If the matrix \(A=\left[\begin{array}{ccc}0 & -3 & x+y \\ 3 & x-2 y & 5 \\ -6 & -5 & 0\end{array}\right]\) is skew-symmetric then values of \(x\) and \(y\) respectively are :

The maximum value of \(y=x^3-3 x\) is :

If \(y=\log \left(x+\sqrt{x^2+a^2}\right)\) then \(\frac{d y}{d x}\) =

The area bounded by \(y=3 x+1, x=0, y=0\) and \(x=a\) is 8 Sq.units. Then value of \(a\) (where \(a>0\) ) is

Let \(f(x)=\left\{\begin{array}{ll}|x|+3 & \text { if } x \leq-3 \\ -2 x & \text { if }-3 < x < 3, \text { then which of the following is true? } \\ 6 x+2 & \text { if } x \geq 3\end{array}\right.\)

The value of b for which the function \(f(x) = \sin x - bx + C\), where b and C are constants is decreasing for \(x \in R\) is given by

Match List 1 with List 2.

List - 1 (Matrix)	List - 2 (Determinants)
(A) \(\operatorname{Matrix}(A)=\left[\begin{array}{cc}1 & 7 \\ -3 & 5\end{array}\right]\)	(I) 24
(B) \(\operatorname{Matrix}(B)=\left[\begin{array}{cc}-2 & 5 \\ -3 & -3\end{array}\right]\)	(II) 32
(C) \(\operatorname{Matrix}(C)=\left[\begin{array}{ll}-12 & 8 \\ -16 & 8\end{array}\right]\)	(III) 21
(D) \(\operatorname{Matrix}(C)=\left[\begin{array}{ll}-12 & 8 \\ -16 & 8\end{array}\right]\)	(IV) 26

Choose the correct answer from the options given below :

Arrange the following alcohols in decreasing order of acidity:

Choose the correct answer from the options given below:

A cell is prepared by dipping a Cu rod in \(1\ M\ CuSO_4\) solution and Sn rod in \(1\ M\ SnCl_2\) solution.
The standard electrode potential of Cu is \(+0.34\ V\) and Sn is \(-0.14\ V\). Emf of cell will be :

Read the following paragraph and answer the given questions.
Cancer detection is based on biopsy and histopathological studies. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Do you know why mother's milk is considered very essential for the new-born infant? The yellowish fluid colostrum secreted by mother during the initial days of lactation has abundant antibodies (IgA) to protect the infant. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. The exaggerated response of the immune system to certain antigens present in the environment is called allergy. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused. Morphine is a very effective sedative and painkiller, and is very useful in patients who have undergone surgery.
A pregnant female is advised not to discard the yellowish fluid called colostrum, secreted during the initial days of lactation, because it is rich in:

If \(A\) and \(B\) are square matrices of order 3 such that \(|A|=-1\) and \(|B|=5\), then the value of \(|3 A B|\) is

Decide which of the following atomic numbers are the atomic numbers of the inner transition elements
(A) 59
(B) 95
(C) 102
(D) 74
Choose the correct answer from the options given below:

The function \(f(x)=|x-3|, x \in R\) is: