Mathematics Tes...

A balloon is moving upwards with a speed of 20 m/s. When it is at a height of 14 m from ground in front of a plane mirror in  as shown in figure, a boy drops himself from the balloon. Find the time duration for which he will see the image of source S placed symmetrically before plane mirror during free fall.

The peak emission from a body at a certain temperature occurs at a wavelength of $\mathrm{9000 }\AA \mathrm{.}$ On increasing its temperature the total radiation emitted is increased to 81 times. At the initial temperature when the peak radiation from the black body is incident on a metal surface it does not cause any photoemission from the surface. After the increase of temperature the peak radiation from the black body causes photoemission. To bring these photoelectrons to rest, potential equivalent to the excitation energy between the n = 2 to n = 3 Bohr levels of hydrogen atom is required. Find the work function of the metal. [h = 6.62 × 10^-34 J-s and c = 3 × 10⁸ m/s]

Q charge is uniformly distributed over the curve surface of a right circular cone of semi-vertical angle θ and height h. The cone is uniformly rotated about its axis at angular velocity ω. Calculated associated magnetic dipole moment.(H>R)

A beam of ultraviolet radiation having wavelength between 100 nm and 200 nm is incident on a sample of atomic hydrogen gas. Assuming that the atoms are in ground state, which wavelengths will have low intensity in the transmitted beam ?

A large tank filled with water to a height 'h' is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from \(\mathrm{h}\) to \(\frac{\mathrm{h}}{2}\) and from \(\frac{\mathrm{h}}{2}\) to zero is :

Initially car A is 10.5 m ahead of car B. Both start moving at time t = 0 in the same direction along a straight line. The velocity time graph of two cars is shown in figure. The time when the car B will catch the car A, will be :

The intensity of the light coming from one of the slits in YDSE is double the intensity from the other slit. Find the ratio of maximum intensity to minimum intensity in the interference fringe pattern observed.

A truck starts from origin, accelerating with 'a' m/sec² in positive x - axis direction. After 2 seconds a man standing at the starting point of the truck projected a ball at an angle 30⁰ with velocity 'v' m/s. Find the relation between 'a' and 'v' such that ball hits the truck. (assume truck is moving on horizontal plane and man projected the ball from the same horizontal level of truck).

A battery is supplying power to a tape-recorder by cable of resistance of 0.2 $\Omega$ . If the battery is generating 50 W power at 5V, then power received by tape-recorder is :

Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is (are) correct ?