The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is: (mass of the moon \(= 7.36 \times 10^{22}\,kg,\) radius of the moon's orbit \(= 3 .8 \times 10^8\,m\) ).

The parameter that remains the same for molecules of all gases at a given temperature is _______.

An ideal transformer with purely resistive load operates at \(12\,kV\) on the primary side. It supplies electrical energy to a number of nearby houses at \(120\,V\). The average rate of energy consumption in the houses served by the transformer is \(60\,kW\). The value of resistive load (Rs) required in the secondary circuit will be \(.........\,m \Omega\).

Assume there are two identical simple pendulum Clocks\(-1\) is placed on the earth and Clock\(-2\) is placed on a space station located at a height \(h\) above the earth surface. Clock\(-1\) and Clock\(-2\) operate at time periods \(4\,s\) and \(6\,s\) respectively. Then the value of \(h\) is \(....km\) (consider radius of earth \(R _{ E }=6400\,km\) and \(g\) on earth \(10\,m / s ^{2}\) )

A force \(\overrightarrow{\mathrm{F}}=2 \hat{i}+\mathrm{b} \hat{j}+\hat{k}\) is applied on a particle and it undergoes a displacement \(\hat{i}-2 \hat{j}-\hat{k}\). What will be the value of \(b\), if work done on the particle is zero.

A transparent block A having refractive index \(\mu=1.25\) is surrounded by another medium of refractive index \(\mu=1.0\) as shown in figure. A light ray is incident on the flat face of the block with incident angle \(\theta\) as shown in figure. What is the maximum value of \(\theta\) for which light suffers total internal reflection at the top surface of the block?

Two capacitors, each having capacitance \(40\,\mu F\) are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant \(K\) such that the equivalence capacitance of the system became \(24\,\mu F\). The value of \(K\) will be.

Two blocks of masses \(m\) and \(M,(M \gt m)\), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then
(\(\mu=\) coefficient of friction between the two blocks)

(A) The time period of small oscillation of the two blocks is \(\mathrm{T}=2 \pi \sqrt{\frac{(\mathrm{~m}+\mathrm{M})}{\mathrm{k}}}\)
(B) The acceleration of the blocks is \(\mathrm{a}=\frac{\mathrm{kx}}{\mathrm{M}+\mathrm{m}}\) (\(\mathrm{x}=\) displacement of the blocks from the mean position)
(C) The magnitude of the frictional force on the upper block is \(\frac{m \mu|x|}{M+m}\)
(D) The maximum amplitude of the upper block, if it does not slip, is \(\frac{\mu(M+m) g}{k}\)
(E) Maximum frictional force can be \(\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}\).
Choose the correct answer from the options given below:

A boy of mass \(20\, kg\) is standing on a \(80\, kg\) free to move long cart. There is negligible friction between cart and ground. Initially, the boy is standing \(25\, m\) from a wall. If he walks \(10\, m\) on the cart towards the wall, then the final distance of the boy from the wall will be ........ \(m\)

lf a line \(L\) is perpendicular to the line \(5x - y\,= 1\) , and the area of the triangle formed by the line \(L\) and the coordinate axes is \(5\), then the distance of line \(L\) from the line \(x + 5y\, = 0\) is

If \(\int {\frac{{dx}}{{{x^3}{{\left( {1 + {x^6}} \right)}^{2/3}}}} = xf\left( x \right){{\left( {1 + {x^6}} \right)}^{\frac{1}{3}}} + C} \) where \(C\) is a constant of integration, then the function \(f(x)\) is equal to

Match List I with List II

List - I	List - II
A. AM Broadcast	I. \(88-108 MHz\)
B. FM Broadcast	II. \(540-1600 kHz\)
C. Television	III. \(3.7-4.2GHz\)
D. Satellite Communication	IV. \(54 MHz-590MHz\)

Choose the correct answer from the options given below:

Let \(g: R \rightarrow R\) be a non constant twice differentiable such that \(g^{\prime}\left(\frac{1}{2}\right)=g^{\prime}\left(\frac{3}{2}\right)\). If a real valued function \(f\) is defined as \(\mathrm{f}(\mathrm{x})=\frac{1}{2}[\mathrm{~g}(\mathrm{x})+\mathrm{g}(2-\mathrm{x})]\), then