List of top Mathematics Questions asked in JEE Main

Let $f:(-\frac{\pi}{4}, \frac{\pi}{4}) \rightarrow R$ be defined as 

If f is continuous at $x=0$, then the value of $6a+b^2$ is equal to : 
 

Let $\alpha, \beta$ be two roots of the equation $x^2 + (20)^{1/4}x + (5)^{1/2} = 0$. Then $\alpha^8 + \beta^8$ is equal to :
Let the plane passing through the point (-1, 0, -2) and perpendicular to each of the planes $2x+y-z=2$ and $x-y-z=3$ be $ax+by+cz+8=0$. Then the value of $a+b+c$ is equal to :
Two tangents are drawn from the point P(-1, 1) to the circle $x^2 + y^2 - 2x - 6y + 6 = 0$. If these tangents touch the circle at points A and B, and if D is a point on the circle such that length of the segments AB and AD are equal, then the area of the triangle ABD is equal to :

Let $\vec{a} = \hat{i}+\hat{j}+2\hat{k}$ and $\vec{b} = -\hat{i}+2\hat{j}+3\hat{k}$. Then the vector product $(\vec{a}+\vec{b}) \times ((\vec{a} \times ((\vec{a}-\vec{b}) \times \vec{b})) \times \vec{b})$ is equal to :
If $y=y(x)$, $y \in [0, \pi/2)$ is the solution of the differential equation $\sec y \frac{dy}{dx} - \sin(x+y) - \sin(x-y) = 0$, with $y(0)=0$, then $5y'(\pi/2)$ is equal to _________.
The value of $\lim_{n \to \infty} \frac{1}{n}\sum_{j=1}^{n}\frac{(2j-1)+8n}{(2j-1)+4n}$ is equal to :
The value of the definite integral $\int_{-\pi/4}^{\pi/4} \frac{dx}{(1+e^{x\cos x})(\sin^4 x + \cos^4 x)}$ is equal to :
If $\log_3 2, \log_3(2^x-5), \log_3(2^x-\frac{7}{2})$ are in an arithmetic progression, then the value of x is equal to _________.
Let the domain of the function $f(x) = \log_4(\log_5(\log_3(18x-x^2-77)))$ be $(a, b)$. Then the value of the integral $\int_a^b \frac{\sin^3 x}{\sin^3 x + \sin^3(a+b-x)} dx$ is equal to _________.
Let F : [3, 5] $\rightarrow$ R be a twice differentiable function on (3, 5) such that
$F(x) = e^{-x} \int_3^x (3t^2 + 2t + 4F'(t))dt$.
If $F'(4) = \frac{\alpha e^\beta - 224}{(e^\beta-4)^2}$, then $\alpha+\beta$ is equal to _________.
Let $f:R \rightarrow R$ be a function such that $f(2)=4$ and $f'(2)=1$. Then, the value of $\lim_{x\to 2}\frac{x^2f(2) - 4f(x)}{x-2}$ is equal to :
The compound statement $(P \lor Q) \land (\sim P) \Rightarrow Q$ is equivalent to :
The probability that a randomly selected 2-digit number belongs to the set $\{n \in N : (2^n - 2) \text{ is a multiple of } 3\}$ is equal to :
If the mean and variance of the following data : 6, 10, 7, 13, a, 12, b, 12 are 9 and $\frac{37}{4}$ respectively, then $(a-b)^2$ is equal to :
If $\sin\theta + \cos\theta = \frac{1}{2}$, then $16(\sin(2\theta) + \cos(4\theta) + \sin(6\theta))$ is equal to :
Let $y=y(x)$ be solution of the differential equation $\log_e\left(\frac{dy}{dx}\right) = 3x+4y$, with $y(0)=0$. If $y\left(-\frac{2}{3}\log_e 2\right) = \alpha \log_e 2$, then the value of $\alpha$ is equal to :
A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes through the point (5, 3). If this reflected ray is the directrix of an ellipse with eccentricity $\frac{1}{3}$ and the distance of the nearer focus from this directrix is $\frac{8}{\sqrt{53}}$, then the equation of the other directrix can be :
If the area of the bounded region $R = \left\{(x, y) : \max\{0, \log_e x\} \le y \le 2^x, \frac{1}{2} \le x \le 2\right\}$ is, $\alpha(\log_e 2)^{-1} + \beta(\log_e 2) + \gamma$, then the value of $(\alpha + \beta - 2\gamma)^2$ is equal to :
If the coefficients of $x^7$ in $\left(x^2 + \frac{1}{bx}\right)^{11}$ and $x^{-7}$ in $\left(x - \frac{1}{bx^2}\right)^{11}$, $b \neq 0$, are equal, then the value of b is equal to :
Let C be the set of all complex numbers. Let $S_1 = \{z \in C : |z-3-2i|^2 = 8\}$, $S_2 = \{z \in C : \text{Re}(z) \ge 5\}$ and $S_3 = \{z \in C : |z - \bar{z}| \ge 8\}$. Then the number of elements in $S_1 \cap S_2 \cap S_3$ is equal to :
Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes through origin O. If OC is perpendicular to both the line segments CP and CQ, then the set\{P, Q\} is equal to :
A function \( f \) is defined on \([-3, 3]\) as \( f(x) = \begin{cases} \min\{|x|, 2-x^2\}, & -2 \le x \le 2 \\ |x|, & 2 < |x| \le 3 \end{cases} \), where \( [x] \) denotes the greatest integer \( \le x \). The number of points, where \( f \) is not differentiable in \((-3, 3)\) is ________ .
A plane passes through the points A(1, 2, 3), B(2, 3, 1) and C(2, 4, 2). If O is the origin and P is (2, -1, 1), then the projection of $\vec{OP}$ on this plane is of length :