A magnetic needle of magnetic moment \(6.7 \times 10^{-2} \) \(Am^2\) and moment of inertia \(7.5 \times  10^{-6}\) \( kgm^2\) is performing simple harmonic oscillations in a magnetic field of \(0.01\ T\). Time taken for \(10\) complete oscillations is.....\(s\)

Two \(10 \; cm\) long, straight wires, each carrying a current of \(5 \; A\) are kept parallel to each other. If each wire experienced a force of \(10^{-5} \; N\), then separation between the wires is \(\dots \; cm\).

A zener diode with 5 V zener voltage is used to regulate an unregulated dc voltage input of 25 V. For a \(400 \Omega\) resistor connected in series, the zener current is found to be 4 times load current. The load current \(\left(I_L\right)\) and load resistance \(\left(R_{\mathrm{L}}\right)\) are :

A thin rod having a length of \(1\; m\) and area of cross-section \(3 \times 10^{-6}\,m ^2\) is suspended vertically from one end. The rod is cooled from \(210^{\circ}\,C\) to \(160^{\circ}\,C\). After cooling, a mass \(M\) is attached at the lower end of the rod such that the length of rod again becomes \(1\,m\). Young's modulus and coefficient of linear expansion of the rod are \(2 \times 10^{11} Nm ^{-2}\) and \(2 \times 10^{-5} K ^{-1}\), respectively. The value of \(M\) is \(.......kg .\left(\right.\) Take \(\left.g=10\,m s ^{-2}\right)\)

Two ions of masses \(4 \,{amu}\) and \(16\, amu\) have charges \(+2 {e}\) and \(+3 {e}\) respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :

Figure shows elliptical path \(abcd\) of a planet around the sun \(S\) such that the area of triangle \(csa\) is \(\frac {1}{4}\) the area of the ellipse. (See figure) With \(db\)  as the semimajor axis, and  \(ca\) as the semiminor axis. If \(t_1\)  is the time taken for planet to go over path \(abc\) and \(t_2\) for path taken over \(cda\) then

In a Frank-hertz experiment, an electron of energy \(5.6\,eV\) passes through mercury vapour and emerges with an energy \(0.7\,eV.\) The minimum wavelength of photons emitted by mercury atoms is close to ............. \(nm\)

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of \(10 \,m\) in \(t \;s ,\) the distance travelled by the toy in the next \(t s\) will be .........\(m\)

A charged particle carrying charge \(1\,\mu C\) is moving with velocity \((2 \hat{ i }+3 \hat{ j }+4 \hat{ k })\, ms ^{-1} .\) If an external magnetic field of \((5 \hat{ i }+3 \hat{ j }-6 \hat{ k }) \times 10^{-3}\, T\) exists in the region where the particle is moving then the force on the particle is \(\overline{ F } \times 10^{-9} N\). The vector \(\overrightarrow{ F }\) is :

Given below are two statements : Statement \(I\) : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation \(\mathrm{P}_1-\mathrm{P}_2=\rho \mathrm{g}\left(\mathrm{h}_2-\mathrm{h}_1\right)\) Statement \(II\) : In ventury tube shown \(2 \mathrm{gh}=v_1^2-v_2^2\) In the light of the above statements, choose the most appropriate answer from the options given below.

A cylindrical container of volume \(4.0 \times 10^{-3} \,{m}^{3}\) contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is \(400 \,{K}\) The pressure of the mixture of gases is: [Take gas constant as \(8.3\, {J} {mol}^{-1} {K}^{-1}\)]

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A :\) The escape velocities of planet \(A\) and \(B\) are same. But \(A\) and \(B\) are of unequal mass. Reason \(R :\) The product of their mass and radius must be same, \(M _{1} R _{1}= M _{2} R _{2}\) In the light of the above statements, choose the most appropriate answer from the options given below

Two satellites \(A\) and \(B\) move round the earth in the same orbit. The mass of \(A\) is twice the mass of \(B\). The quantity which is same for the two satellites will be :