Let A = {1,2,3}.
The number of relations on A containing (1, 2) and (2, 3),
which is reflexive and transitive but not symmetric, is:

Minimum value of the function \(f(x) = \sin(3x) + 5\) is equal to :

Let \(y=\sin \left(\cos x^2\right)\), then the value of \(\frac{d y}{d x}\) at \(x=\frac{\sqrt{\pi}}{2}\) is equal to:

Value of \(\mu(20)+\sigma(20)\) is (where \(\mu(n)\) is the Mobius function and \(o(n)\) is the sum of all positive divisors of \(n\) )

If \(\vec{a}=2 \hat{i}-\hat{j}+3 \hat{k}\) and \(\vec{b}=2 \hat{i}+2 \hat{j}+\hat{k}\) then
Match List-I with List-II

List-I	List-II
(A) Projection of \(\vec{a}\) on \(\vec{b}\) is	(I) \(-7 \hat{i}+4 \hat{j}+6 \hat{k}\)
(B) \(\vec{a} \times \vec{b}\) is	(II) \(\frac{1}{\sqrt{101}}(-7 \hat{i}+4 \hat{j}+6 \hat{k})\)
(C) Unit vector along \(\vec{a}+\vec{b}\) is	(III) \(\frac{5}{3}\)
(D) Unit vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) is	(IV) \(\frac{1}{\sqrt{33}}(4 \hat{i}+\hat{j}+4 \hat{k})\)

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Three numbers are chosen at random without replacement from {1, 2, 3, 4, 5, 6, 7, 8}. The probability that their minimum is 3, (given that their maximum is 6)is:

If the matrix \(A=\left[\begin{array}{ccc}0 & x+y & 1 \\ 3 & z & 2 \\ x-y & -2 & 0\end{array}\right]\) is skew-symmetric, then:

Which of the following hormones are secreted by placenta during pregnancy?
(A) Human Chorionic Gonadotropin
(B) Human Placental Lactogen
(C) Progestogens
(D) Cortisol
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Match List I with List II

LIST I	LIST II
A. Soda Water	I. A solution of gas in gas
B. Sugar Solution	II. A solution of solid in solid
C. German Silver	III. A solution of solid in liquid
D. Air	IV. A solution of gas in liquid

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An ammeter should have very low resistance

Read the passage carefully and answer the given questions.
DNA Fingerprinting Polymorphism in DNA sequence is the basis of genetic mapping of the human genome as well as of DNA fingerprinting. DNA fingerprinting involves identification of differences in some specific regions in the DNA sequence called repetitive DNA. It works on the principle of polymorphisms in DNA sequences. The repetitive DNA are separated from bulk genomic DNA. The bulk DNA forms a major peak and the other small peaks are referred to as satellite DNA. These repetitive/satellite DNA sequences show a high degree of polymorphisms and form the basis of DNA fingerprinting.
DNA fingerprinting is meant for:

Arrange the given steps involved in Polymerase Chain Reaction in correct sequence?
(A) Annealing
(B) Extension
(C) Denaturation
(D) Amplification
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Match List - I with List - II.

List - I	List - II
(A) Mutualism	(I) Abingdon tortoise in Galapagos island and goat
(B) Commensalism	(II) Crow and Cuckoo
(C) Brood Parasitism	(III) Sea anemone and Clown fish
(D) Competition	(IV) Lichen

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