For \(LED's\)  to emit light in visible region of electromagnetic light, it should have energy band gap in the range of

The length of wire becomes \(l_1\) and \(l_2\) when \(100\,N\) and \(120\,N\) tensions are applied respectively. If \(10l_2=11l_1\), the natural length of wire will be \(\frac{1}{x} l_1\). Here the value of \(x\) is ........

At a given instant, say \(t = 0,\) two radioactive substances \(A\) and \(B\) have equal activates. The ratio \(\frac{{{R_B}}}{{{R_A}}}\) of their activities. The ratio \(\frac{{{R_B}}}{{{R_A}}}\) of their activates after time \(t\) itself decays with time \(t\) as \(e^{-3t}.\) If the half-life of \(A\) is \(ln2,\) the half-life of \(B\) is

Two particles having masses \(4\, g\) and \(16\, g\) respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is \(n : 2 .\) The value of \(n\) will be ...... .

The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation: \(K(x) = K_0 + \lambda x\) ( \(\lambda  =\) constant) The capacitance \(C,\) of the capacitor, would be related to its vacuum capacitance \(C_0\) for the relation

A capacitor \(C _{1}\) of capacitance \(5\,\mu F\) is charged to a potential of \(30\,V\) using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor \(C _{2}\) of capacitance \(10\,\mu F\) as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor \(C _{2}\) is________ \(\mu C\)

A wire of cross sectional area \(A\), modulus of elasticity \(2 \times 10^{11} \mathrm{Nm}^{-2}\) and length \(2 \mathrm{~m}\) is stretched between two vertical rigid supports. When a mass of \(2 \mathrm{~kg}\) is suspended at the middle it sags lower from its original position making angle \(\theta=\frac{1}{100}\) radian on the points of support. The value of \(A\) is _______ \(\times 10^{-4} \mathrm{~m}^2\) (consider \(\mathrm{x}<\mathrm{L}\) ). (given: \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )

A force is represented by \(\mathrm{F}=a \mathrm{x}^2+\mathrm{bt}^{1 / 2}\). Where \(\mathrm{x}=\) distance and \(\mathrm{t}=\) time. The dimensions of \(\mathrm{b}^2 / \mathrm{a}\) are _______.

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension \(70 \mathrm{dyn} / \mathrm{cm}\) and glass water contact angle \(\simeq 0^{\circ}\)) with \(30^{\circ}\) inclined with vertical. The length of water risen in the capillary is ________ cm.
\(\left(\right.\) Take \(\left.\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2\right)\)

A particle is subjected two simple harmonic motions as :
\(\mathrm{x}_1=\sqrt{7} \sin 5 \mathrm{tcm}\)
and \(x_2=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}\right) \mathrm{cm}\)
where x is displacement and \(t\) is time in seconds. The maximum acceleration of the particle is \(\mathrm{x} \times 10^{-2} \mathrm{~ms}^{-2}\). The value of x is :

Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\): If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude. Reason \(R \): At equator, the direction of acceleration due to the gravity is towards the center of earth. In the light of above statements, choose the correct answer from the options given below

A cylindrical vessel of cross-section \(A\) contains water to a height \(h\) . There is a hole in the bottom of radius \('a'\) . The time in which it will be emptied is

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is \(200 \mathrm{~N} / \mathrm{m}\). The block is pushed such that the length of the spring becomes 1 m and then released. At distance \(\mathrm{x} \mathrm{m}(\mathrm{x} \lt 2)\) from the wall. the speed of the block will be :