List of top Mathematics Questions asked in JEE Main

Let $ w_1 $ be the point obtained by the rotation of $ z_1 = 5 + 4i $ about the origin through a right angle in the anticlockwise direction, and $ w_2 $ be the point obtained by the rotation of $ z_2 = 3 + 5i $ about the origin through a right angle in the clockwise direction. Then the principal argument of $ w_1 - w_2 $ is equal to:

$ Let f(x) = | x^2 - x | + |x|, \text{ where } x \in \mathbb{R} \text{ and } | t | \text{ denotes the greatest integer less than or equal to } t. \text{ Then, } f \text{ is:} $

Suppose $ f: \mathbb{R} \to (0, \infty) $ be a differentiable function such that: $ 5f(x + y) = f(x) \cdot f(y), \quad \forall x, y \in \mathbb{R} $. If $ f(3) = 320 $, then the value of:$ \sum_{n=0}^{5} f(n) $ is equal to:

A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is

Let $𝑆={𝑤_1,𝑤_2,…….}$ be the sample space associated to a random experiment. Let $𝑃(𝑤_𝑛)= \frac{𝑃(𝑤_{𝑛−1})}{2} ,𝑛≥2.$ Let 𝐴=${(2𝑘+3𝑙:k,𝑙∈ℕ)}$ and $𝐵={𝑤_𝑛:𝑛∈𝐴}$. Then 𝑃( 𝐵) is equal to

Let the probability of getting head for a biased coin be $\frac{1}{4}$ . It is tossed repeatedly until a head appears. Let N be the number of tosses required. If the probability that the equation $64x² + 5Nx + 1 = 0$ has no real root is $\frac{p}{q}$ , where p and q are co-prime, then q – p is equal to _______.

The negation of the statement
(p v q) ∧ (q v(∼r)) is

Let (a+bx+cx²)¹⁰ = $ \sum_{i=0}^{20} $ p_ixⁱ, a,b,c∈N. If p₁=20 and P₂ = 210, then 2(a+b+c) is equal to

Negation of $ p \land (q \land \neg (p \land q)) $ is:}

Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is

Three dice are rolled. If the probability of getting different numbers on the three dice is $\frac{p}{q}$, where $p$ and $q$ are co-prime, then $q - p$ is equal to:

If the equation of the normal to the curve $ y = \frac{x - a}{(x + b)(x - 2)} $ at the point $ (1, -3) $ is $ x - 4y = 13 $, then the value of $ a + b $ is:

Let $ f: [2, 4] \to \mathbb{R} $ be a differentiable function such that $ (x \log x) f'(x) + (\log x) f(x) \geq 1 $, $ x \in [2, 4] $ with $ f(2) = \frac{1}{2} $ and $ f(4) = \frac{1}{4} $. Consider the following two statements:
$ (A) \quad f(x) \geq 1 \quad \text{for all} \quad x \in [2, 4] $
$ (B) \quad f(x) \leq \frac{1}{8} \quad \text{for all} \quad x \in [2, 4] $ Then,

Let $y = y(x)$ be a solution curve of the differential equation $$(1 - x^2 y)\,dx = y\,dx + x\,dy.$$ If the line $x = 1$ intersects the curve $y = y(x)$ at $y = 2$ and the line $x = 2$ intersects the curve $y = y(x)$ at $y = \alpha$, then a value of $\alpha$ is:

Area of the region $(x, y) : x^2 + (y - 2)^2 \leq 4, \, x^2 \geq 2y$ is:

Let S = {1, 2, 3, 4, 5, 6}. Then the number of one-one functions $f : S → P(S)$, where $P(S)$ denotes the power set of S, such that $f(n) ⊂ f(m)$ where $n < m,$ is:

Let $f(x)$ be a quadratic polynomial with leading coefficient 1 such that $f(0) = p, p≠0$ and $f(1)=\frac{1}{3}$. If the equation $f(x) = 0$ and $fofofof(x) = 0$ have a common real root, then $f(–3)$ is equal to.......................

Let $𝑎_1=𝑏_1=1$and $𝑎_𝑛=𝑎_{𝑛−1}+(𝑛−1)$, $𝑏_𝑛=𝑏_{𝑛−1}+𝑎_{𝑛−1}$, $∀𝑛≥2$. If $𝑆= \displaystyle\sum_{ 𝑛=1}^{10}\frac {𝑏_𝑛}{2^𝑛}$ and $𝑇= \displaystyle\sum_{𝑛=1}^{8} \frac {𝑛}{2^{𝑛−1}}$, then $2^7(2𝑆−𝑇)$ is equal to ____ .

Let $\sum_{n=0}^{\infty }\frac{n^{3}((2n)!+(2n-1)(n!))}{(n!)((2n)!)}=ae+\frac{b}{e}+c$, where $a, b, c \in Z$ and $e=\displaystyle\sum_{n=0}^{\infty} \frac{1}{n !}$ Then $a^2-b+c$ is equal to _______

Let sets A and B have 5 elements each. Let mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of A and adding 2 to each element of B. Then the sum of the mean and variance of the elements of C is:

The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is: