List of top Mathematics Questions asked in JEE Main

Let $$ B = \begin{bmatrix} 1 & 3 \\ 1 & 5 \end{bmatrix} $$ and $A$ be a $2 \times 2$ matrix such that $$ AB^{-1} = A^{-1}. $$ If $BCB^{-1} = A$ and $$ C^4 + \alpha C^2 + \beta I = O, $$ then $2\beta - \alpha$ is equal to:

Let $A = \{1, 2, 3, 4, 5\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $4x \leq 5y$. Let $m$ be the number of elements in $R$ and $n$ be the minimum number of elements from $A \times A$ that are required to be added to $R$ to make it a symmetric relation. Then $m + n$ is equal to:

Let A= {2, 3, 6, 8, 9, 11} and B = {1, 4, 5, 10, 15} Let R be a relation on A × B define by (a, b)R(c, d) if and only if 3ad – 7bc is an even integer. Then the relation R is

Let $ S = (-1, \infty) $ and $ f : S \rightarrow \mathbb{R} $ be defined as \[ f(x) = \int_{-1}^{x} (e^t - 1)^{11} (2t - 1)^5 (t - 2)^7 (t - 3)^{12} (2t - 10)^{61} \, dt \] Let $ p = $ Sum of squares of the values of $ x $, where $ f(x) $ attains local maxima on $ S $. And $ q = $ Sum of the values of $ x $, where $ f(x) $ attains local minima on $ S $. Then, the value of $ p^2 + 2q $ is ______

A square is inscribed in the circle $ x^2 + y^2 - 10x - 6y + 30 = 0 $. One side of this square is parallel to $ y = x + 3 $. If $ (x_i, y_i) $ are the vertices of the square, then $ \sum (x_i^2 + y_i^2) $ is equal to:

If $\sin x = -\frac{3}{5}$, where $\pi<x<\frac{3\pi}{2}$, then $80(\tan^2 x - \cos x)$ is equal to:

Let $A = I_2 - MM^T$, where $M$ is a real matrix of order $2 \times 1$ such that the relation $M^T M = I_1$ holds. If $\lambda$ is a real number such that the relation $AX = \lambda X$ holds for some non-zero real matrix $X$ of order $2 \times 1$, then the sum of squares of all possible values of $\lambda$ is equal to:

Let $ R $ be the interior region between the lines $ 3x - y + 1 = 0 $ and $ x + 2y - 5 = 0 $ containing the origin. The set of all values of $ a $, for which the points $ (a^2, a + 1) $ lie in $ R $, is:

If $a=sin^{-1}(sin\ 5)$ and $b=cos^{-1}(cos\ 5)$, then $a^2+b^2=$

If P(6, 1) be the orthocentre of the triangle whose vertices are A(5, –2), B(8, 3) and C(h, k), then the point C lies on the circle.

Let $ x_1, x_2, x_3, x_4 $ be the solution of the equation \[ 4x^4 + 8x^3 - 17x^2 - 12x + 9 = 0 \] and \[ \left(4 + x_1^2\right)\left(4 + x_2^2\right)\left(4 + x_3^2\right)\left(4 + x_4^2\right) = \frac{125}{16} m.\] Then the value of $ m $ is ______.

Given: $5f (x) 4f(\frac 1x) = x^2 - 4 $ & $y = 9f(x) × x^2$ If y is strictly increasing, then find interval of $x$.

If the system of equations
$ 2x + 3y - z = 5 $
$ x + \alpha y + 3z = -4 $
$ 3x - y + \beta z = 7 $
has infinitely many solutions, then $ 13 \alpha \beta $ is equal to:

Let \[ \vec{a} = 2\hat{i} + \alpha \hat{j} + \hat{k}, \quad \vec{b} = -\hat{i} + \hat{k}, \quad \vec{c} = \beta \hat{j} - \hat{k}, \] where $ \alpha $ and $ \beta $ are integers and $ \alpha \beta = -6 $. Let the values of the ordered pair $ (\alpha, \beta) $ for which the area of the parallelogram of diagonals $ \vec{a} + \vec{b} $ and $ \vec{b} + \vec{c} $ is $ \frac{\sqrt{21}}{2} $, be $ (\alpha_1, \beta_1) $ and $ (\alpha_2, \beta_2) $. Then $ \alpha_1^2 + \beta_1^2 - \alpha_2 \beta_2 $ is equal to:

If $ (a, b) $ be the orthocenter of the triangle whose vertices are $ (1, 2) $, $ (2, 3) $, and $ (3, 1) $, and $ I_1 = \int_a^b x \sin(4x - x^2) dx $, $ I_2 = \int_a^b \sin(4x - x^2) dx $, then $ 36 \frac{I_1}{I_2} $ is equal to:

Let $ A = \{1, 3, 7, 9, 11\} $ and $ B = \{2, 4, 5, 7, 8, 10, 12\} $. Then the total number of one-one maps $ f: A \to B $, such that $ f(1) + f(3) = 14 $, is:

Suppose $ 2 - p $, $ p $, $ 2 - \alpha $, $ \alpha $ are the coefficients of four consecutive terms in the expansion of $ (1 + x)^n $. Then the value of $ p^2 - \alpha^2 + 6\alpha + 2p $ equals

Let

$ A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha \end{bmatrix} $

and $|2A|^3 = 2^{21}$ where $\alpha, \beta \in \mathbb{Z}$. Then a value of $\alpha$ is:

Let $ r $ and $ \theta $ respectively be the modulus and amplitude of the complex number $ z = 2 - i \left( 2 \tan \frac{5\pi}{8} \right) $, then $ (r, \theta) $ is equal to

The distance of the point $ (2, 3) $ from the line $ 2x - 3y + 28 = 0 $, measured parallel to the line $ \sqrt{3}x - y + 1 = 0 $, is equal to

Let the foci of a hyperbola $ H $ coincide with the foci of the ellipse $ E : \frac{(x - 1)^2}{100} + \frac{(y - 1)^2}{75} = 1 $ and the eccentricity of the hyperbola $ H $ be the reciprocal of the eccentricity of the ellipse $ E $. If the length of the transverse axis of $ H $ is $ \alpha $ and the length of its conjugate axis is $ \beta $, then $ 3\alpha^2 + 2\beta^2 $ is equal to:

If the mirror image of the point $P(3, 4, 9)$ in the line $\frac{x-1}{3} = \frac{y+1}{2} = \frac{z-2}{1}$ is $(\alpha, \beta, \gamma)$, then $14(\alpha + \beta + \gamma)$ is:

Let $\alpha, \beta$ be the roots of the equation $x^2 + 2\sqrt{2}x - 1 = 0$. The quadratic equation, whose roots are $\alpha^4 + \beta^4$ and $\frac{1}{10} \left( \alpha^6 + \beta^6 \right)$, is:

The value of $\frac{1 \times 2^2 + 2 \times 3^2 + \dots + 100 \times (101)^2}{1^2 \times 2 + 2^2 \times 3 + \dots + 100^2 \times 101}$ is:

Let the line $L$ intersect the lines
$x - 2 = -y = z - 1$, $\quad 2(x + 1) = 2(y - 1) = z + 1$
and be parallel to the line
$\frac{x-2}{3} = \frac{y-1}{1} = \frac{z-2}{2}$.
Then which of the following points lies on $L$?