An air column in a tube \(32 \mathrm{~cm}\) long, closed at one end, is in resonance with a tuning fork. The air column in another tube, open at both ends, of length \(66 \mathrm{~cm}\) is in resonance with
another tuning fork. When these two tuning forks are sounded together, they produce 8 beats per second. Then the frequencies of the two tuning forks are, (Consider fundamental frequencies only)

Match the following.

Codes
\(\begin{array}{llll}A & B & C & D\end{array}\)

In an atom the difference between two energy levels is \(3.31 \mathrm{eV}\), then the wavelength of the radiation emitted when the transition takes place between these levels is nearly

When a spiral spring is stretched by suspending a load with it, the strain produced is called strain.

A body moving along a straight line collides another body of same mass moving in the same direction with half of the velocity of the first body. If the coefficient of restitution between the two bodies is 0.5, then the ratio of the velocities of the two bodies after collision is (treat the collision as one dimensional)

Two towers \(A\) and \(B\), each of height \(20 \mathrm{~m}\) are situated a distance \(200 \mathrm{~m}\) apart. A body thrown horizontally from the top of the tower \(A\) with a velocity \(20 \mathrm{~ms}^{-1}\) towards the tower \(B\) hits the ground at point \(P\) and another body thrown horizontally from the top of tower \(B\) with a velocity \(30 \mathrm{~ms}^{-1}\) towards the tower \(A\) hits the ground at point \(Q\). If a car starting from rest from \(P\) reaches \(Q\) in 10 seconds, then the acceleration of the car is \(\left(\right.\) acceleration due to gravity \(\left.=10 \mathrm{~ms}^{-2}\right)\)

Simultaneously, from the top of a tower, when ball- 1 is thrown horizontally and ball- 2 is just dropped, in the absence of air resistance which among the following options is correct?

In $\mathrm{\Delta }ABC$, if $a:b:c=3:5:7$, then $\cos A+\cos B=$

The probability for a contractor to get a road contract is \(\frac{2}{9}\) and to get a building contract is \(\frac{5}{9}\), if the probability to get both the contract is \(\frac{1}{6}\), then what is the probability to get neither of these two contracts?

The minimum number of quantum numbers required to specify an orbital in an atom is

If the eleventh term in the binomial expansion of \((x+a)^{15}\) is the geometric mean of the eighth and twelfth terms, then the greatest term in the expansion is

Sum of the squares of the imaginary roots of the equation \(z^8-20 z^4+64=0\) is

The domain of the real valued function
\(f(x)=\frac{1}{\sqrt{\log _{0.5}(2 x-3)}}+\sqrt{4-9 x^2}\)