The angle between the line \(2 x=3 y=z\) and \(x\) - axis is :

Two nuclei with mass numbers A and B have density ratios of :

In the context of linear programming, Match List I with List II

List - I	List - II
(A) Z = 250x +75y	I. non-trivial constraints
(B) \(5 x+y \leq 100, x-y \leq 4\)	II. feasible solution
(C) \(x, y \geq 0\)	III. objective function
(D) points within and on the boundary of shaded region	IV. Trivial constraints

The maximum value of \(z=4 x+3 y\) subject to constraint \(x+y \leq 6, x, y \geq 0\) is:

If \(A=\left[\begin{array}{ll}5 & 2 \\ 4 & 3\end{array}\right]\) is a given matrix, then which statements are correct?
(A) \(|A|=7\)
(B) minor of \(3=-5\)
(C) co-factor of \(2=-4\)
(D) \(\operatorname{adj}(A)=\left[\begin{array}{cc}3 & -2 \\ -4 & 5\end{array}\right]\)

For which values of \(a, f(x)=a(x+\sin x)\) is an increasing function?

The system of equations
\(\begin{array}{l}x+y+z=4 \\x+2 y+3 z=12 \\x+3 y+\lambda z=\mu\end{array}\)
has a unique solution if

A bridge circuit is shown in the diagram. The equivalent resistance between A and B is

A piece of silver and another of silicon are cooled from 15 ℃ to 3 ℃. What will be the effect on resistance of each?

Current is a__________ quantity and it's SI unit is__________.

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).
In anaerobic sludge digesters, the biogas produced by the bacteria, is composed of -

Hybridization of carbon atoms attached with halogens in haloalkanes \\& haloarenes are

A proton is projected with a speed of \( v = 4 \times 10^6 \text{ m s}^{-1} \) horizontally from east to west. A uniform magnetic field \( \vec{B} \) of strength \( B = 1.5 \times 10^{-3} \text{ T} \) exists in the vertically upward direction. What is the acceleration produced? (Use charge on the proton \( q = 1.6 \times 10^{-19} \text{ C} \) and mass of the proton \( m = 1.67 \times 10^{-27} \text{ kg} \))