacitor without any dielectric within its plates, has a capacitance C and is connected to a battery of emf V. The battery is disconnected and the plates of the capacitor are pulled apart until the separation between the plates is doubled. What is the work done by the agent pulling the plates apart, in this process?
A) \[\frac{1}{2}C{{V}^{2}}\]
B) \[\frac{3}{2}C{{V}^{2}}\]
C) \[-\frac{3}{2}C{{V}^{2}}\]
D) \[C{{V}^{2}}\]
View Answer play_arrowquestion_answer50) Consider a copper wire of length L, cross-sectional area A. It has n number of free electrons per unit volume. Which of the following is the correct expression of drift velocity of the electrons when the wire carries a steady current I?
A) \[\frac{I}{neL}\]
B) \[\frac{I}{{{n}^{2}}eL}\]
C) \[\frac{I}{neA}\]
D) \[\frac{I}{n{{e}^{2}}LA}\]
View Answer play_arrowquestion_answer51) A resistor has the following colour code, sequentially from the left Black Brown Orange Red and Black What is the resistance of the resistor?
A) \[13\,\Omega \]
B) \[1300\text{ }\Omega \]
C) \[130\text{ }\Omega \]
D) \[13000\,\,\Omega \]
View Answer play_arrowquestion_answer52) Which of the following is false for interference of light?
A) Coherence of the sources is an essential condition for interference
B) The minima of the interference pattern need not be of zero intensity
C) Interference simply redistributes light energy, without destroying any of it
D) The minima of the interference pattern must always be of zero intensity
View Answer play_arrowquestion_answer53) Totally unpolarized light of intensity \[{{I}_{0}}\] is incident normally on a polarizer and the emerging light is made to pass through a second, parallel polarizer with its axis making an angle of 60? with that of the first. What is the intensity of light emerging out of the second polarizer?
A) Zero
B) \[\frac{{{I}_{0}}}{8}\]
C) \[\frac{{{I}_{0}}}{4}\]
D) \[\frac{{{I}_{0}}}{16}\]
View Answer play_arrowquestion_answer54) A concave mirror has a focal length of\[5\text{ }cm\]. When an object is placed at a distance of \[15\text{ }cm\]from the mirror, where is the image formed?
A) \[10\text{ }cm\]in front of the mirror
B) \[7.5\text{ }cm\]behind the mirror
C) \[2.5\text{ }cm\]in front of the mirror
D) \[7.5\text{ }cm\]in front of the mirror
View Answer play_arrowquestion_answer55) The power of a convex lens is 2 dioptre. Its power is t6 be reduced to 1.5 dioptre, by putting another lens in combination with it. Which of the following lenses will serve the purpose?
A) A concave lens of focal length \[2\text{ }m\]
B) A concave lens of focal lens \[\text{4 }m\]
C) A convex lens of focal lens \[2\text{ }m\]
D) A concave lens of focal length \[\text{1 }m\]
View Answer play_arrowquestion_answer56) Spherical wave fronts, emanating from a point source, strike a plane reflecting surface. What will happen to these wave fronts, immediately after reflection?
A) They will remain spherical with the same curvature, both in magnitude and sign
B) They will become plane wave fronts
C) They will remain spherical, with the same curvature, but sign of curvature reversed
D) They will remain spherical, but with different curvature, both in magnitude and sign
View Answer play_arrowquestion_answer57) Which of the following is true for the minimum angular separation of two stars, \[\Delta {{\theta }_{\min }}\] can be resolved by a telescope? In the following aperture is the diameter of the objective
A) it decreases with the increase in aperture of the telescope
B) it is independent of the aperture of the telescope
C) it increases linearly with the aperture of the telescope
D) it increases quadratic ally with the aperture of the telescope
View Answer play_arrowquestion_answer58) The flux density of mass is defined as the amount of mass crossing unit area per unit time. The dimensions of this quantity is
A) \[[M{{L}^{-2}}{{T}^{-1}}]\]
B) \[[M{{L}^{2}}{{T}^{-1}}]\]
C) \[[ML{{T}^{-1}}]\]
D) \[[{{M}^{-1}}{{L}^{-2}}T]\]
View Answer play_arrowquestion_answer59) A physical quantity z, depends upon two other physical quantities x and y, as follows. \[z=a{{x}^{2}}{{y}^{1/2}}\] where, a is a constant. In an experiment, the quantity x is determined by measuring z and y and using the above expression. If the percentage of error in the measurement of z and y are \[10%\] and \[12%\]respectively, then the percentage of error in the determined value of x is
A) \[2%\]
B) \[8%\]
C) \[15%\]
D) without the value of the constant a, the percentage of error cannot be calculated
View Answer play_arrowquestion_answer60) If a particle moves with an acceleration, then which of the following can remain constant?
A) Both speed and velocity
B) Neither speed nor velocity
C) Only the velocity
D) Only the speed
View Answer play_arrowquestion_answer61) A rubber ball is bounced on the floor of a room which has its ceiling at a height of \[3.2\text{ }m\]from the floor. The ball hits the floor with a speed. of \[10\text{ }m/s\]and rebounds vertically up. If all collisions simply reverse the velocity of the ball, without changing its speed, then how long does it take the ball for a round trip, from the moment it bounces from the floor to the moment it returns back to it? Acceleration due to gravity is. \[10\text{ }m/{{s}^{2}}\].
A) \[4\text{ }s\]
B) \[2\text{ }s\]
C) \[0.8\,s\]
D) \[1.2\,\,s\]
View Answer play_arrowquestion_answer62) Two vectors a and b, add up to Vector c. When vector a is made 3 times as long and vector b is doubled in length, without changing their directions, then it is found that vector c is also doubled in length, without change in direction. Then which of the following is true?
A) All three vectors must be parallel
B) b and c must be parallel to each other, but a need not be parallel to b and c
C) a and b must be perpendicular to each other
D) It is impossible for three non-zero vectors a, b and c to have the property stated above
View Answer play_arrowquestion_answer63) Which of the following is not an assumption of the kinetic theory of gases?
A) The molecules travel in straight paths until they undergo collision with other molecules
B) Molecules of the gas are small hard spheres, occupying negligible volume compared with the total volume of the gas
C) The molecules do not undergo any collisions at all
D) The molecules undergo elastic collisions only
View Answer play_arrowquestion_answer64) The equation describing the motion of a simple harmonic oscillator along the x axis is given as \[x=A\,\,\cos (\omega t+\phi ).\]. If at time \[t=0,\] the oscillator is at \[x=0\]and moving in the negative x-direction, then the phase angle \[\phi \] is
A) \[\frac{\pi }{2}\]
B) \[-\frac{\pi }{2}\]
C) \[\pi \]
D) \[0\]
View Answer play_arrowquestion_answer65) At a displacement from the equilibrium position, that is one-half the amplitude of oscillation, what fraction of the total energy of the oscillator is kinetic energy?
A) \[\frac{1}{2}\]
B) \[\frac{1}{4}\]
C) \[\frac{1}{\sqrt{2}}\]
D) \[\frac{3}{4}\]
View Answer play_arrowquestion_answer66) Which of the following does not change as a wave moves from one medium to another?
A) Wavelength
B) Wave velocity
C) Frequency
D) None of these
View Answer play_arrowquestion_answer67) An organ pipe is closed at one end and open at the other. What is the ratio of frequencies of the 3rd and 4th fundamental modes of vibration?
A) \[\frac{3}{4}\]
B) \[\frac{5}{7}\]
C) \[\frac{3}{5}\]
D) \[\frac{9}{11}\]
View Answer play_arrowquestion_answer68) The Doppler shift in the frequency received by a stationary receiver when the source is moving towards it, was measured to be \[\Delta {{v}_{air}}\] when both receiver and source are in air, and it was measured to be \[\Delta {{v}_{water}}\] when both are under water. Then,
A) \[\Delta {{v}_{air}}>\Delta {{v}_{water}}\]
B) \[\Delta {{v}_{air}}<\Delta {{v}_{water}}\]
C) \[\Delta {{v}_{air}}=\Delta {{v}_{water}}\]
D) \[\Delta {{v}_{water}}=0,\,\,\Delta {{v}_{air}}<0\]
View Answer play_arrowquestion_answer69) Which of the following is false for electric lines of force?
A) They always start from positive charges and terminate on negative charges
B) They are always perpendicular. to the surface of a charged conductor
C) They always form closed loops
D) They are parallel and equally spaced in a region of uniform electric field
View Answer play_arrowquestion_answer70) A uniform magnetic field B points vertically up and is slowly changed in magnitude, but not in direction. The rate of change of the magnetic field is a. A conducting ring of radius r and resistance R is held perpendicular to the magnetic field, and is totally inside it. The induced current in the ring is
A) zero
B) \[\frac{2\pi rB}{R}\]
C) \[\frac{r\alpha }{R}\]
D) \[\frac{\pi {{r}^{2}}\alpha }{R}\]
View Answer play_arrowquestion_answer71) A plane electromagnetic wave is propagating along the z-direction. If the electric field component of this wave is in the direction \[(i+j),\] then which of the following is the direction of the magnetic field component?
A) \[(-i+j)\]
B) \[(i-j)\]
C) \[(-i-j)\]
D) \[(i+k)\]
View Answer play_arrowquestion_answer72) Which of the following is the correct arrangement of the electromagnetic spectrum in the increasing order of frequency?
A) Microwaves, infrared, radio waves, visible light. X-rays
B) Radio waves, microwaves, infrared, visible light. X-rays
C) X-rays, visible light, infrared, microwaves, radio waves
D) Microwaves, radio waves, infrared, visible light. X-rays
View Answer play_arrowquestion_answer73) Which of the following optical phenomena is involved in the propagation of light in an optical fiber?
A) Refraction
B) Dispersion
C) interference
D) Total internal reflection
View Answer play_arrowquestion_answer74) In a Young's double-slits experimental arrangement, the light used has wavelength \[5000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,,\] the slit separation is \[2\text{ }mm\]and slits to screen distance is\[1\text{ }m\]. What is the width of the fringes produced on the screen?
A) \[0.25\text{ }mm\]
B) \[0.1\text{ }mm\]
C) \[0.5\text{ }mm\]
D) \[0.025\text{ }mm\]
View Answer play_arrowquestion_answer75) In a single-slit diffraction experiment, the width of the slit is reduced by half. Which of the following needs to be done if the width of the central maxima has to remain the same?
A) Reduce the distance between the slit and screen by half
B) Reduce the distance between the slit and the screen to \[{{\left( \frac{1}{4} \right)}^{th}}\]the original separation
C) Double the distance between the slit and the screen
D) No need to do anything, as the width of the central maxima does not depend on the slit width
View Answer play_arrowquestion_answer76) Molar conductivity decreases with decrease in concentration
A) for strong electrolytes
B) for weak electrolytes
C) both for strong and weak electrolytes
D) for non-electrolytes
E) None of these
View Answer play_arrowquestion_answer77) A nucleophilic substitution reaction proceeds through \[{{\text{S}}_{\text{N}}}\text{1}\]mechanism. So, the reaction is
A) unimolecular
B) bimolecular
C) trimolecular
D) rate depends on concentration of incoming nucleophile
View Answer play_arrowquestion_answer78) For an electrophilic aromatic substitution reaction
A) chlorine is o-p directing group and also electron releasing group
B) chlorine is o-p directing group and also electron with drawing group
C) chlorine is meta directing group and also electron relasing group
D) chlorine is meta directing group and also electron withdrawing group
View Answer play_arrowquestion_answer79) Enthalpy of combustion of carbon to \[\text{C}{{\text{O}}_{\text{2}}}\] is \[-393.52\,\text{kJ/mol}\text{.}\] The heat released upon formation of 11 g of \[\text{C}{{\text{O}}_{\text{2}}}\]from carbon and dioxygen is
A) 35.77 kJ
B) 98.38 kJ
C) 1574.08 kJ
D) 393.52 kJ
View Answer play_arrowquestion_answer80) Entropy change in a process where 1 L of liquid He is poured into ice cold water is
A) finite and positive
B) finite and negative
C) zero
D) infinity
View Answer play_arrowquestion_answer81) Anode reaction of a fuel cell is
A) \[Zn(Hg)+2O{{H}^{-}}H\xrightarrow[{}]{{}}ZnO(s)+{{H}_{2}}O+2{{e}^{-}}\]
B) \[Pb(s)+SO_{4}^{2-}(aq)\xrightarrow{{}}PbS{{O}_{4}}(s)+2{{e}^{-}}\]
C) \[2{{H}_{2}}(g)+4O{{H}^{-}}(aq)\xrightarrow{{}}4{{H}_{2}}O(l)+4{{e}^{-}}\]
D) \[2Fe(s)\xrightarrow{{}}2F{{e}^{2+}}+4{{e}^{-}}\]
View Answer play_arrowquestion_answer82) For an ideal system at thermal equilibrium, the velocity distribution of the constituent particles will be governed by
A) Gaussian distribution
B) Maxwell-Boltzmann distribution
C) Lorentzian distribution
D) Log-normal distribution
View Answer play_arrowquestion_answer83) During spontaneous discharge of an electrochemical cell Gibbs free energy will
A) increase
B) decrease
C) not change
D) be infinity
View Answer play_arrowquestion_answer84) Standard electrode potential of half-cell reactions are given below \[C{{u}^{2+}}+2{{e}^{-}}\xrightarrow{{}}Cu;\] \[{{E}^{o}}=0.34\,V\] \[Z{{n}^{2+}}+2{{e}^{-}}\xrightarrow{{}}Zn;\] \[{{E}^{o}}=-\,0.76\,V\] What is the emf of the cell?
A) \[~+\text{ }1.10\,V\]
B) \[-1.10\,V\]
C) \[-0.42\,V\]
D) \[+\,0.42\,V\]
View Answer play_arrowquestion_answer85) Tollen's test can be used to distinguish
A) propionaldehyde and acetone
B) propanol and propionic acid
C) propene and isobutene
D) isopropanol and propanol
View Answer play_arrowquestion_answer86) The product of reaction between aniline and acetic anhydride is
A) \[o-\]ammoacetophenone
B) \[m-\]aminoacetophenone
C) \[p-\]aminoacetophenone
D) acetanilide
View Answer play_arrowquestion_answer87) According to Le-Chateliefs principle, the equilibrium constant of a reversible reaction will not shift by
A) increasing the temperature of an exothermic reaction
B) increasing the temperature of an endothermic reaction
C) changing the concentrations of the reactants
D) the effect of a catalyst
View Answer play_arrowquestion_answer88) Properties of elements are periodic function of number of...... present in the nucleus.
A) protons
B) electrons
C) neutrons
D) mesons
View Answer play_arrowquestion_answer89) The complex\[{{[Co{{(N{{H}_{3}})}_{5}}Br]}^{2+}}SO_{4}^{2-}\]and \[{{[Co{{(N{{H}_{3}})}_{5}}S{{O}_{4}}]}^{+}}B{{r}^{-}}\]are
A) coordination isomers
B) linkage isomers
C) stereoisomers
D) ionisation isomers
View Answer play_arrowquestion_answer90) Maximum number of electrons in a shell with principal quantum number n is given by
A) \[n\]
B) \[2n\]
C) \[{{n}^{2}}\]
D) \[2{{n}^{2}}\]
View Answer play_arrowquestion_answer91) Anti-Markownikoff addition of HBr is not observed in
A) propene
B) butene
C) 2-butene
D) 2-pentene
View Answer play_arrowquestion_answer92) A ketone gives a yellow ppt when treated with \[{{\text{I}}_{\text{2}}}\] in an alkaline solution. Thus, the ketone is
A) a cyclic ketone
B) a methyl ketone
C) an unsaturated ketone
D) None of the above
View Answer play_arrowquestion_answer93) Wrought iron contains
A) Cr
B) Cu
C) C
D) Ag
View Answer play_arrowquestion_answer94) The ore magnetite is
A) \[F{{e}_{3}}{{O}_{4}}\]
B) \[ZnC{{O}_{3}}\]
C) \[CuC{{O}_{3}}.Cu{{(OH)}_{2}}\]
D) \[Fe{{S}_{2}}\]
View Answer play_arrowquestion_answer95) The first step in the extraction of Cu from copper pyrites is
A) reduction by carbon
B) electrolysis of ore
C) roasting of ore in \[{{\text{O}}_{\text{2}}}\]
D) magnetic separation
View Answer play_arrowquestion_answer96) Desalination of sea water can be done by
A) osmosis
B) reverse osmosis
C) filtration
D) diffusion
View Answer play_arrowquestion_answer97) A compound with nitro group was reduced by \[\text{Sn/HCl,}\]followed by treatment with \[\text{NaN}{{\text{O}}_{\text{2}}}\text{/HCl}\]and followed by phenol. The chromophore group in the final compound is
A) \[\text{N}{{\text{O}}_{2}}\] group
B) \[\text{ }\!\!~\!\!\text{ N}{{\text{H}}_{\text{2}}}\] group .
C) azo group
D) OH group
View Answer play_arrowquestion_answer98) Certain reactions follow die relation between concentrations of the reactant \[vs\]time as What is the expected order for such reactions?
A) 0
B) 1
C) 2
D) Infinity
View Answer play_arrowquestion_answer99) A first order reaction has a rate constant \[k=3.01\times {{10}^{-3}}/s.\]How long it will take to decompose half of the reaction?
A) \[2.303\text{ }s\]
B) \[~23.03\text{ }s\]
C) \[~230.23s\]
D) \[~2303s\]
View Answer play_arrowquestion_answer100) The shape of the ammonia molecule is
A) tetrahedral
B) trigonal pyramidal
C) trigonal bipyramid
D) trigonal planar
View Answer play_arrowquestion_answer101) \[{{\text{H}}_{\text{5}}}\text{I}{{\text{O}}_{\text{6}}}\]is a
A) strong reducing agent
B) strong base
C) strong oxidising agent
D) weak base
View Answer play_arrowquestion_answer102) If a compound gives an orange or red precipitate with 2,4-dinitrophenylhydrazine, then the compound is
A) an alkyl halide
B) an aryl halide
C) an amine
D) a carbonyl compound
View Answer play_arrowquestion_answer103) Isotones have
A) same neutron number but different proton number
B) same proton number but different neutron number
C) same proton and neutron number
D) same proton but different electron number
View Answer play_arrowquestion_answer104) \[{{(C{{H}_{3}})}_{3}}C-OH\]on treatment with \[\text{NaCl}\]in aqueous medium gives
A) no reaction
B) \[{{\text{(C}{{\text{H}}_{3}}\text{)}}_{3}}{{C}^{-}}N{{a}^{+}}\]
C) \[(C{{H}_{3}})CC{{l}^{-}}\]
D) isobutylene
View Answer play_arrowquestion_answer105) The de-Broglie wavelength of a particle is
A) proportional to its mass
B) proportional to its velocity
C) inversely proportional to its momentum
D) proportional to its total energy
View Answer play_arrowquestion_answer106) The \[C-H\]bond distance is the longest in
A) \[{{C}_{2}}{{H}_{2}}\]
B) \[{{C}_{2}}{{H}_{4}}\]
C) \[{{C}_{2}}{{H}_{6}}\]
D) \[{{C}_{2}}{{H}_{2}}B{{r}_{2}}\]
View Answer play_arrowquestion_answer107) Dimension of universal gas constant (R) is
A) \[[VP{{T}^{-1}}{{n}^{-1}}]\]
B) \[[V{{P}^{-1}}T{{n}^{-1}}]\]
C) \[[VPT{{n}^{-1}}]\]
D) \[[VP{{T}^{-1}}n]\]
View Answer play_arrowquestion_answer108) Entropy of a perfectly crystalline solid at 0 K is
A) positive
B) negative
C) zero
D) either positive or negative
View Answer play_arrowquestion_answer109) The hybridisation of carbon in molecular \[\text{C}{{\text{O}}_{\text{2}}}\]is
A) \[sp\]
B) \[s{{p}^{2}}\]
C) \[s{{p}^{3}}\]
D) \[s{{p}^{3}}d\]
View Answer play_arrowquestion_answer110) \[\text{CC}{{\text{l}}_{\text{4}}}\]and freons
A) are green compounds because they are green coloured
B) deplete ozone
C) cause increase in ozone concentration
D) have no effect on ozone concentration
View Answer play_arrowquestion_answer111) Total number of metal atoms per unit cell in a face-centred cubic lattice is
A) 14
B) 8
C) 6
D) 4
View Answer play_arrowquestion_answer112) Bakelite is formed by polymerisation between
A) acrylonitrile molecules
B) tetrafluoroethene molecules
C) urea and formaldehyde molecules
D) phenol and formaldehyde molecules
View Answer play_arrowquestion_answer113) Chromatographic analysis is done based on the property of
A) diffusion
B) absorption
C) adsorption
D) condensation
View Answer play_arrowquestion_answer114) Avogadro number\[(6.023\,\times \,{{10}^{23}})\]of carbon atoms are present in
A) \[12\,g\]of \[{{\,}^{12}}C{{O}_{2}}\]
B) \[22.4\,L\,{{\,}^{12}}C{{O}_{2}}\]at room temperature
C) \[44\,g\]of \[{{\,}^{12}}C{{O}_{2}}\]
D) \[12\]moles of \[{{\,}^{12}}C{{O}_{2}}\]
View Answer play_arrowquestion_answer115) Glucose can be converted into ethyl alcohol using
A) invertase
B) zymase
C) maltase
D) diastase
View Answer play_arrowquestion_answer116) When \[\text{FeC}{{\text{l}}_{\text{3}}}\]is added to phenol
A) no reaction occurs
B) a coloured complex will be formed
C) \[\text{F}{{\text{e}}^{\text{3+}}}\] will be oxidised to higher state
D) \[~o-\] chlorophenol will be formed
View Answer play_arrowquestion_answer117) The correct order of decreasing Lewis acidity is
A) \[B{{F}_{3}}>BC{{l}_{3}}>BB{{r}_{3}}>B{{I}_{3}}\]
B) \[B{{I}_{3}}>BC{{l}_{3}}>BB{{r}_{3}}>B{{F}_{3}}\]
C) \[B{{I}_{3}}>BB{{r}_{3}}>BC{{l}_{3}}>B{{F}_{3}}\]
D) \[BC{{l}_{3}}>B{{F}_{3}}>BB{{r}_{3}}>B{{I}_{3}}\]
View Answer play_arrowquestion_answer118) The buffer present in blood plasma is
A) borax, sodium hydroxide
B) carbonic acid, bicarbonate ion
C) acetic acid, sodium acetate
D) citric acid, potassium dihydrogen phosphate
View Answer play_arrowquestion_answer119) Conduction in a p-type semiconductor is increased by
A) increasing the band gap
B) decreasing the temperature
C) adding appropriate electron deficient impurities
D) adding appropriate electron rich impurities
View Answer play_arrowquestion_answer120) The volume of \[\text{0}\text{.1 M Ca(OH}{{\text{)}}_{\text{2}}}\] required to neutralise 10 mL of \[\text{0}\text{.1 N HC1}\]is
A) 10 mL
B) 20 mL
C) 5 mL
D) 15 mL
View Answer play_arrowquestion_answer121) Boron is unable to form \[\text{BF}_{6}^{3-}\]because of
A) high electronegativity of boron
B) high electronegativity of fluorine
C) lack of d-orbitals in boron
D) less difference in electronegativity between B and F
View Answer play_arrowquestion_answer122) The rate of reactions exhibiting negative activation energy
A) decreases with increasing temperature
B) increases with increasing temperature
C) does not depend on temperature
D) depends on the height of the potential barrier
View Answer play_arrowquestion_answer123) Addition of a non-volatile solute in a volatile ideal solvent
A) increases the vapour pressure of the solvent
B) decreases the vapour pressure of the solvent
C) decreases the boiling pomt of the solvent
D) increases the freezing point of the solvent
View Answer play_arrowquestion_answer124) The dissolution of a gas in a liquid is governed by
A) Raoult?s law
B) Henry's law
C) Dalton's law of partial pressure
D) van't Hoff factor
View Answer play_arrowquestion_answer125) Normal human blood sugar range is 65-105 mg/dL Considering density of human blood is 1.06 kg/L, if a patient's sugar level reads 720 ppm, his/her blood sugar at that time is
A) normal
B) high
C) low
D) cannot say
View Answer play_arrowquestion_answer126) pH of 0.0002 M formic acid\[[{{K}_{a}}=2\times {{10}^{-4}}]\] approximately is
A) 1.35
B) 0.5
C) 3.7
D) 1.85
View Answer play_arrowquestion_answer127) At room temperature, for the reaction \[N{{H}_{4}}SH(S)N{{H}_{3}}(g)+{{H}_{2}}S(g)\]
A) \[{{K}_{p}}={{K}_{c}}\]
B) \[{{K}_{p}}>{{K}_{c}}\]
C) \[{{K}_{p}}<{{K}_{c}}\]
D) \[{{K}_{p}}\]and \[{{K}_{c}}\]do not relate
View Answer play_arrowquestion_answer128) The molecule NO is
A) paramagnetic
B) diamagnetic
C) ferromagnetic
D) an even electron molecule
View Answer play_arrowquestion_answer129) The most stable oxidation state exhibited by thallium is
A) 0
B) \[+\,1\]
C) \[~+\,2\]
D) \[~+\,3\]
View Answer play_arrowquestion_answer130) Which of the following elements has the highest value of electron affinity?
A) O
B) S
C) Se
D) Te
View Answer play_arrowquestion_answer131) The correct order of electron gain enthalpy \[({{\Delta }_{eg}}H)\] of the halogen atoms is
A) \[F<Cl<Br<I\]
B) \[~Cl<F<Br<~I\]
C) \[~I<Br<Cl<F\]
D) \[~Cl<Br<I<F\text{ }\]
View Answer play_arrowquestion_answer132) Which of the following statements is correct?
A) The equivalent mass of KMn04 in alkaline medium is molar mass divided by five.
B) The equivalent mass of KMn04 in strongly alkaline medium is molar mass divided by three.
C) The equivalent mass of KMn04 in neutral medium is molar mass divided by three.
D) The equivalent mass of \[\text{Kmn}{{\text{O}}_{\text{4}}}\]in weakly acidic medium is molar mass divided by three.
View Answer play_arrowquestion_answer133) Bohr model of hydrogen atom was unable to explain
A) Rydberg?s formula of atomic spectra
B) Heisenberg?s uncertainty principle
C) Planck's law of energy quantisation
D) Rutherford's model of atomic structure
View Answer play_arrowquestion_answer134) The correct order of bond energy is
A) \[C{{l}_{2}}>B{{r}_{2}}>{{F}_{2}}>{{I}_{2}}\]
B) \[C{{l}_{2}}>{{F}_{2}}>B{{r}_{2}}>{{I}_{2}}\]
C) \[{{I}_{2}}>B{{r}_{2}}>C{{l}_{2}}>{{F}_{2}}\]
D) \[{{I}_{2}}>B{{r}_{2}}>{{F}_{2}}>C{{l}_{2}}\]
View Answer play_arrowquestion_answer135) The correct order of increasing oxidizing power in the series is
A) \[VO_{2}^{+}<C{{r}_{2}}O_{7}^{2-}<MnO\,_{4}^{-}\]
B) \[C{{r}_{2}}O_{7}^{2-}<VO_{2}^{+}<MnO_{4}^{-}\]
C) \[C{{r}_{2}}O_{7}^{2-}<MnO_{4}^{-}<VO_{2}^{+}\]
D) \[MnO_{4}^{-}<C{{r}_{2}}O_{7}^{2-}<VO_{2}^{+}\]
View Answer play_arrowquestion_answer136) Paramagnetism is shown by
A) \[~{{N}_{2}}\]
B) \[{{O}_{2}}\]
C) \[{{F}_{2}}\]
D) \[C{{O}_{2}}\]
View Answer play_arrowquestion_answer137) The spin only magnetic moment of \[{{[Cr{{F}_{6}}]}^{4-}}\] (at. no. for Cr is 24) is
A) 0
B) 1.7 3BM
C) 2.83 BM
D) 4.9 BM
View Answer play_arrowquestion_answer138) The reduction of zinc oxide with coke occurs at temperature
A) greater than that for\[\text{CuO}\].
B) less than that for\[\text{CuO}\]
C) less than that for\[\text{ }\!\!~\!\!\text{ A}{{\text{g}}_{\text{2}}}\text{O}\]
D) equal to that for \[\text{CuO}\]
View Answer play_arrowquestion_answer139) The effective atomic number for \[{{[Rh{{({{H}_{2}}O)}_{6}}]}^{3+}}\](at. no. for Rh is 45) is
A) 42
B) 45
C) 48
D) 54
View Answer play_arrowquestion_answer140) The crystal structure of solid Mn(II) oxide is
A) \[\text{ }\!\!~\!\!\text{ NaCl}\] structure
B) \[\text{ }\!\!~\!\!\text{ F}{{\text{e}}_{\text{2}}}{{\text{O}}_{\text{3}}}\] structure
C) \[\text{ }\!\!~\!\!\text{ Ca}{{\text{F}}_{\text{2}}}\] structure
D) \[\text{ }\!\!~\!\!\text{ N}{{\text{a}}_{\text{2}}}\text{O}\] structure
View Answer play_arrowquestion_answer141) The nitration (using nitration mixture) of aniline gives
A) \[~p-\] nitroaniline
B) \[~o-\] nitroaniline
C) \[~m-\] nitroaniline
D) All of these
View Answer play_arrowquestion_answer142) The order of basic strength for methyl substituted amine in aqueous solution is
A) \[N{{(C{{H}_{3}})}_{3}}>N{{(C{{H}_{3}})}_{2}}H>N(C{{H}_{3}}){{H}_{2}}>N{{H}_{3}}\]
B) \[N(C{{H}_{3}}){{H}_{2}}>N{{(C{{H}_{3}})}_{2}}H>N{{(C{{H}_{3}})}_{3}}>N{{H}_{3}}\]
C) \[N{{H}_{3}}N(C{{H}_{3}}){{H}_{2}}>N{{(C{{H}_{3}})}_{2}}H\] \[>\,N{{(C{{H}_{3}})}_{3}}\]
D) \[N{{(C{{H}_{3}})}_{2}}H>N(C{{H}_{3}}){{H}_{2}}>N{{(C{{H}_{3}})}_{3}}\]\[>N{{H}_{3}}\]
View Answer play_arrowquestion_answer143) The strongest acid among the choices is
A) dichloroacetic acid
B) dimethylacetic acid
C) trifluoroacetic acid
D) triiodoacetic acid
View Answer play_arrowquestion_answer144) Glucose and fructose can be distinguished by
A) Lucas test
B) Ninhydrin test
C) Benedict reagent test
D) All of the above
View Answer play_arrowquestion_answer145) Which is the most stable compound among the following?
A)
B)
C)
D) All the compounds have same stability
View Answer play_arrowquestion_answer146) Among the following, which is the least stable conformation of cyclohexane?
A) Boat conformation
B) Half chair conformation
C) Twist boat conformation
D) Chair conformation
View Answer play_arrowquestion_answer147) The correct relation between the following pair of compounds is
A) constitutional isomers
B) enantiomers
C) diastereomers
D) None of the above
View Answer play_arrowquestion_answer148) Among the choices of alkyl bromide, the least reactive bromide in a \[{{\text{S}}_{\text{N}}}\text{2}\]reaction is
A) 1-bromopentane
B) 2-bromo-2-methylbutane
C) 1-bromo-3-methylbutane
D) 1-bromo-2-methylbutane
View Answer play_arrowquestion_answer149) The correct order of leaving group ability in a nucleophilic substitution reaction is
A) \[B{{r}^{-}}>C{{l}^{-}}>C{{H}_{3}}CO_{2}^{-}>H{{O}^{-}}>{{H}^{-}}\]
B) \[{{H}^{-}}>O{{H}^{-}}>C{{H}_{3}}CO_{2}^{-}>C{{l}^{-}}>B{{r}^{-}}\]
C) \[B{{r}^{-}}C{{H}_{3}}CO_{2}^{-}C{{l}^{-}}>O{{H}^{-}}>{{H}^{-}}\]
D) \[C{{H}_{3}}CO_{2}^{-}>B{{r}^{-}}>C{{l}^{-}}>O{{H}^{-}}>{{H}^{-}}\]
View Answer play_arrowquestion_answer150) 2-bromobutane reacts with \[\text{O}{{\text{H}}^{-}}\]in \[{{\text{H}}_{\text{2}}}\text{O}\]to give 2-butanol. The reaction involves
A) retention in configuration
B) inversion in configuration
C) racemization
D) mutarotation
View Answer play_arrowquestion_answer151) The number of points at which the function \[f(x)=\frac{1}{{{\log }_{e}}\,|x|}\]is discontinuous, is
A) \[1\]
B) \[2\]
C) \[3\]
D) \[\infty \]
View Answer play_arrowquestion_answer152) The value of \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{\sin \,(\pi \,co{{s}^{2}}x)}{{{x}^{2}}}\] is equal to
A) \[\frac{\pi }{2}\]
B) \[\pi \]
C) \[-\pi \]
D) \[1\]
View Answer play_arrowquestion_answer153) The function \[f(x)=\frac{x}{1+{{x}^{2}}}\] decreases in the interval
A) \[(-\infty ,\,\,-1]\cup [1,\infty )\]
B) \[(-1,1)\]
C) \[(-\infty ,\infty )\]
D) None of the above
View Answer play_arrowquestion_answer154) Let \[f:R\to R\] be a function such that the third derivative of/(x) vanishes for all x. If \[f(0)=1,\,f'(2)=4\]and \[f'\,'(1)=2,\] then \[f(x)\] equals to
A) \[{{x}^{2}}+1\]
B) \[{{x}^{2}}+2x+1\]
C) \[4x+1\]
D) \[{{x}^{2}}-2x+1\]
View Answer play_arrowquestion_answer155) If \[f'(x)=g(x)\] and \[g'(x)=-f(x)\] for all x and \[f(1)=5,\,\,f'(1)=4,\]then the value of \[{{f}^{2}}(1)+{{g}^{2}}(1)\]is equal to
A) \[25\]
B) \[16\]
C) \[41\]
D) \[9\]
View Answer play_arrowquestion_answer156) The degree of the differential equation satisfied by the curve \[\sqrt{1+x}-a\,\sqrt{1+y}=1,\] where a is a parameter, is
A) \[1\]
B) \[2\]
C) \[3\]
D) None of these
View Answer play_arrowquestion_answer157) The probability that atleast one of the events A and B occurs is \[0.5\]. If A and B occur simultaneously with probability \[0.2,\] then \[P({{A}^{c}})+P({{B}^{c}})\]is equal to
A) \[1.0\]
B) \[1.1\]
C) \[0.7\]
D) \[1.3\]
View Answer play_arrowquestion_answer158) The following table gives the probability that certain computer will malfunction 0, 1, 2, 3, 4, 5 or 6 times on any day
Number of malfunctions X | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
Probability f(x) | 0.17 | 0.29 | 0.27 | 0.16 | 0.07 | 0.03 | 0.01 |
A) \[1.74\]
B) \[1.80\]
C) \[0.74\]
D) None of these
View Answer play_arrowquestion_answer159) For the married couple living in Jammu, the probability that a husband will vote in an election is \[0.5\] and the probability that his wife will vote is \[0.4\]. The probability that the husband votes, given that his wife also votes is\[0.7\]. Then, the probability that husband and wife both will vote is
A) \[0.28\]
B) \[0.20\]
C) \[0.35\]
D) \[0.15\]
View Answer play_arrowquestion_answer160) Let \[f(x)=\frac{k}{1+{{x}^{2}}},\,-\infty <x<\infty \] be the probability density of a random variable. Then, k equals to
A) \[\pi \]
B) \[-\pi \]
C) \[\frac{1}{\pi }\]
D) \[1\]
View Answer play_arrowquestion_answer161) If mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value atleast one is
A) \[\frac{1}{16}\]
B) \[\frac{3}{16}\]
C) \[\frac{5}{16}\]
D) \[\frac{15}{16}\]
View Answer play_arrowquestion_answer162) Let A and B be two mutually exclusive events such that \[P(A\cap {{B}^{c}})=0.25\]and \[P({{A}^{c}}\cap B)=0.5\]. Then, \[P\{(A\cup {{B}^{c}})\}\] is equal to
A) \[0.25\]
B) \[0.50\]
C) \[0.75\]
D) \[0.40\]
View Answer play_arrowquestion_answer163) If the product of n positive real numbers is one, then their sum is
A) \[n+\frac{1}{n}\]
B) \[n-\frac{1}{n}\]
C) \[2n+\frac{1}{n}\]
D) never less than n
View Answer play_arrowquestion_answer164) The sum of the series \[5-\frac{10}{3}+\frac{20}{9}-\frac{40}{27}+....\] is equal to
A) \[1\]
B) \[2\]
C) \[3\]
D) None of these
View Answer play_arrowquestion_answer165) The sum of n terms of the series \[\frac{3}{{{1}^{2}}{{.2}^{2}}}+\frac{5}{{{2}^{2}}{{.3}^{2}}}+\frac{7}{{{3}^{2}}{{.4}^{2}}}+.....\] is equal to
A) \[\frac{{{n}^{2}}-2n}{{{(n+1)}^{2}}}\]
B) \[\frac{{{n}^{2}}-2}{{{(n+1)}^{2}}}\]
C) \[\frac{{{n}^{2}}+2n}{{{(n+1)}^{2}}}\]
D) \[\frac{{{n}^{2}}+2}{{{(n+1)}^{2}}}\]
View Answer play_arrowquestion_answer166) If \[^{m+n}P{{ }_{2}}=90\] and \[^{m-n}P{{ }_{2}}=30,\] then \[(m,n)\] is given by (where, m and n are positive integers)
A) \[(8,\,2)\]
B) \[(5,\,\,6)\]
C) \[(3,\,\,7)\]
D) \[(8,\,\,3)\]
View Answer play_arrowquestion_answer167) In the binomial expansion of \[{{(a-b)}^{n}},\,\,n\,\,\ge \,5,\] the sum of 5th and 6th term is zero. Then, \[\frac{a}{b}\]is equal to
A) \[\frac{n-4}{2}\]
B) \[\frac{n-4}{3}\]
C) \[\frac{n-4}{5}\]
D) \[\frac{n-4}{4}\]
View Answer play_arrowquestion_answer168) The value of \[\tan \,\left( {{\cos }^{-1}}\frac{4}{5}+{{\tan }^{-1}}\frac{2}{3} \right)\] is equal to
A) \[\frac{17}{6}\]
B) \[\frac{22}{15}\]
C) \[\frac{16}{5}\]
D) \[\frac{16}{9}\]
View Answer play_arrowquestion_answer169) If A is a skew-symmetric matrix of order \[3\times 3,\] then determinant of A equals to
A) \[0\]
B) \[1\]
C) \[2\]
D) \[-1\]
View Answer play_arrowquestion_answer170) The trajectory of the differential equation \[\frac{dx}{dt}=rx\left( 1-\frac{x}{k} \right),\,\,\,\,r>0\] is monotonically increasing, if
A) \[0<x<k\]
B) \[x(0)>k\]
C) \[\frac{k}{2}<x(0)<2k\]
D) None of these
View Answer play_arrowquestion_answer171) If \[f(x)={{(1+x)}^{n}},\] then the value of \[f(0)+f'(0)+\frac{f'\,'(0)}{2!}+.....+\frac{{{f}^{(n)}}(0)}{n!}\] is equal to
A) \[{{2}^{n-1}}\]
B) \[2\,n\]
C) \[n\]
D) \[{{2}^{n}}\]
View Answer play_arrowquestion_answer172) If \[f:R\to R\] be a differentiable function such that \[f(4)=6\] and \[f'(4)=2,\] then \[\underset{x\to 4}{\mathop{\lim }}\,\,\,\frac{x\,\,f(4)-4f(x)}{x-4}\]is equal to
A) \[2\]
B) \[-2\]
C) \[0\]
D) \[1\]
View Answer play_arrowquestion_answer173) If \[x{{e}^{xy}}=y+{{\sin }^{2}}x,\]then \[\frac{dy}{dx}\]at \[x=0\]is equal to
A) \[0\]
B) \[1\]
C) \[e\]
D) \[-1\]
View Answer play_arrowquestion_answer174) Let \[P(x,y)\] be a point on the curve \[{{y}^{2}}=4x\] at which the tangent is perpendicular to the line \[2x+y=-2.\]Then, the coordinates of the point P are
A) \[(4,\,4)\]
B) \[(4,\,\,-\,4)\]
C) \[(-4,\,\,4)\]
D) \[(-4,\,\,-4)\]
View Answer play_arrowquestion_answer175) Let a line makes an angle of \[{{60}^{o}}\] with each of the x and y-axes. Then, the- angle made by the line with z-axis is
A) \[{{30}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{60}^{o}}\]
D) None of these
View Answer play_arrowquestion_answer176) The value of a for which the volume of parallelepiped formed by the vectors \[i+aj+k,\,\,j+ak\] and \[ai+k\] is minimum, is
A) \[\frac{1}{\sqrt{3}}\]
B) \[3\]
C) \[-3\]
D) \[1\]
View Answer play_arrowquestion_answer177) The angle between the two lines \[\frac{2-x}{1}=\frac{y}{2}=\frac{z+3}{1}\]and \[\frac{x-4}{4}=\frac{y-1}{1}=\frac{z-5}{2}\] is
A) \[{{0}^{o}}\]
B) \[{{90}^{o}}\]
C) \[{{45}^{o}}\]
D) None of these
View Answer play_arrowquestion_answer178) If the foot of perpendicular from the origin to a plane is \[(1,2,3),\] then equation of the planets
A) \[2x-y+z=3\]
B) \[x+y+z=6\]
C) \[x-y-z=-4\]
D) \[x+2y+3z=14\]
View Answer play_arrowquestion_answer179) The length of perpendicular from the point \[(1,0,1)\] to the plane \[3x+\sqrt{6}y+7z+6=0\]is
A) \[2\]
B) \[6\]
C) \[8\]
D) \[7\]
View Answer play_arrowquestion_answer180) If the line \[\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}\]lies in the plane \[2x-4y+z=5,\] then k is equal to
A) \[0\]
B) \[1\]
C) \[7\]
D) \[5\]
View Answer play_arrowquestion_answer181) If A and B be two independent events such that \[P(A)=\frac{2}{3}\] and \[P(B)=\frac{1}{5},\] the \[P(A\cup B)\]equals to
A) \[\frac{1}{15}\]
B) \[\frac{11}{15}\]
C) \[\frac{2}{15}\]
D) \[\frac{13}{15}\]
View Answer play_arrowquestion_answer182) If \[i\,\,{{z}^{3}}-{{z}^{2}}+z+i=0,\] then z lies on
A) a circle with centre \[(0,\,\,0)\] and radius 1
B) a circle with centre and radius 1
C) a circle with centre (0, 1) and radius 1
D) a straight line
View Answer play_arrowquestion_answer183) If \[|z|=1\] and \[w=\frac{z+1}{z-1}\] (where, \[z\ne 1\]), then Re (w) equals to
A) \[\frac{1}{|z-1|}\]
B) \[\frac{1}{|z+1|}\]
C) \[\left| \frac{z}{z-1} \right|\]
D) \[0\]
View Answer play_arrowquestion_answer184) If \[f(x)=\sin \left\{ \log \left( \frac{\sqrt{16-{{x}^{2}}}}{2-x} \right) \right\},\] then domain of \[f(x)\] is equal to
A) \[(-4,\,2)\]
B) \[(-4,\,\,4)\]
C) \[(-4,\,\,4]\]
D) \[[-4,\,\,4]\]
View Answer play_arrowquestion_answer185) The real value of \[\theta \] for which the expression \[\frac{1+i\,\sin \theta }{1-2i\,\sin \theta }\] is a real number
A) \[2n\pi ,\], n is an integer
B) \[2n\pi +\frac{\pi }{2},\] n is an integer
C) \[2n\pi -\frac{\pi }{2},\] n is an integer
D) \[n\pi +\frac{\pi }{2},\] n is an integer
View Answer play_arrowquestion_answer186) Let \[\alpha \] and \[\beta \] be the roots of equation \[{{x}^{2}}-(a-2)x-a-1=0,\] then \[{{\alpha }^{2}}+{{\beta }^{2}}\] assumes the least value, if
A) \[a=0\]
B) \[a=1\]
C) \[a=-1\]
D) \[a=2\]
View Answer play_arrowquestion_answer187) For a real x, the equation \[{{e}^{\sin x}}-{{e}^{-\sin x}}-16=0\] has
A) one and only one solution
B) four solutions
C) infinite number of solutions
D) no solution
View Answer play_arrowquestion_answer188) The number of distinct real roots of \[\left| \begin{matrix} \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x \\ \end{matrix} \right|=0\]in the interval \[-\frac{\pi }{4}\le x\le \frac{\pi }{4}\]is
A) \[0\]
B) 1
C) \[2\]
D) \[4\]
View Answer play_arrowquestion_answer189) Let \[a>0,b>0\]and \[f(x)=\left| \begin{matrix} x & a & a \\ b & x & a \\ b & b & x \\ \end{matrix} \right|,\] then which of the following statement is true?
A) \[f(x)\] has a local minimum at \[x=\sqrt{ab}.\]
B) \[f(x)\] has a local maximum at \[x=\sqrt{ab}.\]
C) \[f(x)\]has a neither local minimum at \[x=\sqrt{ab}.\] nor local maximum at \[x=\sqrt{ab}.\].
D) None of the above
View Answer play_arrowquestion_answer190) The system of homogeneous equations \[tx+(t+1)y+(t-1)z=0,\] \[(t+1)x+ty+(t+2)z=0\] \[(t-1)x+(t+2)y+tz=0,\] has non-trival solutions for
A) exactly three real values oft
B) exactly two real values oft
C) exactly one real value oft
D) infinite number of values oft
View Answer play_arrowquestion_answer191) Matrix A is such that \[{{A}^{2}}=2A-I,\]where \[I\] is the identity matrix, then for \[n\ge 2,\,\,{{A}^{n}}\] is equal to
A) \[{{2}^{n-1}}A-(n-1)I\]
B) \[{{2}^{n-1}}A-I\]
C) \[nA-(n-1)I\]
D) \[nA-I\]
View Answer play_arrowquestion_answer192) If A is a matrix of order n, then determinant \[|-A|\] is equal to
A) \[|A|\]
B) \[-|A|\]
C) \[{{(-1)}^{n}}|A|\]
D) \[n\,|A|\]
View Answer play_arrowquestion_answer193) The value of the integral \[\int_{-\pi /2}^{\pi /2}{\sqrt{1-{{\cos }^{2}}\theta }}\,\,d\theta \]is equal to
A) \[0\]
B) \[1\]
C) \[2\]
D) \[-2\]
View Answer play_arrowquestion_answer194) If \[f(x)=\int_{1}^{x}{\sqrt{4-{{t}^{2}}}}\,\,\,dt,\] then real roots of the equation \[x-f'(x)=0\] are
A) \[\pm \,\,1\]
B) \[\pm \,\,\sqrt{2}\]
C) \[0\] and \[1\]
D) \[\pm \,\,2\]
View Answer play_arrowquestion_answer195) If \[f(x)={{\log }_{e}}\,(1+x)-{{\log }_{e}}(1-x),\]then the value of \[\int_{-1/2}^{1/2}{f(x)\,\,\,dx}\] equals to
A) \[0\]
B) \[1\]
C) \[\frac{1}{2}\]
D) \[-\frac{1}{2}\]
View Answer play_arrowquestion_answer196) Let \[f:(0,\,\,\infty )\to R\] and \[F(x)=\int_{0}^{x}{f(t)\,\,dt.}\]. If \[F({{x}^{2}})={{x}^{2}}(1+x),\]then \[f(1)\] equals to
A) \[\frac{5}{2}\]
B) \[5\]
C) \[\frac{2}{5}\]
D) \[2\]
View Answer play_arrowquestion_answer197) The vectors \[a=i+4j-7k,\,b=\lambda i-j+4k\] and \[c=-9i+18k\] are coplanar, if \[\lambda \] equals to
A) \[0\]
B) \[1\]
C) \[2\]
D) None of these
View Answer play_arrowquestion_answer198) Let a and b be two unit vectors such that \[a+2b\]and \[5\text{ }a-4b\] are perpendicular to each other, then the angle between a and b is
A) \[{{30}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{90}^{o}}\]
View Answer play_arrowquestion_answer199) Let R be the set of real numbers and \[f:R\to R\] be a function defined by \[f(x)={{x}^{2}}+4.\] Then, \[{{f}^{-1}}(29)\]equals to
A) \[\phi \]
B) \[\{5,\,\,\,-5\}\]
C) \[\{4,\,\,\,-4\}\]
D) \[\{2,\,\,\,-4\}\]
View Answer play_arrowquestion_answer200) The function \[f:R\to R\] defined by \[f(x)=\frac{{{e}^{|x|}}-{{e}^{-x}}}{{{e}^{x}}+{{e}^{-x}}}\] is
A) one-one and onto
B) one-one but not onto
C) not one-one but onto
D) neither one-one nor onto
View Answer play_arrowquestion_answer201) The sum of the coefficients of the polynomial \[{{(1+x+{{x}^{2}}-4{{x}^{3}})}^{2149}}\] is
A) \[1\]
B) \[-1\]
C) \[2143\]
D) \[2156\]
View Answer play_arrowquestion_answer202) If \[z=1-i,\] then principal value of arg (z) equals to
A) \[-\frac{\pi }{4}\]
B) \[\frac{\pi }{4}\]
C) \[-\frac{7\pi }{4}\]
D) None of these
View Answer play_arrowquestion_answer203) The number of solutions to the equation \[{{z}^{2}}+\bar{z}=0\] is equal to
A) \[1\]
B) \[2\]
C) \[3\]
D) \[4\]
View Answer play_arrowquestion_answer204) \[{{i}^{i}}\] (when \[i=\sqrt{-1}\]) is
A) a purely real number
B) a purely complex number
C) a complex number whose real part is always a negative real number
D) a complex number whose real part is always a positive integer
View Answer play_arrowquestion_answer205) The equation of the directrix of the parabola \[{{y}^{2}}+4x+4y+2=0\]is
A) \[x=1\]
B) \[x=-1\]
C) \[x=\frac{3}{2}\]
D) \[x=\frac{2}{3}\]
View Answer play_arrowquestion_answer206) Equation of the ellipse having vertices at \[(\pm \,\,5,\,\,0)\] and foci at \[(\pm \,\,4,\,\,0)\] is
A) \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{9}=1\]
B) \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\]
C) \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{16}=1\]
D) \[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{5}=1\]
View Answer play_arrowquestion_answer207) The number of integer values of m, for which the x-coordinate of the point of intersection of the lines \[x+y=3\]and \[y=3mx+1\]is also an integer, is
A) \[0\]
B) \[1\]
C) \[2\]
D) \[4\]
View Answer play_arrowquestion_answer208) The points \[(a,\,\,0),\,\,\,(0,\,\,b)\] and \[(1,\,\,-1)\] are collinear \[(a\ne 0,\,b\ne 0),\] if
A) \[b-a=ab\]
B) \[b+a=ab\]
C) \[a-b=ab\]
D) \[a+b=-ab\]
View Answer play_arrowquestion_answer209) If the points \[(2a,\,a),\,(a,\,2a)\] and \[(a,\,\,a)\] form a triangle of area \[32\text{ }sq\]units, then the centroid of the triangle is
A) \[(32,\,\,32)\]
B) \[(-32,\,\,-32)\]
C) \[(3,\,3)\]
D) \[\left( \frac{32}{3},\,\frac{32}{3} \right)\]
View Answer play_arrowquestion_answer210) If the curve \[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\] intersects the coordinate axes at A and B, then equation of straight line joining A and B is .
A) \[x+y=\sqrt{2}\]
B) \[x+y=1\]
C) \[x-y=1\]
D) \[x-y=\sqrt{2}\]
View Answer play_arrowquestion_answer211) If the system of equations \[(k+1)x+8y=4k\] and \[kx+(k+3)y=3k-1\] has infinitely many solutions, then k is equal to
A) \[0\]
B) \[1\]
C) \[3\]
D) \[-3\]
View Answer play_arrowquestion_answer212) The solution of the differential equation \[\frac{dy}{dx}+\frac{y}{1+{{x}^{2}}}=\frac{{{e}^{x}}}{{{e}^{{{\tan }^{-1}}x}}},\,\,y(0)=1\]is
A) \[y={{e}^{x-{{\tan }^{-1}}x}}\]
B) \[y={{e}^{x}}.{{\tan }^{-1}}x+1\]
C) \[y={{\tan }^{-1}}\,x+1\]
D) \[y={{e}^{x+{{\tan }^{-1}}x}}\]
View Answer play_arrowquestion_answer213) The value of the integral \[\int_{0}^{1}{x{{(1-x)}^{49}}\,dx}\] is equal to
A) \[\frac{1}{2550}\]
B) \[\frac{1}{2500}\]
C) \[\frac{10}{490}\]
D) \[\frac{1}{49}\]
View Answer play_arrowquestion_answer214) The value of \[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{\int_{0}^{x}{\sin \,({{t}^{2}})\,dt}}{{{x}^{3}}}\]is equal to
A) \[0\]
B) \[1\]
C) \[3\]
D) None of these
View Answer play_arrowquestion_answer215) The value of the integral \[\int{\frac{{{e}^{x}}(1+\sin x)}{1+\cos x}}\,\,dx\] is equal to (K is any constant)
A) \[{{\log }_{e}}\,|\tan x|+K\]
B) \[{{e}^{x}}\,\tan \,\left( \frac{x}{2} \right)+K\]
C) \[{{e}^{x}}\,\tan \,x+K\]
D) \[{{e}^{x}}\,{{\log }_{e}}\,|\sec \,x|+K\]
View Answer play_arrowquestion_answer216) The area bounded by the curves \[y=\sqrt{x},\,\,2y+3=x\] and the x-axis lying in the first quadrant, is (in sq units)
A) \[9\]
B) \[27\]
C) \[27/2\]
D) \[18\]
View Answer play_arrowquestion_answer217) In a \[\Delta \,\,ABC,\] let \[\angle A=\frac{\pi }{2}\] and \[(a+b+c)\,(b+c-a)=\lambda bc,\] then \[\lambda \] equals to
A) \[0\]
B) \[1\]
C) \[2\]
D) \[-2\]
View Answer play_arrowquestion_answer218) In a triangle, the lengths of the two larger sides are 10 and 9, respectively. If the angles are in AP, then the length of the third side can be
A) \[4\]
B) \[5\]
C) \[6-\sqrt{6}\]
D) \[5+\sqrt{6}\]
View Answer play_arrowquestion_answer219) If \[\theta \] lies in the second quadrant arid \[3\tan \theta +4=0,\] then the value of \[\sin \theta +\cos \theta \] is equal to
A) \[\frac{1}{5}\]
B) \[\frac{2}{5}\]
C) \[\frac{3}{5}\]
D) \[\frac{4}{5}\]
View Answer play_arrowquestion_answer220) Let A and B be acute angles such that \[\sin \,A={{\sin }^{2}}B\]and \[2{{\cos }^{2}}A=3{{\cos }^{2}}B.\]Then, A equals to
A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{6}\]
C) \[\frac{\pi }{3}\]
D) None of these
View Answer play_arrowquestion_answer221) If \[\sin x\,\cos \,y=\frac{1}{4}\]and \[3\tan x=4\tan y,\], then \[\sin (x-y)\] equals to
A) \[\frac{1}{16}\]
B) \[\frac{1}{8}\]
C) \[\frac{3}{16}\]
D) \[\frac{3}{4}\]
View Answer play_arrowquestion_answer222) If \[A+B+C=\pi \] and \[\sin C+\sin A\,\cos B=0,\] then \[\tan \,A.\,\cot \,B\] is equal to
A) \[0\]
B) \[-\frac{1}{2}\]
C) \[1\]
D) \[-1\]
View Answer play_arrowquestion_answer223) If n is an even integer, then the value of \[^{n}{{C}_{0}}{{+}^{n}}{{C}_{2}}{{+}^{n}}{{C}_{4}}+....{{+}^{n}}{{C}_{n}}\] equals to
A) \[{{2}^{n}}\]
B) \[{{2}^{n+1}}\]
C) \[{{2}^{n-1}}\]
D) \[{{2}^{2n}}\]
View Answer play_arrowquestion_answer224) The coefficient of the term independent of x in the expansion of x\[{{\left( \sqrt{x}+\frac{1}{\sqrt{x}} \right)}^{10}}\] is equal to
A) \[10\]
B) \[252\]
C) \[20\]
D) \[256\]
View Answer play_arrowquestion_answer225) The range of function \[f(x)={{\log }_{a}}x,\,\,a>0\] is
A) \[(0,\,\,\,\infty )\]
B) \[(-\,\infty ,\,\,\infty )\]
C) \[(-\,\infty ,\,\,\infty )-\{\,0\,\}\]
D) None of these
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