Probability that a man speaks truth is \(\frac{3}{4}\). He throws a die and reports that it is a six. The probability that it is actually a

Two numbers are selected without replacement at random, one at a time from the first six positive integers. Let x denotes the larger of the two numbers. Match List-I with List-II

List-I	List-II
(A) \(P(x=2)\)	(I) \(\frac{4}{15}\)
(B) \(P(x=3)\)	(II) \(\frac{1}{15}\)
(C) \(P(x=4)\)	(III) \(\frac{2}{15}\)
(D) \(P(x=5)\)	(IV) \(\frac{1}{5}\)

Choose the correct answer from the options given below:

The probability that A hits a target is \(\frac{1}{5}\) and the probability that B hits it is \(\frac{2}{3}\) The probability that the target will be hit if both A and B shoot at it independently is:

For \(x \in[-1,1]\), if \(4 \sin ^{-1} x+\cos ^{-1} x=\pi\) then \(x\) is equal to :

Which of the following statements are true?
(A) The vector joining the points P(2, 3, 0) Q(- 1, - 2, - 4) directed from P to Q is \(\overrightarrow{P Q}\) = - 3i - 5j - 4k
(B) Projection of a vector vec a on other vector \(\vec{b}\) is \(\frac{\vec{a} \cdot \vec{b}}{|\vec{a}|}\)
(C) If \(\vec{a}=i-2 j+k\) and \(\vec{b}=-2 i+4 j+5 k\) then \(\vec{a}+\vec{b}=-i+2 j+6 k\)
(D) If \(\theta\) is the angle between \(\vec{a}\) and \(\vec{b}\) \(\cos \theta=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}\)
Choose the correct answer from the options given below:

A 95% confidence interval for a population mean was reported to be 152 to 160. If the standard deviation \(\sigma=15\), then the sample size is (given \(Z_{0.025}=1.96\) ) :

For the function \(f(x)=2 x^3-3 x^2-12 x+5\), the difference of maximum and minimum value of \(f(x)\) is

\(\left[ Ag \left( NH _3\right)_2\right] OH\) forms silver when it reacts with:

When the electron in a hydrogen atom jumps from the 2nd orbit to the 1st orbit, the wavelength of the radiation emitted is \(\lambda\).
When the electron jumps from the 3rd orbit to the 1st orbit, the wavelength of emitted radiation is:

Read the passage carefully and answer the questions
Carbohydrates are naturally formed organic compounds from various plants. The common chemical formula, \(C _x\left( H _2 O \right)_y\), was considered as hydrates of carbon to derive the various carbohydrates. For instance, the general formula for glucose ( \(C _6 H _{12} O _6\) ) easily fits into the above formula. Carbohydrates also called saccharides are classified on the basis of their behavior towards hydrolysis. Monosaccharides cannot be hydrolyzed further to simpler units of polyhydroxy aldehyde or ketones. About 20 monosaccharides are known to occur in nature. Carbohydrates that yield large number of monosaccharide units are called polysaccharides. Amino acids contain ( \(- NH _2\) ) and ( - COOH ), which can be classified in various forms. Proteins are polymers of alpha amino acids which are connected to each other by a peptide bond or peptide linkage. When a native protein is subjected to physical change, its globules unfold and helix get uncoiled and the protein loses its biological activity. The protein is said to be denaturated.
The peptide linkage formed between the reaction of glycine and alanine is represented as

Which of the following will increase the mobility of charge carriers?

Read the following passage carefully and answer the given questions.
Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans (tobacco budworm, armyworm), coleopterans (beetles) and dipterans (flies, mosquitoes). B. thuringiensis forms protein crystals during a particular phase of their growth. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (a-1-antitrypsin) used to treat emphysema. In 1997, the first transgenic cow, Rosie, produced human protein-enriched milk (2.4 grams per litre). The milk contained the human alpha-lactalbumin and was nutritionally a more balanced product for human babies than natural cow-milk. A nematode Meloidegyne incognitia infects the roots of tobacco plants and causes a great reduction in yield. A novel strategy was adopted to prevent this infestation which was based on the process of RNA interference (RNAi). This method involves silencing of a specific mRNA due to a complementary dsRNA molecule that binds to and prevents translation of the mRNA (silencing). Biopiracy is the term used to refer to the use of bio-resources by multinational companies and other organisations without proper authorisation from the countries and people concerned without compensatory payment. ELISA is based on the principle of antigen-antibody interaction. Infection by pathogen can be detected by the presence of antigens (proteins, glycoproteins, etc.) or by detecting the antibodies synthesised against the pathogen.
mRNA silencing through RNA interference (RNAi) refers to the:

If \(x, y, z\) are all distinct and \(\left|\begin{array}{lll}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3\end{array}\right|=0\), then the value of \(x y z\) is :