List of top Questions asked in MHT CET

Two simple harmonic progressive waves have displacements \(y_{1}=5\,\sin \left(\frac{2\pi x}{\lambda }-\omega t\right)\) and \(y_{2}=5\,\cos \left(\frac{2\pi x}{\lambda }-\omega t+\frac{\pi }{6}\right)\). The phase difference between the two waves is
The equal charges (say 'q') are placed at a distance of \(4r\) and a third charge \((-2q)\) is placed at a mid-point. The potential energy of the system is (\(\epsilon _{0}=\) permittivity of free space)
A whistle giving out \(400\) Hz approaches a stationary observer at a speed of \(34\) m/s. The frequency heard by the observer (in Hz) is nearly (speed of sound\(=340\) m/s)
A pipe closed at one end vibrating in the sixth overtone is in unison with the open pipe vibrating in its sixth overtone. The ratio \(l_{c}:l_{o}\) is \(\{l_{c}=\) vibrating length of pipe closed at one end, \(l_{o}=\) vibrating length of pipe open at both ends\(\}\)
A simple harmonic progressive wave is given by the equation \(y=a\sin 2\pi \left(nt-\frac{x}{\lambda }\right)\). If the wave velocity is equal to \(\frac{1}{6}\times\) (maximum particle velocity), then the wavelength \(\lambda\) is \(\{a=\) amplitude, \(n=\) frequency, \(t=\) time, \(y=\) displacement, \(x=\) distance\(\}\)
A particle performing S.H.M., has a period of \(12\) s. The particle starts from a mean position. The ratio of distances travelled by the particle in the first and second second is \(\{\cos (\pi /6)=\frac{\sqrt{3}}{2}\}\)
The pressure of a given mass of a gas is decreased by \(20\%\) at constant temperature, then its volume will
A simple harmonic oscillator having four identical springs (as shown in figure) has a time period \(T_{1}\). Another similar simple harmonic oscillator of the same mass \(m\) but the four identical springs with spring constants \(2k\) has a time period \(T_{2}\), then \(\frac{T_{1}}{T_{2}}\) is
Two particles performing simple harmonic motions of maximum accelerations, \(1\) m/s\({}^{2}\) and \(100\) m/s\({}^{2}\), have the same amplitudes. The ratio of their angular frequencies is
Three rods made of the same material and the same cross-sectional areas have been joined as shown in the figure. Each rod is of the same length. The temperature of the junction is
Three spheres, P, Q and R, having radii \(4\) m, \(5\) m and \(6\) m respectively, are coated with lamp black on their outer surfaces. The wavelengths corresponding to maximum intensity (radiated) are \(400\) nm, \(500\) nm and \(600\) nm respectively. If the powers radiated by them are \(P_{P}\), \(P_{Q}\) and \(P_{R}\) respectively, then \(P_{P}:P_{Q}:P_{R}\) is
For any thermodynamic process, the work done by the system depends
The difference between two molar specific heats of a gas is \(7000\) J-kg\({}^{-1}\)-K\({}^{-1}\). If the ratio of two specific heats of gas is \(7/5\), the molar specific heat of the gas at constant pressure in J-kg\({}^{-1}\)-K\({}^{-1}\) is
A rectangular film of liquid is expanded from (\(6\) cm \(\times 5\) cm) to (\(8\) cm \(\times 9\) cm). If the work done is \(4\times 10^{-4}\) J, the surface tension of the liquid is
One mole of a mono-atomic ideal gas is taken through a cycle ABCDA as shown in the P-V diagram, then
In a hydraulic press, the small cylinder has a diameter of \(d_{1}\) cm, while the large cylinder has a diameter of \(d_{2}\) cm. If a force \(F_{1}\) is applied to a piston of small cylinder, then the force on the piston of large cylinder \(F_{2}\) is
Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their gravitational attraction, the speed of each particle is \(\{\sin (45)^{0}=\cos (45)^{\circ }=1/(2)^{0.5}\}\)
Which of the following sentence is true?
a. Moment of a couple is independent of the axis of rotation or the points of application of forces.
b. Moment of a couple produces translational acceleration.
c. Moment of a couple can be balanced by single force.
d. Moment of a couple depends upon the axis of rotation or the points of application of forces.
A vessel contains oil (density\(=0.6\) g/cm\({}^{3}\)) over mercury (density\(=13.6\) g/cm\({}^{3}\)). A homogeneous sphere floats with half its volume immersed in mercury and the remaining half in oil. The density of the material of the sphere in g/cm\({}^{3}\) is
A particular physical quantity is given by \(X=2\pi \sqrt{\frac{a}{b}}\) and the measured value of 'a' is \(40\) unit with \(0.01\) unit accuracy. The value of 'b' is \(\frac{98}{10}\) unit with \(1\) unit accuracy. The % error in \(X\) is nearly
Airplanes A and B are flying with constant velocity in the same vertical plane at angles \(30^{\circ }\) and \(60^{\circ }\) with respect to the horizontal as shown in the figure. The speed of A is \(100\sqrt{3}\) m/s. At time \(t=0\) s, an observer in A finds B at a distance of \(500\) m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at \(t=t_{0}\), A just escapes being hit by B, \(t_{0}\) in second is
\(\{\sin (30)^{\circ }=0.5,\,\cos (30)^{\circ }=3^{0.5}/2\}\)
Two particles A and B are moving in uniform circular motion in concentric circles of radii \(r_{A}\) and \(r_{B}\) with speeds \(v_{A}\) and \(v_{B}\) respectively. \(T_{A}\) and \(T_{B}\) are the time periods of rotation of the particles respectively and their relation is \(T_{A}=3T_{B}\). The ratio of angular speed of B to that of A will be
Four solid spheres, each of diameter \(\sqrt{5}\) cm and mass \(0.5\) kg are placed with their centres at the corners of a square of side \(4\) cm. The M.I. of the system about the diagonal of the square is \(N\times 10^{-4}\) kg-m\({}^{2}\), then \(N\) is
In the case of rotational dynamics, which of the following statements is correct? {\(S\) = linear displacement, \(\alpha\) = angular acceleration, \(r\) = radius vector, \(a\) = linear acceleration, \(L\) = angular momentum, \(p\) = linear momentum, \(\theta\) = angular displacement}

1. \(S=r\times \theta ,a=r\times \alpha ,L=p\times r\)
2. \(S=\theta \times r,a=\alpha \times r,L=r\times p\)
3. \(S=r\cdot \theta ,a=r\cdot \alpha ,L=p\cdot r\)
4. \(S=\omega \times r,a=r\times p,L=r\times f\)
If \(\vec{A}=5\hat{i}+2\hat{j}\) and \(\vec{B}=a\hat{i}+3\hat{j}\) are perpendicular to each other, the value of 'a' is