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Magnitudes of vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are $3,4,5$ respectively. If $\overrightarrow{a}$ and $\overrightarrow{b}+\overrightarrow{c}$, $\overrightarrow{b}$ and $\overrightarrow{c}+\overrightarrow{a}$, $\overrightarrow{c}$ and $\overrightarrow{a}+\overrightarrow{b}$ are mutually perpendicular, then the magnitude of $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}$ is,

A car is pushed by some force from rest. Power delivered to car varies linearly with time as shown, then graph of K.E. with respect to time would be

Question 129(iii)

Astronomy The table shows the mass of the planets, the Sun and the Moon in our solar system.



Which planet has about the same mass as Earth?

An
electron and a proton are detected in a cosmic
ray experiment, the first with kinetic energy 10 keV, and the second
with 100 keV. Which is faster, the electron or the proton? Obtain the
ratio of their speeds. (electron mass = 9.11 × 10^–31
kg, proton mass = 1.67 × 10^–27
kg, 1 eV = 1.60 × 10^–19
J).

Find the amplitude and phase of the vibrations given by $x=A\cos \omega t+\frac{A}{2}\cos (\omega t+\frac{\pi }{2})+\frac{A}{4}\cos (\omega t+\pi )+\frac{A}{8}\cos (\omega t+\frac{3\pi }{2})$

If LHS is $=4\left({\cos }^3\left(10°\right)+{\sin }^3\left(20°\right)\right)$, then RHS will be.

A carnot engine having an efficiency of $\eta =\frac{1}{5}$ is used as a heat engine. Now it is used as a refrigerator. If work done by compressor is $40\text{J}$, the amount of energy delivered to surroundings is

A diatomic gas of moleculer weight $30\text{gm/ mole}$ is filled in a container at ${27}^{\circ }C$. It is moving at a velocity $100\text{m/s}$. If it is suddenly stopped, the rise in temperature of gas( in SI units) is :

Consider the situation shown in following fig. The capacitor A has a charge q on it whereas B is uncharged. The charge appearing on the capacitor B, a long time after the switch S is closed is

A small mass slides down an inclined plane of inclination $\theta$ with the horizontal. The coefficent of friction is $\mu ={\mu }_{o}x$ where the $x$ is the distance through which the mass slides down and ${\mu }_o$ is a positive constant. Then the distance covered by the mass before it stops is

A rectangular block with mass $2\text{kg}$ is sliding down an incline plane at angle of ${30}^{\circ }$. The block is separated from the plane by a lubrication oil with dynamic viscoscity $0.25{\text{Nsm}}^{-2}$ having spacing of $1\text{mm}$. The base of the block has an area of $20\text{cm}\times 50\text{cm}$. Determine the terminal velocity (when acceleration is zero) of the block as it slides down the plane

An ac voltage source $V=V_{0}sin\omega t$ is connected across resistance R and capacitance C as shown in figure. It is given that $R=\frac{1}{\omega C}$.Then peak current is $I_0$. If the angular frequency of the voltage source is changed to $\frac{\omega }{\sqrt{3}}$ keeping R and C fixed, then the new peak current in the circuit is

1. 140

The ratio of angular speeds of minute hand and hour hand of a watch is

Carbon $(Z=6)$ with mass number $11$ decays to boron $(Z=5).$ The half-life of the decay scheme is $20.3\text{minutes}$. How much time will elapse before a mixture of $90\text{\%}\text{carbon}-11$ and $10\text{\%}\text{boron}-11$ (by the number of atoms) converts itself into a mixture of $10\text{\%}\text{carbon}-11$ and $90\%\text{boron}-11?$

$(\ln \frac{1}{9}=-2.1972)$

A pendulum of some length and a bob made of iron, has a time period $T_{iron}$. If another pendulum is made with the same length but with a copper bob, the new time period $T_{copper}$ would be equal to:

If the intensity of two waves is $2$ and $3$ units, then average intensity of light in the overlapping region will be,

Two identical waves interfere at a point in the same medium having amplitudes $3\text{cm}$ and $5\text{cm}$. Which of the resultant amplitude is not possible?

1. 108.6

A hydrogen atom in ground state absorbs a photon of ultraviolet radition of wavelength 50 nm. Assuming that the entire photon energy is taken up by the electron, with what kinetic energy will the electron be ejected ?

A rain drop while falling through a cloud made up of stationary particles gains mass at a rate proportional to its instantaneous momentum. If $m$ is its instantaneous mass, $v$ is its instantaneous velocity and $c$ is the constant of proportionality then

The figure represents a solid uniform sphere of mass M and radius R. A spherical cavity of radius r is at a distance a from the centre of the sphere. The gravitational field inside the cavity is

Find the true power given apparent power = 10 W and power factor = 0.5

The figure shows three progressive waves A, B and C. What can be concluded from the figure that with respect to wave A?

A simple pendulum with lenght $l$ and bob of mass $m$ is executing S.H.M. of small amplitude $a$. The maximum tension in the string will be

Two identical objects each of radii R and masses $m_1$ and $m_2$ are suspended using two strings of equal length L as shown in the figure (R<<L). The angle $\theta$ which mass $m_2$ makes with the vertical is approximately

If $y=x^3$, then $\frac{d^{2}y}{d{x}^2}$ is

A stone is projected at an angle $\theta$ with velocity u to hit a vertical wall at a distance b. If after collision at wall it returns to point of projection, the co-efficient of restitution is given by

A string breaks under the load of $50\text{kg}$. A mass of $1\text{kg}$ is attached to one end of the string $10\text{m}$ long is rotated in a horizontal circle while the other end is attached to the ceiling. Calculate the greatest number of revolutions that the mass can make per second without breaking the string. (Take $g=10m/s^2$)