\(\int_0^a \frac{\sqrt{x}}{\sqrt{x}+\sqrt{a-x}} d x\) is equal to

The maximum value of \(Z=2 x+3 y\) subject to the constraints \(x \geq 0, y \geq 0, x+y \leq 10,3 x+4 y \leq 36\) is:

If the maximum value of the function \(f(x)=\frac{\log _e x}{x}, x>0\) occurs at \(x=a\), then \(a^2 f^{\prime \prime}(a)\) is equal to:

The derivative of \(\sqrt{e^{\sqrt{x}}}\) with respect to \(x\) is :

The shaded region shown in the figure is given by inequalities:

A card is selected at random from a pack of 52 playing cards.The selected card is a queen.The probability that this card is a card of spade is :

A machine costing Rs.50,000 has a useful life of 4 years .The estimated scrap value is Rs 10,000. The rate of depreciation per annum is :

Match List-I with List-II

List-I	List-II
(A) Electric potential V due to a single charge	(I) \(\propto r^0\)
(B) Electric flux due to a positive point charge through sphere of radius r	(II) \(\propto \frac{1}{r^2}\)
(C) Electric intensity E due to a point charge	(III) \(\propto \frac{1}{r}\)
(D) Electric intensity E due to dipole	(IV) \(\propto \frac{1}{r^3}\)

Choose the correct answer from the options given below :

If \(a\) and \(b\) are the order and degree of the differential equation
\(\frac{\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{2}}}{\frac{d^2 y}{d x^2}}=K \text { respectively, then }\)
the value of \(a+2 b\) is :

Phenols are acidic in nature. Which of the following statements is incorrect about them?

Which one of the following seeds is an example of non-albuminous seed?

Read the passage carefully and give the answers to the question :
India was amongst the first countries in the world to initiate action plans and programmes at a national level to attain total reproductive health as a social goal.
These programmes called 'family planning' were initiated in 1951 and were periodically assessed over the past decades. Improved programmes covering wider reproduction-related areas are currently in operation. Creating awareness among the people about various reproduction-related aspects and providing facilities and support for building up a reproductively healthy society are the major tasks under these programmes.
Which of the following statements is incorrect with respect to Medical Termination of Pregnancy?

The reduction of cyclohexanone with LiAlH4 will give: