If \(A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\), then \(A^2=\)

The inverse of the matrix \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]\) is:

The equation of the normal to the curve \(y=\sin x\) at \((0,0)\) is :

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

How many minimum number of times must a man toss a fair coin so that the probability of having at least one head is more than \(90 \%\) ?

The side of an equilateral triangle is increasing at the rate of \(3 cm / sec\).
The rate at which the area of the triangle is increasing, when the side is 4 cm , is:

A random variable X has the following probability distribution

X	0	1	2
\(P ( X )\)	\(1 / 4\)	\(1 / 2\)	\(1 / 4\)

then, which of the following is correct?

The product of the following reaction is :
Reactant: 2,2-Dimethylcyclohexanol
Reagents: \(H ^{ + } /\) heat

Match List I with List II

LIST I	LIST II
A. Alec Jeffreys	I. Operon model
B. Jacob and Monod	II. X-ray diffraction data of DNA
C. Erwin Chargaff	III. DNA Fingerprinting
D. Wilkins and Franklin	IV. (A+G)/(T+C)=1

Choose the correct answer from the options given below:

Answer the question on basis of passage given below :
P block elements are placed in groups 13 to 18 of the periodic table. Their valence shell electronic configuration is \(ns^2 np^{1-6}\). Group 16 of the p block elements are known as the group of chalcogens having \(ns^2 np^4\) as their general electronic configuration. They exhibit number of oxidation states but the stability of \(- 2\) oxidation state decreases down the group. They are sometimes also known as group of chalcogens as the name is derived from the Greek word for brass and points to the association of sulphur and its congeners with copper. Their ionisation enthalpy decreases down the group. Oxygen shows anomalous behaviour due to its small size and high electronegativity.
What will be the products formed in the following equation?

Consider the following hypothesis test :
\(H_0: \mu=15\)
\(H_a: \mu \neq 15\)
A sample of 50 provided a sample mean of 14.15 . If the sample standard deviation is 3 , then the value of the teat statistic in \(t\) - test is

The oxidation number of Co in the complex \(\left[ Co \left( H _2 NCH _2 CH _2 NH _2\right)_3\right]_2\left( SO _4\right)_3\) is:

Read the following paragraph carefully and answer the given questions.
Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. For determining the cause of allergy, the patient is exposed to or injected with very small doses of possible allergens, and the reactions studied. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine. 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. 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.
Which of the following drugs are commonly used to quickly reduce the symptoms of allergy?