The area of the region bounded by the curve \(y^2=x\) and the lines \(x=1, x=4\) is:

Lower half of a convex lens is opaque. The image of an object placed in front will :

The approximate volume of a cube of side a meters on increasing the side by 4% is:

The maximum value of \(4 \sin ^2 x+3 \cos ^2 x\) is:

For the differential equation \((x+y) d y+(x-y) d x=0\), which of the following is/are correct?
(A) Differential equation is homogeneous
(B) Order of differential equation is 1
(C) Integrating factor of differential equation is \(e ^{ x }\)
(D) Degree of the equation is not defined
Choose the correct answer from the options given below:

If \(17^{241} \equiv R(\bmod 13)\), then value of \(R\) is \(:\)

If A is a matrix of order mn and B is a matrix such that AB' and B'A are both defined, the order of matrix B is :

Read the following passage carefully and answer the given questions.
The B-lymphocytes produce an army of proteins in response to pathogens. Each antibody molecule has four peptide chains, two small called light chains and two longer called heavy chains. Virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Symptoms of allergic reactions include sneezing, watery eyes, running nose and difficulty in breathing. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy.
Lymphoid organs are the organs where origin and/or maturation and proliferation of lymphocytes occur. The primary lymphoid organs are bone marrow and thymus. After maturation the lymphocytes migrate to secondary lymphoid organs like spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. Heroin commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine, which is extracted from the latex of poppy plant Papaver somniferum.
Which one of the following organs is not a secondary lymphoid organ in humans?

A card is picked up at random from 52 playing cards. Given that the picked card is a queen, then the probability of this card to be a card of spade is:

Which one of the following is not the autosome-linked recessive Mendelian disorder?

Read the passage carefully and answer the Questions
Amines are classified as primary \(\left(1^{\circ}\right)\), secondary \(\left(2^{\circ}\right)\) and tertiary \(\left(3^{\circ}\right)\) depending upon the number of hydrogen atoms replaced by alkyl or aryl groups in ammonia molecules. Aliphatic amines are a stronger bases due to \(+I\) effect of an alkyl groups. Intermolecular hydrogen bonding in primary and secondary amines affects the boiling points of amines. The intermolecular association is more in primary amines than in secondary amines as there are more number of hydrogen atoms available for hydrogen bond formation. Nitro compounds are reduced to amines by passing hydrogen gas in the presence of finely divided nickel, palladium or platinum and also by reduction with metals in an acidic medium. Gabriel synthesis is used for the preparation of primary amines. Primary amines react with nitrous acid to give unstable diazonium-salts which can be used to synthesize a variety of compounds.
The reaction is an example of

The value of \(\tan ^{-1}(2)+\tan ^{-1}(3)\) is equal to

Match List-l with List-II

LIST-I	LIST-II
A. Planck's constant	(I) \(\left[M L^2 T^{-2}\right]\)
B. Work function	(II) \([L]\)
C. Stopping potential	(III) \(\left[M L^2 T^{-3} A^{-1}\right]\)
D. de Broglie wavelength	(IV) \(\left[M L^2 T^{-1}\right]\)

Choose the correct answer from the options given below :