A body cools in \(7\) minutes from \(60^{\circ}\,C\) to \(40^{\circ}\,C\). The temperature of the surrounding is \(10^{\circ}\,C\). The temperature of the body after the next \(7\) minutes will be

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water.
(Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is \(1 \mathrm{gm} / \mathrm{cm}^3\).) The unknown mass is ________ kg.

An electron with energy \(0.1\,ke\,V\) moves at right angle to the earth's magnetic field of \(1 \times 10^{-4}\,Wbm ^{-2}\). The frequency of revolution of the electron will be. (Take mass of electron \(=9.0 \times 10^{-31}\,kg\) )

The maximum range of a bullet fired from a toy pistol mounted on a car at rest is \(R_0= 10\, m\). What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity \(v = 20\, m/s\), on a horizontal surface ......... \(^o.\) \((g = 10\, m/s^2)\)

A thin convex lens made from crown glass \(\left( {\mu = \frac{3}{2}} \right)\) has focal length \(f\). When it is measured in two different liquids having refractive indices \(\frac{4}{3}\) and \(\frac{5}{3}\) it has the focal lengths \(f_1\) and \(f_2\) respectively. The correct relation between the focal lengths is:

A person of \(80\, kg\) mass is standing on the rim of a circular platform of mass \(200\, kg\) rotating about its axis as \(5\) revolutions per minute \((rpm).\) The person now starts moving towards the centre of the platform. What will be the rotational speed (in \(rpm\) ) of the platform when the person reaches its centre \(......rpm\)

The maximum height reached by a projectile is \(64 \mathrm{~m}\). If the initial velocity is halved, the new maximum height of the projectile is _______ \(\mathrm{m}\).

Given below are two statements : one is labeled as Assertion \(A\) and the other is labeled as Reason \(R\) Assertion \(A:\) Photodiodes are used in forward bias usually for measuring the light intensity. Reason \(R:\) For a \(p-n\) junction diode, at applied voltage \(V\) the current in the forward bias is more than the current in the reverse bias for \(\left|V_z\right| > \pm V \geq\left|V_0\right|\) where \(V_0\) is the threshold voltage and \(V _{ z }\) is the breakdown voltage. In the light of the above statements, choose the correct answer from the options given below

Let the system of equations :
\(\begin{aligned}
& 2 x+3 y+5 z=9 \\
& 7 x+3 y-2 z=8 \\
& 12 x+3 y-(4+\lambda) z=16-\mu
\end{aligned}\)
have infinitely many solutions. Then the radius of the circle centred at \((\lambda, \mu)\) and touching the line \(4 x=3 y\) is

If \( z=\frac{\sqrt{3}}{2}+\frac{i}{2}, i=\sqrt{-1} \), then \( (z^{201}-i)^{8} \) is equal to:

\(\mathop {\lim }\limits_{x \to 0} \frac{{{{\left( {1 - \cos \,2x} \right)}^2}}}{{2x\,\tan \,x - x\,\tan \,2x}}\) is

In the circuit diagrams \((A, B, C\) and \(D\)) shown below, \(R\) is a high resistance and \(S\) is a resistance of the order of galvanometer resistance \(G\). The correct circuit, corresponding to the half deflection method for finding the resistance and figure of merit of the galvanometer, is the circuit labelled as

A tuning fork vibrates with frequency \(256\, Hz\) and gives one beat per second with the third normal mode of vibration of an open pipe . What is the length of the pipe? ... \(cm\) (Speed of sound of air is \(340\, ms^{-1}\))