List of top Questions asked in JEE Main

If the truth value of the statement
(P∧(∼R))→((∼R)∧Q)
is F, then the truth value of which of the following is F?

The minimum value of the sum of the squares of the roots of x2 + (3 – a)x + 1 = 2a is

$\sum_{\substack{i,j=0 \\ t \neq j}}^n$ $^nC_i\ ^nC_j $
is equal to

f the maximum value of a, for which the function
$fa(x)=\tan^{−1}\ ⁡2x−3ax+7$
is non-decreasing in $(−\frac{π}{6},\frac{π}{6})$, is a―, then $f\overline{a}(\frac{π}{8}) $
is equal to

Let
$β = \lim_{x →0} \frac{αx-(e^{3x}-1)}{αx(e^{3x}-1) }$for some$ α \in R.$
Then the value of α+β is

The value of $\log_e2\frac{d}{dx}(\log_{cos⁡ x}\cosec x) $ at $x=\frac{\pi}{4}$ is

$\int_{0}^{20\pi} (|\sin x| + |\cos x|)^2 \,dx$
is equal to

The slope of normal at any point $(x, y), x > 0, y > 0$ on the curve $y = y(x)$ is given by $\frac{x^2}{xy-x^2y2^-1}$ If the curve passes through the point (1, 1), then $e · y(e)$ is equal to

Let $E_1$ and $E_2$ be two events such that the conditional probabilities $P(E_1|E_2)=\frac 12$, $P(E_2|E_1)=\frac 34$ and $P(E_1∩E_2)=\frac 18$⋅ Then:

Let $λ^*$ be the largest value of $λ$ for which the function $f_λ(x) = 4λx^3 – 36λx^2 + 36x + 48$ is increasing for all $x ∈ ℝ$. Then $f_λ^* (1) + f_λ^* (– 1)$ is equal to :

If $\frac{dy}{dx} + \frac{2x-y(2^y-1)}{2x-1} = 0, x,y > 0,y(1) = 1$, then $y(2)$ is equal to:

If the solution of the differential equation
$\frac{dy}{dx}$ $+ e^x(x² - 2)y = (x^2 - 2x)(x^2 - 2)e^{2x}$
satisfies y(0) = 0, then the value of y(2) is ______.

If the solution curve $y = y(x)$ of the differential equation$ y^2dx + (x^2 – xy + y^2)dy = 0$, which passes through the point $(1,1)$ and intersects the line $y=\sqrt 3x$ at the point $(α,\sqrt 3α)$, then value of $log_e(\sqrt 3α)$ is equal to :

The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is ________.

Let the abscissae of the two points $P$ and $Q$ be the roots of $2x^2 – rx + p = 0$ and the ordinates of $P$ and $Q$ be the roots of $x^2 – sx – q = 0$. If the equation of the circle described on $PQ$ as diameter is $2(x^2 + y^2) – 11x – 14y – 22 = 0$, then $2r + s – 2q + p$ is equal to _________.

The number of values of x in the interval $(\frac \pi 4, \frac {7\pi }{4})$ for which $14cosec^2x – 2sin^2x = 21 – 4cos^2x$ holds, is ______.

For a natural number $n$, let $α_n = 19n – 12n$. Then, the value of $\frac {31α_9−α_{10}}{57α_8}$ is _____.

Let A be a 3 × 3 matrix having entries from the set {–1, 0, 1}. The number of all such matrices A having sum of all the entries equal to 5, is ______.

The greatest integer less than or equal to the sum of first $100$ terms of the sequence $\frac 13, \frac 59, \frac {19}{27}, \frac {65}{81},…...$ is equal to ______.

Let $ƒ : N→R$ be a function such that $ƒ(x + y) = 2ƒ(x) ƒ(y)$ for natural numbers x and y. If $ƒ(1) = 2$, then the value of α for which $\displaystyle\sum_{k=1}^{10} f(α+k)=\frac {512}{3} (2^{20}−1)$ holds, is:

Let A be a $3×3$ real matrix such that $A\begin{pmatrix} 1 \\1 \\ 0 \end{pmatrix}$=$\begin{pmatrix} 1 \\1 \\ 0 \end{pmatrix}$; $A\begin{pmatrix} 1 \\0 \\ 1 \end{pmatrix}$=$A\begin{pmatrix} -1 \\0 \\ 1 \end{pmatrix}$ and $A\begin{pmatrix} 0 \\0 \\ 1 \end{pmatrix}$=$\begin{pmatrix} 1 \\1 \\ 2 \end{pmatrix}$
If $X = [x_1, x_2, x_3]^T $and $I$ is an identity matrix of order $3$, then the system $[A−2I]X $= $\begin{pmatrix} 4 \\1 \\ 1 \end{pmatrix}$ has:

Let $A = \begin{bmatrix} 0 & -2 \\[0.3em] 2 & 0 \end{bmatrix}$. If $M$ and $N$ are two matrices given by $M = \displaystyle\sum_{k=1}^{10} A^{2k}$ and $N = \displaystyle\sum_{k=1}^{10} A^{2k-1}$
then $MN^2 $ is :

Let $g : (0, ∞) →R$ be a differentiable function such that $∫(\frac {x(cos⁡x−sin⁡x)}{e^x+1} + \frac {g(x)(e^x+1−xe^x)}{(e^x+1)2})dx = \frac {xg(x)}{e^x+1}+c,$ for all $x>0$, where c is an arbitrary constant. Then:

For any real number x, let [ x ] denote the largest integer less than equal to x Let f be a real valued function defined on the interval [-10,10] by $f(x)=\begin{cases} x-[x], & \text { if }(x) \text { is odd } \\ 1+[x]-x & \text { if }(x) \text { is even }\end{cases}$Then the value of$ \frac{\pi^2}{10} \int\limits_{-10}^{10} f(x) \cos \pi x d x$ is :

The slope of the tangent to a curve C : y=y(x) at any point [x, y) on it is $\frac{2 e ^{2 x }-6 e ^{- x }+9}{2+9 e ^{-2 x }}$ If C passes through the points $\left(0, \frac{1}{2}+\frac{\pi}{2 \sqrt{2}}\right) $and $\left(\alpha, \frac{1}{2} e ^{2 \alpha}\right)$$ then $e ^\alpha$ is equal to :