JEE Main 2021 (Online) 27th July Morning Shift

Let \(A = \left[ {\matrix{ 1 & 2 \cr { - 1} & 4 \cr } } \right]\). If A\(-\)1 = \(\alpha\)I + \(\beta\)A, \(\alpha\), \(\beta\) \(\in\) R, I is a 2 \(\times\) 2 identity matrix then 4(\(\alpha\) \(-\) \(\beta\)) is equal to :

For real numbers \(\alpha\) and \(\beta\), consider the following system of linear equations :x + y \(-\) z = 2, x + 2y + \(\alpha\)z = 1, 2x \(-\) y + z = \(\beta\). If the system has infinite solutions, then \(\alpha\) + \(\beta\) is equa...

Let \(f(x) = \left| {\matrix{ {{{\sin }^2}x} & { - 2 + {{\cos }^2}x} & {\cos 2x} \cr {2 + {{\sin }^2}x} & {{{\cos }^2}x} & {\cos 2x} \cr {{{\sin }^2}x} & {{{\cos }^2}x} & {1 + \cos 2x} \cr } } \right|,x \in [0,\pi ]\). Then...

The probability that a randomly selected 2-digit number belongs to the set {n \(\in\) N : (2n \(-\) 2) is a multiple of 3} is equal to :

Let \(\alpha\), \(\beta\) be two roots of the equation x2 + (20)1/4x + (5)1/2 = 0. Then \(\alpha\)8 + \(\beta\)8 is equal to

If \({\log _3}2,{\log _3}({2^x} - 5),{\log _3}\left( {{2^x} - {7 \over 2}} \right)\) are in an arithmetic progression, then the value of x is equal to _____________.

If the mean and variance of the following data : 6, 10, 7, 13, a, 12, b, 12 are 9 and \({{37} \over 4}\) respectively, then (a \(-\) b)2 is equal to :

If \(\sin \theta + \cos \theta = {1 \over 2}\), then 16(sin(2\(\theta\)) + cos(4\(\theta\)) + sin(6\(\theta\))) is equal to :

Let \(\overrightarrow a = \widehat i + \widehat j + 2\widehat k\) and \(\overrightarrow b = - \widehat i + 2\widehat j + 3\widehat k\). Then the vector product $$\left( {\overrightarrow a + \overrightarrow b } \right) \times \left( {\le...

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

A 0.07 H inductor and a 12\(\Omega\) resistor are connected in series to a 220V, 50 Hz ac source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take \(\pi\) as $${{22} \over...

Consider an electrical circuit containing a two way switch 'S'. Initially S is open and then T1 is connected to T2. As the current in R = 6\(\Omega\) attains a maximum value of steady state level, T1 is disconnected from T2 and immediately ...

If 'f' denotes the ratio of the number of nuclei decayed (Nd) to the number of nuclei at t = 0 (N0) then for a collection of radioactive nuclei, the rate of change of 'f' with respect to time is given as :[\(\lambda\) is the radioactive dec...

In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 \(\mathop A\limits^o\). If the speed of electron is 2.2 \(\times\) 166 m/s, then the current associated with the electron will be _____________ $$...

A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance 200 \(\mu\)F is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is ...

A capacitor of capacitance C = 1 \(\mu\)F is suddenly connected to a battery of 100 volt through a resistance R = 100 \(\Omega\). The time taken for the capacitor to be charged to get 50 V is :[Take ln 2 = 0.69]

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be :(Given area of plate = A)

Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across ...

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2m and 2m respectively. A moves towards B with a speed of 9 m/s and makes an elastic collision with it. Thereafter B ...

The amplitude of upper and lower side bands of A.M. wave where a carrier signal with frequency 11.21 MHz, peak voltage 15 V is amplitude modulated by a 7.7 kHz sine wave of 5V amplitude are \({a \over {10}}V\) and \({b \over {10}}V\) respec...

In the given figure, a battery of emf E is connected across a conductor PQ of length 'l' and different area of cross-sections having radii r1 and r2 (r2 < r1). Choose the correct option as one moves from P to Q :

A particle of mass 9.1 \(\times\) 10\(-\)31 kg travels in a medium with a speed of 106 m/s and a photon of a radiation of linear momentum 10\(-\)27 kg m/s travels in vacuum. The wavelength of photon is __________ times the wavelength of the...

The relative permittivity of distilled water is 81. The velocity of light in it will be :(Given \(\mu\)r = 1)

A transistor is connected in common emitter circuit configuration, the collector supply voltage is 10 V and the voltage drop across a resistor of 1000 \(\Omega\) in the collector circuit is 0.6 V. If the current gain factor (\(\beta\)) is 2...

Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle '\(\theta\)' with the vertical?

A prism of refractive index n1 and another prism of refractive index n2 are stuck together (as shown in the figure). n1 and n2 depend on \(\lambda\), the wavelength of light, according to the relation$${n_1} = 1.2 + {{10.8 \times {{10}^{ - ...

Suppose two planets (spherical in shape) in radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' direct...

The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy 2 \(\times\) 10\(-\)9 J per molecules is :

In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A \(\to\) B and C \(\to\) D are T1 and T2 (T1 > T2) respectively.Choose the correct option out of ...

In a uniform magnetic field, the magnetic needle has a magnetic moment 9.85 \(\times\) 10\(-\)2 A/m2 and moment of inertia 5 \(\times\) 10\(-\)6 kg m2. If it performs 10 complete oscillations in 5 seconds then the magnitude of the magnetic ...

A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times of the ball reaching \({h \over 3}\) in both the directions.

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact...

A body takes 4 min. to cool from 61\(^\circ\) C to 59\(^\circ\) C. If the temperature of the surroundings is 30\(^\circ\) C, the time taken by the body to cool from 51\(^\circ\) C to 49\(^\circ\) C is :

A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section 10\(-\)6 m2 stretched by an amount 0.04 m. The velocity of the projected stone is ______________ m/s.(Young's modulus of rubber = 0.5 $$\time...

List-I
List-II




(a) MI of the rod (length L, Mass M, about an axis \(\bot\) to the rod passing through the midpoint)
(i) \(8M{L^2}/3\)


(b) MI of the rod (length L, Mass 2M, about an axis \(\bot\) to...

The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB (Which is \(\bot\) to the plane of the disc and passing through its centre) o...

A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is \({{3E} \over 4}\) then its displacement 'y' is given by :

Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm.Reason R :Least Count = $${{...

Assertion A : If A, B, C, D are four points on a semi-circular are with centre at 'O' such that \(\left| {\overrightarrow {AB} } \right| = \left| {\overrightarrow {BC} } \right| = \left| {\overrightarrow {CD} } \right|\), then $$\overrighta...

In Young's double slit experiment, if the source of light changes from orange to blue then :