List of top Mathematics Questions asked in JEE Main

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 $60^{\circ}$ and the part $PR$ of the tower subtends an angle of $15^{\circ}$ at $A$, then the height of the tower is :

The number of elements in the set $S = \{ \theta \in [-4\pi, 4\pi] : 3 \cos^2(2\theta) + 6 \cos^2(\theta) - 10\cos(2\theta) + 5 = 0 \}$ is______.

Let C be a circle passing through the points A(2, –1) and B (3, 4). The line segment AB is not a diameter of C. If r is the radius of C and its centre lies on the circle
$(x−5)^2+(y−1)^2=\frac{13}{2}$
then r² is equal to

Choose the correct answer:

1. Let A = {x ∈ R : | x + 1 | < 2} and B = {x ∈ R : | x – 1| ≥ 2}. Then which one of the following statements is NOT true?

$cos^{-1}(\frac{2sin^{-1}(\frac{1}{4x^2-1})}{π})$ is:

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

If $cos^{-1}(\frac{y}{2})=log_e(\frac{x}{5})^5, |y| < 2$ then:

The distance between the two points A and A′ which lie on y = 2 such that both the line segments AB and A′B (where B is the point (2, 3)) subtend angle π/4 at the origin, is equal to

The sum of all the real roots of the equation $(e^{2x} – 4)(6e^{2x} – 5e^x + 1) = 0$ is

Let S be the set containing all 3 × 3 matrices with entries from {-1, 0, 1}. The total number of matrices A ∈ S such that the sum of all the diagonal elements of A^TA is 6 is ________.

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 mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to :

A random variable $X$ has the following probability distribution :

x	0	1	2	3	4
P(x)	k	2k	4k	6k	8k

The value of $P(1 < X < 4 | x ≤ 2)$ is equal to

Let the focal chord of the parabola P :y² = 4x along the line L : y = mx + c, m> 0 meet the parabola at the points M and N. Let the line L be a tangent to the hyperbola H :x² – y² = 4. If O is the vertex of P and F is the focus of H on the positive x-axis, then the area of the quadrilateral OMFN is

Let x = x(y) be the solution of the differential equation
$2ye^{\frac{x}{y^2}}dx+(y^2−4xe^{\frac{x}{y^2}})dy=0 $
such that x(1) = 0. Then, x(e) is equal to

if $∫ \frac{(x^2+1)e^x}{(x+1)^2}dx = ƒ(x)e^x+C$ where $C$ is a constant, then $\frac{d^3ƒ}{dx^3}$ at $x = 1$ is equal to :

Let f : R → R be a function defined by:
$ƒ(x) = (x-3)^{n_1} (x-5)^{n_2} , n_1, n_2 ∈ N$
Then, which of the following is NOT true?

If
$\int_{0}^{2} (\sqrt{2x} - \sqrt{2x - x^2}) \,dx = \int_{0}^{1} \left(1 - \sqrt{1 - y^2} - \frac{y^2}{2}\right) \,dy + \int_{1}^{2} (2 - \frac{y^2}{2}) \,dy + I$
then I equal is

$lim _{ n → ∞}\bigg (\frac{n^2}{(n^2+1)(n+1)}+\frac{n^2}{(n^2+4)(n+2)}+\frac{n^2}{(n2+9)(n+3)}.....+ \frac{n^2}{(n^2+n^2)(n+n)}\bigg)$is equal to

Let α be a root of the equation 1 + x² + x⁴ = 0. Then the value of α¹⁰¹¹ + α²⁰²² – α³⁰³³ is equal to

Let P : y² = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of π/4 with the line y = 3x + 5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is

Let $\begin{array}{l}A=\begin{bmatrix}1 & -1 \\2 & \alpha \\\end{bmatrix}\ \text{and}\ B=\begin{bmatrix}\beta & 1 \\1 & 0 \\\end{bmatrix},\alpha, \beta \in R\end{array}$.

Let $α1$ be the value of α which satisfies
$\begin{array}{l}(A + B)^2 =A^2 + \begin{bmatrix}2 & 2 \\2 & 2 \\\end{bmatrix}\end{array}$

and $α2$ be the value of α which satisfies

$\begin{array}{l}\left(A + B\right)^2 = B^2.\end{array}$

Then $|α1 – α2|$ is equal to _________.

Let f(x) be a quadratic polynomial such that f(–2) + f(3) = 0. If one of the roots of f(x) = 0 is –1, then the sum of the roots of f(x) = 0 is equal to:

$sin^{-1}\bigg(sin\frac{2π}{3}\bigg)+cos^{-1}\bigg(cos\frac{7π}{6}\bigg)+tan^{-1}\bigg(tan\frac{3π}{4}\bigg)$ is equal to:

If the coefficient of x10 in the binomial expansion of
$\left(\frac{\sqrt{x}}{5^{\frac{1}{4}}} + \frac{\sqrt{5}}{x^{\frac{1}{3}}}\right)^{60}$
is 5^k.l, where l, k∈N and l is co-prime to 5, then k is equal to ___________.