Two identical metal spheres are kept in contact with each other, each having radius ' \(R\) ' cm and ' \(\rho\) ' is the density of material of metal spheres. The gravitational force ' \(F\) ' of attraction between them is proportional to

The r.m.s. speed of gas at temperature \(T\) is 2 times the r.m.s speed at \(320 \mathrm{~K}\). The value of the Temperature \(T\) is

In Young's double slit experiment the wavelength of light used is \(6000 Å\), the screen is 40 cm from the slits and the fringe width is 0.012 cm , the distance between two slits is

Moving coil galvanometers \(\mathrm{M}_{1}\) and \(\mathrm{M}_{2}\) have resistance, number of turns, area of coil and magnetic field as follows.
\(\mathrm{R}_{1}=10 \Omega, \mathrm{R}_{2}=14 \Omega, \mathrm{N}_{1}=30, \mathrm{~N}_{2}=42\)
\(\mathrm{A}_{1}=3 \cdot 6 \times 10^{-3} \mathrm{~m}^{2}, \mathrm{~A}_{2}=1 \cdot 8 \times 10^{-2} \mathrm{~m}^{2},\) \(\mathrm{~B}_{1}=0 \cdot 25 \mathrm{~T}, \mathrm{~B}_{2}=0 \cdot 50 \mathrm{~T}\)
(Spring constants are same for both materials)
The ratio of (i) current sensitivity and (ii) voltage sensitivity for galvanometer
\(\left(\mathrm{M}_{2}\right.\) to \(\left.\mathrm{M}_{1}\right)\) is respectively

Three identical polaroids \(P_1, P_2\) and \(P_3\) are placed one after another. The pass axis of \(\mathrm{P}_2\) and \(P_3\) are inclined at an angle \(60^{\circ}\) and \(90^{\circ}\) with respect to axis of \(\mathrm{P}_1\). The source has an intensity \(I_0\). The intensity of transmitted light through \(P_3\) is \(\left(\cos 60^{\circ}=0.5, \cos 30^{\circ}=\frac{\sqrt{3}}{2}\right)\)

A series LCR circuit is connected to an a.c. source of \(230 \mathrm{~V}, 50 \mathrm{~Hz}\). The circuit contains resistance of \(80 \Omega\) an inductor having inductive reactance \(70 \Omega\) and a capacitor of capacitive reactance \(130 \Omega\). The power factor of the circuit is \(x\). The value of \(x\) is

The frequency of vibrating air column in a pipe, open at both ends is \(f_1\). When \(\left(\frac{3}{4}\right)^{\text {th }}\) of its length is immersed in water, the frequency of vibrating air column is \(f_2\). The value of \(\frac{f_1}{f_2}\) is

If \(\mathrm{f}(x)=\cos ^{-1} x, \mathrm{~g}(x)=\mathrm{e}^x\) and \(\mathrm{h}(x)=\mathrm{g}(\mathrm{f}(x))\), then \(\frac{\mathrm{h}^{\prime}(x)}{\mathrm{h}(x)}=\)

A spherical rain drop evaporates at a rate proportional to its surface area. If initially its radius is 3 mm and after 1 second it is reduced to 2 mm , then at any time t its radius is (where \(0 \leq \mathrm{t} \lt 3\) )

A bus is moving with a velocity of \(5 \mathrm{~m} / \mathrm{s}\) towards a wall. The driver blows the horn of frequency \(165 \mathrm{~Hz}\). If the speed of sound in air is \(335 \mathrm{~m} / \mathrm{s}\), then after reflection of sound wave, the number of beats per second heard by the passengers in the bus will be

Match the column-I with column-II and select the correct option.

	Column I (Traits)		Column II (Type of inheritance)
i.	Roan cattle	a.	Multiple allelism
ii.	Pink flowered Mirabilis jalapa plant	b.	Co-dominance
iii.	Sickle cell anaemia	c.	Incomplete dominance
iv.	Wings in Drosophila	d.	Pleiotropism

Which of the following is NOT a disaccharide?

In an \(L R\) circuit, the value of \(L\) is \(\left(\frac{0 \cdot 3}{\pi}\right)\) henry and the value of \(R\) is \(40 \Omega\), If in the circuit, an alternating e.m.f of 230 V at 50 cycles per second is connected, the impedance of the circuit and current will be respectively