A bat moving at \(10\,ms^{-1}\) towards a wall sends a sound signal of \(8000\,Hz\) towards it. On reflection it hears a sound of frequency \(f\). The value of \(f\) in \(Hz\) is close to (speed of sound \(= 320\,ms^{-1}\) )

An electron with kinetic energy \(K _{1}\) enters between parallel plates of a capacitor at an angle \('\alpha'\) with the plates. It leaves the plates at angle \(' \beta '\) with kinetic energy \(K _{2}\). Then the ratio of kinetic energies \(K _{1}: K _{2}\) will be ....... .

Match the \(\frac{C _{ P }}{ C _{ v }}\) ratio for ideal gases with different type of molecules

Moleculae type	\(\frac{C _{ P }}{ C _{ v }}\)
\((A)\) Monoatomic	\((I)\) \(\frac{7}{ 5}\)
\((B)\) Diatomic rigid molecules	\((II)\) \(\frac{9}{7}\)
\((C)\) Diatomic non-rigid molecules	\((III)\) \(\frac{4}{3}\)
\((D)\) Triatomic rigid molecules	\((IV)\) \(\frac{5}{3}\)

The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N , the length of the string is 1.56 m. The original length of the string is _____ m.

Primary side of a transformer is connected to \(230 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. Turns ratio of primary to secondary winding is \(10: 1\). Load resistance connected to secondary side is \(46\  \Omega\). The power consumed in it is :

A submarine \((A)\) travelling at \(18\, km/hr\) is being chased along the line of its velocity by another submarine \((B)\) travelling at \(27\, km/hr\). \(B\) sends a sonar signal of \(500\, Hz\) to detect \(A\) and receives a reflected sound of frequency \(v\). The value of \(v\) is close to ... \(Hz\) (Speed of sound in water \(= 1500\, ms^{-1}\))

Consider an equilateral prism (refractive index \( \sqrt{2} \)). A ray of light is incident on its one surface at a certain angle i. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to __________ .

Consider a modified Bernoulli equation.
\(\left( P +\frac{ A }{ Bt ^2}\right)+\rho g ( h + Bt )+\frac{1}{2} \rho V^2=\) constant
If \(t\) has the dimension of time then the dimensions of A and B are _________ , _________ respectively.

Two long parallel conductors \(S_{1}\) and \(S_{2}\) are separated by a distance \(10 \,cm\) and carrying currents of \(4\, A\) and \(2 \,A\) respectively. The conductors are placed along \(x\)-axis in \(X - Y\) plane. There is a point \(P\) located between the conductors (as shown in figure). A charge particle of \(3 \pi\) coulomb is passing through the point \(P\) with velocity \(\overrightarrow{ v }=(2 \hat{ i }+3 \hat{ j }) \,m / s\); where \(\hat{i}\) and \(\hat{j} \quad\) represents unit vector along \(x\) and \(y\) axis respectively. The force acting on the charge particle is \(4 \pi \times 10^{-5}(-x \hat{i}+2 \hat{j}) \,N\). 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 \(A\): A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with same geometry and mass. Reason \(R\): For the magnetic bar, Eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar. In the light of the above statements, choose the correct answer from the options given below

Let \(A=\{1,2,3, \ldots ,100\}\). Let \(R\) be a relation on A defined by \((x, y) \in R\) if and only if \(2 x=3 y\). Let \(R_1\) be a symmetric relation on \(A\) such that \(\mathrm{R} \subset \mathrm{R}_1\) and the number of elements in \(\mathrm{R}_1\) is \(\mathrm{n}\). Then, the minimum value of \(n\) is ...........

The integral \(\int{ \cfrac{d x}{(x+4)^{\frac{8}{7}}(x-3)^{\frac{6}{7}}}}\) is equal to (where \(\mathrm{C}\) is a constant of integration)

A proton, a neutron, an electron and an \(\alpha\,-\)particle have same energy. If \(\lambda_{ p }, \lambda_{ n }, \lambda_{ e }\) and \(\lambda_{\alpha}\) are the de Broglie's wavelengths of proton, neutron, electron and \(\alpha\) particle respectively, then choose the correct relation from the following