List of top Mathematics Questions asked in JEE Main

If (2, 3, 9), (5, 2, 1), (1, λ, 8) and (λ, 2, 3) are coplanar, then the product of all possible values of λ is :

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

Let the function
$f(x)$=$\begin{cases} \frac{\log_e(1+5x) - \log_e(1+\alpha x)}{x}, & \text{if } x ∈ 0 \\ \space 10 & \text;{if } x = 0 \\ \end{cases}$
be continuous at x = 0. Then α is equal to

Which of the following matrices can NOT be obtained from the matrix $\begin{bmatrix} -1 &2 \\ 1 & -1 \end{bmatrix}$ by a single elementary row operation?

Let $y = y(x)$ be the solution curve of the differential equation
$\frac{dy}{dx} + \frac{2x^2 + 11x + 13}{x^3 + 6x^2 + 11x + 6}y = (x+3)(x+1), \quad x > -1.$
which passes through the point $(0, 1)$. Then $y(1)$ is equal to

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

The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2, 3, 4, 5, 6 (repetition of digits is not allowed) and divisible by 55 is ____ .

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 _____.

If the tangents drawn at the points $P$ and $Q$ on the parabola $y^2=2 x-3$ intersect at the point $R (0,1)$, then the orthocentre of the triangle $PQR$ is :

The remainder when $7^{2022}+3^{2022}$ is divided by $5$ is:

For p, q, ∈ R, consider the real valued function $f(x) = (x – p)^2 – q$, x ∈ R and q > 0, Let $a_1, a_2, a_3$ and $a_4$ be in an arithmetic progression with mean p and positive common difference. If |f(a_i)| = 500 for all i = 1, 2, 3, 4, then the absolute difference between the roots of f(x) = 0 is

Let the vectors $\vec{a}=(1+t) \hat{i}+(1-t) \hat{j}+\hat{k},$

$\overrightarrow{ b }=(1-t) \hat{i}+(1+t) \hat{j}+2 \hat{k}$ and

$\vec{c}=t \hat{i}-t \hat{j}+\hat{k},$$t \in R$ be such that for

$\alpha, \beta, \gamma \in R, \alpha \vec{a}+\beta \vec{b}+\gamma \vec{c}=\overrightarrow{0} \Rightarrow \alpha=\beta=\gamma=0$

Then, the set of all values of t is :

Let the coefficients of x^–1 and x^–3 in the expansion of
$(2x^{\frac{1}{5}} - \frac{1}{x^{\frac{1}{5}}} )^{15} , x > 0$be m and n respectively. If r is a positive integer such that
$mn² = ^{15}C_r.2^r$
then the value of r is equal to ______.

If $a =\displaystyle\lim _{ n \rightarrow \infty} \sum_{ k =1}^{ n } \frac{2 n }{ n ^2+ k ^2}$ and $f(x)=\sqrt{\frac{1-\cos x}{1+\cos x}}, x \in(0,1)$, then :

Let the function f(x) = 2x² – log_ex, x> 0, be decreasing in (0, a) and increasing in (a, 4). A tangent to the parabola y² = 4ax at a point P on it passes through the point (8a, 8a –1) but does not pass through the point (-1/a, 0). If the equation of the normal at P is
$\frac{x}{α}+\frac{y}{β}=1$
then α + β is equal to _______ .

A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If $σ^2 $ is the variance of X, then 100 σ² is equal to ____.

The number of real solutions of x⁷ + 5x³ + 3x + 1 = 0 is equal to ______.

Let the solution curve $y = y(x)$ of the differential equation $(1 + e^{2x})\left(\frac{dy}{dx} + y\right) = 1$ pass through the point $(0, \frac{\pi}{2})$. Then, $\lim_{{x \to \infty}} e^x y(x)$ is equal to

The remainder when (2021)²⁰²² + (2022)²⁰²¹ is divided by 7 is

Suppose a₁, a₂, … a_n, … be an arithmetic progression of natural numbers. If the ration of the sum of first five terms to the sum of first nine terms of the progression is 5 : 17 and 110 < a₁₅ < 120, then the sum of the first ten terms of the progression is equal to

If y = y(x) is the solution of the differential equation
$x$ $\frac{dy}{dx}$ $+ 2y =$ $xe^x , y(1) = 0$
then the local maximum value of the function
$z(x) = x²y(x) - e^x , x ∈ R$
is

The sum of the absolute maximum and absolute minimum values of the function $\begin{array}{l} f\left(x\right)=\tan^{-1}\left(\sin x-\cos x\right) \end{array}$in the interval$ [0, π]$ is

Let
$\frac{x-2}{3} = \frac{y+1}{-2} = \frac{z+3}{-1}$
lie on the plane px – qy + z = 5, for some p, q ∈ ℝ. The shortest distance of the plane from the origin is :

Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing through the point Q and contains the line
$\vec{r}=−\hat{k}+λ(\hat{i}+\hat{j}+2\hat{k}), λ ∈ R.$
Then, which of the following points lies on T?

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