List of practice Questions

The value of $ \int_0^{2\pi} \sqrt{1 + \sin^2 \frac{x}{2}} \, dx \text{ is} $
If $ \int_0^{2a} f(x) \, dx = 2 \int_0^a f(x) \, dx, \text{ then} $
The value of $ \int_0^{\frac{\pi}{2}} \frac{\tan x}{\tan x + \cot x} \, dx \text{ is} $
The domain of the function $ \sin^{-1} x $ is
The derivative of $ \frac{d}{dx} \left( \tan^{-1} \left( \frac{3x - x^3}{1 - 3x^2} \right) \right) \text{ is equal to} $
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} $
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 system of linear equations $ x + y + z = 2, \quad 2x + y - 2 = 3, \quad 3x + 2y + kz = 4 \text{ has a unique solution if} $
If a matrix $ A $ is symmetric as well as skew symmetric then $ A $ is
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
The derivative of $ f(x) = |x| $ at $ x = 0 $ is
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
If $A = \left(\begin{array}{ccc} 2 & 0 & 0 \\ 0 & \cos x & \sin x \\ 0 & -\sin x & \cos x \end{array}\right)$, then $\text{Adj}(A)^{-1}$
"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
The solution of the inequality $ \frac{1}{2x - 5} > 0 $ is
If $ 2 < x < 3 $, then
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
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
The conjugate complex number of $ \frac{2 - i}{1 - 2i^2} $
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