If \(\hat{i}, \hat{j}\) and \(\hat{k}\) are unit vectors along the co-ordinate axes OX, OY and OZ respectively, then
(A) \(\hat{i} \times \hat{j}=\hat{k}\)
(B) \(\hat{k} \times \hat{i}=-\hat{j}\)
(C) \(\hat{j} \cdot \hat{j}=1\)
(D) \(\hat{j} \cdot \hat{k}=0\)
Choose the \{correct} answer from the options given below:

If a sample has \(n\) observations \(x_1, x_2, \ldots, x_n\) with \(m\) constraints on these values, then the degree of freedom of the sample statistic is:

If \(y=7 \sqrt{x}+3 e^x\), then \(\frac{d^2 y}{d x^2}\) is :

The solution of the differential equation \(\frac{d r}{d t}=-r t, r(0)=r_0\) is

The value of \(\lambda\), so that the lines \(\frac{1-x}{3}=\frac{7 y-14}{2 \lambda}=\frac{z-3}{2}\) and \(\frac{7-7 x}{3 \lambda}=\frac{y-5}{1}=\frac{6-z}{5}\) are perpendicular is:

The area (in sq. units) of the region bounded by the curve \(x^2 = 250y, y = 0\) and \(x = 50\) is

Match List - I with List - II

List - I (Matrix/Equations)	List - II (Values)
(A) \(\left[\begin{array}{cc}2 x+1 & 3 y \\ 0 & y^2-5 y\end{array}\right]=\left[\begin{array}{cc}x+3 & y^2+2 \\ 0 & -6\end{array}\right]\)	(I) \(x = 2, y = - 1\)
(B) \(\left[\begin{array}{ccc}1 & 2 & -1 \\ x & 0 & 3 \\ y & 3 & 4\end{array}\right]\) is symmetric	(II) \(x = 2, y = 2\)
(C) \(\left[\begin{array}{ll}x & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -2 & -3\end{array}\right]\left[\begin{array}{ll}5 & 2 \\ 0 & y\end{array}\right]=0\)	(III) \(x = - 2, y = 2\)
(D) \(\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]=\left[\begin{array}{cc}4 & 0 \\ -1 & y / 2\end{array}\right]\)	(IV) \(x = 2, y = 0\)

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The capacity to generate a whole plant from any cell is called:

A parallel plate air capacitor consists of two circular plates of diameter 4 cm. At what distance should the plates be held so as to have the same capacitance as that of a sphere of diameter 16 cm?

Choose the statements that are valid for the molecularity of a reaction
(A) Molecularity is equal to the number of reacting species involved in the overall reaction
(B) Decomposition of ammonium nitrite is an example of unimolecular reaction
(C) Reactions with the molecularity three are very rare
(D) Molecularity can only be determined experimentally
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Read the passage carefully and answer the questions
Optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis are called carbohydrates. They can be broadly classified as monosaccharides, disaccharides and polysaccharides depending on their behavior towards hydrolysis. They are also classified as reducing or non-reducing sugars. Another class of biomolecules is proteins which are polymers of twenty different amino acids linked by peptide bonds. Amino acids can be classified as acidic, basic or neutral depending on the relative number of amino and carboxyl groups in their molecule. The essential amino acids cannot be synthesized by our body and hence must be provided through diet. Nucleic acids are the polymers of nucleotides which in turn consist of a base, pentose sugar and phosphate. There are two types of nucleic acids namely, DNA and RNA which differ in the composition of sugar and a base
The sugar moiety in DNA and RNA molecules, respectively, ar

If 4 individuals in a laboratory population of 40 fruitflies died during a specified time interval, say a week, the death rate in the population during that period is -

Which of the following statements are incorrect?
(A) Fragments of DNA can be separated by ELISA.
(B) Transformation is a procedure through which a piece of DNA is introduced in a host bacterium.
(C) Recombinant DNA technology does not involve isolation of a desired DNA fragment.
(D) DNA ligases are used for stitching DNA fragments into a vector.
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