List of top Mathematics Questions asked in JEE Main

A circle x2 + y2 = 8 and a parabola y2 = 2x are given. Find area bounded by these two curves in first quadrant which lie inside the circle and outside the parabola.
The value of $\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots +\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}$ is :
If $\frac{dy}{dx} +2y = sin 2x$ and $y(0) = \frac{3}4$ , then $y (\frac{π}{8})$ is equal to:
Let relation defined as $(x_1, y_1) \,R (x_2, y_2)\, x_1 ≤ x_2,\, y_1 ≤ y_2$ and given that
(a) R is reflexive but not symmetric.
(b) R is transitive. then
Let $S$ be the set of all solutions of the equation $\cos ^{-1}(2 x)-2 \cos ^{-1}\left(\sqrt{1-x^2}\right)=\pi$, $x \in\left[-\frac{1}{2}, \frac{1}{2}\right]$ Then $\displaystyle\sum_{x \in S} 2 \sin ^{-1}\left(x^2-1\right)$ is equal to
The value of $∫_0^{\frac{\pi}{4}} \frac{dx}{1+tanx} $
The value of $\frac{1\times 2^2+2\times3^2+...+100\times (101)^2}{1^2 \times 2\times2^2 \times3+...+100^2 \times 101}$
Find the numbers of distinct real roots $|x||x + 2| - 5|x + 1| - 1$ =0
Let 'd' be the perpendicular distance from the centre of the ellipse x2a2+y2b2= 1 to the tangent drawn at a point P on the ellipse. If F1 and F are two foci of the ellipse, then (PF1 - PF)2  is equal to;

For x ∈ (0, π), the equation sin x + 2sin2x −sin3x = 3 has 

Let A=(02qrpq−rp−qr). If AAT=I3, then |p| is:
Let A = [1, 2, 3, 4, 5], m be the number of relations such as 4x ≤ 5y XRY and n be the minimum number of elements to be added from A × A to make a symmetric relation. Then the value of n + m.
Let $R$ be a relation on $R$, given by $R=\{(a, b): 3 a-3 b+\sqrt{7}$ is an irrational number $\}$Then $R$ is
If an be the nth  term of the GP of positive numbers. Let ∑n=100100a2n=α and ∑n=1100a2n−1=β such that α≠β then the common ratio is:
If sin 5x+sin 3x+sin x = 0, then the value of x other than zero, lying between π0≤×≤π2 is;

The angle θ between the vectors \(\rm \vec{a} = 5\hat{i} - \hat{j} +  \hat{k}\) and \(\rm \vec{b} = \hat{i} + \hat{j} -  \hat{k}\) equals to

If a→,b→,c→ are non-coplanar vectors and λ is a real number, then[λ(a→+b→)λ2b→λc→]=[a→b→+c→b→] for
If the orthocentre of the triangle, whose vertices are $(1,2),(2,3)$ and $(3,1)$ is $(\alpha, \beta)$, then the quadratic equation whose roots are $\alpha+4 \beta$ and $4 \alpha+\beta$, is
If 4x2 + py2 = 45 and x2 - 4y2 = 5 cut orthogonally, then the value of p is:
The angle θ between the vectors a→=5i^−j^+k^ and b→=i^+j^−k^ is:

If ABCD is a parallelogram, vector AB = 2i + 4j - 5k and vector AD = i + 2j + 3k, then the unit vector in the direction of BD is

If A = {1, 2, 3, 4, 6} and R is a relation on A such that R = {(a, b) : a, b ∈ A and b is exactly divisible by a} then find the number of elements present in the range of R?
For any two statements p and q, the negation of the expression p∨(∼p∧q) is:
What will be the remainder when (428)2024 is divided by 21?
Let $f(x)=\int \frac{2 x}{\left(x^2+1\right)\left(x^2+3\right)} d x$. If $f(3)=\frac{1}{2}\left(\log _e 5-\log _e 6\right)$, then $f(4)$ is equal to