The area (in sq. units) of the region bounded by the curve \(y=\sqrt{16-x^2}\) and x-axis is

If \(f(x)=2 x^3-15 x^2+36 x+1, x \in[1,5]\), then the absolute minimum value of \(f(x)\) is:

Let \(A, B, C, D\) and \(E\) be matrices of \(2 \times n, 3 \times k, 2 \times p\),
\(2 \times p\) and \(3 \times 3\) respectively.
Choose the correct statement(s) from the following :
(A) \(E B+D B\) will be defined if \(k=3, p=n\).
(B) \(E(3 \times 3) \cdot B(3 \times k) \rightarrow(3 \times k) \rightarrow n \times 3\).
(C) If \(n=p=2\), then the order of the matrix \(5 A^2-3 C\) is \(2 \times 2\).
(D) If \(n=p\), then the order of the matrix \(5 A^2-3 C\) is \(2 \times 3\).
Choose the correct answer from the options given below :

The value of \(\left|\begin{array}{lll}2^x & 1 & 6^x \\ 4^x & 1 & 3^x \\ 2^x & 1 & 6^x\end{array}\right|\), where \(x \neq 0 ;\) is:

Which of the following are correct?
(A) The function \(f(x)=3 x+12\) is increasing on \(R\).
(B) The function \(f(x)=e^{2 x}\) is decreasing on \(R\).
(C) The function \(f(x)=x^2-x+1\) is neither increasing nor decreasing on \((-1,1)\).
(D) The function \(f(x)=x^3-3 x^2+4 x\) is increasing on \(R\).
Choose the correct answer from the options given below :

If \(\vec{a}\) and \(\vec{b}\) represent the diagonals of a square, then

The curve \(x=y^2\) and \(x y=k\) cut orthogonally, then \(k^2\) is equal to :

Read the following passage given below and answer the question.
Aldehydes and ketones undergo nucleophilic addition reactions. A nucleophile attacks the electrophilic carbon atom of polar carbonyl group from perpendicular to plane of \(sp^2\) hybridised orbitals of carbonyl carbon. The hybridisation of carbon changes from \(sp^2\) to \(sp^3\) and a tetrahedral alkoxide intermediate is formed. This captures \(H^+\) to give neutral product. In carboxylic acids, carbonyl carbon is less electrophilic than carbonyl carbon in aldehydes and ketones.
An organic compound \(C_3H_6O\) does not give a precipitate with 2,4-dinitrophenylhydrazine and also does not react with metallic sodium. It could be :

A p-type semiconductor can be obtained by adding

The equation of the tangent line to \(y=2 x^2+7\) , which is parallel to the line \(4 x-y+3=0\) is

Read the passage carefully to answer the questions given below
Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans (tobacco budworm, armyworm), coleopterans (beetles) and dipterans (flies, mosquitoes). In Bacillus thuringiensis the toxin is coded by a gene crylAc named cry. There are a number of them, for example, the proteins encoded by the genes crylAc and cryllAb control the cotton bollworms, that of crylAb controls corn borer. Using conventional methods of diagnosis (serum and urine analysis, etc.) early detection is not possible. Recombinant DNA technology, Polymerase Chain Reaction (PCR) and Enzyme Linked Immuno-sorbent Assay (ELISA) are some of the techniques that serve the purpose of early diagnosis. The first clinical gene therapy was given in 1990 to a 4-year old girl with adenosine deaminase (ADA) deficiency. This enzyme is crucial for the immune system to function. The disorder is caused due to the deletion of the gene for adenosine deaminase. RNAi takes place in all eukaryotic organisms as a method of cellular defense. This method involves silencing of a specific mRNA due to a complementary dsRNA molecule that binds to and prevents translation of the mRNA.
RNAi involves involves silencing of a specific mRNA due to a complementary__________ molecule that binds to and prevents translation of the mRNA.

If the mean of Binomial distribution is 5 and Variance is 3 then the value of \(p\) (probability of success) is :

A charged particle with charge 0.01 C rotates on a circular path of radius 0.5 m , with velocity \(0.2 m / s\). What is the value of \(B\) at the center of the circle ?