List of top Mathematics Questions

Given A, B, C represents angles of a  ⃤ AB and cosA + 2 cosB + cosC = 2 and AB = 3 and BC = 7 then cosA – cosC is?

The mean of coefficients of x, x2, ....., x7 in the binomial expansion of (2 + x)9 is?

The number of rational terms in the expansion of (33/4 + 53/2)60?

Maximum value n such that (66)! is divisible by 3n

Three dice are thrown. Then the probability that no outcomes is similar is p/q then q – p is (where p and q are co-prime)

Matrix A is 2×2 matrix and A2=I, no elements of the matrix are zero, let the sum of diagonal elements is a and det(A)=b, then the value of 3a2+b2 is?

The number of points of non-differentiability of the function f(x) = [4 + 13sinx] in (0, 2𝜋) is ____.

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

Consider two sets A and B. Set A has 5 elements whose mean & variance are 5 and 8 respectively. Set B has also 5 elements whose mean & variance are 12 & 20 respectively. A new set C is formed by subtracting 3 from each element of set A and by adding 2 to each element of set B. The sum of mean & variance of the set C is

The mean of coefficients of \(x, x^2, ....., x^7\) in the binomial expansion of \((2 + x)^9\) is?

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

Positive numbers a1, a2, .... 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 ______