A person measures mass of 3 different particles as \(435.42 \mathrm{~g}, 226.3 \mathrm{~g}\) and 0.125 g. According to the rules for arithmetic operations with significant figures, the additions of the masses of 3 particles will be.

For a periodic motion represented by the equation \(Y=\sin \omega t+\cos \omega t\) The amplitude of the motion is 

A circular hole of radius \(\left(\frac{ a }{2}\right)\) is cut out of a circular disc of radius \('a'\) as shown in figure. The centroid of the remaining circular portion with respect to point \('O'\) will be :

A uniformly charged disc of radius \(R\) having surface charge density \(\sigma\) is placed in the \({xy}\) plane with its center at the origin. Find the electric field intensity along the \(z\)-axis at a distance \(Z\) from origin :-

Given below are two statements: Statement \(I :\) \(PN\) junction diodes can be used to function as transistor, simply by connecting two diodes, back to back, which acts as the base terminal. Statement \(II :\) In the study of transistor, the amplification factor \(\beta\) indicates ratio of the collector current to the base current. In the light of the above statements, choose the correct answer from the options given below :

The sum of two forces \(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) is \(\overrightarrow{\mathrm{R}}\) such that \(|\overrightarrow{\mathrm{R}}|=|\overrightarrow{\mathrm{P}}| .\) The angle \(\theta\) (in degrees) that the resultant of \(2 \overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) will make with \(\overrightarrow{\mathrm{Q}}\) is

The mass of the moon is \(1 / 144\) times the mass of a planet and its diameter \(1 / 16\) times the diameter of a planet. If the escape velocity on the planet is \(\mathrm{v}\), the escape velocity on the moon will be _______.

Two identical conducting spheres \(\mathrm{P}\) and \(\mathrm{S}\) with charge \(Q\) on each, repel each other with a force \(16 \mathrm{~N}\). A third identical uncharged conducting sphere \(\mathrm{R}\) is successively brought in contact with the two spheres. The new force of repulsion between \(\mathrm{P}\) and \(\mathrm{S}\) is what?

The image of an object placed in air formed by a convex refracting surface is at a distance of \(10\, m\) behind the surface. The image is real and is at \(\frac{2}{3}\) of the distance of the object from the surface . The wavelength of light inside the surface is \(\frac{2}{3}\) times the wavelength in air. The radius of the curved surface is \(\frac{ x }{13}\, m\). the value of \(^{\prime} x^{\prime}\) is ....... .

A reversible engine has an efficiency of \(\frac{1}{4}\). If the temperature of the sink is reduced by \(58^{\circ} {C}\), its efficiency becomes double. Calculate the temperature of the sink. (In \(^{\circ} {C}\))

A series \(L C R\) circuit with \(L=\frac{100}{\pi} \mathrm{mH}, C=\frac{10^{-3}}{\pi} \mathrm{F}\) and \(R=10 \Omega\), is connected across an ac source of \(220 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. The power factor of the circuit would be___________.