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A musician using an open flute of length $50\text{cm}$ produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of $10\text{km/h}$. If the wave speed is $330\text{m/s}$, the frequency heard by the running person shall be close to

If a simple harmonic motion is represented by $\frac{d^{2}x}{d{t}^2}+\alpha x=0$ its time period is

In a $\text{YDSE}$ experiment, if a slab whose refractive index can be varied is placed in front of one of the slits then the variation of resultant intensity at the mid-point of the screen with $\mu$ will be best represented by ($\mu \ge 1)$. $[$Assume slits of equal width and there is no absorption by slab$]$

The square coil shown in the figure has a side of $30\text{cm}$ and $20$ turns of wire on it. It is moving to the right at a speed of $3{\text{ms}}^{-1}$ as shown, inside there exists a magnetic field whose left boundary is $\text{KL}.$ The induced e.m.f. and the direction of induced current in the coil :

(i) At the instant shown and

(ii) When the coil is completely inside the field region

Two mercury drops each of radius $r$ merge to form a bigger drop. The surface energy of the bigger drop, if $T$ is the surface tension of mercury, is

A racer can bend his bike at a maximum angle of ${53}^{\circ }$ with the vertical plane. If he approaches a curve driving with a velocity of $126\text{km/h}$, what should be the turning radius to make a safe turn?

Read the following and write the correct pairs. Initially, the two plates (A and B) are given charges as shown. Find the final charges on the plates after the key k is closed. All plates are conducting, parallel and of infinite length and breadth.



$\begin{array}{cccc}& \text{List-I}& & \text{List-II}\\ \text{(P)}& \text{Final charge on plate A}& \left(1\right)& \frac{Q}{2}\\ \text{(Q)}& \text{Final charge on plate B}& \left(2\right)& \text{Q}\\ \text{(R)}& \text{Final charge on plate C}& \left(3\right)& \text{0}\\ \text{(S)}& \text{Final charge on plate D}& \left(4\right)& \frac{3Q}{2}\end{array}$

Which of the following option has the correct combination considering column –I and column – II

A milling cutter having $8$ teeth is rotating at $100rpm$. The workpiece feed is set at $40mm/min$ the feed per tooth is

1. 0

Image formed by a convex mirror is [MP PET 1993]

An aero plane is flying horizontally with a constant velocity of 100 kmph at a height of 1 km from the ground level. At
t = 0, it start dropping packets at constant time interval of $I_0$. If R represents the separation between two consecutive points of impact on the ground then for the first 3 packets $R_1:R_2$ is

Two tuning forks are struck and the sounds from each reach your ears at the same time. One sound has a frequency of 256 Hz, and the second sound has a frequency of 258 Hz. The underlying beat frequency is:

A hollow M.S. pipe is kept on a smooth straight edge with the pipe mid point sitting on it. A load 'W' Newton is applied at the ends which is keeping the pipe balanced in the horizontal condition. What is the safe maximum load 'w' that can be applied without yielding the tube consider the self weight of tube as $\rho$ N/m.

Diameter of the pipe is 'd', youngs modulus of pipe is E, allowable yields stress is $\sigma$.

A capacitor of capacitance 100 $\mu$ F is connected across a battery of emf 6.0 V through a resistance of 20 k $\Omega$ for 4.0 s. The battery is then replaced by a thick wire. What will be the charge on the capacitor 4.0 s after the battery is disconnected ?

In the given figure below, there are $2$ convex lenses $L_1$ and $L_2$ having focal length $f_1$ and $f_2$ respectively. The distance between $L_1$ and $L_2$ will be:

In Young's double slit experiment, the wavelength of light used is doubled and the distance between the two slits is halved, the new fringe width becomes,

Two identical batteries,each of emf $2V$ and internal resistance r=1 $\Omega$ by passing a current through it. The maximum power that can be developed across $R=1\Omega$ using these batteries is

Monochromatic light of frequency of $6\times {10}^{14}Hz$ is produced by a laser. Power emitted is $2\times {10}^{-3}W.$ Approximately how many photons per second are emitted by the source?

A hollow prism with side ABCD as open is kept in a region of electric field E. The field is parallel to the sides. BEC and AFD. Find the flux coming out of the pyramid?

A body travels half of its total path in the last second of its fall from rest. If $t$ and $H$ are the time and height of its fall (take $g=10{\text{m/s}}^2$). Then,

Two charges $q_1$ and $q_2$ are kept on $x-$ axis and electric field at different points on $x-$ axis is plotted against $x$. Choose correct statement about nature and magnitude of $q_1$ and $q_2$.

An electromagnetic wave of wavelength ${\lambda }_0$ (in vacuum) passes from $P$ towards $Q$ crossing three different media of refractive index $\mu ,2\mu$ and $3\mu$ respectively as shown in figure. ${\varphi }_P$ and ${\varphi }_Q$ are the phase of the wave at point $P$ and $Q$. Find the phase difference ${\varphi }_Q-{\varphi }_P$ [Take: $\mu =1$]

Find:

(i) (ii) (iii)

You have learnt in the
text how Huygens’ principle leads to the laws of reflection and
refraction. Use the same principle to deduce directly that a point
object placed in front of a plane mirror produces a virtual image
whose distance from the mirror is equal to the object distance from
the mirror.

A
circular disc of mass 10 kg is suspended by a wire attached to its
centre. The wire is twisted by rotating the disc and released. The
period of torsional oscillations is found to be 1.5 s. The radius of
the disc is 15 cm. Determine the torsional spring
constant of the wire. (Torsional spring constant α is defined
by the relation J
=
–α θ,
where J
is
the restoring couple and θ
the angle of twist).

1. 652.5

The acceleration of the particle moving in $x-$direction with an initial velocity $3\text{m/s}$ is $2{m/s}^2$. Then its displacement at $t=3s$ will be

P, Q and R are three tuning forks. Frequency of tuning fork P is $380\text{Hz}$. Number of beats produced by tuning forks P and Q is $10\text{Hz}$ and by tuning forks Q and R is $8\text{Hz}$. When wax is put on P, beat frequency produced by tuning forks P and Q becomes $4\text{Hz}$ and by tuning forks P and R becomes $12\text{Hz}$. Frequency of fork Q is greater than the frequency of fork R. Find natural frequency of tuning forks Q and R respectively.

A jet of water is projected at an angle $\theta$ = ${45}^{\circ }$ with horizontal from the point A which is situated at a distance $x$ = $OA$ = $\frac{1}{2}m$ from a vertical wall. If the speed of projection is $v_0=\sqrt{10}m/s$ , find the point $P$ of striking of the water jet with the vertical wall.

The plates of a parallel plate capacitor are charged up to $100\text{V}$. Now, after removing the battery, a $2\text{mm}$ thick plate is inserted between the plates . Then, to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6\text{mm}$. The dielectric constant of the plate is

The r.m.s. value of an alternating current which when passed through a resistor produces heat which is twice of that produced by a direct current of 2 amperes in the same resistor is