List of top Mathematics Questions asked in JEE Main

If \[ \frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ} = \frac{\alpha + \sqrt{5}\,\beta}{2}, \] then the value of $(\alpha + \beta)$ is

The value of \[ \int_{\frac{\pi}{2}}^{\pi} \frac{dx}{[x]+4} \] where $[\,\cdot\,]$ denotes the greatest integer function, is

The number of values of $x$ satisfying \[ \tan^{-1}(4x)+\tan^{-1}(6x)=\frac{\pi}{6}, \quad x\in\left[-\frac{1}{2\sqrt{6}},\,\frac{1}{2\sqrt{6}}\right] \] is

Let $ M = \{1,2,3,\ldots,16\} $ and $ R $ be a relation on $ M $ defined by $ xRy $ if and only if $ 4y = 5x - 3 $. Then, the number of ordered pairs required to be added to $ R $ to make it symmetric is

If the sum of first 4 terms of an A.P. is $6$ and the sum of first 6 terms is $4$, then the sum of first 12 terms of the A.P. is

Let $ A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix} $ and $ B = \begin{bmatrix} 29 & 49 \\1 & 2 \end{bmatrix} $. If $ (A^5 + B)\begin{bmatrix} x\\ y \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} $, then find $ (x, y) $.

Let $ A = \{1, 2, 3, 4\} $ and $ B = \{1, 4, 9, 16\} $. Then the number of many-one functions $ f: A \to B $ such that $ 1 \in f(A) $ is equal to:

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include at least 4 batsmen and at least 4 bowlers. One batsman and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is:

Number of functions $ f: \{1, 2, \dots, 100\} \to \{0, 1\} $, that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to:

Let $ f(x) = \begin{cases} (1+ax)^{1/x} & , x<0 \\1+b & , x = 0 \\\frac{(x+4)^{1/2} - 2}{(x+c)^{1/3} - 2} & , x>0 \end{cases} $ be continuous at x = 0. Then $ e^a bc $ is equal to

Let $ C_1 $ be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let $ C_2 $ be the circle with center $ (1, 3) $ that touches $ C_1 $ externally at the point $ (\alpha, \beta) $. If $ (\beta - \alpha)^2 = \frac{m}{n} $, and $ \gcd(m, n) = 1 $, then $ m + n $ is equal to:

The number of singular matrices of order 2, whose elements are from the set $ \{2, 3, 6, 9\} $ is:

Let the matrix $ A = \begin{pmatrix} 1 & 0 & 0 \\1 & 0 & 1 \\0 & 1 & 0 \end{pmatrix} $ satisfy $ A^n = A^{n-2} + A^2 - I $ for $ n \geq 3 $. Then the sum of all the elements of $ A^{50} $ is:

Let the angle $ \theta, 0<\theta<\frac{\pi}{2} $ between two unit vectors $ \hat{a} $ and $ \hat{b} $ be $ \sin^{-1} \left( \frac{\sqrt{65}}{9} \right) $. If the vector $ \vec{c} = 3\hat{a} + 6\hat{b} + 9(\hat{a} \times \hat{b}) $, then the value of $ 9(\vec{c} \cdot \hat{a}) - 3(\vec{c} \cdot \hat{b}) $ is:

Let $ f: \mathbb{R} \to \mathbb{R} $ be a function defined by $ f(x) = \left( 2 + 3a \right)x^2 + \left( \frac{a+2}{a-1} \right)x + b, a \neq 1 $. If \[ f(x + y) = f(x) + f(y) + 1 - \frac{2}{7}xy, \] then the value of $ 28 \sum_{i=1}^5 f(i) $ is:

Let the points $A(a,-1,2)$, $B(1,b,-4)$, $C(-1,1,c)$ and $D(1,-2,8)$ be the vertices of a parallelogram $ABCD$. Then its area is equal to:

If the range of the function $ f(x) = \sqrt{3 - x} + \sqrt{5 + x} $ is $[\alpha, \beta]$, then $ \alpha^2 + \beta^2 $ is equal to:

Let $f: [0, \infty) \to \mathbb{R}$ be a differentiable function such that $f(x) = 1 - 2x + \int_0^x e^{x-t} f(t) \, dt$ for all $x \in [0, \infty)$. Then the area of the region bounded by $y = f(x)$ and the coordinate axes is

Let the system of equations $ x + 5y - z = 1 $ $ 4x + 3y - 3z = 7 $ $ 24x + y + \lambda z = \mu $ where $ \lambda, \mu \in \mathbb{R} $, have infinitely many solutions. Then the number of the solutions of this system, if $x, y, z$ are integers and satisfy $7 \leq x + y + z \leq 77$, is:

The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is:

The distance of the line $ \frac{x - 2}{2} = \frac{y - 6}{3} = \frac{z - 3}{4} $ from the point $ (1, 4, 0) $ along the line $ \frac{x}{1} = \frac{y - 2}{2} = \frac{z + 3}{3} $ is:

The total number of ways the word 'DAUGHTER' can be arranged so that all vowels don't occur together:

Two biased dice are rolled. Out of which one die contains 1, 1, 2, 2, 3, 3, and another die contains 1, 2, 2, 3, 3, 4. Then the probability of getting a sum of 4 or 5 is:

Line $ L_1 $ passes through the point (1, 2, 3) and is parallel to z-axis. Line $ L_2 $ passes through the point $ (\lambda, 5, 6) $ and is parallel to y-axis. Let for $ \lambda = \lambda_1, \lambda_2, \lambda_2<\lambda_1 $, the shortest distance between the two lines be 3. Then the square of the distance of the point $ (\lambda_1, \lambda_2, 7) $ from the line $ L_1 $ is

If $ f(x) = \frac{2^x}{2^x + \sqrt{2}} $, $x \in \mathbb{R}$, then $ \sum_{k=1}^{81} f\left(\frac{k}{82}\right) $ is equal to: