Two cards are drawn simultaneously from a well shuffled pack of 52 cards. Then variance of the number of kings is:

The value of \(\lambda\) when the projection of \(\vec{a}=\lambda \hat{i}+\hat{j}+2 \sqrt{5} \hat{k}\) on \(\vec{b}=2 \hat{i}+4 \hat{j}+\sqrt{5} \hat{k}\) is 6 , is :

Let \(A, B, C, D\) and \(E\) be matrices of \(2 \times n, 3 \times k, 2 \times p\),
\(2 \times p\) and \(3 \times 3\) respectively.
Choose the correct statement(s) from the following :
(A) \(E B+D B\) will be defined if \(k=3, p=n\).
(B) \(E(3 \times 3) \cdot B(3 \times k) \rightarrow(3 \times k) \rightarrow n \times 3\).
(C) If \(n=p=2\), then the order of the matrix \(5 A^2-3 C\) is \(2 \times 2\).
(D) If \(n=p\), then the order of the matrix \(5 A^2-3 C\) is \(2 \times 3\).
Choose the correct answer from the options given below :

One person speaks truth in \(60 \%\) of the cases and another person in \(80 \%\) of the cases. They are likely to agree in stating the same fact in:

If the line drawn from the point (-2, -3, -4) meets a plane at right angle at the point (1, -2, 4), then equation of plane is:

The random variable X can take only the values 0, 1, 2. Given that \(P(X = 0) = P(X = 1) = p\) and \(E(X^2) = E(X) + 1\), then the value of p is:

The speed of a motorboat in still water and that of the current of water is in a ratio of \(27: 5\).
The boat goes along the current from point \(A\) to point \(B\) in 3 hours 40 minutes.
How much time will it take to come back from \(B\) to \(A\)?

Which of the following statements with reference to a solution are correct?
(A) the molarity of the solution changes with the change in the temperature.
(B) the volume of the solution changes with the change in the temperature.
(C) the molality of the solution changes with the change in the temperature.
(D) the normality of the solution changes with the change in the temperature.
Choose the correct answer from the options given below:

Clarias gariepinus, the African catfish is an example of

Match List-I (vitamin) with List-II (deficiency disease)

List-l (Vitamin)	List-II (Deficiency disease)
(A) Thiamine	(I) Convulsions
(B) Pyridoxine	(II) Cheilosis
(C) Vitamin E	(III) Retarded Growth
(D) Riboflavin	(IV) Muscular weakness

Choose the correct answer from the options given below :

Read the passage carefully and answer the questions
Biomolecules are the organic compounds present as an essential constituents of living organisms in different cells.Themolecules are generally termed as macromolecules, which are carbohydrates, enzymes, nucleic acids, amino acids andproteins etc. Carbohydrates are classified as sugars and non-sugars include sucrose, glucose, fructose, starch and cellulose. Enzymes are coordinated with various chemical reactions in nucleic acid. Nucleic acids are found in living organisms made up of proteins and natural polymers. Two types that are generally found in biological systems are DNA and RNA nucleic acid. Amino acids are bifunctional groups of carboxyl and amino groups. Proteins are a class of biologically important compounds. They are crucial to virtually all processes in living systems. Some of them are hormones, which serve as chemical messengers that coordinate certain biochemical activities.
Cane sugar on boiling with HCI or \(\ H_2SO_4\) hydrolysis yields

When a transistor is used as an Amplifier, the phase difference between the input and the output signal voltage is

A cell of constant emf is first connected to a resistance \( R_1 \) and then connected to a resistance \( R_2 \). If power delivered in both cases is same, then the internal resistance of the cell is