\(\int_{-1}^1\left(x^7+x^5+x^3+x+1\right) d x\) is equal to:

A money lender charges Rs 10 for Rs 100 per month in advance then effective rate of interest per annum charged by money lender is : \(\left[\right.\) given \(\left.\left(\frac{10}{9}\right)^{12}=3.541\right]\)

The sides of an equilateral triangle are increasing at the rate of \(5 cm / sec\). The rate at which the area increases when the side is 20 cm , is

A and B throw a die alternatively till one of them gets 3 or 6 and wins the game. If B starts the game, then the probability of winning the game by A is

Consider the LPP, Min \(Z=3 x-2 y\) subject to the conditions
\(
\begin{array}{l}
4 x+3 y \geq 12 \\
4 x+y \geq 4 \\
x \geq 0, y \geq 0
\end{array}
\)
then which of the following is correct?

Let R be the feasible region for a Linear Programming Problem and let \(z=a x+b y\) be the objective function. If R is bounded, then the objective function z has :

Two events A and B are independent, if
(A) A and B are mutually exclusive
(B) \(P\left(A^{\prime} \cap B^{\prime}\right)=[1-P(A)][1-P(B)]\)
(C) \(P\left(A^{\prime}\right)=P\left(B^{\prime}\right)\)
(D) P(A) + P(B) = 1
(E) P(A) = P(B)

Match List-I with List-II

List-I	List-II
(A) Electric potential V due to a single charge	(I) \(\propto r^0\)
(B) Electric flux due to a positive point charge through sphere of radius r	(II) \(\propto \frac{1}{r^2}\)
(C) Electric intensity E due to a point charge	(III) \(\propto \frac{1}{r}\)
(D) Electric intensity E due to dipole	(IV) \(\propto \frac{1}{r^3}\)

Choose the correct answer from the options given below :

An objective function \(z=a x+b y\) is maximum at points \((15,15)\) and \((0,20)\). If \(a, b \geq 0\) and \(a b=27\), then the maximum value of the objective function is

A foetal genetic disorder can be studied by which of the following?

The electric field \( E \) associated with a progressive electromagnetic wave is given by \( E = E_0 \sin(kx - \omega t) \). If \( B_0 \) is the amplitude of the magnetic field associated with the wave, then

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.
Arrange the following in the increasing order of their \(p K_{ a }\) values :
(A) \(CF _3- COOH\)
(B) \(O _2 N- CH _2- COOH\)
(C) \(NC - CH _2- COOH\)
(D) \(H - COOH\)
Choose the correct answer from the options given below :

Answer the question on the basis of passage given below :
For the transition elements
Sc \(\quad\) Ti \(\quad\) V \(\quad\) Cr \(\quad\) Mn\(\quad\) Fe \(\quad\) Co \(\quad\) Ni \(\quad\) Cu \(\quad\) Zn
Atomic numbers :
21 \(\quad\) 22 \(\quad\) 23 \(\quad\) 24 \(\quad\) 25 \(\quad\) 26 \(\quad\) 27 \(\quad\) 28 \(\quad\) 29 \(\quad\) 30 \(\quad\)
Which transition element ion \(\text{M}^{3+}\) has electronic configuration \(3d^5 4s^0\)?