The rise and fall of share market is an example of

The vector equation of line passing through (2, -1, 3) and perpendicular to the lines \(\frac{x-2}{3}=\frac{y-1}{1}=\frac{z+2}{2} \quad\) and \(\quad \frac{x+3}{-4}=\frac{y-5}{-3}=\frac{z+1}{2}\)
(Here \(\lambda\) is a parameter)

If \(A=\left[\begin{array}{ccc}5 & 1 & 0 \\ 6 & 2 & -1\end{array}\right], B^T=\left[\begin{array}{cc}2 & 1 \\ -2 & 0 \\ 1 & 3\end{array}\right]\), then \(B A^T\) is :

The value of \(\tan ^2\left(\sec ^{-1} 2\right)+\cot ^2\left(\operatorname{cosec}^{-1} 3\right)\) in equal to

If \(\left|\begin{array}{ccc}-a^2 & a b & a c \\ a b & -b^2 & b c \\ a c & b c & -c^2\end{array}\right|=\lambda a^2 b^2 c^2\), then the value of \(\lambda\) is:

The value of \(\int_0^{\pi / 2} \log _e\left(\frac{5+2 \sin x}{5+2 \cos x}\right) d x\) is

Match List I with List II

(List I)	(List II)
A. \(\frac{d}{d x}\left(a^x\right)\)	\(I.\) \(0\)
B. \(\frac{d}{d x}\left(x^a\right)\)	\(II.\) \(x^x\left(1+\log _e x\right)\)
C. \(\frac{d}{d x}\left(a^a\right)\)	\(III.\) \(a x^{a-1}\)
D. \(\frac{d}{d x}\left(x^x\right)\)	\(IV.\) \(a^x \log _e a\)

Choose the correct answer from the options given below:

Read the passage carefully and answer the given questions.
Recombinant DNA Technology Asexual reproduction preserves the genetic information, while sexual reproduction permits variation. Traditional hybridization procedures used in plants and animals breeding very often lead to inclusion and multiplication of undesirable genes along with the desired genes. The techniques of genetic engineering, which include creation of recombinant DNA, use of gene cloning and gene transfer, overcome this limitation and allow us to isolate and introduce only one or a set of desirable genes without introducing genes into the target organism.
Which one of the following techniques is used to amplify a specific DNA sequence?

Read the given passage and answer the following questions:
Secondary treatment or biological treatment: The primary effluent is passed into large tanks where air is pumped into it. This allows vigorous growth of aerobic microbes. While growing, these microbes consume the major part of the organic matter in the effluent. This significantly change the BOD (biochemical oxygen demand) of the effluent. The effluent in then passed into a tank a small part of the sludge is pumped back into the aeration tank to serve as the inoculum. The remaining major part of the sludge is pumped into large tanks called sludge digesters. Here, other kinds of bacteria grow anaerobically in the sludge. The biogas produced can be used source of energy as it is inflammable. The effluent from the secondary treatment plant is generally released into natural water bodies like rivers and streams.
Which of the following gas is not produced in anaerobic digestion?

If the matrix \(\begin{bmatrix} 3 & a+b & 4 \\ 2 & 0 & -1 \\ a-b & c & 5 \end{bmatrix}\) is symmetric, then the value of a, b and c is given by:

The forbidden energy band gap in conductors, semi conductors and insulators are \( E_{G1}, E_{G2} \) and \( E_{G3} \), respectively. The relation among them is

Match List-l with List-II

List-l (Terms)	List-II (Features)
(A) Selectable marker	(I) Site that commonly used for cutting the DNA by restriction enzyme
(B) Origin of replication	(II) Removes nucleotides from the ends of the DNA
(C) Exonuclease	(III) Helps in identification and elimination of non- transformants
(D) Recognition site	(IV) The sequence responsible for controlling the copy number of linked DNA

Choose the correct answer from the options given below:

The angle between \(x\) axis and the vector \(\hat{i}+\hat{j}+\hat{k}\) is :