Free questions

If a line makes angles $90^{\circ },60^{\circ }$ and $30^{\circ }$ with the positive direction of the $x$, $y$ and $z$-axis respectively, find its direction cosines.

Find the rate of change of the area of a circle with respect to its radius $r$ when $r=5$ cm.

Area lying in the first quadrant and bounded by the circle $x^2+y^2=4$ and the lines $x=0$ and $x=2$ is

1. $\pi$
2. $\frac{\pi }{2}$
3. $\frac{\pi }{3}$
4. $\frac{\pi }{4}$

Check the continuity of the function $f$ given by $f(x)=2x+3$ at $x=1$.

Evaluate $\left|\begin{array}{cc}2& 4\\ -1& 2\end{array}\right|$.

Verify that the function $y=e^{-3x}$ is a solution of the differential equation $\frac{d^{2}y}{d{x}^2}+\frac{dy}{dx}-6y=0$.

Find $\int (2x^2+e^x)dx$.

If ${\sin }^{-1}x=y$, then

1. $0\le y\le \pi$
2. $-\frac{\pi }{2}\le y\le \frac{\pi }{2}$
3. $0<y<\pi$
4. $-\frac{\pi }{2}<y<\frac{\pi }{2}$

In a Linear Programming Problem, the linear function which has to be maximised or minimised is called a linear $\underline{}$ function.

If $A=[a_{ij}{]}_{m\times n}$, then $A$ is a square matrix if

1. $m<n$
2. $m>n$
3. $m=n$
4. None of these