List of practice Questions

If ${\sec }^2\theta +{\tan }^2\theta =3$ then find the value of $\cot \theta$.

Consider the following.1. $z\overline{z}=|z{|}^2$2. $z^{-1}=\frac{z}{|z{|}^2}$, where $z=$ complex numberWhich of the above statement is/are correct?

General solution of $(x^2+y^2)dx-2xydy=0$ is:

If the radius of a sphere is measured as 6 m with an error of 0.02 m, then find the approximate error in calculating its surface area.

$\frac{\sin 7x+6\sin 5x+17\sin 3x+12\sin x}{\sin 6x+5\sin 4x+12\sin 2x}$ equals:

Consider the function $f(x)=|x|$ in the interval $-1\le x\le 1$. At the point $x=0,f(x)$ is:

Find the maximum value of 15sin θ + 20cos θ.

Find the value of $y-x$ from the following equation:$2\left[\begin{array}{cc}x& 5\\ 7& y-3\end{array}\right]+\left[\begin{array}{cc}3& -4\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}7& 6\\ 15& 14\end{array}\right]$

Calculate the area under the curve $y=2\sqrt{x}$ and included between the lines $x=0,x=4$.

Evaluate ${\int }_0^{\frac{\pi }{2}}\frac{\cos x}{1+{\sin }^{2}x}dx$:

Find the area of the region (in square unit) bounded by the curve $y=x-2$ and $x=0$ to $x=4$.

Find the domain for function $$f(x)=[\sin x]\cos \left(\frac{\pi }{[x-1]}\right)$$

Find the equation of the line passing through $(-3,5)$ and perpendicular to the line through the points $(2,5)(-3,6)$.

If $2x^3-3y^2=7$, what is $\frac{dy}{dx}$ equal to $(y\ne 0)$:

If ${\cos }^{-1}\left(\frac{p}{a}\right)+{\cos }^{-1}\left(\frac{q}{b}\right)=\alpha$, then $\frac{p^2}{a^2}+k\cos \alpha +\frac{q^2}{b^2}={\sin }^2\alpha$ where $\mathrm{k}$ is equal to:

If, $y=9\sqrt{x+\sqrt{x+\sqrt{x+....\infty }}}$ find $\left(\frac{dy}{dx}\right)$ at a point where y = 3.

The equation of the locus of a point equidistant from the point A(1, 3) and B(-2, 1) is:

The maximum value of $\frac{\ln x}{x}$ is:

What is the value of ${\int }_4^9\frac{1}{\sqrt{x}}dx$ ?

Find the equation of tangent of $y=x^2$ at $x=1$

Find the equation of the line perpendicular to the line $x-3y+5=0$ and passes through the point $(2,-4)$.

Find the value $f^{\prime }(x)$, if $f(x)={\sin }^{-1}(1-x^2)$

If $A=\left[\begin{array}{ccc}1& -1& 0\\ 3& 2& -1\end{array}\right]$ and $B=\left[\begin{array}{l}1\\ 3\\ 5\end{array}\right]$, find $(AB{)}^T$.

If $\underset{x\to \mathrm{\infty }}{lim}(\frac{x^2+x+1}{x+1}-px-q)=-3$, then $p$ and $q$ is:

What is the area of the parabola $x^2=y$ bounded by the line $y=1$?