List of top Mathematics Questions asked in JEE Main

The function $ f: (-\infty, \infty) \to (-\infty, 1) $, defined by \[ f(x) = \frac{2^x - 2^{-x}}{2^x + 2^{-x}}, \] is:

The term independent of $ x $ in the expansion of $$ \left( \frac{x + 1}{x^{3/2} + 1 - \sqrt{x}} \cdot \frac{x + 1}{x - \sqrt{x}} \right)^{10} $$ for $ x>1 $ is:

The radius of the smallest circle which touches the parabolas $ y = x^2 + 2 $ and $ x = y^2 + 2 $ is

The focus of the parabola $ y^2 = 4x + 16 $ is the center of the circle $ C $ with radius 5. If the values of $ \lambda $, for which $ C $ passes through the point of intersection of the lines $ 3x - y = 0 $ and $ x + \lambda y = 4 $, are $ \lambda_1 $ and $ \lambda_2 $, $ \lambda_1 <\lambda_2 $, then $ 12\lambda_1 + 29\lambda_2 $ is equal to:

Let $( f(x) =$ $\int_0^{x^2 \frac{t^2 - 8t + 15}{e^t} dt}$, $x \in \mathbb{R}$. Then the numbers of local maximum and local minimum points of $ f $, respectively, are:

If $ \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + ... \infty = \frac{\pi^4}{90}, $ $ \frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + ... \infty = \alpha, $ $ \frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + ... \infty = \beta, $ then $ \frac{\alpha}{\beta} $ is equal to:

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $ L_1 : 2x + y + 6 = 0 $ and $ L_2 : 4x + 2y - p = 0 $, $ p>0 $, at the points A and B, respectively. If $ AB = \frac{9}{\sqrt{2}} $ and the foot of the perpendicular from the point A on the line $ L_2 $ is M, then $ \frac{AM}{BM} $ is equal to

In an arithmetic progression, if $ S_{40} = 1030 $ and $ S_{12} = 57 $, then $ S_{30} - S_{10} $ is equal to:

The line $ L_1 $ is parallel to the vector $ \mathbf{a} = -3\hat{i} + 2\hat{j} + 4\hat{k} $ and passes through the point $ (7, 6, 2) $, and the line $ L_2 $ is parallel to the vector $ \mathbf{b} = 2\hat{i} + \hat{j} + 3\hat{k} $ and passes through the point $ (5, 3, 4) $. The shortest distance between the lines $ L_1 $ and $ L_2 $ is:

What is the solution to the differential equation $ \frac{dy}{dx} = \frac{y}{x} $ with the initial condition $ y(1) = 2 $?

If the probability that the random variable X takes the value x is given by $ P(X = x) = k(x + 1)3^{-x} $, $ x = 0, 1, 2, 3, ... $, where k is a constant, then $ P(X \ge 3) $ is equal to

Let the points $ \left( \frac{11}{2}, \alpha \right) $ lie on or inside the triangle with sides $ x + y = 11 $, $ x + 2y = 16 $, and $ 2x + 3y = 29 $. Then the product of the smallest and the largest values of $ \alpha $ is equal to:

The system of equations \[ x + y + z = 6, \] \[ x + 2y + 5z = 9, \] \[ x + 5y + \lambda z = \mu, \] has no solution if:

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together is:

If for the solution curve $ y = f(x) $ of the differential equation \[ \frac{dy}{dx} + (\tan x) y = 2 + \sec^2 x, \quad y(\frac{\pi}{3}) = \sqrt{3}, \] $\text{then}$ $ y(\frac{\pi}{4}) $ is equal to:

Let $ y = y(x) $ be the solution of the differential equation $ \frac{dy}{dx} + 3(\tan^2 x) y + 3y = \sec^2 x $, with $ y(0) = \frac{1}{3} + e^3 $. Then $ y\left(\frac{\pi}{4}\right) $ is equal to

If the sum of the first 20 terms of the series $$ \frac{4.1}{4 + 3.1^2 + 1^4} + \frac{4.2}{4 + 3.2^2 + 2^4} + \frac{4.3}{4 + 3.3^2 + 3^4} + \frac{4.4}{4 + 3.4^2 + 4^4} + ... $$ is $ \frac{m}{n} $, where $ m $ and $ n $ are coprime, then $ m + n $ is equal to:

For the function $ f(x) = \ln(x^2 + 1) $, what is the second derivative of $ f(x) $?