The value of c in Rolle's theorem for the function \(f(x)=x^3-3 x\) in the interval \([0, \sqrt{3}]\) is :

Consider the following test:
\(H _0: \mu \leq 12\)
\(H _{ a }: \mu>12\)
A sample of 36 provided a sample mean \(\bar{x}\) = 16 and a sample standard deviation S = 4.2 Then the value of the t-test statistic is:

A steamer can row at the speed of 16 km/hr in still water. If the river is flowing at 8 km/hr and it takes 12 hours for a round trip, then the distance between the two places is :

The value of the integral \(\int_2^4 \frac{x}{x^2+1} d x\) is :

If \(y=\log _e\left(\frac{e^2}{x^2}\right)\) for \(x \neq 0\), then \(\frac{d^2 y}{d x^2}\) equals

The value of the determinant \(\left|\begin{array}{ccc}a+b & b+c & c+a \\ c & a & b \\ 1 & 1 & 1\end{array}\right|\) is :

If the elementary column transformation \(C_1 \rightarrow 2 C_1\) is carried out on the following matrix equation.
\(\left[\begin{array}{ll}1 & 3 \\ 2 & 4\end{array}\right]\left[\begin{array}{cc}-1 & 2 \\ 5 & 0\end{array}\right]=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\) Then the transformed equation will be:

An equiconvex lens has a focal length of 20 cm and its radius of curvature is 30 cm. Its refractive index is

Area of a rectangle having vertices A, B, C, D with position vectors \(-\hat{i} + \frac{1}{2}\hat{j} + 4\hat{k}, \hat{i} + \frac{1}{2}\hat{j} + 4\hat{k}, \hat{i} - \frac{1}{2}\hat{j} + 4\hat{k}\) and \(-\hat{i} - \frac{1}{2}\hat{j} + 4\hat{k}\) respectively is:

Match List I with List II

LIST I	LIST II
A. Alec Jeffreys	I. Operon model
B. Jacob and Monod	II. X-ray diffraction data of DNA
C. Erwin Chargaff	III. DNA Fingerprinting
D. Wilkins and Franklin	IV. (A+G)/(T+C)=1

Choose the correct answer from the options given below:

What is the full form of ELISA ?

Read the given passage carefully and answer the questions
Salmonella typhi is a pathogenic bacterium which causes typhoid fever in human beings. Sustained high fever (39° to 40°C), weakness, stomach pain, constipation, headache and loss of appetite are some of the common symptoms of this disease. Typhoid fever could be confirmed by Widal test. Plasmodium enters the human body as sporozoites. The parasites initially multiply within the liver cells and then attack the red blood cells (RBCs) resulting in their rupture. The rupture of RBCs is associated with release of a toxic substance, haemozoin, which is responsible for the chill and high fever recurring every three to four days. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa-associated lymphoid tissue (MALT). In our body, cell growth and differentiation is highly controlled and regulated. In cancer cells, there is breakdown of regulatory mechanisms. Normal cells show a property called contact inhibition by virtue of which contact with other cells inhibits their uncontrolled growth. Cancerous cells just continue to divide giving rise to masses of cells called tumors. Tumors are of two types: benign and malignant. Cannabinoids are a group of chemicals, which interact with cannabinoid receptors present principally in the brain. Generally taken by inhalation and oral ingestion, these are known for their effects on cardiovascular system of the body.
Which one of the following statements is not true?

Read the following passage carefully and answer the given questions.
Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans (tobacco budworm, armyworm), coleopterans (beetles) and dipterans (flies, mosquitoes). B. thuringiensis forms protein crystals during a particular phase of their growth. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (a-1-antitrypsin) used to treat emphysema. In 1997, the first transgenic cow, Rosie, produced human protein-enriched milk (2.4 grams per litre). The milk contained the human alpha-lactalbumin and was nutritionally a more balanced product for human babies than natural cow-milk. A nematode Meloidegyne incognitia infects the roots of tobacco plants and causes a great reduction in yield. A novel strategy was adopted to prevent this infestation which was based on the process of RNA interference (RNAi). This method involves silencing of a specific mRNA due to a complementary dsRNA molecule that binds to and prevents translation of the mRNA (silencing). Biopiracy is the term used to refer to the use of bio-resources by multinational companies and other organisations without proper authorisation from the countries and people concerned without compensatory payment. ELISA is based on the principle of antigen-antibody interaction. Infection by pathogen can be detected by the presence of antigens (proteins, glycoproteins, etc.) or by detecting the antibodies synthesised against the pathogen.
Some strains of Bacillus thuringiensis produce proteins that do not kill certain arthropods, such as: