List of top Questions asked in MHT CET

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.

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:

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?

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 $A+B$ $=$

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 _______.

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?

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:

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:

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 tank is filled with water of density $1\frac{g}{{cm}^3}$ and oil of density $0.9\frac{g}{{cm}^3}$. The height of water layer is $100cm$ and that of oil layer is 400 $cm$. If $g=980\frac{cm}{s^2}$, then the velocity of efflux from an opening in the bottom of the tank will be-

A $240V,60Hz$ voltage source is connected to resistor of $60\mathrm{\Omega }$. Find the value of net power consumed by resistance over a complete cycle.

Water is flowing through a horizontal pipe in stream line flow at the narrowest part of the pipe?

The height from earth's surface at which acceleration due to gravity becomes g/ where g is acceleration due to gravity on the surface of earth and R is radius of earth?