List of top Mathematics Questions

The equation of normal to the curve \[ y=\log_e x \] at the point \(P(1,0)\) is

If \( A=\begin{bmatrix}\sec\theta & -\tan\theta-\tan\theta & \sec\theta\end{bmatrix} \) and \( A+\operatorname{adj}A=4I \), then find the value of \( \theta \).

If \( \vec{a}=2\hat{i}-\hat{j}+3\hat{k} \) and \( \vec{b}=\hat{i}+2\hat{j}-\hat{k} \), then the vector perpendicular to both \( \vec a \) and \( \vec b \) is:

If \(A = \begin{bmatrix} 1 & -2 & 2 0 & 2 & -3 3 & -2 & 4 \end{bmatrix}\), find the value of the matrix expression \(A(I + \text{adj } A)\), where \(I\) is the identity matrix of the same order as \(A\).

If \( A = \begin{bmatrix} 4 & 5 2 & 1 \end{bmatrix} \), find \( A^{-1} \).

If $A = \begin{bmatrix} \sin \alpha & -\cos \alpha\\ \cos \alpha & \sin \alpha \end{bmatrix}$ and $\alpha \in (\frac{\pi}{2}, \frac{3\pi}{2})$. If $A + A^T = I$, then $\alpha =$}

Evaluate: \[ \int_0^1 x^3\ln(1+x)\,dx \]

If a real matrix \(A\) satisfies \[ A^T=A \quad \text{and} \quad A^2=I, \] then the eigenvalues of \(A\) must be:

If \[ f(x)=\ln\left(\frac{\sin x}{1+\cos x}\right), \] then \(f'(x)\) is equal to:

Evaluate the definite integral: \( \int_{0}^{\pi/2} \sin^2(x) \, dx \).

If \( z_1, z_2, \ldots, z_n \) are complex numbers such that \( |z_1| = |z_2| = \ldots = |z_n| = 1 \), then \( |z_1 + z_2 + \ldots + z_n| \) is equal to:

A person invites 10 friends to dinner and places them such that 4 are at one round table and 6 are at another round table. The total number of ways in which he can arrange the guests is:

Find the sum of the series \( \left(x + \frac{1}{x}\right)^2 + \left(x^2 + \frac{1}{x^2}\right)^2 + \left(x^3 + \frac{1}{x^3}\right)^2 + \cdots \) up to \( n \) terms.

A pair of fair dice is thrown simultaneously. What is the probability that the sum of the numbers appearing on the top faces is at least 10?

In how many ways can the letters of the word COCHIN be arranged such that the two 'C's are never separated by any other letter?

The sum of the series $\left(x + \frac{1}{x}\right)^2 + \left(x^2 + \frac{1}{x^2}\right)^2 + \left(x^3 + \frac{1}{x^3}\right)^2 \dots\dots\dots$ up to $n$ terms is:

General solution of $\tan 5\theta = \cot 2\theta$ is:

The distance from the origin to the image of $(1, 1)$ with respect to the line $x + y + 5 = 0$ is:

If $p$ and $q$ be the longest and the shortest distance respectively of the point $(-7, 2)$ from any point $(\alpha, \beta)$ on the curve whose equation is $x^2 + y^2 - 10x - 14y - 51 = 0$, then find the Geometric Mean (G.M.) of $p$ and $q$.

Let \(\text{L}_1\) be the length of the common chord of the curves \(x^2 + y^2 = 9\) and \(y^2 = 8x\), and \(\text{L}_2\) be the length of the latus rectum of \(y^2 = 8x\), then:

The eccentricity of the ellipse whose major axis is three times the minor axis is:

If the eccentricity and length of latus rectum of a hyperbola are \(\frac{\sqrt{13}}{3}\) and \(\frac{10}{3}\) units respectively, then what is the length of the transverse axis?

Let \(\text{A} = \{1, 2, 3, 4, 5\}\) and \(\text{R}\) be a relation defined by \(\text{R} = \{(x, y) : x, y \in \text{A}, x + y = 5\}\). Then, \(\text{R}\) is