A closed organ pipe of length ' \(L\) ' and an open organ pipe contain gases of densities \(\rho_1\) and \(\rho_2\) respectively. The compressibility of gases are equal in both the pipes. If the frequencies of their first overtones are same, then the length of the open organ pipe is

An infinite number of electric charges each equal to 5 nano-coulomb (magnitude) are placed along \(X\)-axis at \(x=1 \mathrm{~cm}, x=2 \mathrm{~cm}\), \(x=4 \mathrm{~cm}, x=8 \mathrm{~cm} . . .\). and so on. In this set up if the consecutive charges have opposite sign, then the electric field in newton/coulomb at \(x=0\) is :
\(\left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~N}-\mathrm{m}^2 / \mathrm{C}^2\right)\)

A uniform chain of length \(L\) is lying on the horizontal table. If the coefficient of friction between the chain and the table top is \(\mu\), what is the maximum length of the chain that can hang over the edge of the table without disturbing the rest of the chain on the table?

As shown in the figure, two blocks of masses \(m_1\) and \(\mathrm{m}_2\) are connected to a spring of force constant k . The blocks are slightly displaced in opposite directions to \(\mathrm{x}_1\), \(x_2\) distances and released. If the system executes simple harmonic motion, then the frequency of oscillation of the system ( \(\omega\) ) is

A wire of length 0.5 m and area of cross-section \(4 \times 10^{-6} \mathrm{~m}^2\) at a temperature of \(100^{\circ} \mathrm{C}\) is suspended vertically by fixing its upper end to the ceiling. The wire is then cooled to \(0^{\circ} \mathrm{C}\), but is prevented from contracting, by attaching a mass at the lower end. If the mass of the wire is negligible, then the value of the mass attached to the wire is
[Young's modulus of material of the wire \(=10^{11} \mathrm{~N} \mathrm{~m}^{-2}\); coefficient of linear expansion of the material of the wire \(=10^{-5} \mathrm{~K}^{-1}\) and acceleration due to gravity \(\left.=10 \mathrm{~m} \mathrm{~s}^{-2}\right]\)

The angle of polarisation for a medium with respect to air is \(60^{\circ}\). The critical angle of this medium with respect to air is

Two blocks of equal masses are tied with a light string passing over a massless pulley (Assuming frictionless surfaces) acceleration of centre of mass of the two blocks is \(\left(g=10 \mathrm{~ms}^{-2}\right)\)

Two capacitors of capacities \(1 \mu \mathrm{F}\) and \(C \mu \mathrm{F}\) are connected in series and the combination is charged to a potential difference of \(120 \mathrm{~V}\). If the charge on the combination is \(80 \mu \mathrm{C}\), the energy stored in the capacitor of capacity \(C\) in \(\mu \mathrm{J}\) is

What is the concentration (in \(\mathrm{mol} \mathrm{L}^{-1}\) ) of the product after \(20 \mathrm{~s}\) in the following reaction. Given that \(A \longrightarrow 3 B\), rate \(=k[\mathrm{~A}]^0\)

Which one of the following liberates oxygen immediately when passed into water?

The locus of a point at which the line joining the points \((-3,1,2),(1,-2,4)\) subtends a right angle, is

Let \([x]\) represents the greatest integer not more than \(x\). The discontinuous points of the function \(f(x)=\frac{5+[x]}{\sqrt{11+[x]-6 \sqrt{2+[x]}}}\) lies in the interval

\(0 < \mathrm{x} < 1, \int \frac{d x}{\sqrt{x^2-x^5}}=\frac{1}{3} \log |f(x)|+C\), then \(f\left(\frac{1}{2}\right)=\)