A coin is biased so that head is 4 times as likely to occur as tails. If X represents the number of heads when coin is tossed 4 times then \(P(X=2)\) is equal to:

The matrix \(X\) in the equation \(A X=B\), such that \(A=\left[\begin{array}{ll}1 & 3 \\ 0 & 2\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right]\) is given by

The slope of tangent on the curve \(y=6 x^2-x-12\), at the point where curve meets positive \(x\)-axis is ___________ .

The function \(f(x)=x^x\) has a critical point at :

Two persons A and B throw a die alternately till one of them gets a six and wins the game. If A begins, then the probabilities of winning of A and B respectively are

\(\int x^2 \tan ^{-1} x d x\)=

If it is 7:00 pm currently in the clock, what will the clock show (in am or pm) after 674 hours?

Answer the question on basis of passage given below
The noble gases have closed shell electronic configuration and are monatomic gases under normal conditions. The low boiling points of lighter noble gases are due to the weak dispersion forces between the atoms and the absence of other inter atomic interaction. The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers \(+2, +4\) and \(+6\).
\(\text{XeF}_4\) reacts violently with water to give \(\text{XeO}_3\). The compound of Xenon exhibit stereoisomerism and their geometries can be deduced considering the total number of electrons in the valence shell.
Which noble gas is generally used in illuminating warning signals?

Choose the correct option, which explains the term alleles.

Threatened animals and plants are taken out from their natural habitat and placed in special settings, protected and given special care is.

Which of the following statements are correct about restriction enzymes?
(A). Each restriction endonuclease recognizes a specific palindromic nucleotide sequence in the DNA.
(B). Endonuclease removes nucleotides from the terminal end of the DNA.
(C). The first discovered restriction endonuclease is Hind II.
(D). Restriction enzymes belong to a larger class of enzyme polymerase.
Choose the correct answer from the options given below:

The smaller area between the ellipse \(\frac{x^2}{4}+\frac{y^2}{36}=1\) and the line \(\frac{x}{2}+\frac{y}{6}=1\) is given by:

If A and B are two matrices of order \(4 \times m\) and \(4 \times n\), respectively and \(m=n\),
then the order of matrix \((5 A-2 B)\) is: