List of top Mathematics Questions asked in JEE Main

The integral \(\displaystyle\int_{\pi/6}^{\pi/3}\sec^{2/3}x\;\mathrm{cosec}^{4/3}x\,dx\) is equal to :

If \(\displaystyle\int x^5e^{-x^2}\,dx=g(x)e^{-x^2}+c\), where \(c\) is a constant of integration, then \(g(-1)\) is equal to :

Let \(\lambda\) be a real number for which the system of linear equations \(x+y+z=6,\; 4x+\lambda y-\lambda z=\lambda-2,\; 3x+2y-4z=-5\) has infinitely many solutions. Then \(\lambda\) is a root of the quadratic equation :

A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm\(^3\)/min. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min) of the ice decreases, is :

Let \(f(x)=\log_e(\sin x)\), \((0\lt x\lt\pi)\) and \(g(x)=\sin^{-1}(e^{-x})\), \((x\ge 0)\). If \(\alpha\) is a positive real number such that \(a=(f\circ g)^{\prime}(\alpha)\) and \(b=(f\circ g)(\alpha)\), then :

The distance of the point having position vector \(-\hat{i}+2\hat{j}+6\hat{k}\) from the straight line passing through the point \((2,3,-4)\) and parallel to the vector \(6\hat{i}+3\hat{j}-4\hat{k}\) is :

If \(\displaystyle\lim_{x\to 1}\frac{x^2-ax+b}{x-1}=5\), then \(a+b\) is equal to :

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is :

The sum of the real roots of the equation
\(\begin{vmatrix} x & -6 & -1 \\ 2 & -3x & x-3 \\ -3 & 2x & x+2 \end{vmatrix}=0\)
is equal to :

The sum
\(\frac{3\times 1^3}{1^3} + \frac{5\times(1^3 + 2^3)}{1^2 + 2^2} + \frac{7\times(1^3 + 2^3 + 3^3)}{1^2 + 2^2 + 3^2} + \dots\)
upto 10 terms is:

Which one of the following Boolean expressions is a tautology?

If the circles \(x^2 + y^2 + 5Kx + 2y + K = 0\) and \(2(x^2 + y^2) + 2Kx + 3y - 1 = 0\), \((K \in \mathbb{R})\), intersect at the points \(P\) and \(Q\), then the line \(4x + 5y - K = 0\) passes through \(P\) and \(Q\), for :

The line \(x = y\) touches a circle at the point \((1, 1)\). If the circle also passes through the point \((1, -3)\), then its radius is :

If the line \(x - 2y = 12\) is tangent to the ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) at the point \(\left(3, -\frac{9}{2}\right)\), then the length of the latus rectum of the ellipse is :

If \(\int \frac{dx}{(x^2 - 2x + 10)^2} = A\left(\tan^{-1}\left(\frac{x-1}{3}\right) + \frac{f(x)}{x^2 - 2x + 10}\right) + C\)
where \(C\) is a constant of integration then :

If the system of linear equations
\(x + y + z = 5\)
\(x + 2y + 2z = 6\)
\(x + 3y + \lambda z = \mu\), \((\lambda, \mu \in \mathbb{R})\), has infinitely many solutions, then the value of \(\lambda + \mu\) is :

If the coefficients of \(x^2\) and \(x^3\) are both zero, in the expansion of the expression \((1 + ax + bx^2)(1 - 3x)^{15}\) in powers of \(x\), then the ordered pair \((a, b)\) is equal to :

Let \(A(3, 0, -1)\), \(B(2, 10, 6)\) and \(C(1, 2, 1)\) be the vertices of a triangle and \(M\) be the midpoint of \(AC\). If \(G\) divides \(BM\) in the ratio \(2 : 1\), then \(\cos(\angle GOA)\) (\(O\) being the origin) is equal to :

If \(y = y(x)\) is the solution of the differential equation
\(\frac{dy}{dx} = (\tan x - y)\sec^2 x\), \(x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\),
such that \(y(0) = 0\), then \(y\left(-\frac{\pi}{4}\right)\) is equal to :

All the pairs \((x, y)\) that satisfy the inequality
\(2^{\sqrt{\sin^2 x - 2\sin x + 5}} \cdot \frac{1}{4^{\sin^2 y}} \le 1\)
also satisfy the equation

The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is :

If \(\Delta_1 = \begin{vmatrix} x & \sin\theta & \cos\theta \\ -\sin\theta & -x & 1 \\ \cos\theta & 1 & x \end{vmatrix}\) and \(\Delta_2 = \begin{vmatrix} x & \sin 2\theta & \cos 2\theta \\ -\sin 2\theta & -x & 1 \\ \cos 2\theta & 1 & x \end{vmatrix}\), \(x \ne 0\); then for all \(\theta \in \left(0, \frac{\pi}{2}\right)\) :

Let \(f(x) = x^2\), \(x \in R\). For any \(A \subseteq R\), define \(g(A) = \{x \in R : f(x) \in A\}\). If \(S = [0, 4]\), then which one of the following statements is not true ?

Let \(f(x) = e^x - x\) and \(g(x) = x^2 - x\), \(\forall\, x \in R\). Then the set of all \(x \in R\), where the function \(h(x) = (f \circ g)(x)\) is increasing, is :

The region represented by \(|x - y| \le 2\) and \(|x + y| \le 2\) is bounded by a :