The minimum value of the function \(f(x)=x^3+(10-x)^3\) occurs at :

\(\text{If} A \text{ and } B \text{ are independent events with }P(A)=0.8 \text{ and } P(B)=0.4,\text{ then the value of } P(A\cup B) \text{ is: \)

The lines \(\frac{x}{1}=\frac{y}{2}=\frac{z}{3}\) and \(\frac{x-3}{-3}=\frac{y-4}{-6}=\frac{z-5}{-9}\) are :

Number of defective bulbs in a lot of 500 bulbs follows a binomial distribution with probability of a randomly selected bulb to be defective equal to 0.3.
A sample of 50 bulbs is drawn. Probability of 2 defective bulbs in the sample is:

The domain of the function \(\cos ^{-1}(2 x-3)\) is

The minimum value of \(\left|\begin{array}{ccc}2 & 2 & 2 \\ 2 & 2+x & 2 \\ 2 & 2 & 2+x\end{array}\right|, x \in R\) is

A unit vector perpendicular to the vectors \(\hat{i}-\hat{j}\) and \(\hat{i}+\hat{j}\) is

Read the passage carefully and answer the Questions
Haloalkanes undergo nucelophilic substitution reactions owing to the polarity of CX bond. The nucleophile reacts with the haloalkane on the carbon possessing a partial positive charge holding the halogen atom. The halogen atom X is replaced by a nucleophile. Depending on the kinetics and mode of bond breaking, the mechanism can be either SN1 or SN2 reaction. The rate of SN1 reaction is governed by the stability of carbocation and in SN2 reaction, the rate of reaction is governed by steric factor. Chirality is the main factor in both SN1and SN2. In SN1 reaction, the chirality of alkyl halide is accompanied by racemization of the product, while in SN2 reaction, the product is characterized by inversion of configuration. The structure of alkyl halide and the nature of the solvent also governs the mechanism of the substitution.
Hydrolysis of 2-Chlorobutane will result in formation of

Which isomerism is shown by the following pairs ?
\(CH_3CH_2CH_2OH\) and \(CH_3CH_2OCH_3\)

In an intrinsic semiconductor at room temperature ;

Which of the following can be prepared from Sandmeyer's reaction?
(A) Chlorobenzene
(B) Bromobenzene
(C) lodobenzene
(D) Fluorobenzene
Choose the correct answer from the options given below:

A motorbike costing Rs. 1, 25, 000 has a scrap value of Rs. 25, 000.
If the annual depreciation charge is Rs. 12, 500, then the useful life of the bike is (by using linear method):

Read the following passage carefully and answer the given questions. During anaerobic sludge digestion, bacteria produce a mixture of gases such as methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as source of energy as it is inflammable. The bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. You must have noticed that bottled fruit juices bought from the market are clearer as compared to those made at home. This is because the bottled juices are clarified by the use of pectinases and proteases. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. 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.
During anaerobic sludge digestion, bacteria produce the biogas. The composition of this biogas is -