List of top Questions asked in JEE Main- 2021

Let (1 + x + 2x²)²⁰ = a₀ + a₁x + a₂x² + ⋯ + a₄₀x⁴⁰. Then, a₁ + a₃ + a₅ + ⋯ + a₃₇ is equal to :
The value of 3 + 1/(4 + 1/(3 + 1/(4 + 1/(3 + ⋯ ∞))) is equal to :
1/(3² - 1) + 1/(5² - 1) + 1/(7² - 1) + ⋯ + 1/(201)² - 1 is equal to :
If α, β are natural numbers such that 100$^α - 199 β = (100)(100) + (99)(101) + (98)(102) + ⋯ + (1)(199)$, then the slope of the line passing through (α, β) and origin is :
If f(x) = { 1/|x| if |x| ≥ 1 ; a x² + b if |x| $< 1$ } is differentiable at every point of the domain, then the values of a and b are respectively :
The real valued function f(x) = csc⁻¹x / √(x - [x]), where [x] denotes the greatest integer less than or equal to x, is defined for all x belonging to :
If \( \lim_{x \to 0} \dfrac{\sin^{-1} x - \tan^{-1} x}{3x^3} \) is equal to \( L \), then the value of \( (6L + 1) \) is :
The integral ∫ (2x - 1) cos√((2x - 1)² + 5) / √(4x² - 4x + 6) dx is equal to : (where c is a constant of integration)
The differential equation satisfied by the system of parabolas y² = 4a(x + a) is :
Choose the correct statement about two circles whose equations are given below : x² + y² - 10x - 10y + 41 = 0 ; x² + y² - 22x - 10y + 137 = 0
Match circles M, N, O, P and determine the shape formed by joining their centers in order.
The equation of one of the straight lines which passes through the point (1, 3) and makes an angle tan⁻¹(√2) with the straight line, y + 1 = 3√2 x is :

The solutions of the equation : 

Rotation of axes: Vector ā (3p, 1) becomes (p+1, √10) in new system. Find p.
Let z₁, z₂ be the roots of the equation z² + a z + 12 = 0 and z₁, z₂ form an equilateral triangle with origin. Then, the value of |a| is ________.
Let f(x) and g(x) be two functions satisfying f(x²) + g(4-x) = 4x³ and g(4-x) + g(x) = 0, then the value of ∫$_{-4}^{4}$ f(x²) dx is __________.
If f(x) = ∫$_{x}^{1}$ (5x⁸ + 7x⁶)/(x² + 1 + 2x⁷)² dx, (x ≥ 0), f(0) = 0 and f(1) = 1/K, then the value of K 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 __________.
Let the plane ax + by + cz + d = 0 bisect the line joining the points (4, -3, 1) and (2, 3, -5) at the right angles. If a, b, c, d are integers, then the minimum value of (a² + b² + c² + d²) is __________.
The equation of the planes parallel to the plane x - 2y + 2z - 3 = 0 which are at unit distance from the point (1, 2, 3) is ax + by + cz + d = 0. If (b - d) = K(c - a), then the positive value of K 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 appointed teacher is __________.
The number of times the digit 3 will be written when listing the integers from 1 to 1000 is __________.

Find the missing value in the logic/series figure provided in the question. 

The number of solutions of the equation |cot x| = cot x + 1/sin x in the interval [0, 2π] is __________.
The period of oscillation of a simple pendulum is $T = 2\pi \sqrt{\frac{L}{g}}$. Measured value of 'L' is 1.0 m from meter scale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured from stopwatch of 0.01 s resolution. The percentage error in the determination of 'g' will be :