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A siren emitting a sound of frequency $800\text{ Hz}$ moves away from an observer towards a cliff at a speed of $15\text{ ms}^{-1}$. The frequency of sound that the observer hears in the echo reflected from the cliff will be: (Take, velocity of sound in air = $330\text{ ms}^{-1}$)
The initial velocity of a particle is $10 \text{ m/sec}$ and its retardation is $2 \text{ m/sec}^2$. The distance moved by the particle in the 5th second of its motion is:
The position of a particle with respect to time t along the x-axis is given by x = 9t² - t³ where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the +x-direction?
A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to $L_1$ when mass M is suspended from its free end. The expression for Young's modulus is :
Six similar bulbs are connected as shown in the figure with a DC source of emf E and zero internal resistance. The ratio of power consumption by the bulbs when (i) all are glowing and (ii) in the situation when two from section A and one from section B are glowing, will be :
The correct Boolean operation represented by the circuit diagram drawn is :
<p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">When an object is shot from the bottom of a</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">long smooth inclined plane kept at an angle $60^\circ$</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">with horizontal, it can travel a distance $x_1$</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">along the plane. But when the inclination is</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">decreased to $30^\circ$ and the same object is shot</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">with the same velocity, it can travel $x_2$ distance.</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">Then $x_1 : x_2$ will be:</p>
A particle moving with velocity $\vec{v}$ is acted by three forces shown by the vector triangle PQR. The velocity of the particle will :
A 800 turn coil of effective area $0.05 \text{ m}^2$ is kept perpendicular to a magnetic field $5 \times 10^{-5} \text{ T}$. When the plane of the coil is rotated by $90^\circ$ around any of its coplanar axis in $0.1 \text{ s}$, the emf induced in the coil will be:
The radius of inner most orbit of hydrogen atom is $5.3 \times 10^{-11} \text{ m}$. What is the radius of third allowed orbit of hydrogen atom?
Light with an average flux of $20 \text{ W/cm}^2$ falls on a non-reflecting surface at normal incidence having surface area $20 \text{ cm}^2$. The energy received by the surface during time span of 1 minute is :
A ball is thrown vertically downward with a velocity of $20 \text{ m/s}$ from the top of a tower. It hits the ground after some time with a velocity of $80 \text{ m/s}$. The height of the tower is : ($g = 10 \text{ m/s}^2$)
Find the value of the angle of emergence from the prism. Refractive index of the glass is $\sqrt{3}$.
In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original frequency of B will be:
A resistance wire connected in the left gap of a metre bridge balances a $10 \ \Omega$ resistance in the right gap at a point which divides the bridge wire in the ratio $3 : 2$. If the length of the resistance wire is $1.5 \text{ m}$, then the length of $1 \ \Omega$ of the resistance wire is :
If E and G respectively denote energy and gravitational constant, then $\frac{E}{G}$ has the dimensions of
An inductor of inductance $L$, a capacitor of capacitance $C$ and a resistor of resistance $R$ are connected in series to an ac source of potential difference $V$ volts as shown in figure. Potential difference across $L$, $C$ and $R$ are 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through $LCR$ series circuit is $10\sqrt{2}$ A. The impedance of the circuit is
A spherical conductor of radius $10 \text{ cm}$ has a charge of $3.2 \times 10^{-7} \text{ C}$ distributed uniformly. What is the magnitude of electric field at a point $15 \text{ cm}$ from the centre of the sphere? ($\frac{1}{4\pi \epsilon_0} = 9 \times 10^9 \text{ Nm}^2/\text{C}^2$)
Column-I gives certain physical terms associated with flow of current through a metallic conductor. Column-II gives some mathematical relations involving electrical quantities. Match Column-I and Column-II with appropriate relations. Column-I: (A) Drift Velocity, (B) Electrical Resistivity, (C) Relaxation Period, (D) Current Density. Column-II: (P) $\frac{m}{ne^2\rho}$, (Q) $nev_d$, (R) $\frac{eE}{m}\tau$, (S) $\frac{E}{J}$
A particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it equals $4R$. The angle of projection, $\theta$, is then given by :