List of top Questions asked in JEE Main

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 $ƒ : R→R$ be defined as $ƒ(x) = x^3 + x – 5$ . If g(x) is a function such that $ƒ(g(x)) = x$, ∀‘x‘∈R. Then $g^′(63)$ is equal to_____.

Let a, b and c be the length of sides of a triangle ABC such that:
$\frac {a+b}{7}=\frac {b+c}{8}=\frac {c+a}{9}$
If $r$ and $R$ are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of $\frac Rr$ is equal to :

Let $Q$ be the mirror image of the point $P(1, 0, 1)$ with respect to the plane $S$: $x + y + z = 5$. If a line L passing through $(1, –1, –1)$, parallel to the line $PQ$ meets the plane $S$ at $R$, then $QR_2$ is equal to :

In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured from time of 100 oscillations with a watch of 1 s resolution. If measured value of length is 10 cm known to 1 mm accuracy, the accuracy in the determination of g is found to be x %. The value of 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 $60^{\circ}$ 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

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