List of top Mathematics Questions asked in JEE Main

Let $ A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 0 & 3 \\ 1 & 0 & 0 \end{bmatrix} $, where $ a, c \in \mathbb{R} $. If $ A^n = A $ and the positive value of $ a $ belongs to the interval $ (n-1, n] $, where $ n \in \mathbb{N} $, then $ n $ is equal to:

Let $ S = 109 + \frac{108}{5} + \frac{107}{5^2} + \frac{106}{5^3} + \cdots $. Then the value of $ (16S - (25)^{3}) $ is equal to:

The number of ordered triplets of the truth values of $ p, q, r $ and such that the truth value of the statement \[ (p \lor q) \land (p \lor r) \implies (q \lor r) \text{ is True, is equal to:} \]

Let (\alpha, \beta, \gamma) \text{ be the image of the point } P(3, 3, 5) \text{ in the plane } 2x + y - 3z = 6. \text{ Then } \alpha + \beta + \gamma \text{ is equal to:}

For any vector $ \mathbf{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k} $, with $ 10 | \mathbf{a} |<1 $, $ i = 1, 2, 3 $, consider the following statements:

The number of integral solutions of $ \log_2 \left( \frac{x - 7}{2x - 3} \right) \geq 0 $ is:

The number of elements in the set $S = \{ \theta \in [0, 2\pi] : 3 \cos^4 \theta - 5 \cos^2 \theta - 2 \sin^2 \theta + 2 = 0 \}$ is:

The value of the integral \[ \int_{\log_2}^{-\log_2} e^x \left( \log \left( e^x + \sqrt{1 + e^{2x}} \right) \right) dx \] is equal to:

Let A be a $ 2 \times 2 $ matrix with real entries such that $ A^T = \alpha A + I $, where $ \alpha \in \mathbb{R} \setminus \{-1, 1\} $. If $ \text{det}(A^2 - A) = 4 $, then the sum of all possible values of $ \alpha $ is equal to:

Let $x_1, x_2, \dots, x_{100}$ be in an arithmetic progression, with $x_1 = 2$ and their mean equal to 200. If $y_i = (i \cdot x_i)$, then the mean of $y_1, y_2, \dots, y_{100}$ is:

Let $ m $ and $ n $ be the numbers of real roots of the quadratic equations $ x^2 - 12x + [x] + 31 = 0 $ and $ x^2 - 5|x+2| - 4 = 0 $, respectively, where $ [x] $ denotes the greatest integer less than or equal to $ x $. Then $ m^2 + mn + n^2 $ is equal to ___________.

The negation of $ (p \land (\sim q)) \lor (\sim p) $ is equivalent to:

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

The area of the quadrilateral having vertices as (1,2), (5,6), (7,6), (-1,-6) is?

Let $ A = \{1, 2, 3, 4, 5, 6, 7\} $. Then the relation $ R = \{(x, y) \in A \times A : x + y = 7\} $ is:

A circle passing through the point P$( \alpha , \beta )$ in the first quadrant touches the two coordinate axes at the points A and B. The point P is above the line AB. The point Q on the line segment AB is the foot of perpendicular from P on AB. If PQ is equal to 11 units, then value of $( \alpha \beta )$ is ___

Let the mean and variance of 8 numbers $x, y, 10, 12, 6, 12, 4, 8$ be $9$ and $9.25$ respectively. If $x > y$, then $3x - 2y$ is equal to:

Let $(\alpha, \beta, \gamma)$ $\text{ be the image of the point }$ $P(3, 3, 5) \text{ in the plane } 2x + y - 3z = 6$. $\text{ Then } \alpha + \beta + \gamma \text{ is equal to:}$

Let O be the origin and OP and OQ be the tangents to the circle $ x^2 + y^2 - 6x + 4y + 8 = 0 $ at the points P and Q on it. If the circumcircle of the triangle OPQ passes through the point $ \left( \alpha, \frac{1}{2} \right) $, then a value of $ \alpha $ is.

A bolt manufacturing factory has three products A, B and C. 50% and 30% of the products are A and B type respectively and remaining are C type. Then probability that the product A is defective is 4%, that of B is 3% and that of C is 2%. A product is picked randomly picked and found to be defective, then the probability that it is type C.

Consider the word INDEPENDENCE. The number of words such that all the vowels are together is?

For two groups of 15 sizes each, mean and variance of first group is 12, 14 respectively, and second group has mean 14 and variance of σ². If combined variance is 13 then find variance of second group?

If 5f(x) + 4f ($\frac{1}{x}$) = $\frac{1}{x}$+ 3, then $18\int_{1}^{2}$ f(x)dx is:

Let $a_1, a_2, \ldots, a_n$ be in AP If $a_5=2 a_7$ and $a_{11}=18$, then $12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$ is equal to

The remainder on dividing $5^{99}$ by 11 is