The area (in sq. units) of the region in the first quadrant bounded by \(y=3 \sqrt{1-x^2}, x \in[0,1]\) and the x-axis is equal to

An LPP defined by the objective function Z = 2x + 2y has to be maximized.
The corner points are (0,0), (5, 0), (8, 2), (4, 6) and (0,8).
The maximum value occurs at :

On 1st April 2024, person ' \(X\) ' purchased a machinery costing ₹ 65000 and spent ₹ 10000 on its installation. The estimated effective life of the machinery is 5 years with a scrap value of ₹ 10000 . The annual depreciation using the straight-line method with the accounting year ending on 31st March 2025 is :

The common region determined by all constraints of a Linear programming problem is called:

If the cost function of a product is given by \(C(x)=\frac{3}{4} x^2-5 x+21\), then the marginal cost when \(x=10\) is

The function f defined by \((x)=\left\{\begin{array}{ll}a x+1, & x \leq 3 \\ b x+3, & x>3\end{array}\right.\) is continuous at x = 3 if

The graph given below represents which of the following function?

Five species of warblers studied by Mac Arthur is an example of :

A copper wire of area of cross-section \( 2 \times 10^{-6} \, \text{m}^2 \) and electron density \( 10^{28} \, \text{m}^{-3} \) carries a current of 1.6 A. Time taken by an electron to drift from one end of a 1.0 m long wire to its other end will be

Organic compounds derived from NH3 by replacing one or more H-atoms with alkyl or aryl groups will form primary, secondary and tertiary amines. The common methods which include their preparations are reduction of nitro group, amide group and nitrile group, Gabriel phthalimide synthesis and ammonolysis of alkyl halides. Amines are basic in nature due to the presence of a lone pair of electrons on the nitrogen atom. Important chemical properties of amines include acylation, alkylation and their interaction with nitrous acid. There are various tests which can distinguish different types of amines from each other, for e.g. carbylamine test, Hinsberg's test, coupling reaction etc. Another important class of compounds which can be derived from primary amines is azo compounds. These compounds are intensely colored and widely used as dyes in textile, leather and food industries.
Correctly predict the final product and the type of reaction for the following reaction:
\(C _6 H _5- N _2^{+} Cl ^{-}+ C _6 H _5- OH \xrightarrow{ HO ^{-}}\)?

The spin-only magnetic moment of \(\left[ MBr _4\right]^{2-}\) is 5.9 BM.
The metal M is:

Salicylaldehyde is formed as a main product from phenol by :

The mutation theory of saltation given by Hugo deVries based on his work on: