List of top Mathematics Questions

If \( S_1: x^2 + y^2 - 6x - 8y + 21 = 0 \) and \( S_2: x^2 + y^2 + 6x + 8y + \lambda = 0 \), then the distance of the centre of \( S_2 \) to the farthest point on \( S_1 \) is:
Consider an equilateral \( \Delta PQR \), where \( P(3, 5) \) and the side \( QR \) lies on the line \( x + y = 4 \). If the orthocentre of \( \Delta PQR \) is \( (\alpha, \beta) \), then \( 9(\alpha + \beta) \) is equal to:
The area enclosed between the region given by \( xy \le 27 \) and \( 1 \le y \le x^2 \) is:
Let \( S_n \) be the sum of the first \( n \) terms of an A.P. If \( S_n = 3n^2 + 5n \), then the sum of the squares of the first 10 terms of the given A.P. is:
If \( x_1, x_2, \dots, x_{25} \) be 25 observations such that \( \sum_{i=1}^{25} (x_i + 5)^2 = 2500 \) and \( \sum_{i=1}^{25} (x_i - 5)^2 = 1000 \). Then, the ratio of Mean and Standard deviation of the given observations is:
In the expansion of \( (1 + \alpha x)^{26} \) and \( (1 - \alpha x)^{28} \), the coefficient of the middle term is the same, then the value of \( \alpha \) is:
\( \int_{-\pi/4}^{\pi/4} \frac{32 \cos^4 \theta}{1 + e^{\sin \theta}} \, d\theta \) is equal to:
The value of \( 1^3 - 2^3 + 3^3 - 4^3 + \dots + 15^3 \) is equal to:
The value of \( \lim_{x \to 0} \frac{x^2 \sin^2 x}{x^2 - \sin^2 x} \) is equal to:
Let $A$ is a matrix of order 3 such that $|A| = -4$, then the value of $|\text{adj}(\text{adj}(2\text{adj} A)^{-1})|$ is
A circle $x^2 + y^2 + x - 3y = 0$ passes through $P(1, 2)$. If 2 chords (PS \& PR) drawn from P are bisected by $y$-axis, then mid point of RS is $(\alpha, \beta)$, find $6(\alpha + \beta)$
If $S = \{ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}, A^2 - 4A + 3I = \text{Null matrix}, a, b, c, d \in \{0, 1, 2, 3, 4\} \text{ and } \text{Tr}(A) = 4 \}$. Then the number of elements of set $S$ is/are
Find number of ways of arranging 4 Boys \& 3 Girls such that all girls are not together :
If $\int_{-2}^2 ([\sin x] + |x \sin x|) dx = 2 \sin 2 - 4 \cos 2 - \beta$, then the value of $|\beta|$ where $[\cdot]$ is GIF is
If $f(x) = \min \{2x^2 + 3, 6x\} + |x-1| \cos(x^2 - \frac{1}{4})$, then the number of points of non derivability of $f(x)$ is/are
If $A = \frac{\sin 3^\circ}{\cos 9^\circ} + \frac{\sin 9^\circ}{\cos 27^\circ} + \frac{\sin 27^\circ}{\cos 81^\circ}$ and $B = \tan 81^\circ - \tan 3^\circ$, find $\frac{B}{A}$
If coefficient of $x^3$ in $(1+x)^3 + (1+x)^4 + \dots + (1+x)^{99} + (1+kx)^{100}$ is $\binom{100}{3} \left( \frac{101}{4} - 43n \right)$, then the value of $(k^3 + 43n)$ is
The domain of $f(x) = \cos^{-1} \left( \frac{4x + 2[x]}{3} \right)$ (where $[x]$ denotes greatest integer function) is
Let mean and median of 9 observations 8, 13, a, 17, 21, 51, 103, b, 67 are 40 and 21 respectively where a > b. If mean deviation about median is 26 then 2a is :-
If Latus rectum of parabola $y^2 = 4kx$ and ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ coincide then the value of $e^2 + 2\sqrt{2}$ is, where $e$ is eccentricity of ellipse
If $f(x)$ is a non-constant polynomial satisfying $f(x) = f'(x)f''(x)$ and $f(0) = 0$. Then the value of $\int_0^2 f(x) dx + f'(2) + f''(2)$ is :
In an A.P. first term is $\frac{10}{3}$ and first 30 terms are non-negative such that sum of first 30 terms = $(T_{30})^3$, then d is equal to (where $T_n$ is $n^{\text{th}}$ term of A.P., and d is the common difference of A.P.)
If \( L_1 : x - y = 0 \), \( L_2 : y = -3x \), \( L_3 \) is the obtuse angle bisector of \( L_1 \) and \( L_2 \), and \( L_4 : x + 3 = 0 \). Let \( A \) be the point of intersection of \( L_4 \) and \( L_1 \), \( B \) be the point of intersection of \( L_4 \) and \( L_2 \), and \( C \) be the point of intersection of \( L_4 \) and \( L_3 \). Then the value of \( \dfrac{(BC)^2}{(AC)^2} \) is:
Let $y = \tan^{-1}\left( \frac{3\cos x - 4\sin x}{4\cos x + 3\sin x} \right) + \tan^{-1}\left( \frac{x}{1 + \sqrt{1 + x^2}} \right)$. Then the value of $\frac{dy}{dx}$ at $x = \frac{\sqrt{3}}{2}$ is :
Let in a $\triangle ABC$, given that $A \equiv (1, 2)$, mid-point of $AB$ is $(-5, -1)$ and centroid is $(3, 4)$ then circumcentre is $(\alpha, \beta)$, then the value of $21(\alpha + \beta)$ is :