List of top Mathematics Questions

Which one of the following curves correctly represents (schematically) the solution for the equation $\dfrac{df}{dx}+2f=3;\; f(0)=0$ ?

Let matrix $M=\begin{pmatrix} 4 & x \\ 6 & 9\end{pmatrix}$. If $\det(M)=0$, then

The coefficient of $x^3$ in the Taylor expansion of $\sin(\sin x)$ around $x = 0$ is .............. (Specify your answer up to two digits after the decimal point.)
Let $f(x)=3x^6 - 2x^2 - 8$. Which of the following statements is (are) true?
The value of \[ \lim_{n \to \infty} \left( 1 + \frac{2}{n} \right)^{n^2} e^{-2n} \text{ is } \]

The value of \[ \lim_{n \to \infty} \frac{3n^2 + 5n + 4}{4 + 2n^2} \] is 
 

If \( \varphi(x) = x^2 \) and \( \psi(x) = 2^x \), then \( \psi(\varphi(x)) \) is
Consider the equation \( x^3 - 1 = 0 \). If one of the solutions to this equation is 1, the other solution(s) is/are
The value of \( \log_n 4^{16} = -32 \). The value of \( n \) is ................

The determinant of the matrix \[ \left[ \begin{array}{ccc} 1 & 3 & 0 \\ 2 & 6 & 4 \\ -1 & -1 & 2 \end{array} \right] \] is ........... 
 

For \( a = \) ..............., the following simultaneous equations have an infinite number of solutions: \[ 10x + 13y = 6 \] \[ ax + 32.5y = 15 \]
If A and B are events such that \( P(A) = 0.3, P(B) = 0.2 \) and \( P(A \cup B) = 0.45 \), the value of \( P(A \cap B) \) is .............

What is the solution of \( \int x^2 \ln x \, dx \)? Given \( C \) is an arbitrary constant. 
 

Let \( H \) be the quotient group \( \mathbb{Q} / \mathbb{Z} \). Consider the following statements.
I. Every cyclic subgroup of \( H \) is finite.
II. Every finite cyclic group is isomorphic to a subgroup of \( H \).
Which one of the following holds?
A vector \( \vec{A} = i + xj + 3k \) is rotated through an angle and is also doubled in magnitude resulting in \( \vec{B} = 4i + (4x - 2)j + 2k \). An acceptable value of x is
The value of integral \( \int_{-2}^{2} x e^{-2x^2} dx \) is
The number of three-letter words, with or without meaning, which can be formed using letters of the word 'VIRUS' without repetition of letters is
The area of an equilateral triangle with sides of length \( \alpha \) is
Three vectors are as follows: \[ \mathbf{a} = 3\hat{i} - 10\hat{j} + 7\hat{k}, \mathbf{b} = -9\hat{i} + 6\hat{j} - 47\hat{k}, \mathbf{c} = 11\hat{i} - 17\hat{k} \] The value of \((\mathbf{a} + \mathbf{b}) \cdot \mathbf{c}\) is
Choose the most appropriate option. If \(y = a^b x\), then
Evaluate the limit: \[ \lim_{x \to a} \frac{\log{(x^{a-1})}}{x-a} \]
Choose the most appropriate option. \[ \int_{-2}^{2} \frac{3x^7 - 2x^5 + x^3 - 3}{x^4 + 3x^2 + 1} \, dx \]
If the line \( x - 1 = 0 \) is the directrix of the parabola \( y^2 - kx + 8 = 0 \), then one of the values of \( k \) is
Choose the most appropriate option. \(\lim_{x \to 1} x^{(1-x)}\) is equal to:
Evaluate the limit: \[ \lim_{x \to 0} \frac{1 - \cos 4x}{2 \sin^2 x + x \tan 7x} \]