List of practice Questions

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?

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

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

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

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

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

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

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

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

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

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

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

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:

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

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

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 $y=1$?

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

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 $(AB{)}^T$.

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

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

Graphic location of mode is done with reference to:

The point of intersection of diagonals of a square ABCD is at the origin and one of its vertices is at A(4, 2). What is the equation of the diagonal BD?

Find the equation of tangent to the curve $y=\sqrt{5x-3}-2$, which is parallel to the line $4x-2y+3=0$?

If $\int \frac{x^2+1}{x(x+1{)}^2}dx=A\ln |x|+\frac{B}{1+x}+C$, where C is the constant of integration, then $A+B$ $=$