JEE Main 2021 (Online) 16th March Evening Shift

Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB, CD, BC, DA respectively. Let \(\alpha\) be the number of triangles having these points from different sides as vertices and \(\beta\) be the number ...

Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then probability of event A is equal to :

In \(\Delta\)ABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of \(\Delta\)ABC is 30 cm2 and R and r are respectively the radii of circumcircle and incircle of \(\Delta\)ABC, then the value of 2R + r (in cm)...

Let \({1 \over {16}}\), a and b be in G.P. and \({1 \over a}\), \({1 \over b}\), 6 be in A.P., where a, b > 0. Then 72(a + b) is equal to ___________.

Sn(x) = loga1/2x + loga1/3x + loga1/6x + loga1/11x + loga1/18x + loga1/27x + ...... up to n-terms, where a > 1. If S24(x) = 1093 and S12(2x) = 265, then value of a is equal to ____________.

Let A = {2, 3, 4, 5, ....., 30} and '\(\simeq\)' be an equivalence relation on A \(\times\) A, defined by (a, b) \(\simeq\) (c, d), if and only if ad = bc. Then the number of ordered pairs which satisfy this equivalence relation with or...

Consider the statistics of two sets of observations as follows :



Size
Mean
Variance




Observation I
10
2
2


Observation II
n
3
1


If the variance of the combined set of thes...

Let A(\(-\)1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0, intersects lines AC and BC at point P and Q respectively. Let A1 and A2 be the areas of \(\Delta\)ABC and \(\Delta\)PQC respectively, such that A1 = 3A2, the...

Let \(\overrightarrow c\) be a vector perpendicular to the vectors, \(\overrightarrow a\) = \(\widehat i\) + \(\widehat j\) \(-\) \(\widehat k\) and \(\overrightarrow b\) = \(\widehat i\) + 2\(\widehat j\) + \(\widehat k\). If $$\overrig...

Let \(\overrightarrow a\) = \(\widehat i\) + 2\(\widehat j\) \(-\) 3\(\widehat k\) and \(\overrightarrow b = 2\widehat i\) \(-\) 3\(\widehat j\) + 5\(\widehat k\). If \(\overrightarrow r\) \(\times\) \(\overrightarrow a\) = $$\overright...

For the given circuit, comment on the type of transformer used.

The half-life of Au198 is 2.7 days. The activity of 1.50 mg of Au198 if its atomic weight is 198 g mol\(-\)1 is, (Na = 6 \(\times\) 1023/mol).

Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.

In a parallel plate capacitor set up, the plate area of capacitor is 2 m2 and the plates are separated by 1 m. If the space between the plates are filled with a dielectric material of thickness 0.5 m and area 2 m2 (see fig.) the capacitance...

A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical di...

Statement I : A cyclist is moving on an unbanked road with a speed of 7 kmh\(-\)1 and takes a sharp circular turn along a path of radius of 2m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and...

Two identical antennas mounted on identical towers are separated from each other by a distance of 45 km. What should nearly be the minimum height of receiving antenna to receive the signals in line of sight? (Assume radius of earth is 6400 ...

The energy dissipated by a resistor is 10 mJ in 1 s when an electric current of 2 mA flows through it. The resistance is ___________\(\Omega\). (Round off to the Nearest Integer)

A resistor develops 500 J of thermal energy in 20 s when a current of 1.5A is passed through it. If the current is increased from 1.5A to 3A, what will be the energy developed in 20 s.

The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V. What should nearly be the ratio of their wavelengths? (mp = 1.00727u me = 0.00055u)

The magnetic field in a region is given by \(\overrightarrow B = {B_o}\left( {{x \over a}} \right)\widehat k\). A square loop of side d is placed with its edges along the x and y axes. The loop is moved with a constant velocity $$\overrigh...

The following logic gate is equivalent to :

Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the region of uniform line charge of 8 nC/m lying along the z-axis in free space.

A deviation of 2\(^\circ\) is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass as 0.02 and 0.03 respectively and refractive index for yellow light ...

Red light differs from blue light as they have :

The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is placed in a medium of same refractive index? Assume the radii of curvature of the faces of lens are R1 and R2 respectively.

If one wants to remove all the mass of the earth to infinity in order to break it up completely.The amount of energy that needs to be supplied will be \({x \over 5}{{G{M^2}} \over R}\) where x is __________ (Round off to the Nearest Integer...

A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold bath, it will :

For an ideal heat engine, the temperature of the source is 127\(^\circ\)C. In order to have 60% efficiency the temperature of the sink should be ___________\(^\circ\)C. (Round off to the Nearest Integer)

Calculate the value of mean free path (\(\lambda\)) for oxygen molecules at temperature 27\(^\circ\)C and pressure 1.01 \(\times\) 105 Pa. Assume the molecular diameter 0.3 nm and the gas is ideal. (k = 1.38 \(\times\) 10\(-\)23 JK\(-\)1)

A body of mass 2 kg moves under a force of \(\left( {2\widehat i + 3\widehat j + 5\widehat k} \right)\)N. It starts from rest and was at the origin initially. After 4s, its new coordinates are (8, b, 20). The value of b is _____________. (R...

A charge Q is moving \(\overrightarrow {dl}\) distance in the magnetic field \(\overrightarrow {B}\). Find the value of work done by \(\overrightarrow {B}\).

A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just o...

A mosquito is moving with a velocity \(\overrightarrow v = 0.5{t^2}\widehat i + 3t\widehat j + 9\widehat k\) m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2 s?

What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of water are 0.5 cm and 10\(-\)3 Pa s, respectively. (Density of water : 103 kg/m3...

A force \(\overrightarrow F\) = \({4\widehat i + 3\widehat j + 4\widehat k}\) is applied on an intersection point of x = 2 plane and x-axis. The magnitude of torque of this force about a point (2, 3, 4) is ___________. (Round off to the Ne...

A solid disc of radius 'a' and mass 'm' rolls down without slipping on an inclined plane making an angle \(\theta\) with the horizontal. The acceleration of the disc will be \({2 \over b}\)g sin\(\theta\) where b is ____________. (Round off...

Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500g, Decay constant = 20 g/s then how much time is required for the amplitude of the system to drop to drop to half of its initial ...

In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1m (measured using a scale of least count = 1 mm), a weight of mass 1 kg (measured using a scale of least cou...

A closed organ pipe of length L and an open organ pipe contain gases of densities \(\rho\)1 and \(\rho\)2 respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same...