List of top Mathematics Questions asked in JEE Main

The value of $ tan^{-1}(\frac{cos\frac{15}{4}-1}{sin(\frac{π}{4})} )$ is equal to:

The value of the integral
$\frac{48}{\pi^4} \int_{0}^{\pi}(\frac{3\pi x^2}{2} - x^3) \frac{ \sin(x)}{1 + \cos^2x} \, dx$
is equal to ________

Let the lines$ \begin{array}{l} \frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}\ \text{and}\ \frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda}\end{array}$be coplanar and P be the plane containing these two lines. Then which of the following points does NOT lie on P?

Let $f : R \rightarrow R$ be a continuous function such that $f (3x)- f(x)= x$. If $f(8)=7$, then $f (14)$ is equal to :

If $f(x)=\begin{cases} x+a, & x \leq 0 \\ |x-4|, & x\gt0\end{cases}$ and
$g(x)= \begin{cases}x+1 & , x\lt0 \\ (x-4)^2+b, & x \geq 0\end{cases}$
are continuous on $R$, then $(gof) (2)+(fog)(-2)$ is equal to:

If the minimum value of $f(x)=\frac{5 x^2}{2}+\frac{\alpha}{x^5}, x>0$, is 14 , then the value of $\alpha$ is 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

A tower PQ stands on a horizontal ground with base Q on the ground. The point R divides the tower in two parts such that QR = 15 m. If from a point A on the ground the angle of elevation of R is 60° and the part PR of the tower subtends an angle of 15° at A, then the height of the tower is :

The number of solutions of the equation sin x = cos² x in the interval (0, 10) is _____.

The value of
$\lim_{{n \to \infty}} 6\tan\left\{\sum_{{r=1}}^{n} \tan^{-1}\left(\frac{1}{{r^2+3r+3}}\right)\right\}$
is equal to :

For k ∈ R, let the solution of the equation
$\cos\left(\sin^{-1}\left(x \cot\left(\tan^{-1}\left(\cos\left(\sin^{-1}\right)\right)\right)\right)\right) = k, \quad 0 < |x| < \frac{1}{\sqrt{2}}$
Inverse trigonometric functions take only principal values. If the solutions of the equation x² – bx – 5 = 0 are
$\frac{1}{α^2}+\frac{1}{β^2} $and $\frac{α}{β}$
, then b/k2 is equal to_____.

The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to:

Let H: $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1, a > 0, b > 0,$ be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is $4(2\sqrt 2 + \sqrt {14}).$ If the eccentricity H is $\frac{\sqrt {11}}{2}$, then the value of $a^2 + b^2 $ is equal to ______.

The number of points, where the function $f: \mathbb{R} \to \mathbb{R}$, $$ f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x - 3)|x^2 - 5x + 4|, $$ is NOT differentiable, is

If α, β, γ, δ are the roots of the equation x⁴ + x³ + x² + x + 1 = 0, then α²⁰²¹ + β²⁰²¹ + γ²⁰²¹ + δ²⁰²¹ is equal to

If the system of equations
$ x + y + z = 6 $,
$ 2x + 5y + \alpha z = \beta $,
$ x + 2y + 3z = 14 $
has infinitely many solutions, then $ \alpha + \beta $ is equal to:

The mean and standard deviation of 15 observations are found to be 8 and 3, respectively. On rechecking, it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _______.

The number of elements in the set { $z = a + ib ∈ C : a,b ∈ Z$ and $1 < | z - 3 + 2i | < 4$ } is _______ .

Let
$A = \{z \in \mathbb{C} : |\frac{z+1}{z-1}| < 1\}$
and
$B = \{z \in \mathbb{C} : \text{arg}(\frac{z-1}{z+1}) = \frac{2\pi}{3}\}$
Then $A∩B$ is :

Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola
$\frac{x^2}{a^2}−\frac{y^2}{b^2}=1$
Let e′ and l′ respectively be the eccentricity and length of the latus rectum of its conjugate hyperbola. If
$e^2=\frac{11}{14}l$ and $(e^′)^2=\frac{11}{8}l^′$
then the value of 77a + 44b is equal to :

Five numbers, $x_1, x_2, x_3, x_4, x_5$ are randomly selected from the numbers $1, 2, 3$,….., $18$ and are arranged in the increasing order $(x_1<x_2<x_3<x_4<x_5)$. The probability that $x_2 = 7$ and $x_4 = 11$ is:

A circle touches both the y-axis and the line x + y = 0. Then the locus of its center is

Let the tangents at two points A and B on the circle$ x^2 + y^2 – 4x + 3 = 0$ meet at origin O(0, 0). Then the area of the triangle OAB is

If the absolute maximum value of the function $f(x)=\left(x^2-2 x+7\right) e^{\left(4 x^3-12 x^2-180 x+31\right)}$ in the interval [-3,0] is $f(\alpha)$, then:

The minimum value of the twice differentiable function $f(x)=\int\limits_0^x e^{x-1} f^{\prime}(t) d t-\left(x^2-x+1\right) e^x, x \in R$, is :