Match List-I with List-II

List - I	List - II
(A) \(\sin ^{-1}(-1)\)	(I) \(\frac{5 \pi}{6}\)
(B) \(\cot ^{-1}(-1)\)	(II) \(-\frac{\pi}{2}\)
(C) \(\sec ^{-1}\left(-\frac{2}{\sqrt{3}}\right)\)	(III) \(\frac{\pi}{4}\)
(D) \(\tan ^{-1}(1)\)	(IV) \(\frac{3 \pi}{4}\)

Choose the correct answer from the options given below :

Let \(x=t^2, y=t^3\). Then \(\frac{d^2 y}{d x^2}\) is equal to

Match List - I with List - II

List - I	List - II
(A) The number of possible matrices of order 3 × 3 with each entry 1 or 0	(I) \(2^4\)
(B) The number of possible matrices of order 2 × 3 with each entry 1 or 0	(II) \(2^9\)
(C) The number of possible matrices of order 2 × 3 with each entry 0, 1, 2	(III) \(2^6\)
(D) The number of possible matrices of order 2 × 2 with each entry 1 or 0	(IV) \(3^6\)

Choose the correct answer from the options given below:

A machine costing ₹1,00,000 has a useful life of 5 years. The estimated scrap value is ₹20,000.
Using straight line method, the annual depreciation is:

Ishita is rowing a boat. She takes 24 hours to row 72 km against the stream and she takes 9 hours to return to the starting point in the direction of the stream. The speed of the boat in still water is :

If \(\int_0^1 \frac{e^x}{1+x} d x=m\), then the value of \(\int_0^1 \frac{e^x}{(1+x)^2} d x\) is :

The particular solution of the differential equation \(\left\{x \sin ^2\left(\frac{y}{x}\right)-y\right\} d x+x d y=0, y=\frac{\pi}{4}\) when \(x=1\) is

If the frequency of light in a photoelectric experiment is doubled the stopping potential will be:

Which of the following pair of nuclides are Isobars?

Optically active alkyl halide undergoing S_N2 substitution involves

Question based on following passage :
Adsorption is the process of attracting and retaining the adsorbate molecules on the surface of adsorbent. It is of two types i.e. Physisrption and chemisorption. To increase the rate of reaction, the substance called 'catalyst' is added. Promotors enhance the activity of catalyst while poison decrease the catalyst activity. Solutions may be true solution, suspension and colloids. Colloids are heterogenous but quite stable. On the basis of nature of interaction, colloids may be Lyophilic or Lyophobic. On the basis of type of dispersed phase particles, there may be multimolecular colloids, macromlecular colloids and associated colloids. The congulation of colloids may be done by boiling, dialysis or by mixing oppositely charged sols.
The substances which behave as normal electrolyte at low concentration but become colloids at higher concentration, are known as :

If \(A=\left[\begin{array}{ccc}0 & x^2-6 & -3 \\ -x & 0 & -8 \\ x^2-2 x & 8 & 0\end{array}\right]\) is a skew symmetric matrix, then the value(s) of \(x\) is/ are -
(A) 3
(B) -3
(C) -2
(D) -1
Choose the correct answer from the options given below :

The chromosome number per cell is 46 in: