JEE Main 2018 (Online) 16th April Morning Slot

The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is not allowed) and are multiple of 3 is :

Two different families A and B are blessed with equal numbe of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to ...

Let A, B and C be three events, which are pair-wise independent and \(\overrightarrow E\) denotes the completement of an event E. If \(P\left( {A \cap B \cap C} \right) = 0\) and \(P\left( C \right) > 0,\) then $$P\left[ {\left( {\overline...

If an angle A of a \(\Delta\)ABC satiesfies 5 cosA + 3 = 0, then the roots of the quadratic equation, 9x2 + 27x + 20 = 0 are :

Let p, q and r be real numbers (p \(\ne\) q, r \(\ne\) 0), such that the roots of the equation \({1 \over {x + p}} + {1 \over {x + q}} = {1 \over r}\) are equal in magnitude but opposite in sign, then the sum of squares of these roots...

Let \({1 \over {{x_1}}},{1 \over {{x_2}}},...,{1 \over {{x_n}}}\,\,\) (xi \(\ne\) 0 for i = 1, 2, ..., n) be in A.P. such that x1=4 and x21 = 20. If n is the least positive integer for which \({x_n} > 50,\) then $$\sum\limits_{i = 1}^n {\...

The sum of the first 20 terms of the series
\(1 + {3 \over 2} + {7 \over 4} + {{15} \over 8} + {{31} \over {16}} + ...,\) is :

Let N denote the set of all natural numbers. Define two binary relations on N as R = {(x, y) \(\in\) N \(\times\) N : 2x + y = 10} and R2 = {(x, y) \(\in\) N \(\times\) N : x + 2y = 10}. Then :

The mean and the standard deviation(s.d.) of five observations are9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :

Let \(\overrightarrow a = \widehat i + \widehat j + \widehat k,\overrightarrow c = \widehat j - \widehat k\) and a vector \(\overrightarrow b\) be such that \(\overrightarrow a \times \overrightarrow b = \overrightarrow c\) and $$\ove...

A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns, giving the output power at 230 V. If the current in the primary of the transformer is 5 A, and its efficiency i...

At some instant, a radioactive sample S1 having an activity 5 \(\mu\)Ci has twice the number of nuclei as another sample S2 which has an activity of 10 \(\mu\)Ci. The half lives of S1 and S2 are :

In the following circuit, the switch S is closed at t = 0. The charge on the capacitor C1 as a function of time will be given by \(\left( {{C_{eq}} = {{{C_1}{C_2}} \over {{C_1} + {C_2}}}} \right)\)

A carrier wave of peak voltage 14 V is used for transmitting a message signal. The peak voltage of modulating signal given to achieve a modulation index of 80% will be :

In a circuit for finding the resistance of a galvanometer by half deflection method, a 6 V battery and a high resistance of 11 k\(\Omega\) are used. The figure of merit of the galvanometer is 60 \(\mu A/\)division. In the absence of shu...

A heating element has a resistance of 100 \(\Omega\) at room temperature. When it is connected to a supply of 220 V, a steady current of 2 A passes in it and temperature is 500oC more than room temperature. what is the temperature coeffic...

A galvanometer with its coil resistance 25 \(\Omega\) requires a current of 1 mA for its full deflection. In order to construct an ammeter to read upto a current of 2 A, the approximate value of the shunt resistance should be :

The de-Broglie wavelength (\(\lambda\)B) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state (\(\lambda\)G) by :

Both the nucleus and the atom of some element arein their respective first excited states. They get de-excted by emitting photons of wavelengths \(\lambda\)N, \(\lambda\)A respectively. The ratio \({{{}^\lambda N} \over {{}^\lambda A}}\)...

A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B. When it is rotated with an angular velocity \(\omega ,\) the maxium e.m.f. induced in the coil will be:

A plane electromagnetic wave of wavelength \(\lambda\) has an intensity I. It is propagatting along the positive Y-direction. The allowed expressions for the electric and magnetic fields are givn by :

In the given circuit, the current through zener diode is :

Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between theis F. A third identical conducting sphere, C, is uncharged. Sphere C is first touh...

A ray of light is incident at an angle of 60o on one face of a prism of angle 30o. The emergent ray of light makes an angle of 30o with incident ray. The angle made by the emergent ray with second face of prism will be :

Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence :

One mole of an ideal monoatomic gas is taken along the path ABCA as show in the PV diagram. The maximum temperature attained by the gas along the path BC is given by :

Two moles of helium are mixed with n moles of hydrogen. If \({{Cp} \over {Cv}} = {3 \over 2}\) for the mixture, then the value of n is :

A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity \(\omega\) with resect to normal axis then the magnetic moment of the loop is :

A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let P2 be the pressure inside the inner bubble and P0, the pressure outside the outer bubble. Radius of another bubble with pressure dif...

A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and z' axes will be :

A particle executes simple harmonic motion and is located at x = a, b and c at times t0, 2t0 and 3t0 respectively. The freqquency of the oscillation is :

An oscillator of mass M is at rest in its equilibrium position in a potential
V = \({1 \over 2}\) k(x \(-\) X)2. A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This proce...

The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity A = \({{{P^3}{Q^2}} \over {\sqrt R S}}.\)
The maximum percentage error in the value of A will be :

The relative uncertainly in the period of a satellite orbiting around the earth is 10-2. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :

Let \(\overrightarrow A\) = \(\left( {\widehat i + \widehat j} \right)\) and, \(\overrightarrow B = \left( {2\widehat i - \widehat j} \right).\) The magnitude of a coplanar vector \(\overrightarrow C\) such that $$\overrightarrow A .\ove...

Unpolarized light of intensity I is incident on a system of two polarizers, A followed by B. The intensity of emergent light is I/2. If a third polarizer C is placed between A and B, the intensity of emergent light is reduced to I/3. The a...

Two sitar strings, A and B, playing the note 'Dha' are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B s slightly increased and the beat frequency is found to decrease by 3Hz. If the frequency of A is ...

The end correction of a resonance column is 1 cm. If the shortest length resonating with the tunning fork is 10 cm, the next resonating length should be :

A body of mass m starts moving from rest along x-axis so that its velocity varies as \(\upsilon = a\sqrt s\) where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the ...

Two particles of the same mass m are moving in circular orbits because of force, given by \(F\left( r \right) = {{ - 16} \over r} - {r^3}\)
The first particle is at a distance r = 1, and the second, at r = 4. The best estimate for the ratio...