List of top Mathematics Questions

If \( \alpha = \frac{\pi}{4} + \sum_{p=1}^{11} \tan^{-1} \left( \frac{2^{p-1}}{1 + 2^{2p-1}} \right) \), then the value of \( \tan(\alpha) \) is:

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:

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:

Find number of ways of arranging 4 Boys \& 3 Girls such that all girls are not together :

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

The domain of $f(x) = \cos^{-1} \left( \frac{4x + 2[x]}{3} \right)$ (where $[x]$ denotes greatest integer function) is

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 :

Consider the differential equation $\frac{dy}{dx} = (x^2 + x + 1)(y^2 - y + 1)$. If $y(0) = \frac{1}{2}$, then the value of $2(y(1)) - 1$ is

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 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

Let $A = \{1, 2, 3, 4, 5\}$ and $B = \{a, b, c\}$ then total number of functions from $A$ to $B$ which are not onto are

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 :

If $Z$ be a complex number such that $|Z + 2| = |Z - 2|$ and $\text{arg} \left( \frac{Z - 3}{Z + 1} \right) = \frac{\pi}{4}$, then the value of $|Z|^2$ 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 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