A radioactive element \({ }_{92}^{242} X\) emits two \(\alpha\)-particles, one electron and two positrons. The product nucleus is represented by \({ }_{ P }^{234} Y\). The value of \(P\) is \(..................\)

When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called:

The total number of turns and cross-section area in solenoid is fixed. However, its length \(L\) is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to

The displacement of a particle executing SHM is given by \(x=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{m}\). The time period of motion is \(3.14 \mathrm{~s}\). The velocity of the particle at \(\mathrm{t}=0\) is_________ \(\mathrm{m} / \mathrm{s}\).

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion \(A\) : If \(dQ\) and \(dW\) represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics \(d Q=d U-d W\). Reason \(R :\) First law of thermodynamics is based on law of conservation of energy. In the light of the above statements, choose the correct answer from the option given below :

A conducting circular loop of area \( 1.0 m^{2} \) is placed perpendicular to a magnetic field which varies as \( B = \sin(100 t) \) Tesla. If the resistance of the loop is 100 \( \Omega \), then the average thermal energy dissipated in the loop in one period is ___________ J.

For extrinsic semiconductors; when doping level is increased;

A wire of resistance \(R\) and length \(L\) is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be _______.

Two vectors \(\overrightarrow{{X}}\) and \(\overrightarrow{{Y}}\) have equal magnitude. The magnitude of \((\overrightarrow{{X}}-\overrightarrow{{Y}})\) is \({n}\) times the magnitude of \((\overrightarrow{{X}}+\overrightarrow{{Y}})\). The angle between \(\overrightarrow{{X}}\) and \(\overrightarrow{{Y}}\) is -

A series \(LCR\) circuit of \(R=5\, \Omega, L=20\, {mH}\) and \({C}=0.5 \,\mu \,{F}\) is connected across an \({AC}\) supply of \(250\, V\), having variable frequency. The power dissipated at resonance condition is \(.....\,\times 10^{2}\, {W}\)

An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity \(10^6 \mathrm{~m} / \mathrm{s}\). If the magnitude of the electric field between the plates is \(9.1 \mathrm{~V} / \mathrm{cm}\), then the vertical component of velocity of electron is (mass of electron \(=9.1 \times 10^{-31} \mathrm{~kg}\) and charge of electron \(=1.6 \times 10^{-19} \mathrm{C}\) )

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) A pendulum clock when taken to Mount Everest becomes fast. Reason \(R:\) The value of \(g\) (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth. In the light of the above statements, choose the most appropriate answer from the options given below