List of top Questions asked in MHT CET

A step up transformer operates on $220\text{ V}$ and supplies current of $2\text{ A}$. The ratio of primary and secondary windings is $1 : 20$. The current in the primary is
The electric field intensity on the surface of a charged solid sphere of radius $r$ and volume charge density $\rho$ is given by ($\varepsilon_0$ = permittivity of free space)
A particle performing linear S.H.M. of amplitude $0.1\text{ m}$ has displacement $0.02\text{ m}$ and acceleration $0.5\text{ m/s}^2$. The maximum velocity of the particle in m/s is
A thin metal disc of radius $r$ floats on a water surface and bends the surface downwards along the perimeter making an angle $\theta$ with the vertical edge of the disc. If the weight of water displaced by the disc is $W$, the weight of the metal disc is [$T$ = surface tension of water]
Two tuning forks of frequencies $320\text{ Hz}$ and $480\text{ Hz}$ are sounded together to produce sound waves. The velocity of sound in air is $320\text{ ms}^{-1}$. The difference between wavelengths of these waves is nearly
A sonometer wire of length $25\text{ cm}$ vibrates in unison with a tuning fork. When its length is decreased by $1\text{ cm}$, $6$ beats are heard per second. What is the frequency of the tuning fork?
The plates of a parallel plate capacitor of capacity $C_1$ are moved closer together until they are at half their original separation. The new capacitance $C_2$ is
A p-n junction photodiode is fabricated from a semiconductor with a band gap of $2.5\text{ eV}$. It can detect a signal of wavelength [Planck's constant = $6.6 \times 10^{-34}\text{ Js}$, $c = 3 \times 10^8\text{ m/s}$, $e = 1.6 \times 10^{-19}\text{ C}$]
For a monoatomic gas, the work done at constant pressure is $W$. The heat supplied at constant volume for the same rise in temperature of the gas is
A monoatomic ideal gas initially at temperature $T_1$ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. $L_1$ and $L_2$ are the lengths of the gas columns before and after the expansion respectively. Then $\frac{T_2}{T_1}$ is
A glass tube of uniform cross-section is connected to a tap with a rubber tube. The tap is opened slowly. Initially the flow of water in the tube is streamline. The speed of flow of water to convert it into a turbulent flow is [radius of tube = $1\text{ cm}$, $\eta = 1 \times 10^{-3}\text{ Ns/m}^2$, $R_n = 2500$ and density of water = $10^3\text{ kg/m}^3$]
The radii of curvature of both the surfaces of a convex lens of focal length $f$ and focal power $P$ are equal. One of the surfaces is made plane by grinding. The new focal length and focal power of the lens is respectively
A photon has wavelength $3\text{ nm}$, then its momentum and energy respectively will be $[h = 6.63 \times 10^{-34}\text{ Js}, c = 3 \times 10^8\text{ m/s}]$
A glass slab has refractive index $\mu$ with respect to air and the critical angle for a ray of light in going from glass to air is $\theta$. If a ray of light is incident from air on the glass with angle of incidence $\theta$, then the corresponding angle of refraction is
A stone is projected vertically upwards with velocity $V$. Another stone of same mass is projected at an angle of $60^\circ$ with the vertical with the same speed ($V$). The ratio of their potential energies at the highest points of their journey, is
An electron makes a transition from an excited state to the ground state of a hydrogen like atom. Out of the following statements which one is correct?
The common region of the solutions of the inequations $x + 2y \ge 4$, $2x - y \le 6$ and $x, y > 0$ is
If $\int \frac{\cos x - \sin x}{8 - \sin 2x} \, dx = \frac{1}{p} \log \left[ \frac{3 + \sin x + \cos x}{3 - \sin x - \cos x} \right] + c$, then $p = $
Two identical springs of constant $K$ are connected in series and parallel in shown in figure. A mass $M$ is suspended from them. The ratio of their frequencies is series to parallel combination will be
If the horizontal velocity given to a satellite is greater than critical velocity but less than the escape velocity at the height, then the satellite will
Two identical particles each of mass $m$ are separated by a distance $d$. The axis of rotation passes through the midpoint of $d$ and is perpendicular to the length $d$. If $K$ is the average rotational kinetic energy of the system, then the angular frequency is
If $A = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 1 & a \\ 2 & 4 & 7 \end{bmatrix}$ and $B = \begin{bmatrix} 13 & 2 & b \\ -3 & -1 & 2 \\ -2 & 0 & 1 \end{bmatrix}$ where matrix $B$ is the inverse of matrix $A$, then the values of $a$ and $b$ are
A die is thrown four times. The probability of getting a perfect square in at least one throw is
For a $3 \times 3$ matrix $A$, if $A(\operatorname{adj}A) = \begin{bmatrix} -10 & 0 & 0 \\ 0 & -10 & 0 \\ 0 & 0 & -10 \end{bmatrix}$, then the value of the determinant of $A$ is
In any $\triangle ABC$, with usual notations, $c(a \cos B - b \cos A) = $