List of top Mathematics Questions asked in JEE Main

A six faced die is biased such that
3 × P (a prime number) = 6 × P (a composite number) = 2 × P (1).
Let X be a random variable that counts the number of times one gets a perfect square on some
throws of this die. If the die is thrown twice, then the mean of X is :

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is :

Let
\(x = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}\) and \(A = \begin{bmatrix} -1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1 \end{bmatrix}\)
For k ∈ N, if X’A^kX = 33, then k is equal to ____ .

Let P(a, b) be a point on the parabola y² = 8x such that the tangent at P passes through the centre of the circle x² + y² – 10x – 14y + 65 = 0. Let A be the product of all possible values of a and B be the product of all possible values of b. Then the value of A + B is equal to

The remainder when \(7^{2022}+3^{2022}\) is divided by \(5\) is:

Let S = {4, 6, 9} and T = {9, 10, 11, …,1000}. If A = {a1 + a2 + … +ak :k∈N, a1, a2, a3, …, ak∈S}, then the sum of all the elements in the set T – A is equal to ____________.

\(\lim_{x\rightarrow \frac{\pi}{4}}\) 8\(\sqrt2\)−(cosx+sinx)\(^{\frac{7}{\sqrt2}}\)−\(\sqrt2\)sin2x is equal to

If \(\begin{array}{l}\int_{0}^{\sqrt{3}}\frac{15x^3}{\sqrt{1+x^2 + \sqrt{(1+x^2)^3}}}dx = \alpha \sqrt{2}+\beta\sqrt{3},\end{array}\)where \(α, β\) are integers, then \(α + β\) is equal to

The statement
\((p⇒q)∨(p⇒r) \)
is NOT equivalent to

Let
\(\vec{a}\) and \(\vec{b}\) be two vectors such that
\(|\vec{a} + \vec{b}|^2 = |\vec{a}|^2 + 2|\vec{b}|^2,\ \vec{a} \cdot \vec{b} = 3\) and \(|\vec{a} \times \vec{b}|^2 = 75\)
Then \(|\vec{a}|^2\) is equal to _____.

Let the tangents at the points P and Q on the ellipse

\(\begin{array}{l} \frac{x^2}{2}+\frac{y^2}{4}=1\ \text{meet at the point}\ R\left(\sqrt{2},2\sqrt{2}-2\right).\end{array}\)

If S is the focus of the ellipse on its negative major axis, then SP² + SQ²is equal to ________.

Let y = y₁(x) and y = y₂(x) be two distinct solution of the differential equation
\(\frac{dy}{dx} = x+y,\)
with y₁(0) = 0 and y₂(0) = 1 respectively. Then, the number of points of intersection of y = y₁ (x) and y = y₂(x) is

Let α→ = \(2\^{i}-\^{j}+5\^{k} and b→= α\^{i}+β\^{j}+2\^{k}. If ((α→×b→)×\^{i}).\^{k} \)=\(\frac{ 23}{2}\),then \(|b→×2\^{j}\| \)is equal to

Let
\(\begin{array}{l} \vec{a},\vec{b},\vec{c}\ \text{be three non-coplanar vectors such that}\end{array}\)
\(\begin{array}{l} \overrightarrow{a}\times\vec{b}=4\vec{c},\vec{b}\times\vec{c}=9\vec{a}\ \text{and}\ \vec{c}\times\vec{a}=\alpha\vec{b},\alpha>0.\end{array}\)

If
\(\begin{array}{l} \left|\overrightarrow{a}\right|+\left|\overrightarrow{b}\right|+\left|\overrightarrow{c}\right|=\frac{1}{36}\end{array}, \)

then \(α\) is equal to___.

\(\begin{array}{l} \text{Consider a matrix}~A=\begin{bmatrix}\alpha & \beta & \gamma \\\alpha^2 & \beta^2 & \gamma^2 \\\beta+\gamma & \gamma+\alpha & \alpha+\beta \\\end{bmatrix}\end{array}\)

where \(α, β, γ\) are three distinct natural numbers.
If \(\begin{array}{l}\frac{\text{det(adj(adj(adj(adj A))))}}{\left(\alpha-\beta\right)^{16}\left(\beta-\gamma\right)^{16}\left(\gamma-\alpha\right)^{16}}=2^{32}\times3^{16},\end{array}\)
then the number of such 3-tuples \((α, β, γ)\) is _________.

Let for the 9^th term in the binomial expansion of (3 + 6x)ⁿ, in the increasing powers of 6x, to be the greatest for x = 3/2, the least value of n is n₀. If k is the ratio of the coefficient of x⁶ to the coefficient of x³, then k + n₀ is equal to :

Let R₁ and R₂ be two relations defined on ℝ by a R₁b ⇔ ab ≥ 0 and aR₂b ⇔ a ≥ b. Then,

Let
f,g:N = {1} → N be functions defined by
f(a) = α, where α is the maximum of the powers of those primes p such that p^α divides a, and g(a) = a + 1, for all a ∈ N – {1}. Then, the function f + g is

Let the minimum value v₀ of
v = |z|²+|z-3|²+|z-6i|²,z∈C
is attained at z = z₀. Then
\(|2z^2_0-\overline{z}^3_0+3|^2+v^2_0\)
is equal to

Let
\(I = ∫^{\frac{π}{3}}_{\frac{π}{4}}(\frac{8sinx-sin2x}{x})dx\)
Then

The area of the smaller region enclosed by the curves y² = 8x + 4 and
x²+y²+4√3x-4=0
is equal to

Let R be a relation from the set \(\{1, 2, 3, ….., 60\}\) to itself such that \(R = \{(a, b) : b = pq,\) where \(p, q≥ 3\) are prime numbers\(\}\). Then, the number of elements in R is :

If z ≠ 0 be a complex number such that\(|z-\frac{1}{z}|=2\), then the maximum value of |z| is

Let a₁, a₂, a₃,…. be an A.P. If
\(\begin{array}{l} \displaystyle\sum\limits_{r=1}^\infty\frac{a_r}{2^r}=4,\end{array}\)
then 4a₂ is equal to ________.

\(\sum_{r=1}^{20}\)(r²+1)(r!) is equal to