List of top Questions asked in MHT CET- 2016

$\int \left(\frac{\left(x^{2}+2\right)a^{\left(x +tan^{-1}x\right)}}{x^{2}+1}\right)dx = $

A simple pendulum of length $l$ has maximum angular displacement $\theta$. The maximum kinetic energy of the bob of mass $m$ is ($g =$ acceleration due to gravity)

If $r. v. x :$ waiting time in minutes for bus and $p.d.f.$ of $x$ is given by $f(x) = \begin{cases} \frac{1}{5} , & 0\le x\le5 \\[2ex] 0, & \text{otherwise} \end{cases}$ then probability of waiting time not more than $4$ minutes is = _______

A mass $m_1$ connected to a horizontal spring performs $S.H.M.$ with amplitude $A$. While mass $m_1$ is passing through mean position another mass $m_2$ is placed on it so that both the masses move together with amplitude $A_1$. The ratio of $\frac{A_{1}}{A}$ is $\left(m_{2} < m_{1}\right)$

Alternating current of peak value $\left(\frac{2}{\pi}\right)$ ampere flows through the primary coil of the transformer. The coefficient of mutual inductance between primary and secondary coil is 1 henry. The peak e.m.f. induced in secondary coil is (Frequency of $AC = 50\, Hz$)

If $A$ and $B$ are foot of perpendicular drawn from point $Q (a, b, c)$ to the planes $yz$ and $zx$, then equation of plane through the points $A, B$ and $O$ is ___________

A particle moves along a circle of radius ?$r$? with constant tangential acceleration. If the velocity of the particle is ?$?$? at the end of second revolution, after the revolution has started then the tangential acceleration is

For a gas $\frac{R}{C_{v}} = 0.4$, where ?$R$? is the universal gas constant and ?$C_v$? is molar specific heat at constant volume. The gas is made up of molecules which are

Two wires having same length and material are stretched by same force. Their diameters are in the ratio $1 : 3$. The ratio of strain energy per unit volume for these two wires (smaller to larger diameter) when stretched is

In vertical circular motion, the ratio of kinetic energy of a particle at highest point to that at lowest point is

When the observer moves towards the stationary source with velocity, $V_1$, the apparent frequency of emitted note is $F_1$. When the observer moves away from the source with velocity $V_1$, the apparent frequency is $F_2$. If $V$ is the velocity of sound in air and $\frac{F_{1}}{F_{2}} = 2$ then $\frac{V}{V_{1}}=$ ?

Wire having tension $225\, N$ produces six beats per second when it is tuned with a fork. When tension changes to $256\, N$, it is tuned with the same fork, the number of beats remain unchanged. The frequency of the fork will be

Assuming the expression for the pressure exerted by the gas on the walls of the container, it can be shown that pressure is

Two strings $A$ and $B$ of same material are stretched by same tension. The radius of the string $A$ is double the radius of string $B$. Transverse wave travels on string $A$ with speed ?$V_A$? and on string $B$ with speed ?$V_B$?. The ratio $\frac{V_{A}}{V_{B}}$ is

If $ 2 \,tan^{-1} (cos\,x) = tan^{-1} (2 \,cosec\,x)$ then $sin\,x + cos\,x $ is equal to

$\int \frac{1}{\sqrt{8+2x-x^{2}}} dx$ is equal to

From Brewster�s law, except for polished metallic surfaces, the polarising angle

If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$

If $p :$ Every square is a rectangle $q :$ Every rhombus is a kite then truth values of $p ? q$ and $p ? q$ are __________ and ___________ respectively.

In an oscillator, for sustained oscillations, Barkhausen criterion is $A\beta$ equal to ($A =$ voltage gain without feedback, $\beta =$ feedback factor)

The differential equation of the family of circles touching $y$-axis at the origin is

Two identical parallel plate air capacitors are connected in series to a battery of e.m.f. $V$. If one of the capacitor is completely filled with dielectric material of constant $K$, then potential difference of the other capacitor will become

Direction cosines of the line $\frac{x+2}{2} = \frac{2y-5}{3}, z = -1$ is

If $r.v. X \sim B \left(n = 5, P=\frac{1}{3}\right)$ then $P(2 < X < 4) =$ ______________

A ring and a disc roll on the horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is $4\, J$ then total kinetic energy of the disc is