List of top Questions asked in JEE Main

If A and B are any two events such that \(P(A)=\frac{2}{5}\) and \(P(A\cap B)=\frac{3}{20}\), then the conditional probability, \(P(A\mid(A'\cup B'))\), where \(A'\) denotes the complement of A, is equal to :

Consider the following two statements :
P : If 7 is an odd number, then 7 is divisible by 2.
Q : If 7 is a prime number, then 7 is an odd number.
If \(V_1\) is the truth value of the contrapositive of P and \(V_2\) is the truth value of contrapositive of Q, then the ordered pair \((V_1, V_2)\) equals :

If the mean deviation of the numbers \(1, 1+d, \ldots, 1+100d\) from their mean is 255, then a value of \(d\) is :

The number of \(x\in[0, 2\pi]\) for which \(\left|\sqrt{2\sin^4x+18\cos^2x}-\sqrt{2\cos^4x+18\sin^2x}\right|=1\) is :

If \(m\) and \(M\) are the minimum and the maximum values of \(4+\frac{1}{2}\sin^2 2x-2\cos^4x,\ x\in\mathbf{R}\), then \(M-m\) is equal to :

In a triangle ABC, right angled at the vertex A, if the position vectors of A, B and C are respectively \(3\hat i+\hat j-\hat k\), \(-\hat i+3\hat j+p\hat k\) and \(5\hat i+q\hat j-4\hat k\), then the point \((p, q)\) lies on a line :

A circle passes through \((-2, 4)\) and touches the \(y\)-axis at \((0, 2)\). Which one of the following equations can represent a diameter of this circle ?

The distance of the point \((1, -2, 4)\) from the plane passing through the point \((1, 2, 2)\) and perpendicular to the planes \(x-y+2z=3\) and \(2x-2y+z+12=0\), is :

Let \(a\) and \(b\) respectively be the semi-transverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation \(9e^2-18e+5=0\). If \(S(5, 0)\) is a focus and \(5x=9\) is the corresponding directrix of this hyperbola, then \(a^2-b^2\) is equal to :

The area (in sq. units) of the region described by \(A=\{(x, y) \mid y \geq x^2-5x+4,\ x+y \geq 1,\ y \leq 0\}\) is :

If \(f(x)\) is a differentiable function in the interval \((0, \infty)\) such that \(f(1)=1\) and \(\lim_{t \to x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1\), for each \(x\gt 0\), then \(f\left(\frac{3}{2}\right)\) is equal to :

The shortest distance between the lines \(\frac{x}{2}=\frac{y}{2}=\frac{z}{1}\) and \(\frac{x+2}{-1}=\frac{y-4}{8}=\frac{z-5}{4}\) lies in the interval :

The minimum distance of a point on the curve \(y=x^2-4\) from the origin is :

If \(\lim_{x\to\infty}\left(1+\frac ax-\frac{4}{x^2}\right)^{2x}=e^3\), then 'a' is equal to :

If the function \(f(x)=\begin{cases}-x, & x\lt 1\\ a+\cos^{-1}(x+b), & 1\le x\le 2\end{cases}\) is differentiable at \(x=1\), then \(\frac ab\) is equal to :

If \(2\int_0^1\tan^{-1}x\,dx=\int_0^1\cot^{-1}(1-x+x^2)\,dx\), then \(\int_0^1\tan^{-1}(1-x+x^2)\,dx\) is equal to :

If \(\int\frac{dx}{\cos^3x\sqrt{2\sin2x}}=(\tan x)^{A}+C(\tan x)^{B}+k\), where \(k\) is a constant of integration, then \(A+B+C\) equals :

If the equations \(x^2+bx-1=0\) and \(x^2+x+b=0\) have a common root different from \(-1\), then \(|b|\) is equal to :

Let \(x,\ y,\ z\) be positive real numbers such that \(x+y+z=12\) and \(x^3y^4z^5=(0.1)(600)^3\). Then \(x^3+y^3+z^3\) is equal to :

The value of \(\sum_{r=1}^{15}r^2\left(\frac{{}^{15}C_r}{{}^{15}C_{r-1}}\right)\) is equal to :

If \(P=\begin{bmatrix}\frac{\sqrt3}{2}&\frac12\\-\frac12&\frac{\sqrt3}{2}\end{bmatrix},\ A=\begin{bmatrix}1&1\\0&1\end{bmatrix}\) and \(Q=PAP^{T}\), then \(P^{T}Q^{2015}P\) is :

For \(x\in\mathbf{R},\ x\neq-1\), if \((1+x)^{2016}+x(1+x)^{2015}+x^2(1+x)^{2014}+\ldots+x^{2016}=\sum_{i=0}^{2016}a_i\,x^i\), then \(a_{17}\) is equal to :

The point represented by \(2+i\) in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there \(2\sqrt{2}\) units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by :

Which of the following statements about low density polythene is FALSE ?

The pair in which phosphorous atoms have a formal oxidation state of +3 is :