A coin is biased so that the head is three times as likely to occur as tail. If the coin is tossed twice, the mean of the number of tails is:

The area of the region bounded by the lines x = 2y + 3, x = 0, y = 1 and y = - 1 is:

The area of the region bounded by the parabola \(y^2=8 x\) and its latus rectum in the first quadrant, is

\(\int \frac{\sin 2 x d x}{\sqrt{9-\cos ^4 x}}\) equals

The number of all possible matrices of order 2 × 2 with each entry 0 or 1 is:

If \(A\) and \(B\) are invertible matrices of same order, then which one of the following is NOT true?

The value of the determinant \(\left|\begin{array}{cc}a \cos \theta & a \sin \theta \\ -a \sin \theta & a \cos \theta\end{array}\right|\) is:

During denaturation of proteins which structure of proteins remain intact?

The relation \(R\) in the set \(\{1,2,3\}\) given by \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3)\}\) is:

Arrange the following events of human embryo development in a correct sequence:
(A) Blastocyst formation
(B) Implantation
(C) Formation of morula
(D) Cleavage in zygote
Choose the correct answer from the options given below:

Read the following paragraph and answer the given questions.
Repeated amplification is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermus aquaticus), which remain active during the high temperature induced denaturation of double stranded DNA. 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 separated bands of DNA are cut out from the agarose gel and extracted from the gel piece. The convention for naming these 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, e.g., EcoRI comes from Escherichia coli RY 13. In EcoRI, the letter 'R' is derived from the name of strain. Roman numbers following the names indicate the order in which the enzymes were isolated from that strain of bacteria. Stanley Cohen and Herbert Boyer accomplished this in 1972 by isolating the antibiotic resistance gene by cutting out a piece of DNA from a plasmid which was responsible for conferring antibiotic resistance. Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA, RNA, protein, polysaccharides etc. The RNA can be removed by treatment with ribonuclease whereas proteins can be removed by treatment with protease. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol.

Stanley Cohen and Herbert Boyer constructed the first recombinant DNA by isolating the antibiotic resistance gene by cutting out a piece of DNA from a plasmid of ____________ resistance. which was responsible for conferring antibiotic

If \(x=a \sec ^3 \theta, y=a \tan ^3 \theta\) then \(\frac{d^2 y}{d x^2}\) equals.

In an LCR circuit, which of the following expression has the dimension of frequency :