List of top Mathematics Questions

The turning point of the function $ y = \frac{ax-b}{(x-1)(x-4)} $ at the point $ P(2, -1) $ is
Evaluate the following expression: $ \sqrt{2 + \sqrt{2} + \sqrt{2 + 2 \cos(2\theta)}} \quad \text{where} \quad \theta \in \left[ -\frac{\pi}{8}, \frac{\pi}{8} \right] $

If $A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix} \quad \text{and} \quad A \, \text{adj} \, A = A A^t, \quad \text{then} \, 5a + b \, \text{is equal to}$ 
 

Which of the following relations on the set of real numbers $ \mathbb{R} $ is an equivalence relation?
If two cards are drawn at random simultaneously from a well shuffled pack of 52 playing cards, then the probability of getting a card having a composite number and a card having a number which is a multiple of 3 is:

The solution set for the inequality $ 13x - 5 \leq 15x + 4<7x + 12;  x \in W $

What is the nature of the function $ f(x) = x^3 - 3x^2 + 4x $ on real numbers?
The maximum value of $ P = 500x + 400y $ for the given constraints $ x + y \leq 200, \quad x \geq 20, \quad y \geq 4x, \quad y \geq 0 $
Evaluate: $ \cos^{-1} \left( \cos \frac{35\pi}{18} \right) - \sin^{-1} \left( \sin \frac{35\pi}{18} \right) $
What is the probability of a randomly chosen 2-digit number being divisible by 3?
If $ \frac{dy}{dx} = y + 3 \quad \text{and} \quad y(0) = 2, \quad \text{then} \quad y(\log 2) \text{ is equal to:} $
If $ y = \sin^{-1} \left( \frac{5x + 12\sqrt{1 - x^2}}{13} \right) $ then $ \frac{dy}{dx} $ equals
Two finite sets have $ m $ and $ n $ number of elements respectively. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Then the values of $ m $ and $ n $ are respectively.
The area bounded by the curve $ y = \cos x $, $ x = 0 $, and $ x = \pi $ is
If $ I_n = \int_0^\pi \tan^n x \, dx $, for $ n \geq 2 $, then $ I_n + I_{n-2} = $
The integral $ \int e^x \left[ \frac{x^2 + 1}{(x+1)^2} \right] \, dx $
If $ (1 - 4i)^3 = a + ib $, then the value of $ a $ and $ b $ is
Find the value of 'b' such that the scalar product of the vector $ \hat{i} + \hat{j} + \hat{k} $ with the unit vector parallel to the sum of the vectors $ 2\hat{i} + 4\hat{j} - 5\hat{k} $ and $ b\hat{i} + 2\hat{j} + 3\hat{k} $ is unity.
Value of $ \cos 105^\circ $
The co-ordinate of the foot of the perpendicular from $ P(1, 8, 4) $ on the line joining $ R(0, -1, 3) $ and $ Q(2, -3, -1) $ is
The general solution of the differential equation $ (1 + \tan y)(dx - dy) + 2x \, dx \, dy = 0 $
If a real number $ a $ is such that $ \int_0^a x \, dx \leq a + 4 $, then what is the range of $ a $?
The side of a cube is equal to the diameter of a sphere. If the side and radius increase at the same rate then the ratio of the increase of their surface area is
A coin is tossed until a head appears or until the coin has been tossed three times. Given that 'head' does not appear on the first toss, what is the probability that the coin is tossed thrice?
The value of $ \int \frac{dx}{\sqrt{2ax - x^2}} $