List of top Mathematics Questions

Let $a : \sim(p \wedge \sim r) \vee (\sim q \vee s)$ and $b : (p \vee s) \leftrightarrow (q \wedge r)$. If the truth values of $p$ and $q$ are true and that of $r$ and $s$ are false, then the truth values of $a$ and $b$ are respectively

If $$\int_{0}^{a} \sqrt{\frac{a-x}{x}} \, dx = \frac{k}{2}$$ then $k =$

If $f(x) = [8x] - 3$, where $[x]$ is the greatest integer function of $x$, then $f(\pi) =$ (where $\pi = 3.14$)

If lines represented by the equation $px^2 - qy^2 = 0$ are distinct, then

The slant height of a right circular cone is $\sqrt{3}\text{ cm}$. The height of the cone for maximum volume is

$$\int \cos^{-1} x \, dx =$$

$$\int \frac{1}{\cos x + \sqrt{3}\sin x} \, dx =$$

If $\omega$ is the complex cube root of unity, then $(3 + 5\omega + 3\omega^2)^2 + (3 + 3\omega + 5\omega^2)^2 =$

If $x^y \cdot y^x = 16$, then $\frac{dy}{dx}$ at $(2,2)$ is

The common region of the solution of the inequations $x+y \ge 5$, $y \le 4$, $x \ge 2$, $x, y \ge 0$ is

If the line joining two points $A(2,0)$ and $B(3,1)$ is rotated about $A$ in anticlockwise direction through an angle of $15^\circ$, then the equation of the line in its new position is

$$\int_{0}^{2} |2x - 3| \, dx =$$

The vector equation of the line whose Cartesian equations are $y = 2$ and $4x - 3z + 5 = 0$ is

If the mean and variance of a binomial distribution are 4 and 2 respectively, then probability of getting 2 successes is

If $A = \begin{bmatrix} 1 & 2 & 1 \\ -1 & 1 & 3 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 2 \\ -3 & 1 \\ 0 & 2 \end{bmatrix}$, then $(AB)^{-1} =$

First bag contains 3 red and 5 black balls and second bag contains 6 red and 4 black balls. A ball is drawn from each bag. The probability that one ball is red and the other is black, is

A line drawn from a point $A(-2,-2,3)$ and parallel to the line $\frac{x}{-2} = \frac{y}{2} = \frac{z}{-1}$ meets the $YOZ$ plane in point $P$, then the coordinates of the point $P$ are

The general solution of $\frac{dy}{dx} = \frac{x+y}{x-y}$ is

A fair coin is tossed 4 times. If $X$ is a random variable which indicates number of heads, then $P[X \lt 3] =$

With usual notations, in any $\Delta ABC$, if $a\cos B = b\cos A$, then the triangle is

$$\int \frac{\tan^4 \sqrt{x} \cdot \sec^2 \sqrt{x}}{\sqrt{x}} \, dx =$$

If the points $P(4,5,x)$, $Q(3,y,4)$ and $R(5,8,0)$ are collinear, then the value of $x+y$ is

The statement pattern $(p \wedge q) \wedge [(p \wedge q) \vee (\sim p \wedge q)]$ is equivalent to

The particular solution of the differential equation $\frac{dy}{dx} = \frac{y+1}{x^2-x}$, when $x=2$ and $y=1$ is

The line $\frac{x-2}{3} = \frac{y-1}{-5} = \frac{z+2}{2}$ lies in the plane $x + 3y - \alpha z + \beta = 0$, then value of $\alpha \beta$ is