The sum of order and degree of the differential equation \(\frac{\left\{1+\left(\frac{d y}{d x}\right)^2\right\}^{\frac{5}{2}}}{\frac{d^2 y}{d x^2}}= p\) is :

The area of the region bounded by the circle \(x^2+y^2=1\) is ___________ sq. units.

The number of arbitrary constants in the particular solution of a differential equation of order 4 and degree 3 is

For the differential equation \((x+y) d y+(x-y) d x=0\), which of the following is/are correct?
(A) Differential equation is homogeneous
(B) Order of differential equation is 1
(C) Integrating factor of differential equation is \(e ^{ x }\)
(D) Degree of the equation is not defined
Choose the correct answer from the options given below:

Match \(List - I\) with \(List - II\)

\(List - I\)	\(List - II\)
(A) \(\frac{d}{d x}\left(\sin x^2\right)\)	(I) \(\frac{1}{5}\)
(B) \(\frac{d}{d x}\left(e^{\sin x}\right)\)	(II) 0
(C) \(f(x)=\tan ^{-1} x\) then \(f^{\prime}(2)\)	(III) \(2 x \cos x^2\)
(D) If \(y=3 \cos x-2 \sin x\), then \(\frac{d^2 y}{d x^2}+y\)	(IV) \(e^{\sin x} \cos x\)

The feasible region of a LPP is bounded. The corresponding objective function is \(Z=6 x-7 y\). Then the objective function attains:

A solenoid with \(2 \times 10^4\) turns per meter, diameter 0.1 m , has a coil of 100 turns and 0.01 m radius placed inside. If solenoid current decreases from 4 A to 0 in 0.05 s , total charge through coil is :

The Roquefort cheese are ripened by growing a specific_______ on them, which gives them a particular flavour.

Read the passage carefully and answer the Questions:
Amines are classified as primary \(\left(1^{\circ}\right)\), secondary \(\left(2^{\circ}\right)\) and tertiary \(\left(3^{\circ}\right)\) depending upon the number of hydrogen atoms replaced by alkyl or aryl groups in ammonia molecules. Aliphatic amines are a stronger bases due to \(+I\) effect of an alkyl groups. Intermolecular hydrogen bonding in primary and secondary amines affects the boiling points of amines. The intermolecular association is more in primary amines than in secondary amines as there are more number of hydrogen atoms available for hydrogen bond formation. Nitro compounds are reduced to amines by passing hydrogen gas in the presence of finely divided nickel, palladium or platinum and also by reduction with metals in an acidic medium. Gabriel synthesis is used for the preparation of primary amines. Primary amines react with nitrous acid to give unstable diazonium-salts which can be used to synthesize a variety of compounds.

The reaction is an example of:

\(\int \frac{1 - \sin x}{\cos^2 x} dx\) is equal to:

What is the IUPAC name of m-cresol?

The value of \(\cot \left(\cos ^{-1} \frac{7}{25}\right)\) is

Read the passage carefully and answer the following questions
Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms. They play a pivotal role in various biochemical processes of life. Their presence in nature adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C-OH bond and the O-H bond along with the reactions involving the complete - COOH group.
Identify the incorrect statement for Cannizaro reaction.