A water heater of power \(2000\,W\) is used to heat water. The specific heat capacity of water is \(4200\,J\,kg ^{-1}\, K ^{-1}\). The efficiency of heater is \(70 \%\). Time required to heat \(2\,kg\) of water from \(10^{\circ}\,C\) to \(60^{\circ}\,C\) is \(..........s\). (Assume that the specific heat capacity of water remains constant over the temperature range of the water).

A galvanometer of resistance \(G\) is converted into a voltmeter of range \(0-1\, V\) by connecting a resistance \(R _{1}\) in series with it. The additional resistance that should be connected in series with \(R _{1}\) to increase the range of the voltmeter to \(0-2\, V\) will be

The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation: \(K(x) = K_0 + \lambda x\) ( \(\lambda  =\) constant) The capacitance \(C,\) of the capacitor, would be related to its vacuum capacitance \(C_0\) for the relation

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is \(\left(\frac{a-1}{a}\right)\) then the value of \(a\) is _______.

Consider following statements:
A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid.
B. As the temperature of liquid rises, the coefficient of viscosity increases.
C. As the temperature of gas increases, the coefficient of viscosity increases
D. The onset of turbulence is determined by Reynold's number.
E. In a steady flow two stream lines never intersect.
Choose the correct answer from the options given below:

A car is moving with speed of \(150\,km / h\) and after applying the brake it will move \(27\,m\) before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling \(....m\) distance.

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason \(R\) Assertion \(A:\) The beam of electrons shows wave nature and exhibit interference and diffraction. Reason \(R\) : Davisson Germer Experimentally verified the wave nature of electrons. In the light of the above statements. Choose the most appropriate answer from the options given below :

Three masses \(m_1 = 4\) kg, \(m_2 = 4\) kg and \(m_3 = 6\) kg are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of \(T_1/T_2\) is _____.
(take \(g = 10\) m/s\(^2\))

A \(1 \,kg\) block attached to a spring vibrates with a frequency of \(1\, Hz\) on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an \(8\, kg\) block placed on the same table. So, the frequency of vibration of the \(8\, kg\) block is ..... \(Hz\)

The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between \(t=0\) to \(t=4 \mathrm{~s}\) ?

At any instant the velocity of a particle of mass \(500\,g\) is \(\left(2 t \hat{ i }+3 t ^2 \hat{ j }\right)\,ms ^{-1}\). If the force acting on the particle at \(t=1 s\) is \((\hat{i}+x \hat{j}) N\). Then the value of \(x\) will be: