List of practice Questions

The least value of $n$ so that ${}^{n-1}C_3 + {}^{n-1}C_4>{}^nC_3$ is
A natural number $n$ such that $n!$ ends in exactly 1000 zeros is
If $\dfrac{13x + 43}{2x^2 + 17x + 30} = \dfrac{A}{2x + 5} + \dfrac{B}{x + 6}$, then $A^2 + B^2 = $
If $A + B + C = \pi$, $\cos B = \cos A \cos C$, then $\tan A \tan C =$
In a triangle $ABC$, $\left(\tan \dfrac{A}{2} \tan \dfrac{B}{2} \tan \dfrac{C}{2} \right)^2 \le$
The value of $\tan\left(\dfrac{7\pi}{8}\right)$ is
$1 + \sec^2 x \cdot \sin^2 x = $
If $e^{i\theta = \cos\theta + i\sin\theta$ then}
$\sum_{n=0}^{\infty} \dfrac{\cos(n\theta)}{2^n} \div \sum_{n=0}^{\infty} \dfrac{\cos(n\theta)}{5^n} =$
If $f(f(0)) = 0$, where $f(x) = x^2 + ax + b$, $b \neq 0$, then $a + b =$
The sum of the real roots of the equation $|x - 2|^2 + |x - 2| - 2 = 0$ is
If the difference between the roots of $x^2 + ax + b = 0$ and that of $x^2 + bx + a = 0$ is same and $a \ne b$, then
For what values of $a \in \mathbb{Z}$, the quadratic expression $(x + a)(x + 1991) + 1$ can be factorised as $(x + b)(x + c)$, where $b, c \in \mathbb{Z}$?
If a set $A$ has $m$ elements and the set $B$ has $n$ elements, then the number of injections from $A$ to $B$ is
If $A = \begin{bmatrix} 2 & -3\\ -4 & 1 \end{bmatrix}$, then $(A^T)^2 + (12A)^T = $
If $a$, $b$, $c$ are respectively the $5^{\text{th}$, $8^{\text{th}}$, $13^{\text{th}}$ terms of an arithmetic progression, then}
$\begin{vmatrix} a & 5 & 1 \\ b & 8 & 1\\ c & 13 & 1 \end{vmatrix} = $
If $A = \begin{bmatrix} 1 & 0 & 0 \\ a & -1 & 0 \\ b & c & 1 \end{bmatrix}$ is such that $A^2 = I$, then
Let $A = \begin{bmatrix} -2 & x & 1 \\ x & 1 & 1 \\ 2 & 3 & -1 \end{bmatrix}$. If the roots of the equation $\det A = 0$ are $l, m$ then $l^3 - m^3 =$
Multiplicative inverse of the complex number $(\sin\theta, \cos\theta)$ is
$\sum_{k=0}^{440} i^k = x + iy \Rightarrow x^{100} + x^{99} y + x^{342} y^2 + x^{97} y^3 =$
A true statement among the following identities is
Identify the major product formed from the following:
the major product formed from the following
Identify the correct trend of acidic strength for the given alcohols:
correct trend of acidic strength for the given alcohols:
Which of the following can undergo disproportionation reaction on heating with Conc. Alkali?
Identify the major product from the following reaction sequence:
the major product from the following reaction sequence
$\left\{ x \in \mathbb{R} \,\middle|\, \frac{\sqrt{|x^2 - 2|x| - 8}}{\log(2 - x - x^2)} \text{ is a real number} \right\} =$