The value of integral \(\int_0^1 \sqrt{1-x^2} d x\) is :

If \(\alpha, \beta\) and \(\gamma\) are angle of inclinations of a line with \(x, y\) and \(z\) ares respectively, then the value of \(2(\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma)\) is

The value of \(\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)\) at \(x=\frac{1}{5}\) is

If \(x_1, x_2, x_3,\)........,\(x_n\) are \(n\) observations in a sample then which of following is/are TRUE?
(A) The mean \(\bar{x}\) has \(n\) degree of freedom
(B) The mean \(\bar{x}\) has ( \(n-1\) ) degree of freedom
(C) The standard deviation of the sample has ( \(n-1\) ) degree of freedom
(D) The standard deviation of the sample has \(n\) degree of freedom
Choose the correct answer from the options given below :

A measure of an average yearly growth of an investment over a certain time period when returns are reinvested is

The value of the definite integral \(I=\int_{-1}^1 \frac{1}{1+\sqrt{e^x}} d x\) is :

The value of \(C\) which satisfies Rolle's Theorem for \(f(x)=\sin ^4 x+\cos ^4 x\) in \(\left[0, \frac{\pi}{2}\right]\). Then \(C\) is :

Match List - I with List - II.

List - I	List - II
(A) Barrier methods	(I) Prevents physical contact between ovum and sperm
(B) IUD	(II) Sterilizes physical contact between ovum and sperm
(C) Oral Contraceptives	(III) Increases phagocytosis of sperms and suppress sperm motility:

Choose the correct answer from the options given below :

The Wheatstone bridge is an arrangement of four resistances \( R_1, R_2, R_3, R_4 \) as shown in the figure given below. The null-point condition is not given by:

Which of the following complexes are square planar?
(A) \(\left[ Ni ( CN )_4\right]^{2-}\)
(B) \(\left[ NiCl _4\right]^{2-}\)
(C) \(\left[ PtCl _4\right]^{2-}\)
(D) \(\left[ PdCl _4\right]^{2-}\)
Choose the correct answer from the options given below

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.
Steps in primary treatment does not include:

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 is not used as a vector in recombinant DNA technology?

If A is any non-zero square matrix, then the matrix \(P=\frac{1}{2}\left(A-A^T\right)\) is: