List of top Questions asked in JEE Main- 2021

Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A²B² - B²A²) X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has :
Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2-x) for all x ∈ (0, 2), f(0) = 1 and f(2) = e². Then the value of ∫ from 0 to 2 f(x) dx is :
If the curve y = ax² + bx + c passes through (1, 2) and the tangent at origin is y = x, then a, b, c are :
If n ≥ 2 is a positive integer, then the sum of the series $^{n+1}C_2 + 2( ^2C_2 + ^3C_2 + ^4C_2 + ....... + ^nC_2 )$ is :
Let f(x) = -55x (x<-5), 2x³ - 3x² - 120x (-5 ≤ x ≤ 4), 2x³ - 3x² - 36x - 336 (x>4). Let A = {x ∈ ℝ : f is increasing}. Then A is equal to :
A possible value of \( \tan\!\left(\frac{1}{4}\sin^{-1}\!\left(\frac{\sqrt{63}}{8}\right)\right) \) is :
The angle of elevation of a jet plane from a point A on the ground is 60°. After 20 s at speed 432 km/h, the angle changes to 30°. If the jet plane is at constant height, then its height is :
The vector equation of the plane passing through the intersection of r · (i + j + k) = 1 and r · (i - 2j) = -2, and the point (1, 0, 2) is :
The area of the region : R = {(x, y) : 5x² ≤ y ≤ 2x² + 9} is :
If the variance of 10 natural numbers 1, 1, 1, ......., 1, k is less than 10, then the maximum possible value of k is ______
Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (-5, 0). If the locus of the point P is a circle of radius r, then 4r² is equal to ________
If the area of the triangle formed by the positive x-axis, the normal and the tangent to the circle \( (x-2)^2 + (y-3)^2 = 25 \) at the point \( (5, 7) \) is \( A \), then \( 24A \) is equal to _______
Let i = √-1. If $\frac{(-1 + i\sqrt{3})^{21}}{(1 - i)^{24}} + \frac{(1 + i\sqrt{3})^{21}}{(1 + i)^{24}} = k$, and $n = \lfloor |k| \rfloor$. Then $\sum_{j=0}^{n+5} (j + 5)^2 - \sum_{j=0}^{n+5} (j + 5)$ is equal to __________.
The students S1, S2, ......., S10 are to be divided into 3 groups A, B and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is _________
The maximum value of k for which the sum $\sum_{i=0}^k \binom{10}{i} \binom{15}{k-i} + \sum_{i=0}^{k+1} \binom{12}{i} \binom{13}{k+1-i}$ exists, is equal to __________.
If a + α = 1, b + β = 2 and a f(x) + α f(1/x) = b x + β / x, then [f(x) + f(1/x)] / [x + 1/x] is ________
If the shortest distance between x - λ = 2y - 1 = -2z and x = y + 2λ = z - λ is √7 / 2√2, then |λ| is _______
An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90 W. How long it would take to increase the internal energy by $2.5 \times 10^3$ J ?
A body of mass 2 kg moving with a speed of 4 m/s makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is $\frac{x}{10}$ m/s. Then the value of $x$ is ________.
The unit cell of copper corresponds to a face centered cube of edge length 3.596 Å with one copper atom at each lattice point. The calculated density of copper in kg/m³ is ________ . [Molar mass of Cu: 63.54 g; Avogadro Number=6.022$\times$10²³]
Water does not produce CO on reacting with:
The major product (A) formed in the reaction given below is :
\includegraphics[width=0.6\linewidth]{image43.png}
A metal surface is exposed to 500 nm radiation. The threshold frequency of the metal for photoelectric current is 4.3 \(\times\) 10\(^{14}\) Hz. The velocity of ejected electron is ___________ \(\times\) 10\(^{5}\) ms\(^{-1}\). (Nearest integer)
[Use: h = 6.63\(\times\)10\(^{-34}\) Js, m\(_e\) = 9.0\(\times\)10\(^{-31}\) kg]