A bubble in a glass slab (refractive index1.5) when viewed from one side appears at \(5 \mathrm{~cm}\) and at \(2 \mathrm{~cm}\) from other side then thickness of the slab is

A particle of mass \(m\) is rotating in a plane in circularpath of radius \(r\). Its angular momentum is \(L\). The centripetal force acting on the particle is

Two capacitors \(\mathrm{C}_1=3 \mu \mathrm{F}\) and \(\mathrm{C}_2=2 \mu \mathrm{F}\) are connected in series across d.c. source of \(100 \mathrm{~V}\). The ratio of the potential across \(C_2\) to \(C_1\) is

A resistor of \(50 \Omega\), inductor of self inductance \(\left(\frac{2}{\pi^2}\right) \mathrm{H}\) and a capacitor of unknown capacity are connected in series to an a.c. source of \(100 \mathrm{~V}, 50\) Hz supply. When the voltage and current are in phase, the value of capacitance is

A bar magnet has length \(3 \mathrm{~cm}\), cross-sectional area \(2 \mathrm{~cm}^2\) and magnetic moment \(3 \mathrm{Am}^2\). The intensity of magnetization of bar magnet is

A thin rod of length ' \(L\) ' is bent in the form of a circle. Its mass is ' \(M\) '. What force will act on mass ' \(\mathrm{m}\) ' placed at the centre of this circle?
\((\mathrm{G}=\text { constant of gravitation) }\)

A student measures time for 20 oscillations of a simple pendulum as \(30 \mathrm{~s}, 32 \mathrm{~s}, 35 \mathrm{~s}\) and 35 s . If the minimum division in the measuring clock is \(1 s\), then correct mean time (in second) is

The co-factors of the elements of second column of \(\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 2 & 1 \\ -1 & 3 & 4\end{array}\right]\) are

The area (in sq. units) of the region \(\left\{(x, y) / x \geq 0, x+y \leq 3, x^2 \leq 4 y\right.\) and \(\left.y \leq 1+\sqrt{x}\right\}\) is

If \(8.84 \mathrm{~kJ}\) heat is liberated for formation of \(3 \mathrm{~g}\) ethane, calculate its \(\Delta_{\mathrm{f}} \mathrm{H}^{\circ}\).

The variation of intensity of magnetisation (I) and the applied magnetic field
intensity (H) for three magnetic materials ' \(\mathrm{X}^{\prime}\), \({ }^{\prime} \mathrm{Y}^{\prime}\) and ' \(\mathrm{Z}\) ' are shown in the graph as
OX, OY and OZ respectivley. The materials ' \(\mathrm{X}^{\prime},{ }^{\prime} \mathrm{Y}^{\prime}\) and ' \(\mathrm{Z}\) ' respectively are

If \(\bar{x}=\frac{\overline{\mathrm{b}} \times \overline{\mathrm{c}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}, \bar{y}=\frac{\overline{\mathrm{c}} \times \overline{\mathrm{a}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}\) and \(\overline{\mathrm{z}}=\frac{\overline{\mathrm{a}} \times \overline{\mathrm{b}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}\) where \(\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) are non-coplanar vectors, then value of \(\bar{x} \cdot(\overline{\mathrm{a}}+\overline{\mathrm{b}})+\bar{y} \cdot(\overline{\mathrm{~b}}+\overline{\mathrm{c}})+\overline{\mathrm{z}} \cdot(\overline{\mathrm{c}}+\overline{\mathrm{a}})\) is

If the gametes of an individual are RY and Ry only, then the genotype of the same individual will be _________ .