List of top Mathematics Questions asked in JEE Main

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 ________.
Choose the correct statement about two circles whose equations are given below : x² + y² - 10x - 10y + 41 = 0 ; x² + y² - 22x - 10y + 137 = 0
The differential equation satisfied by the system of parabolas y² = 4a(x + a) is :
The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is :
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 :
Match circles M, N, O, P and determine the shape formed by joining their centers in order.
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 :
1/(3² - 1) + 1/(5² - 1) + 1/(7² - 1) + ⋯ + 1/(201)² - 1 is equal to :
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 :
The value of 3 + 1/(4 + 1/(3 + 1/(4 + 1/(3 + ⋯ ∞))) is equal to :
The integral ∫ (2x - 1) cos√((2x - 1)² + 5) / √(4x² - 4x + 6) dx is equal to : (where c is a constant of integration)
Let (1 + x + 2x²)²⁰ = a₀ + a₁x + a₂x² + ⋯ + a₄₀x⁴⁰. Then, a₁ + a₃ + a₅ + ⋯ + a₃₇ is equal to :
The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and 3 is :
If the functions are defined as f(x) = √x and g(x) = √(1-x), then what is the common domain of the following functions : f+g, f-g, f/g, g/f, g-f where (f ± g)(x) = f(x) ± g(x), (f/g)(x) = f(x)/g(x)
If the equation a|z|² + āz + a z̄ + d = 0 represents a circle where a, d are real constants, then which of the following condition is correct ?
Let A + 2B = [1 2 0; 6 -3 3; -5 3 1] and 2A - B = [2 -1 5; 2 -1 6; 0 1 2]. If Tr(A) denotes the sum of all diagonal elements of the matrix A, then Tr(A) - Tr(B) has value equal to :
The area (in sq. units) of the region, given by the set $\{(x, y) \in R \times R \mid x \ge 0, 2x^2 \le y \le 4 - 2x\}$ is :
Let $f:[0, \infty) \to [0, \infty)$ be defined as $f(x) = \int_0^x [y] dy$, where $[x]$ is the greatest integer less than or equal to $x$. Which of the following is true ?

Let $g: N \to N$ be defined as $g(3n+1) = 3n+2, g(3n+2) = 3n+3, g(3n+3) = 3n+1$, for all $n \ge 0$. Then which of the following statements is true ?
Let the foot of perpendicular from a point $P(1, 2, -1)$ to the straight line $L: \frac{x}{1} = \frac{y}{0} = \frac{z}{-1}$ be $N$. Let a line be drawn from $P$ parallel to the plane $x + y + 2z = 0$ which meets $L$ at point $Q$. If $\alpha$ is the acute angle between the lines $PN$ and $PQ$, then $\cos \alpha$ is equal to ________.
A spherical gas balloon of radius 16 meter subtends an angle $60^{\circ}$ at the eye of the observer A while the angle of elevation of its center from the eye of A is $75^{\circ}$. Then the height (in meter) of the top most point of the balloon from the level of the observer's eye is :
Let $S_n$ be the sum of the first n terms of an arithmetic progression. If $S_{3n} = 3S_{2n}$, then the value of $\frac{S_{4n}}{S_{2n}}$ is :