List of top Mathematics Questions

The modulus of \((\frac{1+i}{1-i})^{75}-(\frac{1-i}{1+i})^{75}\)is

If \(z^4=7-5i\), then \(\text{Im}((\bar{z})^4)\) is equal to

The value of \(\left[ \frac{5i}{(1-i)(2-i)(3-i)} \right]^{50}\)is equal to

The minimum value of |z+1|+|z-2| is equal to

The principal argument of the complex number \(z=\frac{8+4i}{1+3i}\) is equal to

Let f: R→R be defined by f(x) = cos x. Then

Let \(f(x) =   \begin{cases}     x+2       & for\ x\lt\ 1 \\     4x-1  & for\ 1\leq x \leq3 \\ x^2+5 & for\ x\gt3   \end{cases}\). Then

The domain of the function \(f(x) = (x^2-2x-63)^{\frac{3}{2}}\), x ∈ R is

Let A = {1,2,3,4,5} and let B={1,2,3,4}. If the relation R : A → B is given by (a, b) ∈ R if and only if a+b is even, then n(R) is equal to

Let the system of linear equations \[ x + 2y + z = 2, \quad \alpha x + 3y - z = \alpha, \quad -\alpha x + y + 2z = -\alpha \] be inconsistent. Then $\alpha$ is equal to:

Let
A = \(\begin{pmatrix}1 & 2\\ -2 & -5 \end{pmatrix}\)
Let \( \alpha, \beta \in \mathbb{R} \) be such that \( \alpha A^2 + \beta A = 2I \). Then \( \alpha + \beta \) is equal to 

The sum of the first n terms of the series $$ 1^2 + 2 \cdot 2^2 + 3^2 + 2 \cdot 4^2 + 5^2 + 2 \cdot 6^2 + \cdots $$ is $$ \frac{n(n + 1)^2}{2} \quad \text{when n is even. When n is odd the sum is} $$ 

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line $$ 4x - 5y = 20 $$ to the circle $$ x^2 + y^2 = 9 \text{ is:} $$ 

The equation of the plane which bisects the angle between the planes $$ 3x - 6y + 2z + 5 = 0 \quad \text{and} \quad 4x - 12y + 3z - 3 = 0 \quad \text{which contains the origin is:} $$ 

If the mode of the data 2, 4, 6, 7, 5, 6, 10, 6, 7, 2k + 1, 9, 7, 13 is 7, then the value of k is

Which of the following cannot be determined graphically?

If a data has 25 observations (arranged in ascending order), then which of the following observations represents the median?

If the mean of the following data is k(> 0), then the value of k is

Marks	K	4	K	8	3
Frequency	K	2K	3K	4K	5K

If a card is selected at random from a deck of 52 cards, then the probability of getting a red face card is

The mean of 12 numbers is 19. If 4 is subtracted from each number, then the new mean is

A box contains 3 blue, 2 white and 4 red balls. If a ball is drawn at random from the box, what is the probability that it will not be a white ball?

Two dice are thrown together. The probability of getting the same number on both dice is

Which of the following cannot be the probability of an event?

If sec θ+ tan θ= X, then tan θ =

If two towers of heights h1 and h2 subtend angles of 45° and 30° respectively at the midpoint of the line joining their feet, then the ratio of h₁: h₂ is