The area of the triangle with vertices \((1,4),(2,7)\) and \((4,13)\) is:

The sides of an equilateral triangle are increasing at the rate of \(5 cm / sec\). The rate at which the area increases when the side is 20 cm , is

The function \(f(x)=6-6 x-2 x^2\)

If \(f(x)=\left\{\begin{array}{l}m x+1, x \geq \pi / 2 \\ \sin x+n, x \leq \pi / 2\end{array}\right.\) is continuous at \(x=\pi / 2\), where \(m \in Z\) (set of integers), then \(\sin 2 n=\)

If A and B are symmetric matrices then \((A B+B A)\) is:

Match List - I with List - II regarding the value of the following.

List - I	List - II
(A) \(\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)\)	(I) \(\frac{\pi}{2}\)
(B) \(\cos ^{-1}\left(\cos \frac{5 \pi}{4}\right)\)	(II) \(\frac{\pi}{4}\)
(C) \(\sin ^{-1} \frac{4}{5}+2 \tan ^{-1} \frac{1}{3}\)	(III) \(\frac{5 \pi}{6}\)
(D) \(\tan ^{-1} \frac{x}{y}-\tan ^{-1} \frac{x-y}{x+y}\)	(IV) \(\frac{3 \pi}{4}\)

Choose the correct answer from the options given below :

The volume of spherical balloon is increasing at the rate of 4 \(cm ^3\) / sec. The rate of increase of its surface area, when the radius is 3 cm will be :-

Which one of the following diseases can be treated by human protein (a -1-
antitrypsin) produced by transgenic animals?

Data available for profit (₹ Thousands) of a company as

Year	2004	2005	2006	2007	2008	2009	2010
Profit(000)	114	130	126	144	138	156	164

Based on the above data using least square method the trend value for the year ‘2007’ is

Identify the mammals which live wholly in water:
A. Dolphins
B. Seals
C. Sea Horse
D. Sea cow
Choose the correct answer from the options given below:

Read the passage carefully and answer the questions
Carbohydrates such as cane sugar, glucose, starch etc. belong to a class of naturally occurring organic compounds. Structurally these are polyhydroxy aldehydes or ketones or the compounds which produce such units on hydrolysis. Carbohydrates which are sweet in taste are called sugars. Theses sugars can be reducing or non-reducing. Monosaccharides cannot be hydrolyzed to simpler units whereas Oligosaccharides yield two to ten monosaccharide units on hydrolysis. Polysaccharides yield large number of monosaccharide units on hydrolysis. This class of biomolecules is essential for living systems as they serve as storage molecules in plants and animals. In addition, they provide raw materials for important industries like furniture, textiles, paper, lacquers and breweries. Two aldopentose form important constituents of nucleic acids. Carbohydrates are also called saccharides (Greek: sakcharon which means sugar). Sugar which is used in household and in milk also comes under this class of biomolecules.
Among below given carbohydrates, which one is not a polysaccharides ?

The area (in sq. units) of the region bounded by the curve \(y=\sin x,-2 \pi \leq x \leq 2 \pi\) and the \(x\)-axis is :

Among the following compounds, which will not undergo oxidation reaction?