The differential equation representing the family of curves \(y=a \sin (x+b)\), where \(a\) and \(b\) are arbitrary constants is

Consider two independent events A and B such that P(A) = 0.3, P(B) = 0.6.
match List - I with List - II

List - I	List - II
(A) P(A and B)	(I) 0.28
(B) P(A and not B)	(II) 0.18
(C) P(A or B)	(III) 0.12
(D) P(neither A nor B)	(IV) 0.72

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If \(P(A)=\frac{6}{11}, P(B)=\frac{5}{11}\) and \(P(A \cup B)=\frac{7}{11}\), then
A. \(P(A \cap B)=\frac{4}{11}\)
B. \(P(A \mid B)=\frac{ 4 }{ 5 }\)
C. \(P(B \mid A)=\frac{2}{5}\)
D. \(A\) and \(B\) are independent events
E. \(P(\) neither \(A\) nor \(B)=\frac{4}{11}\)
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The sale of ice creams is higher in summer than in winter is an example of:

Three varieties A, B and C of rice are mixed together in the ratio 1:1:3 respectively. The price of rice A is Rs 127 per kg and that of rice B is Rs 135 per kg. If the price of the mixture is Rs. 152 per kg, then the price per kg of rice of type C is :

A man wishes to ensure that he gets Rs. 75,000/- at the end of each year indefinitely. The amount that he invest now to produce the desired cash flow, if money is worth 2.5% compounded annually is:

The differential coefficient of \(\log _e\left[\log _e\left(\log _e x^5\right)\right]\) with respect to \(x\) is:

Let A be a square matrix of order n, then which of the following are TRUE?
(A) \(|\operatorname{adj} A|=|A|^{n-1}\)
(B) \(|A \cdot \operatorname{adj} A|=|A|^n\)
(C) A. (adj A) = |A|
(D) |KA| = K|A|
(E) \(\left|A^{-1}\right|=\frac{1}{|A|},|A| \neq 0\)
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Which of the following statements are correct?
A. The process of generation of conduction electrons and holes and process of recombination is a simultaneous process.
B. To increase the conductivity of a semiconductor manifold, a few parts per million of a suitable impurity is added.
C. Extrinsic semiconductors doped with trivalent impurity are called n-type semi conductors.
D. During the formation of a p-n junction, two processes diffusion and drift occurs.
E. The thickness of depletion region is of the order of a millimeter.
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A student got data showing productivity of three different ecosystems, but the unit was missing, Choose the correct unit.

Read the passage carefully and answer:
Organic compounds derived from NH3 by replacing one or more H-atoms with alkyl or aryl groups will form primary, secondary and tertiary amines. The common methods which include their preparations are reduction of nitro group, amide group and nitrile group, Gabriel phthalimide synthesis and ammonolysis of alkyl halides. Amines are basic in nature due to the presence of a lone pair of electrons on the nitrogen atom. Important chemical properties of amines include acylation, alkylation and their interaction with nitrous acid. There are various tests which can distinguish different types of amines from each other, for e.g. carbylamine test, Hinsberg's test, coupling reaction etc. Another important class of compounds which can be derived from primary amines is azo compounds. These compounds are intensely colored and widely used as dyes in textile, leather and food industries.
How many different structural isomers that correspond to the molecular formula \(\mathrm{C}_3 \mathrm{H}_9 \mathrm{~N}\) are possible? Out of these, how many will give a positive carbylamine test?

Which of the following is a man-made ecosystem?

Which of the following statements are correct?
A. The relative motion between a magnet and a coil is responsible for induction of electric current in the coil.
B. Magnetic flux is a vector quantity.
C . In a closed coil, the magnitude of emf induced is equal to the time rate of change of magnetic flux.
D. Eddy currents oppose the magnetic braking effect in trains.
E. Lenz's law gives the polarity of the induced emf clearly.
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