JEE Main 2023 (Online) 10th April Morning Shift

The number of permutations, of the digits 1, 2, 3, ..., 7 without repetition, which neither contain the string 153 nor the string 2467, is ___________.

Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then the total number of persons, who participated in the tournament, is ___________.

Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that \({2^N} < N!\) is \({m \over n}\), where m and n are coprime, then \(4m-3n\) is equal to :

Let the first term \(\alpha\) and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033, then the sum of these three terms is equal to

The sum of all those terms, of the arithmetic progression 3, 8, 13, ...., 373, which are not divisible by 3, is equal to ____________.

The number of elements in the set \(\{ n \in Z:|{n^2} - 10n + 19| < 6\}\) is _________.

If the mean of the frequency distribution

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\(96\cos {\pi \over {33}}\cos {{2\pi } \over {33}}\cos {{4\pi } \over {33}}\cos {{8\pi } \over {33}}\cos {{16\pi } \over {33}}\) is equal to :

Let O be the origin and the position vector of the point P be \(- \widehat i - 2\widehat j + 3\widehat k\). If the position vectors of the points A, B and C are $$ - 2\widehat i + \widehat j - 3\widehat k,2\widehat i + 4\widehat j - 2\wide...

An arc PQ of a circle subtends a right angle at its centre O. The mid point of the arc PQ is R. If \(\overrightarrow {OP} = \overrightarrow u ,\overrightarrow {OR} = \overrightarrow v\), and $$\overrightarrow {OQ} = \alpha \overrightarr...

Given below are two statements:
Statement I : Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs
Statement II : Maximum power is dissipate...

The angular momentum for the electron in Bohr's orbit is L. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be

The decay constant for a radioactive nuclide is 1.5 \(\times\) 10\(^{-5}\) s\(^{-1}\). Atomic weight of the substance is 60 g mole\(^{-1}\), (\(N_A=6\times10^{23}\)). The activity of 1.0 \(\mu\)g of the substance is ___________ \(\times\) 1...

The equivalent capacitance of the combination shown is :

A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. After collision, they stick together and continue to move together with velocity

A carrier wave of amplitude 15 V is modulated by a sinusoidal base band signal of magnitude 3 V. The ratio of maximum amplitude to minimum amplitude in an amplitude modulated wave is

The equivalent resistance of the circuit shown below between points a and b is :

10 resistors each of resistance 10 \(\Omega\) can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be ___________.

The de Broglie wavelength of a molecule in a gas at room temperature (300 K) is \(\lambda_1\). If the temperature of the gas is increased to 600 K, then the de Broglie wavelength of the same gas molecule becomes

Given below are two statements:
Statement I : If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double.
Statement II : Increasing current sensitivity of a moving coil galvanomet...

A 1 m long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the circuit is 5\(\Omega\), the force needed to move the rod in d...

The energy of an electromagnetic wave contained in a small volume oscillates with

A zener diode of power rating 1.6 W is to be used as voltage regulator. If the zener diode has a breakdown of 8V and it has to regulate voltage fluctuating between 3 V and 10 V. The value of resistance Rs for safe operation of diode will be...

Three concentric spherical metallic shells X, Y and Z of radius a, b and c respectively [a < b < c] have surface charge densities \(\sigma,-\sigma\) and \(\sigma\) respectively. The shells X and Z are at same potential. If the radii of X & ...

An object is placed at a distance of 12 cm in front of a plane mirror. The virtual and erect image is formed by the mirror. Now the mirror is moved by 4 cm towards the stationary object. The distance by which the position of image would be ...

Two satellites of masses m and 3m revolve around the earth in circular orbits of radii r & 3r respectively. The ratio of orbital speeds of the satellites respectively is

Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth \(d=\frac{R}{2}\) from the surface of earth, if its weight on the surface of earth is 200 N, will be:
(Given R = radius of earth)

If the earth suddenly shrinks to \(\frac{1}{64}\)th of its original volume with its mass remaining the same, the period of rotation of earth becomes \(\frac{24}{x}\)h. The value of x is __________.

Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The gas in A is compressed isothermally to \(\frac{1}{8}\) of its original volume while the gas in B is compressed adiabat...

Match List I with List II :

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The current required to be passed through a solenoid of 15 cm length and 60 turns in order of demagnetise a bar magnet of magnetic intensity \(2.4\times10^3~Am^{-1}\) is ___________ A.

The range of the projectile projected at an angle of 15\(^\circ\) with horizontal is 50 m. If the projectile is projected with same velocity at an angle of 45\(^\circ\) with horizontal, then its range will be

The position-time graphs for two students A and B returning from the school to their homes are shown in figure.

(A) A lives closer to the school
(B) B lives closer to the school
(C) A takes lesser time to reach home
(D) A travels faster th...

Given below are two statements:
Statement I : Pressure in a reservoir of water is same at all points at the same level of water.
Statement II : The pressure applied to enclosed water is transmitted in all directions equally.
In the light of...

Two wires each of radius 0.2 cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is __________ \(\times\) 10\(^{-6}\) m. [Young's modulus for steel = 2 $$...

A particle executes S.H.M. of amplitude A along x-axis. At t = 0, the position of the particle is \(x=\frac{A}{2}\) and it moves along positive x-axis. The displacement of particle in time t is \(x = A\sin (wt + \delta )\), then the value o...

A physical quantity P is given as
\(P = {{{a^2}{b^3}} \over {c\sqrt d }}\)
The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be

Unpolarised light of intensity 32 Wm\(^{-2}\) passes through the combination of three polaroids such that the pass axis of the last polaroid is perpendicular to that of the pass axis of first polaroid. If intensity of emerging light is 3 Wm...

A transverse harmonic wave on a string is given by
\(y(x,t) = 5\sin (6t + 0.003x)\)
where x and y are in cm and t in sec. The wave velocity is _______________ ms\(^{-1}\).

A closed circular tube of average radius 15 cm, whose inner walls are rough, is kept in vertical plane. A block of mass 1 kg just fit inside the tube. The speed of block is 22 m/s, when it is introduced at the top of tube. After completing ...