List of practice Questions

Two stretched strings of same material are vibrating under same tension in fundamental mode. The ratio of their frequencies is 1 : 2 and ratio of the length of the vibrating segments is 1 : 4. Then the ratio of the radii of the strings is

A lamp consumes only $25\%$ of the peak power in an ac circuit. The phase difference between the applied voltage and the current is

Of the three molecules $XeF_4, SF_4 ,SiF_4$ one which have tetrahedral structures is

Differentiate w.r.t. x the function:\(x^x+x^a+a^x+a^a\), for some fixed \(a>0\) and \(x>0\)

An electron accelerated through a potential difference $V_1$ has a de-Broglie wavelength of $\lambda$. When the potential is changed to $V_2$, its de-Broglie wavelength increases by $50 \%$. The value of $\left(\frac{V_1}{V_2}\right)$ is equal to

The magnetic moment of a sample of mass \( 2 \, \text{g} \) is \( 8 \times 10^{-7} \, \text{A}\cdot\text{m}^2 \). If density \( \rho = 4 \, \text{g/cm}^3 \), then the magnetisation \( M \) of the sample is: ?

A sample of drinking water was found to be severely contaminated with chloroform \((CHCl_3)\) supposed to be a carcinogen. The level of contamination was 15ppm (by mass):
(i) express this in percent by mass
(ii) determine the molality of chloroform in the water sample.

Electric lines of force never cross each other. Electric field at a point superimpose to give one resultant electric field.

Write all the factors of the following numbers:

1. 24
2. 15
3. 21
4. 27
5. 12
6. 20
7. 18
8. 23
9. 36