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A plane electromagnetic wave propagating in the $x-$direction in vacuum has wavelength of $6.0\text{mm}$. The electric field is in the $y-$direction and its maximum magnitude is $33{\text{Vm}}^{-1}$.



$\left(ii\right)$ The equation for the magnetic field as a function of $x\left(\text{m}\right)$ and $t\left(\text{s}\right)$ is



​​​​​​​$[$1 Mark$]$

Radius of first orbit of hydrogen is $0.53\dot{A}$. The radius in fourth orbit is:

A circular road of radius $1000\text{m}$ has a banking angle of ${45}^{\circ }$. The maximum safe speed (in $\text{m/s}$) of a car having a mass $2000\text{kg}$ will be (if the coefficient of friction between the tyres and the road is $0.3$) (Take $g=10{\text{m/s}}^2$)

Two friends on roller skates are standing 5m apart facing each other. One of them throws a ball of 2 kg towards the other, who catches it, how will this activity affect the position of the two? Explain your answer.

In the electrical network at $t<0$, key was placed on $\left(1\right),$ until the capacitor becomes fully charged at $t=0$.

Position of key is changed to $\left(2\right)$ at $t=0$. The energy in the capacitor and the inductor will be same for the first time is

A wave travelling along a string is described by $y(x,t)=0.008\sin (85x-4t)$ in $\text{SI}$ units, where $x$ is in metres and $t$ is in seconds . Calculate the wavelength and frequency of the wave.

Two waves passing through a region are represented by

$y=1.0cmsin\left[\right(3.14c{m}^{-1})x-(157s^{-1}\left)t\right]$

and $y=1.5cmsin\left[\right(1.57c{m}^{-1})x-(314s^{-1}\left)t\right]$

Find the displacement of the particle at x = 4.5 cm at time t = 5.0 ms.

In the given figure, a mirror is arranged at an angle ${30}^{\circ }$ to the square shaped wooden board as shown. Find the angle made by the comb with its reflected shadow. [5 MARKS]

The instantaneous values of AC and AC source in a circuit are, $i=\frac{1}{\sqrt{2}}\sin \left(100t\right)$ and $E=\frac{1}{\sqrt{2}}\sin (100t+\pi /3)$ respectively. The total work done in a cycle is -

Calculate the distance covered by a car when it starts from rest and gains a speed of 30 m/s at 2 meter per sq. second.

Block A of mass m is executing SHM on block B which moves with acceleration $a_0$ towards right. All surfaces are frictionless. The spring constant is K. Find the energy of oscillation:

A
horizontal straight wire 10 m long extending from east to west is
falling with a speed of 5.0 m s⁻¹,
at right angles to the horizontal component of the earth’s
magnetic field, 0.30 × 10⁻⁴
Wb m⁻².

(a)
What is the instantaneous value of
the emf induced in the wire?

(b)
What is the direction of the emf?

(c)
Which end of the wire is at the
higher electrical potential?

Which of the following graphs correctly represents the variation of particle momentum with associated de Broglie wavelength?

1. 117.6

The first overtone frequency of a closed organ pipe $P_1$, is equal to the fundamental frequency of an open organ pipe $P_2$. If the length of the pipe $P_1$, is 30 cm, what will be the length of $P_2$ ?

An electron in hydrogen atom first jumps from second excited state to first excited state and then from first excited state to ground state. Let the ratio of wavelength, momentum and energy of photons emitted in these two cases be a, b and c respectively. Then

Question 9

Magnification produced by a rear view mirror fitted in vehicles



(a) is less than one

(b) is more than one

(c) is equal to one

(d) can be more than or less than one depending upon the position of the object in front of it .

Beam $GHI$ is supported by three pontoons as shown in the figure below. The horizontal cross-sectional area of each pontoon is $8m^2,$ the flexural rigidity of the beam is $10000kN-m^2$ and the unit weight of water is $10kN/m^3.$







When the middle pontoon is removed, the deflection at H will be

When a sphere rolls without slipping, the ratio of its kinetic energy of translation to its total kinetic energy is

Let M denote the mass of earth and let R denote its radius . The ratio of g/G at earth's surface is?

A parallel narrow beam of light is incident on the surface of a transparent hemisphere of radius $R$ and refractive index $\mu =1.5$ as shown. The position of the image formed by refraction at the spherical surface only is

For $x\in [0,2\pi ]$, select the correct options.

A person walks up a stalled escalator in $90s$ . When just standing on the same moving escalator, he is carried in $60s$. The time it would take him to walk up the moving escalator will be

Frequency is the function of density $\left(\rho \right)$, length $\left(a\right)$ and surface tension $\left(T\right)$. Then its value is ($k$ is a constant)

What
will be the pressure of the gaseous mixture when 0.5 L of H₂
at 0.8 bar and 2.0 L of dioxygen at 0.7 bar are introduced in a 1L
vessel at 27°C?

The force $F$ acting on a particle of mass $m$ is indicated by the force - time graph shown below. The change in momentum of the particle over the time interval from $0$ to $8\text{s}$ is