If \(y = x^2 \log_e x\), then \(\frac{d^2y}{dx^2}\) is equal to:

Let \(\tan ^{-1} y=\tan ^{-1} x+\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)\). Then \(y\) is :

Which one of the following is not correct.

Let \(X\) denote the number of tails in two tosses of a coin. If the mean and the variance of \(X\) are \(\mu\) and \(\sigma^2\) respectively, then \(\mu+\sigma^2\) is equal to:

The value of a for which \(\int_1^a x^2 d x=\frac{7}{3}\) is:

Which of the following functions is onto?

For the following probability distribution:

X	-4	-3	-2	-1	0
p(x)	0.1	0.2	0.3	0.2	0.2

The slope of the normal to the curve \(x=a \cos ^3 \theta, y=a \sin ^3 \theta\) at \(\theta=\frac{\pi}{4}\) is :

Identify the symptoms of Amoebiasis from the following.
(A) Constipation
(B) Diarrhoea and vomitting
(C) Abdominal pain and cramps
(D) Excess mucous and blood clots in stool
Choose the correct answer from the options given below:

"Answer the question on basis of passage given below:
\(G = \frac{\kappa A}{l}\) =k(both \(A\) and \(l\) are unity in their appropriate units in m or cm)
Molar conductivity of a solution at a given concentration is the conductance of the volume \(V\) of solution containing one mole of electrolyte kept between two electrodes with area of cross section \(A\) and distance of unit length (\(l\)). Therefore,
\(\Lambda_m = \frac{\kappa A}{l}\)
Since \(l = 1\) and \(A = V\) (volume containing 1 mole of electrolyte),
\(\Lambda_m = \kappa V\)
Molar conductance for 0.2 M AgCl solution showing resistance of 40 \(\Omega\) in a cell having distance between electrodes as 2 cm and surface area of 4 cm\(^2\) will be:"

Read the given paragraph and answer the question:
Humans have 23 pairs of chromosomes. 22 pairs are exactly same in both males and females; these are the autosomes. A pair of X-chromosome are present in the female, whereas the presence of an X and Y chromosome are determinant of the male characteristic.
A number of disorders in human beings have been found to be associated with the inheritance of changed or altered genes or chromosomes. Broadly, genetic disorder may be grouped into two categories-Mendelian disorders and Chromosomal disorders.
A disorder caused due to absence of one of the 'X' chromosome is -

Match List - I with List - II.

List-I	List - II
(A) Ranitidine	(I) Tranquilizer
(B) Furacine	(II) Antibiotic
(C) Phenelzine	(III) Antihistamine
(D) Chloramphenicol	(IV) Antiseptic

Choose the correct answer from the options given below :

Which statement is correct for solutions?