If \(0<2 x<1\), which of the following is smallest?

The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is :

The water and milk in two vessels are in the ratio 1:1 and 3: 8 respectively. In what ratio, the mixtures in the vessels be mixed to obtain a new mixture containing water and milk in the ratio 4 : 7?

If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0},|\vec{a}|=7,|\vec{b}|=3\) and \(|\vec{c}|=5\), then angle between \(\vec{b}\) and \(\vec{c}\) is

Which of the following is not correct about the Compound Annual Growth Rate (CAGR)?

The random variable \(X\) can take values 0, 1, 2 . If \(P(X=0)=P(X=1)=\alpha\), and \(E\left(X^2\right)=E(X)\), then which of the following are correct?
\(E(X)=2-3 \alpha\)
\(E\left(X^2\right)=4+7 \alpha\)
\(\alpha=\frac{1}{2}\)
\(\alpha=\frac{1}{5}\)
Choose the correct answer from the options given below :

If \(A=\left[\begin{array}{ll}x & 3 \\ 2 & y\end{array}\right], \quad B=\left[\begin{array}{cc}2 y & 1 \\ 3 & x\end{array}\right]\) and \(A+2 B=\left[\begin{array}{cc}6 & 5 \\ 8 & -2\end{array}\right]\), then the value of \((x, y)\) is:

Read the Passage carefully and answer the the questions
The DNA fragments can be separated by a technique known as gel electrophoresis. Since DNA fragments are negatively charged molecules, they can be separated by forcing them to move towards the anode under an electric field through a medium/matrix. The separated DNA fragments can be visualised only after staining the DNA with a compound known as ethidium bromide followed by exposure to UV radiation. The repeated amplification of DNA is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermus aquaticus). After completion of the biosynthetic stage, the product has to be subjected through a series of processes before it is ready for marketing as a finished product. The downstream processing and quality control testing vary from product to product. The convention for naming restriction enzymes is the first letter of the name comes from the genus and the second two letters come from the species of the prokaryotic cell from which they were isolated.
The thermostable DNA polymerase is isolated from -

In the depletion layer of a reverse biased p-n junction, the :

The reaction in which an amide is treated with bromine in presence of ethanolic solution of sodium hydroxide is called

If \(P, Q\) and \(R\) are matrices of order \(2 \times 3,3 \times 5\) and \(5 \times 3\) respectively. Then which of the following are valid?
(A) \(P Q R\)
(B) \(P R Q\)
(C) \(Q R\)
(D) \(R Q\)
(E) \(P R\)
Choose the correct answer from the options given below :

If \(y=\log _e\left(\sec \left(e^{x^2}\right)\right)\), then \(\frac{d y}{d x}=\)

Arrange the following reactions in increasing order of the value of the ratio of rate constants \(\left(\frac{k_{310}}{k_{300}}\right)\)
\((A): A + B \rightarrow C , E_g=70 kJ mol ^{-1}\)
(B) : \(P + Q \rightarrow R , E_g=45 kJ mol ^{-1}\)
\((C): G + H \rightarrow I , E_g=95 kJ mol ^{-1}\)
(D): \(X + Y \rightarrow Z , E_g=100 kJ mol ^{-1}\)
Choose the correct answer from the options given below :