question_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?
question_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?
question_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?
question_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?
question_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
doneclear
B)
\[0.5\text{ }A\]in the same direction as those in the first and the third
doneclear
C)
\[0.5\text{ }A\]in the opposite direction to those in the first and the third
doneclear
D)
\[0.25\text{ }A\]in the same direction as those in the first and the third
question_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?
question_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)
\[10m/{{s}^{2}}\]
doneclear
B)
Less than \[10m/{{s}^{2}}\]
doneclear
C)
More than \[10m/{{s}^{2}}\]
doneclear
D)
the answer will depend upon which pole of the magnet is up
question_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?
question_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?
question_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
question_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
question_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?
question_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?
question_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
question_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
question_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
doneclear
B)
There is a threshold frequency, below which no photoelectrons are emitted, no matter how long the light is thrown on the metallic surface
doneclear
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
doneclear
D)
For each frequency of light, exceeding the threshold frequency, there is a maximum kinetic energy of the emitted electrons
question_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
question_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?
question_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
question_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
question_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?
question_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?
question_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
doneclear
B)
When it is at the maximum displacement
doneclear
C)
When it passes through the equilibrium point, either way
doneclear
D)
When' it is at a displacement \[\pm \frac{A}{\sqrt{2}}\] from the equilibrium point and moving away from the equilibrium point
question_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?
question_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\[(20\,\,cm,\,\,20\,\,cm)\]?
question_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?
question_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?
question_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?
question_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?
question_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?
question_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?
question_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
doneclear
B)
They will become plane wave fronts
doneclear
C)
They will remain spherical, with the same curvature, but sign of curvature reversed
doneclear
D)
They will remain spherical, but with different curvature, both in magnitude and sign
question_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
doneclear
B)
it is independent of the aperture of the telescope
doneclear
C)
it increases linearly with the aperture of the telescope
doneclear
D)
it increases quadratic ally with the aperture of the telescope
question_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)
\[2%\]
doneclear
B)
\[8%\]
doneclear
C)
\[15%\]
doneclear
D)
without the value of the constant a, the percentage of error cannot be calculated
question_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. \[10\text{ }m/{{s}^{2}}\].
question_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
doneclear
B)
b and c must be parallel to each other, but a need not be parallel to b and c
doneclear
C)
a and b must be perpendicular to each other
doneclear
D)
It is impossible for three non-zero vectors a, b and c to have the property stated above
question_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
question_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?
question_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?
question_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,
question_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
question_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?
question_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?
question_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
doneclear
B)
Reduce the distance between the slit and the screen to \[{{\left( \frac{1}{4} \right)}^{th}}\]the original separation
doneclear
C)
Double the distance between the slit and the screen
doneclear
D)
No need to do anything, as the width of the central maxima does not depend on the slit width
question_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
question_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?
question_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
doneclear
B)
\[\text{ }\!\!~\!\!\text{ N}{{\text{H}}_{\text{2}}}\] group .
question_answer98) Certain reactions follow die relation between concentrations of the reactant \[vs\]time as What is the expected order for such reactions?
question_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
question_answer150) 2-bromobutane reacts with \[\text{O}{{\text{H}}^{-}}\]in \[{{\text{H}}_{\text{2}}}\text{O}\]to give 2-butanol. The reaction involves
question_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
question_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
question_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
question_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
question_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
question_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
question_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
question_answer170) The trajectory of the differential equation \[\frac{dx}{dt}=rx\left( 1-\frac{x}{k} \right),\,\,\,\,r>0\] is monotonically increasing, if
question_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
question_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
question_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
question_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
question_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 \[x=\sqrt{ab}.\]
doneclear
B)
\[f(x)\] has a local maximum at \[x=\sqrt{ab}.\]
doneclear
C)
\[f(x)\]has a neither local minimum at \[x=\sqrt{ab}.\] nor local maximum at \[x=\sqrt{ab}.\].
question_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
question_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
question_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
question_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
question_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 .
question_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
question_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
question_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