The least non-negative remainder when \(2^{75}\) is divided by 5 will be:-

Which of the following are correct?
(A) For a square matrix \(A\), if \(A^3=I\), then \(A^{-1}=A^2\).
(B) The determinant of only a square matrix can be defined.
(C) If \(A\) is a square matrix of order 3 , then the number of minors of the matrix \(A\) is 3 .
(D) If \(A\) and \(B\) are two non-singular matrices of the same order, then \((A B)^{-1}=B^{-1} A^{-1}\).
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Evaluate \(\int_1^{\sqrt{3}} \frac{1}{1+x^2} d x\)

The probability distribution of number of heads in two tosses of a coin is:

If \(A\) is any event associated with sample space and If \(E_1, E_2, E_3\) are mutually exclusive and exhaustive events. Then which of the following are true?
(A) \(P(A)=P\left(E_1\right) P\left(E_1 \mid A\right)+P\left(E_2\right) P\left(E_2 \mid A\right)+P\left(E_3\right) P\left(E_3 \mid A\right)\)
(B) \(P(A)=P\left(A \mid E_1\right) P\left(E_1\right)+P\left(A \mid E_2\right) P\left(E_2\right)+P\left(A \mid E_3\right) P\left(E_3\right)\)
(C) \(P\left(E_i \mid A\right)=\frac{P\left(A \mid E_i\right) P\left(E_i\right)}{\sum_{i=1}^3 P\left(A \mid E_i\right) P\left(E_i\right)}, i=1,2,3\)
(D) \(P\left(A \mid E_i\right)=\frac{P\left(E_i \mid A\right) P\left(E_i\right)}{\sum_{i=1}^3 P\left(E_i \mid A\right) P\left(E_i\right)}, i=1,2,3\)
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Which of the following statements are correct?
(A) In the sinking fund a fixed amount at regular intervals is deposited.
(B) Sinking fund is a long-term account which can be closed any time.
(C) In a saving account, any amount, any time can be deposited.
(D) Sinking fund can be used only for the purpose it was created.
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Match List - I with List - II.

List - I	List - II
(A) The common region determined by all the constraints of LPP is called	(I) objective function
(B) Minimize \(z=c_1 x_1+c_2 x_2+\cdots+c_n x_n\) is	(II) convex set
(C) A solution that also satisfies the non-negative restrictions of a LPP is called	(III) feasible region
(D) The set of all feasible solutions of a LPP is a	(IV) feasible solution

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Match List-I with List-II

List-I (Solute)	List-II (Van't Hoff factor)
(A) Benzoic acid in benzene	(I) 3
(B) \(K _2 SO _4( aq )\)	(II) 2
(C) Urea (aq)	(III) 0.5
(D) \(KOH ( aq )\)	(IV) 1

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The density of a population in a given habitat during a given period, fluctuates due to changes in -
(A) Natality
(B) Immigration
(C) Emigration
(D) Mortality
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If light of wavelength 412.5 nm is incident on each of the metals given below, which ones will show photoelectric emission ?

Metal	Work Function (eV)
Na	1.92
K	2.15
Ca	3.20
Mo	4.17

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Two charged particles, placed at a distance d apart in vacuum, exert a force F on each other. Now, each of the charges is doubled. To keep the force unchanged, the distance between the charges should be changed to :

Which of the following reagents are used for denaturation of alcohol

Which of the following will exhibit only +3 oxidation state?