The area of the region (in square units) bounded by \(x=1, x=2\) and the curve \(y^2=4 x\) in the first quadrant is:

If an investment of Rs. \(12000\) becomes Rs. \(72000\) in \(4\) years, then the compound annual growth rate is:

Choose the wrong statement from the following :

\(\int_2^5|x-3| d x\) equals

A person can row a boat in still water at the rate of \(5 km / hr\). It takes him \(4\) times as long to row upstream of a river as to row downstream to cover same distance in the same river. The speed of flow of the stream is:

A boat can row at the speed of \(16 km / hr\) in still water. If the river is flowing at \(8 km / hr\), and it takes 8 hours for a round trip, then the distance between the two places is :

A simple random sample consists of four observations 1, 3, 5, 7. The point estimate of population standard deviation is :

A vessel contains 56 litres of mixture of milk and water in the ratio \(5: 2\). How much water should be mixed with it so that the milk to water ratio becomes 4:5.

p-block elements are placed in groups 13 to 18 of the periodic table. Group 15 is nitrogen family. Nitrogen makes various compounds like \(NH _3, HNO _3, N_2 O , NO _2\) etc. Phosphorus exists in the form of white and red phosphorus. White phosphorus glows in dark. \(PH _3\) gas is used as smoke screen. Group 16 is called oxygen family. Dry air contains \(21\% O_2\) gas by volume. Combined sulphur exists as sulphates such as gypsum, epsome salt, baryte etc. The allotropic forms of sulphur are Rhombic and monoclinic sulphur. \(S_2\) is paramagnetic like \(O_2\) and it stable at high temperature. Group 17 is Halogen family. \(F_2\) is highly reactive, \(C l_2\) is greenish yellow gas. Both \(S O_2\) and \(C l_2\) are used for bleaching. Group 18 is Noble gas family but some noble gases also form compounds.
Complete hydrolysis of \(XeF _6\) gives HF and \(XeO _3\) as main products.
The product of complete hydrolysis of \(XeF _6\) in the following reaction is
\(XeF _6+ H _2 O \rightarrow ?+ HF\)

Which of the following statements are correct?
(A) In dispersion through a prism of glass, the red color ray deviates most.
(B) In simple microscope, to get a magnified image, the object is placed within the focus of a convex lens.
(C) In compound microscope, total magnification is m = (magnification due to eye lens) x (magnification due to objective)
(D) Magnifying power of telescope M = focal length of eye lens / focal length of objective lens
Choose the correct answer from the options given below:

Match List-I with List-II

List-I (Optical instrument)	List-II (Magnifying power)
(A) Magnifying power m of a simple microscope	(I) \( m = 1 + (D/f) \)
(B) Magnifying power m of a simple microscope if the image is at infinity	(II) \( m = (L/f_0) \times (D/f_e) \)
(C) Magnifying power m of a compound microscope	(III) \( m = f_0 / f_e \)
(D) Magnifying power m of a telescope	(IV) \( m = D/f \)

Choose the correct answer from the options given below:

A metal foil of thickness (3/4)d is introduced between two plates of a capacitor of capacitance C. The distance between the plates of the capacitor is d. The new capacitance of the capacitor will be

Two positive numbers whose sum is 60 and the product of the square of one number and other number is maximum are: