A galvanometer has a \(50\) \(division\) scale. Battery has no internal resistance. It is found that there is deflection of \(40\) \(divisions\) when \(R = 2400\,\Omega \). Deflection becomes \(20\) \(divisions\) when resistance taken from resistance box is \(4900\,\Omega \) . Then we can conclude

A screw gauge has \(50\) divisions on its circular scale. The circular scale is \(4\) units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of \(0.5\, mm\) is noticed on the pitch scale. The nature of zero error involved, and the least count of the screw gauge, are respectively

The solid cylinder of length \(80\, {cm}\) and mass \({M}\) has a radius of \(20\, {cm}\). Calculate the density of the material used if the moment of inertia of the cylinder about an axis \(CD\) parallel to \({AB}\) as shown in figure is \(2.7\, {kg} {m}^{2}\)

In photo electric effect \(A.\) The photocurrent is proportional to the intensity of the incident radiation. \(B.\) Maximum Kinetic energy with which photoelectrons are emitted depends on the intensity of incident light. \(C.\) Max. \(K.E\) with which photoelectrons are emitted depends on the frequency of incident light. \(D.\) The emission of photoelectrons require a minimum threshold intensity of incident radiation. \(E.\) Max. K.E of the photoelectrons is independent of the frequency of the incident light. Choose the correct answer from the options given below:

In the given circuit below inductance values of \(L_1\), \(L_2\) and \(L_3\) are same. The magnetic energy stored in the entire circuit is \((U_t)\) and that stored in the \(L_2\) inductor is \((U_l)\). \(U_t / U_l\) is __________.
(Ignore the mutual inductance if any)

Match List\(-I\) with List\(-II\)

List\(-I\)	List\(-II\)
\((a)\) Isothermal	\((i)\) Pressure constant
\((b)\) Isochoric	\((ii)\) Temperature constant
\((c)\) Adiabatic	\((iii)\) Volume constant
\((d)\) Isobaric	\((iv)\) Heat content is constant

Choose the correct answer from the options given below

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range \(R\). If the time of flight of these bodies are \(5\) s and \(10\) s, respectively, then the value of \(R\) is ________ m. (Take \(g=10\) m/s\(^2\))

Let \(T\) and \(C\) respectively be the transverse and conjugate axes of the hyperbola \(16 x^2-\) \(y^2+64 x+4 y+44=0\). Then the area of the region above the parabola \(x^2=y+4\), below the transverse axis \(T\) and on the right of the conjugate axis \(C\) is:

Consider an A.P.: \( a_1, a_{2},....,a_{n} \), \( a_{1}>0 \). If \( a_{2}-a_{1}=\frac{-3}{4} \), \( a_{n}=\frac{1}{4} a_{1} \) and \(\sum_{i=1}^n a_i=\frac{525}{2}\) , then \(\sum_{i=1}^{17} a_i\) is equal to

A relation on the set \(A\, = \,\{ x\,:\,\left| x \right|\, < \,3,\,x\, \in Z\} ,\) where \(Z\) is the set of integers is defined by \(R= \{(x, y) : y = \left| x \right|, x \ne  - 1\}\). Then the number of elements in the power set of \(R\) is

Number of functions \(f:\{1,2, \ldots, 100\} \rightarrow\{0,1\}\), that assign 1 to exactly one of the positive integers less than or equal to 98 , is equal to ________.

Heat energy of \(184\,kJ\) is given to ice of mass \(600\,g\) at \(-12^{\circ}\,C\), Specific heat of ice is \(2222.3\,J\,kg ^{-1^{\circ}}\,C ^{-1}\) and latent heat of ice in \(336\,kJ / kg ^{-1}\) \((A)\) Final temperature of system will be \(0^{\circ} C\). \((B)\) Final temperature of the system will be greater than \(0^{\circ} C\). \((C)\) The final system will have a mixture of ice and water in the ratio of \(5: 1\). \((D)\) The final system will have a mixture of ice and water in the ratio of \(1: 5\). \((E)\) The final system will have water only. Choose the correct answer from the options given below:

If the radius of earth shrinks by \(2 \%\) while its mass remains same. The acceleration due to gravity on the earth's surface will approximately.