Let \(|\vec{a}|=5,|\vec{b}|=2\) and \(\vec{a} \cdot \vec{b}=6\), then the value of \(|\vec{a} \times \vec{b}|\) is equal to

Match List-l with List-ll
Where \(R\) is set of real numbers

List-l	List-ll
(A) \(f: R \rightarrow R\) s.t \(f(x)=x^4\) is	(I) one-one, Into
(B) \(f: R \rightarrow[0, \infty)\) s.t \(f(x)=x^4\) is	(II) many-one, into
(C) \(f:[0, \infty) \rightarrow R\) s.t \(f(x)=x^4\) is	(III) one-one, onto
(D) \(f:[0, \infty) \rightarrow[0, \infty)\) s.t \(f(x)=x^4\) is	(IV) many-one, onto

Choose the correct answer from the options given below :

Which of the following is a correct statement?

A boat can row at the speed of \(16 km / hr\) in still water. If the river is flowing at \(8 km / hr\), and it takes 8 hours for a round trip, then the distance between the two places is :

A company purchased a machine for ₹ 15,00,000 and its effective life is estimated to be 10 years. A sinking fund is created for replacing the machine at the end of its effective life when its scrap value is ₹ \(2,42,000\). What amount company should provide at the end of every year out of profits for the sinking fund if it accumulates an interest of \(5 \%\) per annum? [Given: \((1.05)^{10}=1.629\)]

If \(\left[\begin{array}{lll}1 & 2 & 1\end{array}\right]\left[\begin{array}{lll}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2\end{array}\right]\left[\begin{array}{l}0 \\ 2 \\ x\end{array}\right]=0\), then value of x is

Area of the region bounded by the curve \(x^2=4 y, x\)-axis and \(x=3\) 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).
Identify, the free living bacteria in soil, which can fix the atmospheric nitrogen.

Which of the following material takes longer time for decomposition?

In Freundlich adsorption isotherm, the value of \(1/\text{n}\) is:

Which one of the followings cells are attacked by HIV?

The equation of the normal to the curve \(y=2 \sin x\) at \((0,0)\) is:

The slope of the normal to the curve \(y=2 x^2\) at \(x=1\) is: