List of top Mathematics Questions

The number of 5-card combinations out of a deck of 52 cards if there is exactly one ace in each combination is:
A question paper consists of two sections having 3 and 4 questions respectively. One question from each section is compulsory. In how many ways can a candidate select the questions?
The product of real roots of the equation \[ 4x^4 - 24x^3 + 57x^2 + 18x - 45 = 0 \] if one of the roots is \(3 + i\sqrt{6}\) is:
The sum of the complex roots of the equation \[ x^4 - 2x^3 + x - 380 = 0 \] is:
The quadratic equation whose sum of roots is 11 and sum of squares of roots is 61 is:
Evaluate \[ \left(\frac{1-i}{1+i}\right)^{2022} + \left(\frac{1+i}{1-i}\right)^{2021} \]
If \(1, \omega, \omega^2\) are the cube roots of unity, then the value of \[ (x+y)^2 + (x\omega + y\omega^2)^2 + (x\omega^2 + y\omega)^2 \] is:
If \(\Arg z_1\) and \(\Arg z_2\) are \(\frac{\pi}{3}\) and \(\frac{\pi}{5}\) respectively, then the value of \(\Arg z_1 + \Arg z_2\) is:
If \(x^2 + px + 1\) is a factor of \(ax^3 + bx + c\), then:
If \[ A= \begin{bmatrix} 1 & -3 & 2\\ -2 & 1 & 3\\ 3 & 2 & -1 \end{bmatrix} \] then \(A^2\operatorname{Adj}A=\)
Area of the triangle formed by the complex numbers \(z\), \(iz\) and \(z+iz\) in the Argand diagram as vertices is:
The set of values of \(k\) for which the system of simultaneous equations \[ x+y+kz = 1, \quad 2x+2y-3, \quad x+2y+2kz = k \] has no real solution is:
If \[ A = \begin{bmatrix}0 & 1 & 2 & 3 \\ 0 & 2 & 4 & 8 \\ 0 & 0 & 4 & 8\end{bmatrix}, \text{ then the rank of } A \text{ is:} \]
Let \(f(x)=\sqrt{\frac{x+1}{x+3}}\) and \(g(x)=\sqrt{\frac{2-x}{x+3}}\) be two real valued functions. Then the domain of \(\frac{f}{g}\) is:
If the system of simultaneous linear equations \[ x+y+z = \lambda, \quad 5x - y + \mu z = 10, \quad 2x + 3y - z = 6 \] has a unique solution, then:
If the function \(f:\mathbb{R}\to\mathbb{R}\) is defined as \(f(x)=x^2-2x-3\), then \(f\) is:
If the system of linear equations.
\(8x + y + 4z = –2\)
\(x + y + z = 0\)
\(λx–3y=μ\)
has infinitely many solutions, then the distance of the point \((λ, μ, -1/2)\) from the plane \(8x + y + 4z + 2 = 0\) is

Let
 \(x = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}\) and \(A = \begin{bmatrix} -1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1 \end{bmatrix}\)
For k ∈ N, if X’AkX = 33, then k is equal to ____ .

Let \(S=\left\{θ∈[0,2π]:8^{2sin^2⁡θ}+8^{2cos^2⁡θ}=16\right\}\) .
Then\(n(S) + \sum_{\theta \in S}\left( \sec\left(\frac{\pi}{4} + 2\theta\right)\cosec\left(\frac{\pi}{4} + 2\theta\right)\right)\)is equal to :

Let the minimum value v0 of
v = |z|2+|z-3|2+|z-6i|2,z∈C
is attained at z = z0. Then
\(|2z^2_0-\overline{z}^3_0+3|^2+v^2_0\)
is equal to

For the parabola represented in the parametric form \[ x=t^2+t+1 \] \[ y=t^2-t+1, \] the length of latus rectum is:
An integrating factor of the differential equation \[ (x^2+1)\frac{dy}{dx}+xy=x^3 \] is
If the general solution of \[ \frac{dy}{dx}=\frac{y^2}{xy-y^2-x^2} \] is \[ \tan^{-1}\left(\frac{y}{x}\right)=f(y)+C, \] then \(f(e^3)=\)
Evaluate \[ \int_{a-1}^{a}\frac{e^x(a-x)}{(x-a+1)^2}\,dx \]
If \(a\) and \(b\) are respectively the order and degree of the differential equation \[ y^2(y'')^2+3x(y')^{1/3}+x^2y^2=\sin x, \] then