JEE Main 2021 (Online) 27th August Evening Shift

Let A(a, 0), B(b, 2b + 1) and C(0, b), b \(\ne\) 0, |b| \(\ne\) 1, be points such that the area of triangle ABC is 1 sq. unit, then the sum of all possible values of a is :

Let [\(\lambda\)] be the greatest integer less than or equal to \(\lambda\). The set of all values of \(\lambda\) for which the system of linear equations x + y + z = 4, 3x + 2y + 5z = 3, 9x + 4y + (28 + [\(\lambda\)])z = [\(\lambda\)] has ...

If two tangents drawn from a point P to the parabola y2 = 16(x \(-\) 3) are at right angles, then the locus of point P is :

Let S = {1, 2, 3, 4, 5, 6, 9}. Then the number of elements in the set T = {A \(\subseteq\) S : A \(\ne\) \(\phi\) and the sum of all the elements of A is not a multiple of 3} is _______________.

Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is :

The probability distribution of random variable X is given by :
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The set of all values of K > \(-\)1, for which the equation \({(3{x^2} + 4x + 3)^2} - (k + 1)(3{x^2} + 4x + 3)(3{x^2} + 4x + 2) + k{(3{x^2} + 4x + 2)^2} = 0\) has real roots, is :

If 0 < x < 1 and \(y = {1 \over 2}{x^2} + {2 \over 3}{x^3} + {3 \over 4}{x^4} + ....\), then the value of e1 + y at \(x = {1 \over 2}\) is :

An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If $$\mu$...

Let S be the sum of all solutions (in radians) of the equation \({\sin ^4}\theta + {\cos ^4}\theta - \sin \theta \cos \theta = 0\) in [0, 4\(\pi\)]. Then \({{8S} \over \pi }\) is equal to ____________.

An ac circuit has an inductor and a resistor resistance R in series, such that XL = 3R. Now, a capacitor is added in series such that XC = 2R. The ratio of new power factor with the old power factor of the circuit is \(\sqrt 5 :x\). The val...

X different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number n = 6 ? The value of X is ______________.

Three capacitors C1 = 2\(\mu\)F, C2 = 6\(\mu\)F and C3 = 12\(\mu\)F are connected as shown in figure. Find the ratio of the charges on capacitors C1, C2 and C3 respectively :

A bullet of 10 g, moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m/s. The length of the pendulum is 0.5 m and mass of the bob is 1 kg. The minimum value of v = ____________ m/s s...

An antenna is mounted on a 400 m tall building. What will be the wavelength of signal that can be radiated effectively by the transmission tower upto a range of 44 km?

The Colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is :

For full scale deflection of total 50 divisions, 50 mV voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is 2 div/mA will be :

The ratio of the equivalent resistance of the network (shown in figure) between the points a and b when switch is open and switch is closed is x : 8. The value of x is ___________.

A monochromatic neon lamp with wavelength of 670.5 nm illuminates a photo-sensitive material which has a stopping voltage of 0.48 V. What will be the stopping voltage if the source light is changed with another source of wavelength of 474.6...

A constant magnetic field of 1T is applied in the x > 0 region. A metallic circular ring of radius 1m is moving with a constant velocity of 1 m/s along the x-axis. At t = 0s, the centre of O of the ring is at x = \(-\)1m. What will be the v...

A plane electromagnetic wave with frequency of 30 MHz travels in free space. At particular point in space and time, electric field is 6 V/m. The magnetic field at this point will be x \(\times\) 10\(-\)8 T. The value of x is ___________.

For a transistor \(\alpha\) and \(\beta\) are given as \(\alpha = {{{I_C}} \over {{I_E}}}\) and \(\beta = {{{I_C}} \over {{I_B}}}\). Then the correct relation between \(\alpha\) and \(\beta\) will be :

A zener diode of power rating 2W is to be used as a voltage regulator. If the zener diode has a breakdown of 10 V and it has to regulate voltage fluctuated between 6 V and 14 V, the value of Rs for safe operation should be ___________ $$\Om...

Figure shows a rod AB, which is bent in a 120\(^\circ\) circular arc of radius R. A charge (\(-\)Q) is uniformly distributed over rod AB. What is the electric field \(\overrightarrow E\) at the centre of curvature O ?

Curved surfaces of a plano-convex lens of refractive index \(\mu\)1 and a plano-concave lens of refractive index \(\mu\)2 have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the co...

A mass of 50 kg is placed at the centre of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the centre is V kg/m. The value of V is :

if the rms speed of oxygen molecules at 0\(^\circ\)C is 160 m/s, find the rms speed of hydrogen molecules at 0\(^\circ\)C.

The height of victoria falls is 63 m. What is the difference in temperature of water at the top and at the bottom of fall?[Given 1 cal = 4.2 J and specific heat of water = 1 cal g\(-\)1 \(^\circ\)0C\(-\)1]

A heat engine operates between a cold reservoir at temperature T2 = 400 K and a hot reservoir at temperature T1. It takes 300 J of heat from the hot reservoir and delivers 240 J of heat to the cold reservoir in a cycle. The minimum temperat...

The boxes of masse 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use g = 10 m/s2)

A coaxial cable consists of an inner wire of radius 'a' surrounded by an outer shell of inner and outer radii 'b' and 'c' respectively. The inner wire carries an electric current i0, which is distributed uniformly across cross-sectional are...

A player kicks a football with an initial speed of 25 ms\(-\)1 at an angle of 45\(^\circ\) from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g = 10 ms\(-\)2)

Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8 m. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the positi...

Wires W1 and W2 are made of same material having the breaking stress of 1.25 \(\times\) 109 N/m2. W1 and W2 have cross-sectional area of 8 \(\times\) 10\(-\)7 m2 and 4 \(\times\) 10\(-\)7 m2, respectively. Masses of 20 kg and 10 kg hang fro...

Two discs have moments of inertia I1 and I2 about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, \(\omega\)1 and \(\omega\)2 respectively and are brought into contact ...

Two simple harmonic motion, are represented by the equations \({y_1} = 10\sin \left( {3\pi t + {\pi \over 3}} \right)\) \({y_2} = 5(\sin 3\pi t + \sqrt 3 \cos 3\pi t)\) Ratio of amplitude of y1 to y2 = x : 1. The value of x is ____________...

Match List - I with List - II.



List - I

List - II




(a)
\({R_H}\) (Rydberg constant)
(i)
\(kg\,{m^{ - 1}}{s^{ - 1}}\)


(b)
h (Planck's constant)
(ii)
\(kg\,{m^2}{s^{ - 1}}\)
...

If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density :

The light waves from two coherent sources have same intensity I1 = I2 = I0. In interference pattern the intensity of light at minima is zero. What will be the intensity of light at maxima?

A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with the tuning fork will be __________ cm. (Take speed of sound in air as 340 ms\(-\)1)