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MHT CET
List of top Questions asked in MHT CET- 2016
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
MHT CET - 2016
MHT CET
Physics
Hooke's Law
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
MHT CET - 2016
MHT CET
Physics
Kinetic Energy
In vertical circular motion, the ratio of kinetic energy of a particle at highest point to that at lowest point is
MHT CET - 2016
MHT CET
Physics
Kinetic Energy
Direction cosines of the line
$\frac{x+2}{2} = \frac{2y-5}{3}, z = -1$
is
MHT CET - 2016
MHT CET
Mathematics
Three Dimensional Geometry
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)
MHT CET - 2016
MHT CET
Physics
Kinetic Energy
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
$\left(m_{2} < m_{1}\right)$
MHT CET - 2016
MHT CET
Physics
Oscillations
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
$\frac{V}{V_{1}}=$
?
MHT CET - 2016
MHT CET
Physics
Waves
In an oscillator, for sustained oscillations, Barkhausen criterion is $A\beta$ equal to ($A =$ voltage gain without feedback, $\beta =$ feedback factor)
MHT CET - 2016
MHT CET
Physics
Semiconductor electronics: materials, devices and simple circuits
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
MHT CET - 2016
MHT CET
Physics
Ideal gas equation
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
MHT CET - 2016
MHT CET
Physics
Uniform Circular Motion
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.
MHT CET - 2016
MHT CET
Mathematics
mathematical reasoning
If Matrix $A = \begin{bmatrix}1&2\\ 4&3\end{bmatrix}$ such that $Ax = I$, then $X = $_______
MHT CET - 2016
MHT CET
Mathematics
Determinants
$\int \left(\frac{\left(x^{2}+2\right)a^{\left(x +tan^{-1}x\right)}}{x^{2}+1}\right)dx = $
MHT CET - 2016
MHT CET
Mathematics
Integrals of Some Particular Functions
If Rolle�s theorem for $f\left(x\right)= e^{x} \left(sinx - cosx\right)$ is verified on $[\pi/4$, $5 \pi/4]$, then the value of $c$ is
MHT CET - 2016
MHT CET
Mathematics
Differentiability
Derivative of $log \left(sec\,\theta +tan \,\theta\right) $ with respect to $sec\, \theta$ at $\theta = \pi/4$ is
MHT CET - 2016
MHT CET
Mathematics
Differentiability
For what value of
$k$
, the function defined by $ f(x) = \begin{cases} \frac{log(1+2x)sin\,x^\circ}{x^2} & \text{for } x \ge \text {0}\\ k & \text{for } x = \text{ 0} \end{cases}$ is continuous at
$x = 0$
?
MHT CET - 2016
MHT CET
Mathematics
Differentiability
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 ___________
MHT CET - 2016
MHT CET
Mathematics
Three Dimensional Geometry
$\int\left(\frac{4e^{2}-25}{2e^{x}-5}\right)dx = Ax+B \,\,log |2e^{x}-5|+c$ then
MHT CET - 2016
MHT CET
Mathematics
Integrals of Some Particular Functions
If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
MHT CET - 2016
MHT CET
Mathematics
Integrals of Some Particular Functions
If $ 2 \,tan^{-1} (cos\,x) = tan^{-1} (2 \,cosec\,x)$ then $sin\,x + cos\,x $ is equal to
MHT CET - 2016
MHT CET
Mathematics
Inverse Trigonometric Functions
If $A=\begin{bmatrix}1&1&0\\ 2&1&5\\ 1&2&1\end{bmatrix}$, then $a_{11}A_{21} +a_{12}A_{22}+a_{13}A_{23} $ is equal to
MHT CET - 2016
MHT CET
Mathematics
Determinants
The differential equation of the family of circles touching $y$-axis at the origin is
MHT CET - 2016
MHT CET
Mathematics
General and Particular Solutions of a Differential Equation
Assuming the expression for the pressure exerted by the gas on the walls of the container, it can be shown that pressure is
MHT CET - 2016
MHT CET
Physics
kinetic theory
The approximate value of $f\left(x\right)= x^{3}+5x^{2}-7x +9$ at $x=1.1 $ is
MHT CET - 2016
MHT CET
Mathematics
Application of derivatives
$\int \frac{1}{\sqrt{8+2x-x^{2}}} dx$ is equal to
MHT CET - 2016
MHT CET
Mathematics
Integrals of Some Particular Functions
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