List of top Mathematics Questions

Negation of $(p \land q) \rightarrow (\sim p \lor r)$ is

The joint equation of pair of lines through the origin and making an equilateral triangle with the line $y=3$ is

If $\vec{r} = -4\hat{i} - 6\hat{j} - 2\hat{k}$ is a linear combination of the vectors $\vec{a} = -\hat{i} + 4\hat{j} + 3\hat{k}$ and $\vec{b} = -8\hat{i} - \hat{j} + 3\hat{k}$, then

The area bounded by the parabola $y = x^2$ and the line $y = x$ is

If $y = \sin^{-1}\left[\cos \sqrt{\frac{1+x}{2}}\right] + x^x$, then $\frac{dy}{dx}$ at $x=1$ is

Water is being poured at the rate of $36\ \text{m}^3/\text{min}$ into a cylindrical vessel, whose circular base is of radius $3\ \text{m}$. Then the water level in the cylinder is rising at the rate of

If the equation $3x^2 - kxy - 3y^2 = 0$ represents the bisectors of angles between the lines $x^2 - 3xy - 4y^2 = 0$, then value of $k$ is

The general solution of $\left(x \frac{dy}{dx} - y\right) \sin \frac{y}{x} = x^3 e^x$ is

If area of the parallelogram with $\vec{a}$ and $\vec{b}$ as two adjacent sides is 20 square units, then the area of the parallelogram having $3\vec{a}+\vec{b}$ and $2\vec{a}+3\vec{b}$ as two adjacent sides in square units is

If $f(x) = \frac{4^{x - \pi} + 4^{\pi - x} - 2}{(x - \pi)^2}$, for $x \ne \pi$, is continuous at $x = \pi$, then $f(\pi)$ is

If $y = \sqrt{e^{\sqrt{x}}}$, then $\frac{dy}{dx} =$

If $2 f(x) - 3 f\left(\frac{1}{x}\right) = x$, then $\int_1^e f(x) dx =$

The equation of tangent to the circle $x^2+y^2=64$ at the point $P\left(\frac{2\pi}{3}\right)$ is

The equation of the plane that contains the line of intersection of the planes $x+2y+3z-4=0$ and $2x+y-z+5=0$ and is perpendicular to the plane $5x+3y-6z+8=0$ is

If $f(x) = 2x^3 - 15x^2 - 144x - 7$, then $f(x)$ is strictly decreasing in

The principal solutions of $\sqrt{3} \sec x + 2 = 0$ are

$\int \operatorname{cosec}(x-a) \operatorname{cosec} x dx = $

If the sum of mean and variance of a binomial distribution for 5 trials is 1.8, then probability of a success is

If the variance of the numbers $2, 3, 11$ and $x$ is $\frac{49}{4}$, then the values of $x$ are

The co-factors of the elements of second column of $\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 2 & 1 \\ -1 & 3 & 4\end{array}\right]$ are

The differential equation of an ellipse whose major axis is twice its minor axis, is

The Cartesian equation of the plane $\overline{\mathrm{r}}=(\hat{\mathrm{i}}-\hat{\mathrm{j}})+\lambda(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})+\mu(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$ is

$\cos^{-1}\left(\frac{4}{5}\right)+\cos^{-1}\left(\frac{12}{13}\right)=$

The solution set for the system of linear inequations $x+y \ge 1 ; 7x+9y \le 63 ; y \le 5 ; x \le 6, x \ge 0$ and $y \ge 0$ is represented graphically in the figure. What is the correct option?

The general solution of the differential equation $\cos x \cdot \sin y dx + \sin x \cdot \cos y dy = 0$ is