List of top Mathematics Questions asked in JEE Main

If [ ] denotes the greatest integer function, then the integral \(\int_0^{\pi}[\cos x]\,dx\) is equal to:

If \(\begin{vmatrix} a^2 & b^2 & c^2 \\ (a+\lambda)^2 & (b+\lambda)^2 & (c+\lambda)^2 \\ (a-\lambda)^2 & (b-\lambda)^2 & (c-\lambda)^2 \end{vmatrix} = k\lambda \begin{vmatrix} a^2 & b^2 & c^2 \\ a & b & c \\ 1 & 1 & 1 \end{vmatrix}, \lambda \ne 0\), then \(k\) is equal to:

If \(f(\theta) = \begin{vmatrix} 1 & \cos\theta & 1 \\ -\sin\theta & 1 & -\cos\theta \\ -1 & \sin\theta & 1 \end{vmatrix}\) and \(A\) and \(B\) are respectively the maximum and the minimum values of \(f(\theta)\), then \((A, B)\) is equal to:

If \(f(x)=x^2-x+5,\ x>\frac{1}{2}\), and \(g(x)\) is its inverse function, then \(g'(7)\) equals:

Statement I: The equation \((\sin^{-1}x)^3+(\cos^{-1}x)^3-a\pi^3=0\) has a solution for all \(a\ge\frac{1}{32}\).
Statement II: For any \(x\in\mathbb{R}\), \(\sin^{-1}x+\cos^{-1}x=\frac{\pi}{2}\) and \(0\le\left(\sin^{-1}x-\frac{\pi}{4}\right)^2\le\frac{9\pi^2}{16}\).

Let \(f,g:\mathbb{R}\to\mathbb{R}\) be two functions defined by \(f(x)=\begin{cases}x\sin\left(\frac{1}{x}\right), & x\ne0\\ 0, & x=0\end{cases}\) and \(g(x)=xf(x)\).
Statement I: \(f\) is a continuous function at \(x=0\).
Statement II: \(g\) is a differentiable function at \(x=0\).

If \(A = \begin{bmatrix} 1 & 2 & x \\ 3 & -1 & 2 \end{bmatrix}\) and \(B = \begin{bmatrix} y \\ x \\ 1 \end{bmatrix}\) be such that \(AB = \begin{bmatrix} 6 \\ 8 \end{bmatrix}\), then:

Let \(p, q, r\) denote arbitrary statements. Then the logically equivalent of the statement \(p \Rightarrow (q \vee r)\) is:

Let \(\bar{X}\) and M.D. be the mean and the mean deviation about \(\bar{X}\) of \(n\) observations \(x_i, i = 1, 2, n\). If each of the observations is increased by 5, then the new mean and the mean deviation about the new mean, respectively, are:

For the two circles \(x^2 + y^2 = 16\) and \(x^2 + y^2 - 2y = 0\), there is/are

A relation on the set \(A = \{x : |x| \lt 3, x \in Z\}\), where \(Z\) is the set of integers is defined by \(R = \{(x, y) : y = |x|, x \ne -1\}\). Then the number of elements in the power set of \(R\) is:

If the three distinct lines \(x + 2ay + a = 0\), \(x + 3by + b = 0\) and \(x + 4ay + a = 0\) are concurrent, then the point \((a, b)\) lies on a:

8-digit numbers are formed using the digits \(1, 1, 2, 2, 2, 3, 4, 4\). The number of such numbers in which the odd digits do not occupy odd places, is:

If \(\left(2 + \frac{x}{3}\right)^{55}\) is expanded in the ascending powers of \(x\) and the coefficients of powers of \(x\) in two consecutive terms of the expansion are equal, then these terms are:

Let \(G\) be the geometric mean of two positive numbers \(a\) and \(b\), and \(M\) be the arithmetic mean of \(\frac{1}{a}\) and \(\frac{1}{b}\). If \(\frac{1}{M} : G\) is \(4 : 5\), then \(a : b\) can be:

The sum of the roots of the equation, \(x^2 + |2x - 3| - 4 = 0\), is:

A set S contains 7 elements. A non-empty subset A of S and an element x of S are chosen at random. Then the probability that \(x \in A\) is:

If \(X\) has a binomial distribution, \(B(n,p)\) with parameters \(n\) and \(p\) such that \(P(X=2)=P(X=3)\), then \(E(X)\), the mean of variable \(X\), is

If \(|\vec{c}|^2 = 60\) and \(\vec{c}\times(\hat{i}+2\hat{j}+5\hat{k}) = \vec{0}\), then a value of \(\vec{c}\cdot(-7\hat{i}+2\hat{j}+3\hat{k})\) is:

If the general solution of the differential equation \(y' = \frac{y}{x} + \Phi\left(\frac{x}{y}\right)\), for some function \(\Phi\), is given by \(y\ln|cx| = x\), where c is an arbitrary constant, then \(\Phi(2)\) is equal to:

The plane containing the line \(\frac{x-1}{1} = \frac{y-2}{2} = \frac{z-3}{3}\) and parallel to the line \(\frac{x}{1} = \frac{y}{1} = \frac{z}{4}\) passes through the point:

Let f be an odd function defined on the set of real numbers such that for \(x \ge 0\), \(f(x) = 3\sin x + 4\cos x\). Then f(x) at \(x = -\frac{11\pi}{6}\) is equal to:

For the curve \(y = 3\sin\theta\cos\theta\), \(x = e^{\theta}\sin\theta\), \(0 \le \theta \le \pi\), the tangent is parallel to x-axis when \(\theta\) is:

The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius \(= \sqrt{3}\) is:

Let \(f(x) = x|x|\), \(g(x) = \sin x\) and \(h(x) = (g\circ f)(x)\). Then