JEE Main 2022 (Online) 28th June Morning Shift

Let A be a matrix of order 3 \(\times\) 3 and det (A) = 2. Then det (det (A) adj (5 adj (A3))) is equal to _____________.

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is :

The probability, that in a randomly selected 3-digit number at least two digits are odd, is :

The number of real solutions of the equation \({e^{4x}} + 4{e^{3x}} - 58{e^{2x}} + 4{e^x} + 1 = 0\) is ___________.

Let A1, A2, A3, ....... be an increasing geometric progression of positive real numbers. If A1A3A5A7 = \({1 \over {1296}}\) and A2 + A4 = \({7 \over {36}}\), then the value of A6 + A8 + A10 is equal to

Let A = {1, a1, a2 ....... a18, 77} be a set of integers with 1 < a1 < a2 < ....... < a18 < 77. Let the set A + A = {x + y : x, y \(\in\) A} contain exactly 39 elements. Then, the value of a1 + a2 + ...... + a18 is equal to _____________.

Let R1 and R2 be relations on the set {1, 2, ......., 50} such that
R1 = {(p, pn) : p is a prime and n \(\ge\) 0 is an integer} and
R2 = {(p, pn) : p is a prime and n = 0 or 1}.
Then, the number of elements in R1 \(-\) R2 is _______________...

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _____________.

A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2 : 1. Let the co-ordin...

If \(\overrightarrow a = 2\widehat i + \widehat j + 3\widehat k\), \(\overrightarrow b = 3\widehat i + 3\widehat j + \widehat k\) and \(\overrightarrow c = {c_1}\widehat i + {c_2}\widehat j + {c_3}\widehat k\) are coplanar vectors and $$...

An AC source is connected to an inductance of 100 mH, a capacitance of 100 \(\mu\)F and a resistance of 120 \(\Omega\) as shown in figure. The time in which the resistance having a thermal capacity 2 J/\(^\circ\)C will get heated by 16$$^\c...

A telegraph line of length 100 km has a capacity of 0.01 \(\mu\)F/km and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in serie...

The Q-value of a nuclear reaction and kinetic energy of the projectile particle, Kp are related as :

A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly car starts moving with velocity 2 ms\(-\)1. The velocity of the running man was ___________ ms\(-\)1, when he jumps into ...

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k2rt2, where k is a constant. The power delivered to the particle by the force acting on it is g...

Match List-I with List-II

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A meter bridge setup is shown in the figure. It is used to determine an unknown resistance R using a given resistor of 15 \(\Omega\). The galvanometer (G) shows null deflection when tapping key is at 43 cm mark from end A. If the end correc...

Current measured by the ammeter (A) in the reported circuit when no current flows through 10 \(\Omega\) resistance, will be ________________ A.

The de Broglie wavelengths for an electron and a photon are \(\lambda\)e and \(\lambda\)p respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie waveleng...

A radar sends an electromagnetic signal of electric field (E0) = 2.25 V/m and magnetic field (B0) = 1.5 \(\times\) 10\(-\)8 T which strikes a target on line of sight at a distance of 3 km in a medium. After that, a part of signal (echo) ref...

In the following circuit, the correct relation between output (Y) and inputs A and B will be :

For using a multimeter to identify diode from electrical components, choose the correct statement out of the following about the diode :

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : n-p-n transistor permits more current than a p-n-p transistor.
Reason R : Electrons have greater mobility as a charge carri...

Given below are two statements :
Statement I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive.
Statement II : An electric dipole is placed in ...

The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side 'a' as shown in figure. The magnitude of electric field (E) at the corner D of the square, is :

The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2). Then the angle of minimum deviation will be -

The aperture of the objective is 24.4 cm. The resolving power of this telescope, if a light of wavelength 2440 \(\mathop A\limits^o\) is used to see th object will be :

Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relat...

Given below are two statements :
Statement I : When \(\mu\) amount of an ideal gas undergoes adiabatic change from state (P1, V1, T1) to state (P2, V2, T2), then work done is \(W = {{\mu R({T_2} - {T_1})} \over {1 - \gamma }}\), where $$\ga...

The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be _____________ J. (Given R = 8.31 J/mol.K)

A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the str...

An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface.
Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.

A singly ionized magnesium atom (A = 24) ion is accelerated to kinetic energy 5 keV, and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be _____________ cm.

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity.
Reason R : Coefficient of ...

A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be :

Match List-I with List-II

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The position vector of 1 kg object is \(\overrightarrow r = \left( {3\widehat i - \widehat j} \right)m\) and its velocity \(\overrightarrow v = \left( {3\widehat j + \widehat k} \right)m{s^{ - 1}}\). The magnitude of its angular momentum ...

Motion of a particle in x-y plane is described by a set of following equations \(x = 4\sin \left( {{\pi \over 2} - \omega t} \right)\,m\) and \(y = 4\sin (\omega t)\,m\). The path of the particle will be :

A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled aside until the string is at 60\(^\circ\) with vertical as shown in the figure. After releasing the bob, the maximum veloc...

The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be :