List of top Mathematics Questions

The function \( y = Ae^x + Be^{-2x} \) satisfies which of the following differential equations?
The derivative of the function $f(x) = \sin(x^2)$ at $x = \sqrt{\pi}$ is
By multiplying with $e^{\int P dx}$ on both sides of the equation $\frac{dy}{dx} + P(x)y = Q(x)$, the left side of the equation takes the form $\frac{d}{dx} (y f(x))$, then $f(x) =$
If a and b are respectively the order and degree of a differential equation \( y^2(y'')^2 + 3x(y')^{1/3} + x^2y^2 = \sin x \), then
Solve the differential equation: $$ \frac{dy}{dx} = \cos^2(3x + y) $$
An integrating factor of the differential equation \( (x^2+1)\frac{dy}{dx} + xy = x^3 \) is
Solve: $iz^3 + z^2 - z + i = 0 \Rightarrow |z| = $ ?
If \( 1, \omega, \omega^2 \) are the cube roots of unity, then evaluate: \[ (2 - \omega)^2 (2 - \omega^2)^2 (2 - \omega^{10})^2 (2 - \omega^{11})^2 \]
The values of \(\theta\), for which \( \frac{3+2i\sin\theta}{1-2i\sin\theta} \) is real are
Multiplicative inverse of the complex number $(\sin\theta, \cos\theta)$ is
If \( x = -5 + 2\sqrt{-4} \), then the value of \( x^4 + 9x^3 + 35x^2 - x + 4 \) is:
If 1, \(\omega, \omega^2\) denote the cube roots of unity, then, the value of \( (1-\omega+\omega^2)^5 + (1+\omega-\omega^2)^5 \) is
\( \frac{(1+i)x-2i}{3+i} + \frac{(2-3i)y+i}{3-i} = i \implies x+y = \)
The number of integer solutions of the equation $|1 - i|^x = 2^x$ is:
Let \( z \) and \( w \) be two complex numbers such that \( \bar{z} + i\bar{w} = 0 \) and \( \text{Arg}(zw) = \pi \). Then \( \text{Arg}(z) = \)
$\sum_{k=0}^{440} i^k = x + iy \Rightarrow x^{100} + x^{99} y + x^{342} y^2 + x^{97} y^3 =$
If the complex numbers \( z_1, z_2, 0 \) are vertices of an equilateral triangle, then \( z_1^2 + z_2^2 = \)
The locus of a point $ z $ satisfying: $$ |z|^2 = \text{Re}(z) $$ is a circle with centre:
By simplifying the expression: $$ i^{18} - 3i^7 + i^2(1 + i^4)(i^{22}) $$ we get:
Evaluate: \[ \sum_{k=1}^{6} \left[ \sin\left( \frac{2\pi k}{7} \right) - i \cos\left( \frac{2\pi k}{7} \right) \right] \]
If \( (x - iy)^{1/3} = a - ib \), then the value of \( \frac{x}{2a} + \frac{y}{2b} \) is:
If $\dfrac{x - 1}{3 + i} + \dfrac{y - 1}{3 - i} = i$, then the true statement among the following is:
Let z and w be two distinct non-zero complex numbers if \(|z|^2w - |w|^2z = z - w\), then
If \( f(x) = \int \cos^{-1} \left( \frac{x}{\sqrt{a + x}} \right) dx + C \), then \( f'(a) = \)
\( \lim_{n \to \infty} \left( \frac{1}{1 + n^5} + \frac{2^4}{2^5 + n^5} + \frac{3^4}{3^5 + n^5} + \ldots + \frac{n^4}{n^5 + n^5} \right) = \)