List of practice Questions

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 $y=1$?

Find the area between the curve $y=x^2$ and $y=x$.

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

Graphic location of mode is done with reference to:

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 $A+B$ $=$

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?

What is the equation of line passing through (0, 1) and making an angle with the y-axis equal to the inclination of the line x - y = 4 with x-axis?

A circle with center $(4,-5)$ is tangent to the $y$ -axis in the standard $(x,y)$ coordinate plane. What is the radius of this circle?

If $A=\left[\begin{array}{cc}\cos 2\theta & -\sin 2\theta \\ \sin 2\theta & \cos 2\theta \end{array}\right]$ and $A+A^T=I$ Where $I$ is the unit matrix of $2\times 2$ and  $A^T$ is the transpose of $A$, then the value of $\theta$ is equal to:

Jobs arrive at a facility at an average rate of $5$ in an $8$ hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is $40$ minutes. The service time follows exponential distribution. Idle time (in hours) at the facility per shift will be _______.

The point which does not belong to the feasible region of the LPP:Minimize: $\mathrm{Z}=60\mathrm{x}+10\mathrm{y}$subject to $3\mathrm{x}+\mathrm{y}\ge 18$$2x+2y\ge 12$$x+2y\ge 10$$\mathrm{x},\mathrm{y}\ge 0$ is:

The value of the term independent of $x$ in the expansion of ${(x^2-\frac{1}{x})}^9$ is:

What is the acute angle between the lines represented by the equations $y-\sqrt{3}x-5=0$ and $\sqrt{3}y-x+6=0?$

A rigid spherical body is spinning around an axis without any external torque. Due to rise of temperature its volume increases by 3% . Then percentage change in its angular speed is