List of top Mathematics Questions asked in JEE Main

The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :

Let the operations $*, \odot \in\{\wedge, \vee\}$. If $(p * q) \odot(p \odot \sim q)$ is a tautology, then the ordered pair $(*, \odot)$ is :

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $\cos ^{-1}(x)-2 \sin ^{-1}(x)=\cos ^{-1}(2 x)$ is equal to:

Considering only the principal values of the inverse trigonometric functions, the domain of the function $f(x)=\cos ^{-1}\left(\frac{x^2-4 x+2}{x^2+3}\right)$ is :

A point $P$ moves so that the sum of squares of its distances from the points $(1,2)$ and $(-2,1)$ is $14$. Let $f(x, y)=0$ be the locus of $P$, which intersects the $x$-axis at the points $A , B$ and the $y$-axis at the point $C, D$. Then the area of the quadrilateral $ACBD$ is equal to

Let $f(x)= \begin{cases} x^3-x^2+10 x-7, & x \leq 1 \\ -2 x+\log _2\left(b^2-4\right), & x>1\end{cases}$ Then the set of all values of $b$, for which $f(x)$ has maximum value at $x=1$, is :

The foot of the perpendicular from a point on the circle \(x ^2+ y ^2=1, z =0\) to the plane \(2 x+3 y+z=6\) lies on which one of the following curves ?

If the function $f(x)= \begin{cases} \frac{\log _e\left(1-x+x^2\right)+\log_e\left(1+x+x^2\right)}{\sec x-\cos x}, x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)-\{0\} \\k, \,\,\,\,\, x=0\end{cases}$ is continuous at $x=0$, then $k$ is equal to :

The sum of first 4 terms of a G.P. is 65/12 and sum of their reciprocals is 65/18. If product of first 3 terms is 1 and the 3rd term is α, then 2α is _________

The students S1, S2, ......., S10 are to be divided into 3 groups A, B and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is _________

The maximum value of k for which the sum $\sum_{i=0}^k \binom{10}{i} \binom{15}{k-i} + \sum_{i=0}^{k+1} \binom{12}{i} \binom{13}{k+1-i}$ exists, is equal to __________.

If a + α = 1, b + β = 2 and a f(x) + α f(1/x) = b x + β / x, then [f(x) + f(1/x)] / [x + 1/x] is ________

Let i = √-1. If $\frac{(-1 + i\sqrt{3})^{21}}{(1 - i)^{24}} + \frac{(1 + i\sqrt{3})^{21}}{(1 + i)^{24}} = k$, and $n = \lfloor |k| \rfloor$. Then $\sum_{j=0}^{n+5} (j + 5)^2 - \sum_{j=0}^{n+5} (j + 5)$ is equal to __________.

Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (-5, 0). If the locus of the point P is a circle of radius r, then 4r² is equal to ________

If the shortest distance between x - λ = 2y - 1 = -2z and x = y + 2λ = z - λ is √7 / 2√2, then |λ| is _______

If the variance of 10 natural numbers 1, 1, 1, ......., 1, k is less than 10, then the maximum possible value of k is ______