MHT CET (PCB) 2024 22th April Morning Shift

In an oscillating LC circuit, the maximum charge on the capacitor is ' $Q$ '. When the energy is stored equally between the electric and magnetic fields, the instantaneous charge on the capacitor ' $q$ ' is

The resistance of a coil for d.c. is $5 \Omega$. In a.c., the resistance will

The instantaneous value of current in an a.c. circuit is $I=2 \sin \left[100 \pi t+\frac{\pi}{3}\right]$ A. The current will be maximum for the first time at $\left(\sin 90^{\circ}=1\right)$

If an electron in hydrogen atom jumps from $3^{\text {rd }}$ orbit to $2^{\text {nd }}$ orbit it emits a photon of wavelength ' $\lambda$ '. When it emits a photon from $4^{\text {th }}$ orbit to $3^{\text {rd }}$ orbit then the correspondi...

The angular momentum of electron in hydrogen atom in first orbit is ' $L$ '. The change in angular momentum if electron is in second orbit of hydrogen atom is

In between the plates of parallel plate capacitor of plate separation 'd' a dielectric plate of thickness ' $t$ ' is inserted. The capacitance becomes one-third of the original capacity without dielectric. The dielectric constant of the pla...

A parallel combination of two capacitors of capacities ' C ' and ' $\frac{\mathrm{C}}{3}$, respectively is connected across a battery of 12 volt. When both capacitors are fully charged, the charge and energy stored in them is $Q_1, Q_2$ and...

Four masses of $1 \mathrm{~kg}, 2 \mathrm{~kg}, 3 \mathrm{~kg}$ and 4 kg are kept at co-ordinates $(0,0) \mathrm{m},(0,1) \mathrm{m}$ and $(1,0) \mathrm{m}$ respectively. Using the co-ordinates of centre of mass its position vector is

In case of well of death which is a vertical cylindrical wall of radius ' $r$ ' inside which vehicle is driven in horizontal circles. If ' $m$ ' is mass of vehicle, ' $V$ ' is the velocity and ' $\mu_s$ ' is the coefficient of static fricti...

A galvanometer of resistance ' $G$ ' can be converted into a voltmeter of range ( $0-\mathrm{V}$ ) volt by connecting a resistance ' $R$ ' in series with it. The resistance ' $R$ required to change its range from $\left(0-\frac{\mathrm{V}}{...

Which one of the following is the correct equation for the electric circuit shown in the figure?

A photon and an electron have an equal energy ' E '. The ratio of wavelength ' $\lambda_{\mathrm{p}}$ ' of photon to that of electron ' $\lambda_{\mathrm{e}}$ ' is proportional to

A metal surface is illuminated by light of two different wavelengths 207 nm and 414 nm . The maximum speeds of photoelectrons corresponding to these wavelengths are $\mathrm{u}_1$ and $\dot{u}_2$ respectively with $u_1: u_2=2: 1$. The work ...

Two different coils have self - inductance $\mathrm{L}_1=9 \mathrm{mH}$ and $\mathrm{L}_2=3 \mathrm{mH}$. The current in first coil is increased at a constant rate. The current in the second coil is also increased at the same constant rate....

Figure shows a rectangular frame situated in a constant magnetic field. A wire BC of length 1 m is moved out with velocity $4 \mathrm{~m} / \mathrm{s}$. Magnetic field strength is 0.15 T . Force acting on the wire $B C$ is

A hollow charged metal sphere has a radius ' $r$ '. If the potential difference between its surface and a point at a distance ' 3 r ' from the centre is ' $v$ ', then the electric field intensity at a distance ' $3 r$ ' is

In the diagram, the total electric flux through the closed surface ' S ' is
[Given $\mathrm{q}=$ charge
$\varepsilon_0=$ permittivity of free space]

Water is flowing through a horizontal pipe in a streamline flow. At the narrowest part of the pipe

A light metal disc of radius ' $r$ ' floats on 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 wei...

Work done to get ' $n$ ' spherical drops of equal size from a single spherical drop of water, is proportional to

A satellite is revolving round the earth with orbital speed ' $\mathrm{V}_0$ '. If it stops suddenly, the speed with which it will strike the surface of the earth would be ( $\mathrm{V}_{\mathrm{e}}=$ escape velocity of a particle on earth'...

The height at which the acceleration due to gravity becomes $\frac{g}{4}$ in terms of $R$ is $[R=$ the radius of the earth $]$

In thermodynamic process, which of the following statements is not true?

The volume of a block of metal at $30^{\circ} \mathrm{C}$ changes by $0.12 \%$ when its temperature is increased to $70^{\circ} \mathrm{C}$. The coefficient of linear expansion of the metal is

A fixed mass of gas at constant pressure occupies a volume ' $V$ '. The gas undergoes a rise in temperature so that the r.m.s. velocity of the molecule is doubled. The new volume will be

Two stars 'A' and 'B' radiate maximum energy at $5200 \mathop {\rm{A}}\limits^ \circ$ and $6500 \mathop {\rm{A}}\limits^ \circ$ respectively. Then the ratio of absolute temperatures of stars ' A ' and ' $B$ ' is

$$\mathop {\rm{A}}\limits^ ...

A monoatomic ideal gas, initially at temperature ' $\mathrm{T}_1$ '' is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature ' $\mathrm{T}_2$ ' by releasing the piston suddenl...

A spherical body of radius ' $r$ ' radiates power ' $P$ ' at $T$ kelvin. If the radius $s$ halved and the temperature doubled the power radiated in the same time ' t ' will be

A solenoid is connected to a battery so that a steady current flows through it, If an iron core is inserted into the solenoid, then the current in the coil

A solenoid having 400 turns/metre has a core of a material with relative permeability 300 . If a current of 0.5 A is passed through it, then the magnetisation of the core material is nearly

A stone is thrown upward with a speed 'u' from the top of a tower reaches the ground with velocity ' $3 u$ '. The height of the tower is ( $g=$ acceleration due to gravity)

The magnetic field at the centre of a current carrying circular coil of area ' $A$ ' is ' $B$ '. The magnetic moment of the coil is ( $\mu_0=$. permeability of free space)

A charged particle is subjected to acceleration in a cyclotron which consists of two dees ' $\mathrm{D}_1$ ' and ' $D_2$ '. The charged particle undergoes increase in its speed.

When a ray of light is refracted from one medium to another, then the wavelength changes from $6000 \mathop {\rm{A}}\limits^ \circ$ to $4000 \mathop {\rm{A}}\limits^ \circ$. The critical angle for the interface will be

For a given medium, the speed of light and the polarising angle are ' $v$ ' and ' $i_p$ ' respectively, then ( $\mathrm{c}=$ speed of light in vaccum )

A transparent sphere of refractive index ' $\mu$ ' and radius of curvature ' $R$ ' is kept in air. A point object is placed at a distance ' d ' from the surface of the sphere so that the real image is formed at the same distance ' $d$ ' fro...

Four point masses, each of mass ' $m$ ' are arranged in $X-Y$ plane as shown in the figure. The moment of inertia of this system about $X$-axis is

A thin rod of length ' 4 L ' and mass ' 4 m ' is bent at the points as shown in the figure. The moment of inertia of the rod about an axis passing through point ' $O$ ' and perpendicular to plane of the paper is

For a common emitter transistor configuration the ratio of $\frac{\mathrm{I}_{\mathrm{C}}}{\mathrm{I}_{\mathrm{E}}}=0.96$, then the current gain in this configuration is

The Boolean expression for $\mathrm{X}-\mathrm{OR}$ gate $C=(A \oplus B)$ is equivalent to

Diode and resistance are connected as shown in figure. Out of the following statements which one is TRUE?

A pendulum is performing simple harmonic motion. The acceleration of the bob is $20 \mathrm{~cm} \mathrm{~s}^{-2}$ at a distance of 5 cm from mean position. The time period of oscillation is

Two particles execute S.H.M. of same amplitude and frequency along the same straight line path. They pass each other when going in opposite directions, each time their displacement is half the amplitude. The phase difference between them is...

A particle of mass ' m ' is executing S.H.M. about the origin on $x$-axis with frequency $\sqrt{\frac{\mathrm{ka}}{\pi \mathrm{m}}}$, where ' $k$ ' is a constant and ' $a$ ' is the amplitude of S.H.M. If ' x ' is a displacement of a particl...

In a biprism experiment, fifth dark fringe is obtained at a point. A thin transparent film of refractive index ' $\mu$ ' is placed in one of the interfering paths. Now $7^{\text {th }}$ bright fringe is obtained at the same point. If ' $\la...

In biprism experiment the maximum intensity is ' $\mathrm{I}_0$ '. If the path difference between the two interfering waves is ' $\lambda / 4$ ' then intensity at the point on the screen is
$$ \left[\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{...

A pipe closed at one end vibrating in fifth overtone is in unison with open pipe vibrating in its fifth overtone. The ratio of $l_{\mathrm{c}}: l_{\mathrm{o}}$ is $\left[l_{\mathrm{c}}=\right.$ vibrating length of closed pipe, $l_0=$ vibrat...

The pitch of whistle of an engine appears to drop by $30 \%$ of the original value when it passes a stationary observer. If speed of sound in air is $350 \mathrm{~m} / \mathrm{s}$, then the speed of engine in $\mathrm{m} / \mathrm{s}$ is

Two uniform strings ' $A$ ' and ' $B$ ' made of steel are made to vibrate under same tension. If the first overtone of ' $A$ ' is equal to second overtone of ' B ' and radius of ' A ' is twice that of ' B '. Then the ratio of length of stri...

The equation of simple harmonic progressive wave is given by $y=A \sin (100 \pi t-4 x)$. The distance between two particles having a phase difference of $\left(\frac{\pi}{4}\right)^c$ is