If \(A=\left[\begin{array}{cc}2 x+y & -3 \\ 4 & 2\end{array}\right]\) and \(B=\left[\begin{array}{cc}5 & 3 x-2 y \\ 2 & 1\end{array}\right]\) are such that \(A+B=\left[\begin{array}{ll}0 & 0 \\ 6 & 3\end{array}\right]\) then values of x and y are respectively:

A boat 10 m high floating at a uniform speed of 13 meters per minute \(( m / min )\) away from a lamp post 15 m high.
Then the rate at which the length of shadow of the boat increases is :

\(\int\left(\frac{1+x+x^2}{1+x^2}\right) e^{\tan ^{-1} x} d x=\)

\(\int_0^1 \tan ^{-1}\left(\frac{2 x-1}{1+x-x^2}\right) d x\) is equal to :

If the matrix \(A = \begin{bmatrix} 0 & a & 3 \\ 2 & b & -1 \\ c & 1 & 0 \end{bmatrix}\) is skew-symmetric, then a + b + c is equal to:

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

Consider the following data of expenses (in lakhs) of an organization year wise:

Year	2001	2002	2003	2004	2005
Expenses (Rs. lakh)	160	185	220	300	510

Then expected expenses trend for the year 2006 using method of least squares is:

Observe the figure and answer the following:


What is the above figure representing?

Which one of the following infections is completely curable?

Let \(\left|\begin{array}{cc}x & 2 \\ 18 & x\end{array}\right|=\left|\begin{array}{ll}-4 & -2 \\ -8 &-4\end{array}\right|\). Then :
(A) \(x=-4\)
(B) \(x=-6\)
(C) \(x=4\)
(D) \(x=6\)
Choose the correct answer from the options given below :

Which of the following is NOT a copper releasing IUDs?

Read the following passage carefully and answer the given questions. During anaerobic sludge digestion, bacteria produce a mixture of gases such as methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as source of energy as it is inflammable. The bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. You must have noticed that bottled fruit juices bought from the market are clearer as compared to those made at home. This is because the bottled juices are clarified by the use of pectinases and proteases. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. The BOD test measures the rate of uptake of oxygen by microorganisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water.
Cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by -

Match List-I with List-II

List-I (Population interactions)	List-II (Species A / Species B)
(A) Competition	(I) - / 0
(B) Amensalism	(II) + / 0
(C) Commensalism	(III) + / -
(D) Parasitism	(IV) - / -

'* + 'sign for beneficial interaction, '-'for detrimental and '0 *' for neutral interaction
Choose the correct answer from the options given below: