Graphs were plotted between stopping potential \( (V_o) \) and frequency of incident radiation \( (\nu) \) for 2 metals namely Cesium (work fn. 2.14) and Aluminium (work fn. 4.28). The ratio of slope of graph of Cesium to the slope of graph for Aluminium is:

The total energy of the electron in a hydrogen atom is \( -1.51 \text{ eV} \).
A. Its Kinetic energy is \( -1.51 \text{ eV} \)
B. Its potential energy is \( -3.02 \text{ eV} \)
C. electron is in second excited state
D. The ground state energy of hydrogen atom is 13.6 eV
Choose the correct answer from the options given below:

A current element \(\Delta \vec{l}=\Delta x \hat{i}\) (where \(\Delta x=1 cm\) ) is placed at the origin and carries a current 10 A . The magnetic field on y -axis at a distance of 0.5 m is :

Two point charges \( q_1 = 10 \times 10^{-8} \text{ C} \) and \( q_2 = -2 \times 10^{-8} \text{ C} \) are separated by a distance of 6 cm. The distance from \( q_1 \) where the electric potential is zero, can be

Arrange the following electromagnetic waves in decreasing order of their wavelength respectively.
A. Gamma Rays
B. UV Rays
C. Infrared Rays
D. X-Rays
E. Microwaves
Choose the correct answer from the options given below:

Which of the following represents Ohm's law for a conducting material?

Which of the following statement is NOT true, when two capacitors charged to different potential are connected in parallel by a conducting wire ?

A particle moves along the curve \(6 y=x^3+2\). The point(s) on the curve at which the \(y\)-coordinate is changing 8 times as fast as the \(x\)-coordinate are:

The function of the soft iron core in the moving coil galvanometer is:

Given that at x = 1, the function \(x^4-62 x^2+a x+90\) attains its maximum value on the interval [0, 2], the value of a is:

Evaluate \(\int_1^{\sqrt{3}} \frac{1}{1+x^2} d x\)

Microbes in human welfare Microbes are a very important component of life on earth. we use microbes and microbially derived products almost every day, like LAB to make curd, yeast to make bread, adding flavor and texture to cheese, producing antibiotics etc. The addition of LAB, improves the milk quality by increasing vit. B12. Cheese is one of the oldest food items in which microbes are used. For example, large holes in Swiss cheese are due to CO2 produced by the bacterium Propionibacterium sharmanii. The BOD test measures the rate of uptake of oxygen by microorganisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water. The greater the BOD of waste water, the more is its polluting potential. In anaerobic sludge digesters, bacteria produce a mixture of gases like methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as a source of energy. Biofertilisers are organisms that enrich the nutrient quality of the soil. The main sources of biofertilisers are bacteria, fungi and cyanobacteria. You have studied about the nodules on the roots of leguminous plants formed by the symbiotic association of Rhizobium. These bacteria fix atmospheric nitrogen into organic forms, which is used by the plant as a nutrient. Other bacteria can fix atmospheric nitrogen while free-living in the soil (examples Azospirillum and Azotobacter).
The large holes in Swiss cheese are generated by-

If \(\left[\begin{array}{cc}2 x+1 & 5 x \\ 0 & y^2+1\end{array}\right]=\left[\begin{array}{cc}x+3 & 10 \\ 0 & 26\end{array}\right]\), then the value of (x + y) is :