List of top Questions asked in JEE Main- 2025

If the image of the point $ (4, 4, 3) $ in the line $ \frac{x-1}{2} = \frac{y-2}{1} = \frac{z-1}{3} $ is $ (a, \beta, \gamma) $, then $ a + \beta + \gamma $ is equal to:

Let a circle $ C $ with radius $ r $ passes through four distinct points $ (0, 0), (k, 3k), (2, 3), (-1, 5) $, such that $ k \neq 0 $, then $ (10k + 2r^2) $ is equal to:

Let (a, b) be the point of intersection of the curve $x^2 = 2y$ and the straight line $y - 2x - 6 = 0$ in the second quadrant. Then the integral $I = \int_{a}^{b} \frac{9x^2}{1+5^{x}} \, dx$ is equal to:

The value of \[ \int_{e^2}^{e^4} \frac{1}{x} \left( \frac{e^{\left( (\log_e x)^2 +1 \right)^{-1}}}{e^{\left( (\log_e x)^2 +1 \right)^{-1}} + e^{\left( (6-\log_e x)^2 +1 \right)^{-1}}} \right) dx \] is:

What is the sum of the infinite series $ S = \sum_{n=0}^{\infty} \frac{1}{3^n} $?

Suppose A and B are the coefficients of the 30th and 12th terms respectively in the binomial expansion of $ (1 + x)^{2n - 1} $. If $ 2A = 5B $, then $ n $ is equal to:

The total number of 10-digit sequences formed by only $ \{0, 1, 2\} $, where 1 should be used at least 5 times and 2 should be used exactly three times, is:

Let ABC be a triangle formed by the lines $ 7x - 6y + 3 = 0 $, $ x + 2y - 31 = 0 $, and $ 9x - 2y - 19 = 0 $. Let the point $ (h, k) $ be the image of the centroid of $ \triangle ABC $ in the line $ 3x + 6y - 53 = 0 $. Then $ h^2 + k^2 + hk $ is equal to:

Let A be a 3 × 3 matrix such that $\text{det}(A) = 5$. If $\text{det}(3 \, \text{adj}(2A)) = 2^{\alpha \cdot 3^{\beta} \cdot 5^{\gamma}}$, then $ (\alpha + \beta + \gamma) $ is equal to:

Let $ A = \{(\alpha, \beta) \in \mathbb{R} \times \mathbb{R} : |\alpha - 1| \leq 4 \text{ and } |\beta - 5| \leq 6\} $ and $ B = \{(\alpha, \beta) \in \mathbb{R} \times \mathbb{R} : 16(\alpha - 2)^2 + 9(\beta - 6)^2 \leq 144\}. $ Then:

If $ A $ and $ B $ are binomial coefficients of the 30$^\text{th}$ and 12$^\text{th}$ terms of the binomial expansion $ (1 + x)^{2n-1} $, and $ 2A = 5B $, then the value of $ n $ is

The sum of all values of $ \theta \in [0, 2\pi] $ satisfying $ 2\sin^2\theta = \cos 2\theta $ and $ 2\cos^2\theta = 3\sin\theta $ is:

Let the product of $ \omega_1 = (8 + i) \sin \theta + (7 + 4i) \cos \theta $ and $ \omega_2 = (1 + 8i) \sin \theta + (4 + 7i) \cos \theta $ be $ \alpha + i\beta $, where $ i = \sqrt{-1} $. Let $ p $ and $ q $ be the maximum and the minimum values of $ \alpha + \beta $ respectively.

Let $ S = \mathbb{N} \cup \{0\} $. Define a relation $ R $ from $ S $ to $ \mathbb{R} $ by: \[ R = \left\{ (x, y) : \log_e y = x \log_e \left(\frac{2}{5}\right), x \in S, y \in \mathbb{R} \right\}. \] Then, the sum of all the elements in the range of $ R $ is equal to:

Let $ a_1, a_2, a_3, \dots $ be an A.P. and $ \sum_{k=1}^{12} a_{2k-1} = -\frac{72}{5} a_1 $ and $ \sum_{k=1}^{n} a_k = 0 $. Then the value of $ n $ is:

Marks obtained by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18, then the total number of students is:

A rod of length eight units moves such that its ends A and B always lie on the lines $ x - y + 2 = 0 $ and $ y + 2 = 0 $, respectively. If the locus of the point $ P $, that divides the rod AB internally in the ratio 2:1, is \[ 9(x^2 + \alpha y^2 + \beta xy + \gamma x + 28 y) - 76 = 0, \] then \[ \alpha - \beta - \gamma \text{ is equal to:} \]

Let the set of all values of $ p \in \mathbb{R} $, for which both the roots of the equation $ x^2 - (p + 2)x + (2p + 9) = 0 $ are negative real numbers, be the interval $ (\alpha, \beta) $. Then $ \beta - 2\alpha $ is equal to:

Let $ f : \mathbb{R} \setminus \{0\} \to (-\infty, 1) $ be a polynomial of degree 2, satisfying $ f(x)f\left( \frac{1}{x} \right) = f(x) + f\left( \frac{1}{x} \right) $. If $ f(K) = -2K $, then the sum of squares of all possible values of $ K $ is:

Let the curve $($$ z(1 + i) + \overline{z(1 - i)} = 4$, $\, z \in \mathbb{C}$ $)$, divide the region $|z - 3| \leq 1$ into two parts of areas $ \alpha $ and $ \beta $. Then $ |\alpha - \beta| $ equals:

If the equation of a circle is $ 4x^2 + 4y^2 - 12x + 8y = 0 $, what is the radius of the circle?