List of top Mathematics Questions asked in JEE Main

R = (a, b) : a + 5b = 42 and a, b ∈ N has m elements and \(\sum\limits_{n=1}^{m}(1+i^{n!})\) = x + iy (where i = √-1). Find x + y + m.

If set A = { z: |z - 1| ≤ 1} and set B = { z: |z - 5i| ≤ |z - 5| }, if z = a + ib, where a, b ∈ I, then find the sum of modulus squares of A ∩ B.

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.

\(I(x)=\int\frac{6dx}{sin^2x(1+\cot x)^2}\)and I(0) then I (\(\frac{\pi}{2}\)) is equal to

If the length of focal chord of y² = 12x is 15 and if the distance of the focal chord from origin is p then 10p² is equal to:

If $f(x)= 3\sqrt{(x-2)}+\sqrt{4-x }$ If minimum value = α Maximum value = β find $α2 + β2 $.

If the normal at point P $$$(a{t}_1^2,2a{t}_1)$ and $Q$$(a{t}_2^2,2a{t}_2)$ on the parabola $y^2=4ax$ meet on the parabola, the$t_1{t}_2$ equals

If 4x² + py² = 45 and x² - 4y² = 5 cut orthogonally, then the value of p is:

$PQ$ and $RS$ are two perpendicular chords of the rectangular hyperbola $xy=c^2$. If $C$ is the centre of the rectangular hyperbola, then the product of the slopes of $CP,CQ,CR$ and $CS$ is equal to:

The circle $x^2+y^2+4x-7y+12=0$ cuts an intercept on $y$ -axis of length

Find the equation of normal to the curve$$y=(1+x{)}^y+{\sin }^{-1}({\sin }^{2}x)\text{at}x=0$$

The derivative of $se{c}^{-1} \left(\frac{1}{2x^2-1}\right)$ with respect to $\sqrt{1-x^2}$ at $x=\frac{1}{2}$ is:

The rate of change of volume of a sphere with respect to its surface area when the radius is 4 cm 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?

The number of terms of an $AP$ is even. The sum of the odd terms is $24$ and of the even terms is $30$. The last term exceeds the first by $10\frac{1}{2}$. Then the number of terms in the series is ______.

If |x + 1||x + 3| – 4|x + 2| + 5 = 0, then sum of squares of solutions is

The sum of the first $16$ terms of an AP whose first term and the third term are $5$ and $15$ respectively is

A=\(\begin{bmatrix}   \alpha & \alpha & \alpha \\   \beta & \alpha & -\beta \\   -\alpha & \alpha & \alpha  \end{bmatrix}\)B is formed by co-factor of A matrix, then find out determinant of AB.

If |a| = 2, |b| = 3 and a = b × 2, then minimum value of \(|\hat{c} - a|^2\) is:

Area bounded by y = -2|x| and y = x|x| is:

Consider the equation ax² + bx + c = 0 . Find probability if a, b, c ∈ A where A = {1,2,3, ... , 8} that the equation has equal roots.

Consider a equation  P(x)= ax² + bx + c =0. If a,b,c ∈ A, were A = {1, 2, 3, 4, 5, 6} . Then the probability that P(x) has real and distinct roots?

If S = {2, 4, 8, 16, ..., 512}. If S is broken in 3 equal subsets A, B and C such that A∩B = B∩C = C∩A = φ and A∪B∪C = S then maximum number of ways to break is

\(\left( \frac{3^{\frac{1}{5}}}{x}+\frac{2x}{5^\frac{1}{3}} \right)^{12}\)Find which term is constant.

Let image of point(8,5,7) with respect to line \(\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{5}\) is (α,β,γ). Then, α+β+γ is equal to______.