List of top Mathematics Questions

Let \( \Delta = \begin{vmatrix} x & y & 1 x+y & y+1 & x+1 1 & x & y \end{vmatrix} \). If \( x+y=-1 \), then the value of \( \Delta \) is equal to
If \(\begin{vmatrix} a & 1 & 1 1 & b & 1 1 & 1 & c \end{vmatrix}=2\), where \(a,b\) and \(c\) are positive integers, then \(a+b+c\) is equal to
\(2+{}^{15}C_{1}+{}^{15}C_{2}+\dots+{}^{15}C_{14}=\)
Four fair dice are rolled. Then the number of ways in which the sum of upper faces of four dices can be six, is
A bag contains \( 5 \) red balls, \( 4 \) black balls, and \( 3 \) white balls. Then the number of ways of selecting three balls at random that contains at least one white ball is
The coefficient of $x^{1}$ in the binomial expansion of $\left(\sqrt{x}+\frac{1}{x}\right)^{10}$ is:
The sum and difference of the arithmetic mean and the geometric mean of two positive integers are respectively, \(18\) and \(8\). Then the values of the two numbers are
The sum of the geometric series \(\sqrt{3}+\sqrt{12}+\sqrt{48}+\dots\) up to \(10\) terms is
If \( 1, a, b, c, 16 \) are in geometric progression, then \( \sqrt[3]{abc} \) is equal to
If the numbers \( x, 6, y, 54, 162 \) are in geometric progression, then \( \dfrac{y}{x} \) is equal to
The point \(z=\frac{1}{\sqrt{2}}(1+i)\) in the complex plane is rotated about the origin through an angle \(\frac{\pi}{4}\) in the clockwise direction, then the new position of \(z\) is
If \(z\) is a complex number, then the minimum value of \(|z-2|+|z-4|\) is
If \( z = \frac{3+i}{2-i} \), then \( z^{-1} \) is equal to
If \( z = 1 + i \tan \theta \), where \( \pi < \theta < \dfrac{3\pi}{2} \), then \( |z| \) is equal to
If \( f(x) = ax + bx^2 \), then the coefficient of \( x^3 \) in \( f(f(x)) \) is
If \(f(x) = [2x]\), where \([x]\) denotes the greatest integer function in \(x\), then the image of \(\{-2.3, 2.9\}\) is
If \(n(A) = 8\), then the number of subsets of \(A\) which contain \(2\) or \(6\) elements is
If $ \mathbf{a} $ and $ \mathbf{b} $ are non-coplanar unit vectors such that $ \mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = \frac{\mathbf{b}}{2} $ then the angle between $ \mathbf{a} $ and $ \mathbf{b} $ is:
If \( A = \{ x : x \text{ is a letter of the word MISSISSIPPI} \} \), then \( n(A) = \)
If the maximum value of the function f(x) = $\frac{\log_e x}{x}$, x > 0 occurs at x = a, then a2f''(a) is equal to
If $ A $ is a $ 2 \times 2 $ matrix and $ |A| = 4 $, then $ |A^{-1}| $ is:
Let \( y=\sin(\cos(x^2)) \). Find \( \frac{dy}{dx} \) at \( x=\frac{\sqrt{\pi}}{2} \).
When a current changes at the rate of $30\ \text{A s}^{-1}$, the induced emf is $12\ \text{V}$. The self-inductance of the coil is:
If an inductor coil of self-inductance 2 H stores 25 J of magnetic energy, then the current I passing through it is:
Which one is not a ferromagnetic material?