List of practice Questions

If $y = \tan^{-1}(\frac{3x - x^3}{1-3x^2}) + \tan^{-1}(\frac{7x}{1-12x^2})$, then at $x=0$, $\frac{dy}{dx} =$

If the day after tomorrow is Wednesday, what day is it today? 
 

If the probability distribution of a random variable X is as follows, then the mean of X is

X = xi-1012
P(X = xi)k32k3 + k4k - 10k24k - 1

The mean deviation about the mean for the following data is 
 

Class Interval0--22--44--66--88--10
Frequency13412
The number of solutions of the equation $\sqrt{3x^2 + x + 5} = x - 3$ is

$\left( 1 + \sqrt{5} + i \sqrt{10 - 2\sqrt{5}} \right)^5$

Which Indian state was renamed as Vijayapuram in 2024? 
 

Which international agreement was India a part of in 2024 to combat climate change? 
 

 A contract is formed when one party makes an offer and the other party accepts it. If A offers to sell his car to B for 5 lakh, and B agrees but later refuses to pay, what is the legal consequence? 
 

In tort law, the principle of `res ipsa loquitur' refers to: 
 

If $(\sqrt{3} - i)^n = 2^n$, $n \in \mathbb{N}$, then the least possible value of $n$ is

Under the Indian Penal Code, which section defines the offense of theft? 
 

If the point $P$ denotes the complex number $z = x + iy$ in the Argand plane and $\frac{z - (2 - i)}{z + (1 + 2i)}$ is purely imaginary, then the locus of $P$ is

Which of the following is NOT a fundamental right under the Indian Constitution? 
 

Who was appointed as the Chief Justice of India in November 2024? 
 

Consider two systems of 3 linear equations in 3 unknowns $AX = B$ and $CX = D$. If $AX = B$ has the unique solution $X = D$ and $CX = D$ has the unique solution $X = B$, then the solution of $(A - C^{-1})X = 0$ is

Which article of the Indian Constitution deals with the Right to Equality? 
 

$f(x)$ is an $n^{th}$ degree polynomial satisfying $f(x) = \frac{1}{2}\left[f(x)f\left(\frac{1}{x}\right) + f\left(\frac{f(x)}{x}\right)\right]$. If $f(2) = 33$, then the value of $f(3)$ is
If $a$ is the determinant of the adjoint of the matrix $\begin{bmatrix} 1 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 3 \end{bmatrix}$ and $b$ is the determinant of the inverse of the matrix $\begin{bmatrix} 2 & 1 & 3 \\ 1 & -4 & -1 \\ 2 & 1 & 4 \end{bmatrix}$, then $\frac{b+1}{18b} = $
For all $n \in \mathbb{N}$, if $n(n^2+3)$ is divisible by $k$, then the maximum value of $k$ is
The domain of the function $f(x) = \ln\left(\frac{1}{\sqrt{x^2-4x+4}}\right) + \sin^{-1}(x^2-2)$ is

What are X and Y in the following reaction sequence?

p-Chlorotoluene is the major product in which of the following reactions?

The final product (C) in the given reaction sequence is

The artificial sweetener X contains glycosidic linkage and Y contains amide and ester linkages. X and Y respectively are