List of top Mathematics Questions asked in JEE Main

If $A = \{x \in \mathbb{R} : |x-2|>1\}$, $B = \{x \in \mathbb{R} : \sqrt{x^2-3}>1\}$, $C = \{x \in \mathbb{R} : |x-4| \geq 2\}$ and $\mathbb{Z}$ is the set of all integers, then the number of subsets of the set $(A \cap B \cap C)^c \cap \mathbb{Z}$ is _________.
$\sum_{k=0}^{20} (^{20}C_k)^2$ is equal to :
If $0<x<1$, then $\frac{3}{2}x^2 + \frac{5}{3}x^3 + \frac{7}{4}x^4 + \dots$, is equal to :
$\int_{6}^{16} \frac{\log_e x^2}{\log_e x^2 + \log_e(x^2 - 44x + 484)} \, dx$ is equal to :
When a certain biased die is rolled, a particular face occurs with probability $\frac{1}{6} - x$ and its opposite face occurs with probability $\frac{1}{6} + x$. All other faces occur with probability $\frac{1}{6}$. Note that opposite faces sum to 7 in any die. If $0<x<\frac{1}{6}$, and the probability of obtaining total sum $= 7$, when such a die is rolled twice, is $\frac{13}{96}$, then the value of $x$ is :
Let $\frac{\sin A}{\sin B} = \frac{\sin(A - C)}{\sin(C - B)}$, where A, B, C are angles of a triangle ABC. If the lengths of the sides opposite these angles are a, b, c respectively, then :
Equation of a plane at a distance $\sqrt{\frac{2}{21}}$ from the origin, which contains the line of intersection of the planes $x - y - z - 1 = 0$ and $2x + y - 3z + 4 = 0$, is :
Let $y = y(x)$ be the solution of the differential equation $\frac{dy}{dx} = 2(y + 2\sin x - 5)x - 2\cos x$ such that $y(0) = 7$. Then $y(\pi)$ is equal to :
If $U_n = \left(1 + \frac{1}{n^2}\right) \left(1 + \frac{2^2}{n^2}\right)^2 \dots \left(1 + \frac{n^2}{n^2}\right)^n$, then $\lim_{n \to \infty} (U_n)^{-\frac{4}{n^2}}$ is equal to :
If $\alpha, \beta$ are the distinct roots of $x^2 + bx + c = 0$, then $\lim_{x \to \beta} \frac{e^{2(x^2 + bx + c)} - 1 - 2(x^2 + bx + c)}{(x - \beta)^2}$ is equal to :
If for $x, y \in \mathbb{R}, x>0, y = \log_{10} x + \log_{10} x^{1/3} + \log_{10} x^{1/9} + \dots$ upto $\infty$ terms and $\frac{2 + 4 + 6 + \dots + 2y}{3 + 6 + 9 + \dots + 3y} = \frac{4}{\log_{10} x}$, then the ordered pair $(x, y)$ is equal to :
If the matrix \( A = \begin{pmatrix} 0 & 2 \\ K & -1 \end{pmatrix} \) satisfies \( A(A^3 + 3I) = 2I \), then the value of \( K \) is :
If $S = \left\{z \in \mathbb{C} : \frac{z - i}{z + 2i} \in \mathbb{R}\right\}$, then :
If $x^2 + 9y^2 - 4x + 3 = 0, x, y \in \mathbb{R}$, then $x$ and $y$ respectively lie in the intervals :
Let n be an odd natural number such that the variance of 1, 2, 3, 4, ..., n is 14. Then n is equal to _________.
A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55, is _________.
The number of distinct real roots of the equation $3x^4 + 4x^3 - 12x^2 + 4 = 0$ is _________.
If $(\sin^{-1} x)^2 - (\cos^{-1} x)^2 = a; 0<x<1, a \neq 0$, then the value of $2x^2 - 1$ is :
The statement $(p \land (p \to q) \land (q \to r)) \to r$ is :
A tangent and a normal are drawn at the point $P(2, -4)$ on the parabola $y^2 = 8x$, which meet the directrix of the parabola at the points A and B respectively. If $Q(a, b)$ is a point such that $AQBP$ is a square, then $2a + b$ is equal to :
The distance of the point $(1, -2, 3)$ from the plane $x - y + z = 5$ measured parallel to a line, whose direction ratios are $2, 3, -6$ is :
Let us consider a curve, $y = f(x)$ passing through the point $(-2, 2)$ and the slope of the tangent to the curve at any point $(x, f(x))$ is given by $f(x) + x f'(x) = x^2$. Then :
A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon. Then the length of the side (in meters) of the hexagon, so that the combined area of the square and the hexagon is minimum, is :
Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of AB and the perpendicular bisector of AB meets the y-axis at C. The locus of the mid-point P of MC is :
If $y = y(x)$ is an implicit function of $x$ such that $\log_e (x + y) = 4xy$, then $\frac{d^2y}{dx^2}$ at $x = 0$ is equal to _________.