List of top Mathematics Questions asked in JEE Main

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 :
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 :
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 :
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 :
The value of the integral, ∫ from 1 to 3 of [x² - 2x - 2] dx, where [x] denotes the greatest integer less than or equal to x, is :
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 be a twice differentiable function defined on ℝ such that f(0) = 1, f'(0) = 2 and f'(x) ≠ 0 for all x ∈ ℝ. If $| f(x) \ f'(x) | \ | f'(x) \ f''(x) | = 0$, then the value of f(1) lies in the interval :
The negation of the statement ~p ∧ (p ∨ q) 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 P is a point on the parabola y = x² + 4 which is closest to the straight line y = 4x - 1, then the co-ordinates of P are :
Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be (10/3, 7/3). If α, β are the roots of the equation ax² + bx + 1 = 0, then the value of α² + β² - αβ is :
Let a, b ∈ R. If the mirror image of the point P(a, 6, 9) with respect to the line (x-3)/7 = (y-2)/5 = (z-1)/(-9) is (20, b, -a - 9), then |a + b| is equal to :
For which of the following curves, the line x + √3 y = 2√3 is the tangent at the point (3√3 / 2, 1/2) ?

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

The solutions of the equation : 

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 :
Let α, β, γ be the real roots of the equation, x³ + a x² + b x + c = 0, (a, b, c ∈ R and a, b ≠ 0). If the system of equations (in u, v, w) given by α u + β v + γ w = 0; β u + γ v + α w = 0; γ u + α v + β w = 0 has non-trivial solution, then the value of a²/b is :
The number of solutions of the equation |cot x| = cot x + 1/sin x in the interval [0, 2π] 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 __________.
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 __________.
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 __________.
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 __________.
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 __________.
Rotation of axes: Vector ā (3p, 1) becomes (p+1, √10) in new system. Find p.