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List of top Mathematics Questions

Sum of first 20 terms: 5, 11, 19, 29, 41

Positive numbers a₁, a_2, .... a₅ are in geometric progression. Their mean and variance are $\frac{31}{10}$ and $\frac{m}{n}$ respectively. The mean of the reciprocals is $\frac{31}{40}$, then m + n is?

If sin^-1x = 2 tan^-1x , then number of integral values of x is equal to:

The area of the region enclosed by the curve $y=x^3$ and its tangent at the point (−1,−1) is

($\frac{2x^3-1}{3x^8}$)⁵$\rightarrow$coefficient of x⁴

In a given data set mean of 40 observations is 50 and standard deviation is 12. Two readings which were 20 and 25, were mistakenly taken as 40 and 45. Find correct variance of data set

Let a differentiable function $f$ satisfy $f(x)+\int\limits_3^x \frac{f(t)}{t} d t=\sqrt{x+1}, x \geq 3$ Then $12 f(8)$ is equal to :

Let the sets A and B denote the domain and range respectively of the function $f(x)=\frac{1}{\sqrt[x]-x}$ where [x] denotes the smallest integer greater than or equal to x . Then among the statements
(S1) : A ∩ B = (1, ∞) – N and
(S2) : A ∪ B = (1, ∞)

Let α be the area of the larger region bounded by the curve y² = 8x and the lines y = x and x = 2, which lies in the first quadrant. Then the value of 3α is equal to:

Let S = {1, 2, 3, 4, 5, 6}. Then the number of one-one functions $f : S → P(S)$, where $P(S)$ denotes the power set of S, such that $f(n) ⊂ f(m)$ where $n < m,$ is:

Let $ A = \begin{pmatrix} m & n \\ p & q \end{pmatrix} $, $ d = |A| \neq 0 $, and $ |A - d(\text{Adj}(A))| = 0 $. Then

The mean and variance of 7 observations are 8 and 16, respectively. If one observation 14 is omitted and a and b are respectively the mean and variance of the remaining 6 observations, then $a+3b−5$ is equal to

Suppose $ f: \mathbb{R} \to (0, \infty) $ be a differentiable function such that: $ 5f(x + y) = f(x) \cdot f(y), \quad \forall x, y \in \mathbb{R} $. If $ f(3) = 320 $, then the value of:$ \sum_{n=0}^{5} f(n) $ is equal to:

Let $ \lambda_1 < \lambda_2 $ be two values of $ \lambda $ such that the angle between the planes:
$ P_1 : \vec{r} \cdot (3\hat{i} - 5\hat{j} + \hat{k}) = 7 $
$ P_2 : \vec{r} \cdot (\lambda\hat{i} + \hat{j} - 3\hat{k}) = 9 $
is $ \sin^{-1}\left(\frac{2\sqrt{6}}{5}\right) $. Then, the square of the length of the perpendicular from the point $ (38\lambda, 10\lambda, 2) $ to the plane $ P_1 $ is:

If the coefficient of x⁷ in expansion of $(ax- \frac{1}{bx^2})^{13}$ is equal to the coefficient of x^-5 in expansion of $(ax + \frac{1}{bx^2})13$, then a⁴b⁴ is ______

If the equation of the normal to the curve $ y = \frac{x - a}{(x + b)(x - 2)} $ at the point $ (1, -3) $ is $ x - 4y = 13 $, then the value of $ a + b $ is:

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:

Let $ H_n : \frac{x^2}{1 + n} + \frac{y^2}{3 + n} = 1, n \in \mathbb{N} $. Let $ k $ be the smallest even value of $ n $ such that the eccentricity of $ H_n $ is a rational number. If $ l $ is the length of the latus rectum of $ H_k $, then 21 $ l $ is equal to:

The mean of the coefficients of $ x^n, x^{n+1}, \dots, x^r $ in the binomial expansion of $ (2 + x)^r $ is:

If a and b are the roots of the equation x² - 7x - 1 = 0, then the value of a² + b² + a³ + b³ is equal to:

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sit on the allotted seat, is:

Let a line $ l $ pass through the origin and be perpendicular to the lines \[ l_1: \vec{r}_1 = i + j + 7k + \lambda(i + 2j + 3k), \quad \lambda \in \mathbb{R} \] \[ l_2: \vec{r}_2 = -i + j + 2k + \mu(i + 2j + k), \quad \mu \in \mathbb{R} \] If $ P $ is the point of intersection of $ l_1 $ and $ l_2 $, and $ Q (a, b, \gamma) $ is the foot of perpendicular from P on $ l $, then $ (a + b + \gamma) $ is equal to:

For $ m, n>0 $, let $ \alpha(m,n) = \int_{0}^{1} (1 + 3t)^{n} \, dt $. If $ \alpha(10,6) = \int_{0}^{1} (1 + 3t)^{6} \, dt $ and $ \alpha(11,5) = p(14)^{5} $, then $ p $ is equal to:

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: