List of top Mathematics Questions

Let $ f(x) = x^3 - 6x^2 + 9x + 8 $, then $ f(x) $ is decreasing in
The function $ f(x) = 2 + 4x^2 + 6x^4 + 8x^6 $ has
The derivative of $ \frac{d}{dx} \left( x \sqrt{a^2} - x^2 + a^2 \sin^{-1} \left( \frac{x}{a} \right) \right) \text{ is equal to} $
The derivative of $ \frac{d}{dx} \left( \tan^{-1} \left( \frac{3x - x^3}{1 - 3x^2} \right) \right) \text{ is equal to} $
The limit $ \lim_{x \to 0} \frac{5^x + 4^x}{4^x - 3^x} $ is equal to
The limit $ \lim_{x \to 0} \left( \frac{\tan x - x}{x} \right) \cdot \left( \sin \frac{1}{x} \right) $ is equal to
If a matrix $ A $ is symmetric as well as skew symmetric then $ A $ is
The system of linear equations $ x + y + z = 2, \quad 2x + y - 2 = 3, \quad 3x + 2y + kz = 4 \text{ has a unique solution if} $
The derivative of $ f(x) = |x| $ at $ x = 0 $ is
If $A = \left(\begin{array}{ccc} 2 & 0 & 0 \\ 0 & \cos x & \sin x \\ 0 & -\sin x & \cos x \end{array}\right)$, then $\text{Adj}(A)^{-1}$
For the positive integer $ n $, $ C_1^{n} + C_2^{n} + C_3^{n} + ... + C_n^{n} \text{ is equal to} $
The term independent of $ x $ in the expansion of $ \left( x - \frac{3}{x^2} \right)^{18} $
If $a^2 + b^2 + c^2 = 0$ and $$\begin{vmatrix} b^2+c^2 & ab & ac \\ ab & c^2+a^2 & bc \\ ac & bc & a^2+b^2 \end{vmatrix}=ka^2b^2c^2$$ then k is equal to
The value of $ n $, for which $ \frac{a^{n+1} + b^{n+1}}{a^n + b^n} $ is the A.M. between $ a $ and $ b $, is
The solution of the inequality $ \frac{1}{2x - 5} > 0 $ is
"The maximum or the minimum of the objectives function occurs only at the corners points of the feasible region". This theorem is known as fundamental theorem of
If $ 2 < x < 3 $, then
The maximum value of $ P = 8x + 3y $, subject to the constraints $ x + y \leq 6, x \geq 0, y \geq 0 $, is
The value of $ \left( \frac{1 + i\sqrt{3}}{1 - i\sqrt{3}} \right)^6 + \left( \frac{1 - i\sqrt{3}}{1 + i\sqrt{3}} \right)^6 $ is
The conjugate complex number of $ \frac{2 - i}{1 - 2i^2} $
Let $ R $ be a relation on set $ A $ such that $ R = R^{-1} $, then $ R $ is
Let $ R $ be a relation on $ \mathbb{N} $ defined as $ x R y $ iff $ x + 2y = 8 $, the domain of $ R $ is
If $ n(A) = 4 $ and $ n(B) = 2 $, then the number of surjections from A to B is:

Let the line $L$ intersect the lines
$x - 2 = -y = z - 1$, $\quad 2(x + 1) = 2(y - 1) = z + 1$
and be parallel to the line
$\frac{x-2}{3} = \frac{y-1}{1} = \frac{z-2}{2}$.
Then which of the following points lies on $L$?

Evaluate the limit: $$ \lim_{n \to \infty} n^4 \left[ \sum_{k=0}^{\infty} \frac{1}{(n^2 + k)^{5/2}} \right]. $$