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If error in measurement of radius of sphere is $1\%$, what will be the error in measurement of volume?

The refractive index of a prism is 2.This prism can have a maximum refracting angle of

In the relation : $\frac{dy}{dt}=2\omega sin(\omega t+\varphi )$, the dimensional formula for $(\omega t+\varphi )$ is

Which of the following is the Fourier transform of $x\left(t\right)=\{\begin{array}{cc}2;& -1\le t<0\\ 1;& 0\le t<1\\ 0;& elsewhere\end{array}$

The mass per unit length of a non-uniform rod $OP$ of length $L$ varies as $m=k\frac{x}{L},$ where $k$ is a constant and $x$ is the distance of point on the rod from end $O$. The distance of the centre of mass of the rod from end $O$ is

Water is flowing continuously from a tap having an internal diameter $8\times {10}^{-3}m$. The water velocity as it leaves the tap is $0.4m{s}^{-1}$. The diameter of the water stream at a distance $2\times {10}^{-1}m$. Below the tap is close to

Water stands at a depth H behind the vertical upstream face of a dam. The total width of the dam is L. The horizontal force acting on the dam is (density of water =$\rho$ )

A thin wire of length L and uniform linear mass density ρ is bent into a circular loop with center O as shown. The moment of inertia of the loop about the axis XX' is

If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be :

A person
with a normal near point (25 cm) using a compound microscope with
objective of focal length 8.0 mm and an eyepiece of focal length 2.5
cm can bring an object placed at 9.0 mm from the objective in sharp
focus. What is the separation between the two lenses? Calculate the
magnifying power of the microscope,

In a fluid flow system two fluids are mixed in appropriate proportion. The concentration at the mixing point is y(t) and it is reproduced without change after $T_d$ seconds at the monitoring point as b(t). What is the transfer function between b(t) and y(t)?

When a body is earth connected electrons from earth flow into the body.the means the body is

A cargo ship has the job of transporting goods from city A to city B on the downstream and come back upstream. If the velocity of ship in still water is 30 km/hr and velocity of the river stream is 15 km/hr. Find the average speed of the ship in the journey.

Some springs are combined in series and parallel arrangement as shown in the figure and a mass $m$ is suspended from them. The ratio of their frequencies will be

Two amplifiers are
connected one after the other in series (cascaded). The first
amplifier has a voltage gain of 10 and the second has a voltage gain
of 20. If the input signal is 0.01 volt, calculate the output ac
signal.

A super dense particle of mass $\frac{M}{2}$ is projected from the surface of the planet of mass M and radius R. Escape velocity for this particle of mass $\frac{M}{2}$ from surface of planet is

A metal block of density $6000kg{m}^{-3}$ and mass $1.2kg$ is suspended through a spring of spring constant $200N{m}^{-1}$. The spring-block system is dipped in water kept in a vessel. The water has a mass of $260g$ and the block is at a height $40cm$ above the bottom of the vessel. If the support to the spring is broken, what will be the rise in the temperature of the water? Specific heat capacity of the block is $250Jk{g}^{-1}{K}^{-1}$ and that of water is $4200Jk{g}^{-1}{K}^{-1}$. Heat capacities of the vessel and the spring are negligible.

In a chemical analysis of a rock, the mass ratio of two radioactive isotopes is found to be $100:1$. The mean lives of the two isotopes are $4\times {10}^9\text{years}$ and $2\times {10}^9\text{years}$, respectively. If it is assumed that at the time of formation, atoms of both the isotopes were in equal proportion, calculate the age of rock. Ratio of the atomic weight of the two isotopes is $1.02:1$.

Given ${\log }_e\left(100/1.02\right)=4.58$

A body is in motion along a straight line. As it crosses a fixed point a stop watch is started. The body travels a distance of 1.80m in the first 3 second and 2.20m in next 5 seconds what will be the velocity at the end of 9 seconds?

Two balls are projected from the same point in directions inclined at ${60}^{\circ }$ and ${30}^{\circ }$ to the horizontal. If they attain the maximum height at the same time, what is the ratio of their velocities of projection?

Give a detailed account of torque and angular momentum

Determine the direction of Poynting vector for an electromagnetic wave when its electric field component is oscillating in the $+y$ direction and the magnetic field component oscillates in the $-z$ direction.

As shown in the figure, water squirts horizontally out of two small holes in the side of cylinder and the two streams strike the ground at the same point. If the level of water stands at height $H=4.25\text{m}$ and hole $P$ is at depth of $0.25\text{m}$ below the surface of water, then find the depth of hole $Q$ from the surface of water.

Convection coefficient depends upon

Four particles of masses $1\text{kg},2\text{kg},3\text{kg}$ and $4\text{kg}$ are placed at the four vertices $\text{A,B,C}$ and $\text{D}$ of a square of side $1\text{m}$ as shown in figure. Find the position of centre of mass of the particles.

A false balance has equal arms. An object weigh X when placed in one pan and Y when placed in other pan, then the weight W of the object is equal to

A ball whose kinetic energy is E, is projected at an angle of ${45}^{\circ }$ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be

A wooden block $A$ of mass $10\text{kg}$ is placed on another identical block $B$ of mass $15\text{kg}$ lying on a horizontal wooden table as shown below. It is found that when a force of $20\text{N}$ is applied on the block $A$, it just begins to slide over the surface of the block $B$. When a body of mass $7.5\text{kg}$ is connected to the block $B$ by a string and pulley arrangement so that both the blocks $A$ and $B$ just move together, the co-efficient of friction between the block $B$ and surface will be:-
(Take $g=10{\text{ms}}^{-2}$)