JEE Main 2016 (Online) 10th April Morning Slot

An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is :

If x is a solution of the equation, \(\sqrt {2x + 1}\) \(- \sqrt {2x - 1} = 1,\) \(\,\,\left( {x \ge {1 \over 2}} \right),\) then \(\sqrt {4{x^2} - 1}\) is equal to :

Let z = 1 + ai be a complex number, a > 0, such that z3 is a real number.
Then the sum 1 + z + z2 + . . . . .+ z11 is equal to :

If   A > 0, B > 0   and    A + B = \({\pi \over 6}\), then the minimum value of tanA + tanB is :

Let a1, a2, a3, . . . . . . . , an, . . . . . be in A.P.
If a3 + a7 + a11 + a15 = 72,
then the sum of its first 17 terms is equal to :

Let P = {\(\theta\) : sin\(\theta\) \(-\) cos\(\theta\) = \(\sqrt 2 \,\cos \theta\)} and Q = {\(\theta\) : sin\(\theta\) + cos\(\theta\) = \(\sqrt 2 \,\sin \theta\)} be two sets. Then

The mean of 5 observations is 5 and their variance is 124. If three of the observations
are 1, 2 and 6 ; then the mean deviation from the mean of the data is :

A ray of light is incident along a line which meets another line, 7x − y + 1 = 0, at the point (0, 1). The ray is then reflected from this point along the line, y + 2x = 1. Then the equation of the line of incidence of the ray of light is :

A straight line through origin O meets the lines 3y = 10 − 4x and 8x + 6y + 5 = 0 at points A and B respectively. Then O divides the segment AB in the ratio :

Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are \(\overrightarrow a ,\overrightarrow b ,\overrightarrow c\) and \({{\overrightarrow a + \overrightarrow b + \overrightarrow c } \over 4}\) ...

Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be 1 \(\mu\)F is :

A neutron moving with a speed ‘v’ makes a head on collision with a stationary
hydrogen atom in ground state. The minimum kinetic energy of the neutron for
which inelastic collision will take place is :

In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then \({{BC} \over {AB}}\) is close to :

A modulated signal Cm(t) has the form Cm(t) = 30 sin 300 \(\pi\)t + 10 (cos 200 \(\pi\)t −cos 400 \(\pi\)t). The carrier frequency c, the modulating frequency (message frequency) f\(\omega\), and the modulation index \(\mu\) are respec...

A galvanometer has a 50 division scale. Battery has no internal resistance. It is found that there is deflection of 40 divisions when R = 2400 \(\Omega\). Deflection becomes 20 divisions when resistance taken from resistance box is 4900 $$...

The resistance of an electrical toaster has a temperature dependence given by R(T) = R0 [1 + \(\alpha\)(T − T0)] in its range of operation. At T0 = 300 K, R = 100 \(\Omega\) and at T = 500 K, R = 120 \(\Omega\). The toaster is connected ...

A photoelectric surface is illuminated successively by monochromatic light of wavelengths \(\lambda\) and \({\lambda \over 2}.\) If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first c...

Consider a thin metallic sheet perpendicular to the plane of the paper
moving with speed ‘v’ in a uniform magnetic field B going into the plane of the paper (See figure). If charge densities \(\sigma\)1 and \(\sigma\)2 are induced on the ...

A conducting metal circular-wire-loop of radius r is placed perpendicular to a
magnetic field which varies with time as
B = B0e\({^{{{ - t} \over r}}}\) , where B0 and \(\tau\) are constants, at time t = 0. If the resistance of the loop i...

Consider an electromagnetic wave propagating in vacuum. Choose the correct
statement :

To get an output of 1 from the circuit shown in figure the input must be :

The ratio (R) of output resistance r0, and the input resistance ri in measurements of input and output characteristics of a transistor is typically in the range:

A realistic graph depicting the variation of the reciprocal of input resistance in an input characteristics measurement in a commonemitter
transistor configuration is :

Within a spherical charge distribution of charge density \(\rho\)(r), N equipotential surfaces of potential V0, V0 + \(\Delta\)V, V0 + 2\(\Delta\)V, .......... V0 + N\(\Delta\)V (\(\Delta\) V > 0), are drawn and have increasing radii r...

To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are :

A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 6 cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirro...

An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth’s surface. The radius of the earth is R, while its mass is M. The gravitational pull FG on the astronaut is :

A Carnot freezer takes heat from water at 0oC inside it and rejects it to the room at a temperature of 27oC. The latent heat of ice is 336×103 J kg−1. If 5 kg of water at 0oC is converted into ice at 0oC by the freezer, then the energy cons...

Which of the following shows the correct relationship between the pressure ‘P’ and density \(\rho\) of an ideal gas at constant temperature ?

A particle of mass m is acted upon by a force F given by the empirical law
F =\({R \over {{t^2}}}\,v\left( t \right).\) If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot :

A fighter plane of length 20 m, wing span (distance from tip of one wing to the tip of the other wing) of 15 m and height 5 m is flying towards east over Delhi. Its speed is 240 ms−1. The earth’s magnetic field over Delhi is 5 \(\times\)1...

A thin 1 m long rod has a radius of 5 mm. A force of 50 \(\pi\)kN is applied at one end to determine its Young’s modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the...

A bottle has an opening of radius a and length b. A cork of length b and radius (a + \(\Delta\)a) where (\(\Delta\)a < < a) is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coe...

Concrete mixture is made by mixing cement, stone and sand in a rotating
cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum r...

In an engine the piston undergoes vertical simple harmonic motion with amplitude 7 cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer sta...

A, B, C and D are four different physical quantities having different
dimensions. None of them is dimensionless. But we know that the equation AD = C ln (BD) holds true. Then which of the combination is not a meaningful quantity ?

Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm. The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be...

A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beats per second. If the velocity of sound in air is 340 m/s, the frequency of the hor...

A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n2 R t2 where n is a constant. The power delivered to the particle by the force acting on it, is :

Velocity-time graph for a body of mass 10 kg is shown in figure. Work-done on
the body in first two seconds of the motion is :