JEE Main 2021 (Online) 18th March Morning Shift

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is :

The value of \(3 + {1 \over {4 + {1 \over {3 + {1 \over {4 + {1 \over {3 + ....\infty }}}}}}}}\) is equal to

\({1 \over {{3^2} - 1}} + {1 \over {{5^2} - 1}} + {1 \over {{7^2} - 1}} + .... + {1 \over {{{(201)}^2} - 1}}\) is equal to

If \(\alpha\), \(\beta\) are natural numbers such that 100\(\alpha\) \(-\) 199\(\beta\) = (100)(100) + (99)(101) + (98)(102) + ...... + (1)(199), then the slope of the line passing through (\(\alpha\), \(\beta\)) and origin is :

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly ...

The equation of one of the straight lines which passes through the point (1, 3) and makes an angles \({\tan ^{ - 1}}\left( {\sqrt 2 } \right)\) with the straight line, y + 1 = 3\({\sqrt 2 }\) x is :

The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is :

A square ABCD has all its vertices on the curve x2y2 = 1. The midpoints of its sides also lie on the same curve. Then, the square of area of ABCD is _________.

The number of solutions of the equation \(|\cot x| = \cot x + {1 \over {\sin x}}\) in the interval [ 0, 2\(\pi\) ] is

A vector \(\overrightarrow a\) has components 3p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to new system, $$\overr...

In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value :

An AC source rated 220 V, 50 Hz is connected to a resistor. The time taken by the current to change from its maximum to the rms value is :

Imagine that the electron in a hydrogen atom is replaced by a muon (\(\mu\)). The mass of muon particle is 207 times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will b...

A radioactive sample disintegrates via two independent decay processes having half lives \(T_{1/2}^{(1)}\) and \(T_{1/2}^{(2)}\) respectively. The effective half-life T1/2 of the nuclei is :

A parallel plate capacitor has plate area 100 m2 and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is 'x' pF.The ...

The circuit shown in the figure consists of a charged capacitor of capacity 3 \(\mu\)F and a charge of \(\mu\)C. At time t = 0, when the key is closed, the value of current flowing through the 5 M\(\Omega\) resistor is 'x' \(\mu\)-A. The va...

A ball of mass 10 kg moving with a velocity 10\(\sqrt 3\) m/s along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One ...

Match List - I with List - II.List - I(a) 10 km height over earth's surface(b) 70 km height over earth's surface(c) 180 km height over earth's surface(d) 270 km height over earth's surfaceList - II(i) Thermosphere(ii) Mesosphere(iii) Strato...

In the experiment of Ohm's law, a potential difference of 5.0 V is applied across the end of a conductor of length 10.0 cm and diameter of 5.00 mm. The measured current in the conductor is 2.00 A. The maximum permissible percentage error in...

The voltage across the 10\(\Omega\) resistor in the given circuit is x volt.The value of 'x' to the nearest integer is _________.

A particle is travelling 4 time as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2 : 1, the mass of the particle is :

A plane electromagnetic wave of frequency 100 MHz is travelling in vacuum along the x-direction. At a particular point in space and time, \(\overrightarrow B = 2.0 \times {10^{ - 8}}\widehat kT\). (where, \(\widehat k\) is unit vector alon...

An npn transistor operates as a common emitter amplifier with a power gain of 106. The input circuit resistance is 100\(\Omega\) and the output load resistance is 10 K\(\Omega\). The common emitter current gain '\(\beta\)' will be ________....

An oil drop of radius 2 mm with a density 3g cm\(-\)3 is held stationary under a constant electric field 3.55 \(\times\) 105 V m\(-\)1 in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will poss...

Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her as non-uniform and distorted. The doctor diagnosed the problem as :

The time period of a satellite in a circular orbit of radius R is T. The period of another satellite in a circular orbit of radius 9R is :

The P-V diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done during an adiabatic process CD is (use \(\gamma\) = 1.4) :

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T? (kB is Boltzmann constant)

A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of bullet before hitting the wood is 10 m/s and it slows down with uniform deceleration, then th...

A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.

Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If the magnetic field at the center of A is 3T, the field at the center of C would be : (Assume that the magnetic field is confined with in the ...

A person is swimming with a speed of 10 m/s at an angle of 120\(^\circ\) with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is 'x' m/s. The value of 'x' to the nearest integer is ___...

The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by :

Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The...

A thin circular ring of mass M and radius r is rotating about its axis with an angular speed \(\omega\). Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become :

The time period of a simple pendulum is given by \(T = 2\pi \sqrt {{l \over g}}\). The measured value of the length of pendulum is 10 cm known to a 1mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using...

A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is \({1 \over a}\)s. The value of 'a' to the nearest integer ...

In Young's double slit arrangement, slits are separated by a gap of 0.5 mm, and the screen is placed at a distance of 0.5 m from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a mon...

As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is x m/s. (Take g = 10 m/s2)The value of...

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to :-