List of top Mathematics Questions

The differential equation whose solution is $Ax^2 + By^2 = 1$ where $A$ and $B$ are arbitrary constants is of

Sultan took a loan from the bank at 8% per annum, and was supposed to pay a sum of Rs.2240 at the end of 4 years. If the same sum is cleared off in four equal annual installments at the same rate, the amount of annual installment will be

If $A = \begin{bmatrix}1&-5&7\\ 0&7&9\\ 11&8&9\end{bmatrix}$, then trace of matrix $A$ is

The value of integral $\int\limits_0^1 \, \sqrt{\frac{1-x}{1+x}}dx$ is

The tangent at $(1, 7)$ to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x + 12y + c = 0$ at

The value of $\displaystyle\lim_{x\to\infty}\left(\frac{\pi}{2} - \tan^{-1} x\right)^{1/x} $ is

$\int \frac{dx}{\sin x - \cos x + \sqrt{2}} $ equals to

There are $5$ letters and $5$ different envelopes. The number of ways in which all the letters can be put in wrong envelope, is

A straight line through the point A(3, 4) is such that its intercept between the axes is bisected at A, its equation is

The coefficient of $x^n$ in the expansion of $\log_a (1 + x)$ is

The maximum value of $4 \, \sin^2 \, x - 12 \sin \, x + 7$ is

Let $x_1 , x_2,...., x_n$ be n observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^2$ be the variance. Variance of $2x_1, 2x_2, ..., 2x_n$ is $4 \sigma^2$. Arithmetic mean $2x_1, 2x_2, ..., 2x_n $ is 4 $\bar{x}$ .

The value of the determinant $\begin{vmatrix}\cos\alpha&-\sin\alpha&1\\ \sin \alpha&\cos\alpha&1\\ \cos\left(\alpha+\beta\right)&-\sin\alpha+\beta&1\end{vmatrix} $ is

Let $x$ and $y$ be two natural numbers such that $xy = 12(x + y)$ and $x \le y$. Then the total number of pairs $(x, y)$ is

The nearest point on the line $3x + 4y = 12$ from the origin is

Let $T(k)$ be the statement $1 + 3 + 5 + ... + (2k - 1)= k^2 +10$ Which of the following is correct?

$\int\limits^{\pi/2}_{0} \frac{2^{\sin x}}{2^{\sin x} + 2^{\cos x}} dx $ equals

The area bounded by the curve $y = \sin x$, $x$-axis and the ordinates $x = 0$ and $x = \pi /2$ is

What is the value of n so that the angle between the lines having direction ratios $(1, 1, 1)$ and $(1, -1, n)$ is $60^{\circ}$ ?

The foot of the perpendicular from the point $(7, 14, 5)$ to the plane $2x + 4y - z = 2$ are

Find the coordinates of the point where the line joining the points $(2, -3, 1)$ and $(3, - 4, - 5)$ cuts the plane $2x + y + z = 7$.

The coefficient of $x^{20}$ in the expansion of $(1 + x^2)^{40} . (x^2 + 2 + \frac{1}{x^2})^{-5}$ is

If $\sin^2 \theta + \sin^2 \phi = 1/2, \cos^2 + \cos^2 \phi = 3/2$, then $\cos^2 (\theta - \phi)$ is equal to

If $a.b = a.c$ and $a \times b = a \times c$, then correct statement is

For the function $f\left(x\right)= \frac{x^{100}}{100} + \frac{x^{99}}{99} + ... \frac{x^{2}}{2} + x + 1 , $ f ' (1) = mf' (0), where m is equal to