if a function \(f: Q \rightarrow R\) defined by \(f(x)=\frac{2 x-1}{2}\) and \(g: Q \rightarrow R\) is defined by \(g(x)=x+2\), then \((g \circ f)\left(\frac{3}{2}\right)\) is :

Magnetic moment of a thin bar magnet is ' M '. If it is bent into a semicircular form, its new magnetic moment will be

Match List - I with List - II

List - I (Example)	List - II (Component of Time Series)
(A) Lockouts and strikes	(I) Secular trend
(B) Rise and fall of share market	(II) Seasonal trend
(C) Continuous decline in death rate	(III) Irregular trend
(D) The rise in prices before Diwali	(IV) Cyclical trend

Choose the correct answer from the options given below:

If \(\theta\) is the angle between two unit vectors \(\hat{a}\) and \(\hat{b}\) then \(|\hat{a}-\hat{b}|=\)

\(\int \frac{d x}{9 x^2-16}\) is equal to:

\(\int e^{-x}\left(\cot x+\mid \operatorname{cosec}^2 x\right) d x\) =

The integral \(\int \frac{d x}{\sqrt{\frac{1}{2}-5 x-x^2}}\) is equal to:

Read the passage carefully and answer the questions
Carboxylic acids are the organic compounds which comprise of carboxyl functional group, -COOH. These are generally found in nature, some higher members are known as fatty acids as they occur in natural fats as esters of glycerol. They can be prepared from oxidation of alcohols and aldehydes, hydrolysis of nitriles and amides and Grignard reagents. They are stronger acids than simple phenols and alcohols. but weaker than mineral acids. Substituents affect the acidity of aliphatic and aromatic carboxylic acids. They undergo reactions involving cleavage of -OH and C-OH bond. Carboxylic acids having an alpha hydrogen get halogenated in the presence of red phosphorus to form alpha halo carboxylic acids. The reaction is known as Hell Volhard Zelinsky reaction. Besides these aromatic carboxylic acids undergo electrophilic substitution reactions. They are versatile and are employed in the manufacture of various useful compounds. For example, methanoic acid is used in rubber, textile, dyeing, leather and electroplating industries. Higher fatty acids are used in the manufacture of soaps and detergents. Esters of Benzoic acid are used in perfumery.
Benzoic acid in the presence of conc. \(HNO _3\) and conc. \(H _2 SO _4\) gives major product as:

A boat covers a distance of 24 km upstream and returns to the same point in a total time of 4 hours. If the speed of the boat in downstream is twice its speed in upstream, then the speed of boat in upstream is:

In a circuit where current 3I enters at A, with semicircular sections ABC and ADC of equal radii r, resistances 2R and R respectively, the magnetic field at the center is :

Match List - I with List - II.

List - I (Disease)	List - II (Pathogen)
(A) Pneumonia	(I) Salmonella typhi
(B) Typhoid	(II) Plasmodium falciparum
(C) Malaria	(III) Wuchereria bancrofti
(D) Filariasis	(IV) Haemophilus influenzae

Choose the correct answer from the options given below :

Match List-I with List-II

List-l (Species)	List-II (Population interaction terms)
(A) Monarch butterfly	(I) Brood parasitism
(B) Cuckoo bird	(II) Commensalism
(C) Cuscuta	(III) Camouflage
(D) Sea anemone and Clown fish	(IV) Parasitism

Choose the correct answer from the options given below:

The second trophic level in an aquatic ecosystem is: