The value of \(\int_{-5}^5|x+3|\) \(dx\) is

If \(X\) is a random variable and \(a, b\) are real numbers, then which of the following statements are correct?
(A) \(E[a X+b]=a E(X)+b\)
(B) \(\operatorname{Var}(a X+b)=a^2 \operatorname{Var}(X)+b\)
(C) \(\operatorname{Var}(a X+b)=a \operatorname{Var}(X)\)
(D) \(\operatorname{Var}(X)=E\left(X^2\right)-[E(X)]^2\)
Choose the correct answer from the options given below:

For an objective function \(z=a x+b y\) where \(a, b>0\).
The corner points of feasible region determined by a set of constraints are \((0,20),(10,10),(30,30),(0,40)\).
The condition on \(a\) and \(b\) such that max \(z\) occurs at both the points \((30,30)\) and \((0,40)\) is:

match List - I with List - II

List - I	List - II
(A) \(\tan ^{-1}\left(\frac{2}{11}\right)+\tan ^{-1}\left(\frac{7}{24}\right)\)	(I) \(\frac{3 \pi}{4}\)
(B) \(\tan ^{-1} 2+\tan ^{-1} 3\)	(II) \(\pi\)
(C) \(\tan ^{-1} 1+\tan ^{-1} 2+\tan ^{-1} 3\)	(III) \(\tan ^{-1}\left(\frac{1}{2}\right)\)
(D) \(\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{13}\right)\)	(IV) \(\tan ^{-1}\left(\frac{2}{9}\right)\)

Choose the correct answer from the options given below:

The solution of the differential equation \((\cot y) d x=x d y\) is:

For a set A = {1, 2, 3}, the following functions are defined from A to A. Which of these functions has an inverse?

Which of the following functions \(f(x)\) are differentiable at \(x=0\) ?
(A) \(|x|\)
(B) \(|x-1|\)
(C) \(|\sin x|\)
(D) \(|\cos x|\)
(E) \(x^2\)
Choose the correct answer from the options given below :

In the formation of a p-n junction diode, arrange the following processes in sequence.
(A) Diffusion of charge carriers
(B) Drift of charge carriers
(C) Doping
(D) Generation of electric field at the junction
Choose the correct answer from the options given below :

In alcohols, C-O-H bond angle is:

Read the passage carefully and answer the questions based on the passage:
Pollen pistil interaction involves all events from the landing of pollen grains on the stigma until the pollen tube enters the embryo sac (when the pollen is compatible). When a pollen tube grows through the style and enters into the ovules, it finally discharges two male gametes in one of the synergids. Syngamy and triple fusion are two fusion events occur in angiosperms. Thus, angiosperms exhibit double fertilization. The products of these fusions are the diploid zygote and triploid primary endosperm nucleus. Zygote develops into embryo and primary endosperm cell forms the endosperm tissue. The developing embryo passes through different stages before maturation.
Formation of diploid zygote is a result of:

Considering the stability of Cu(II) and Cu(I) which of the following statements is true?

Select the correct statements for Hoffmann bromamide degradation reaction:
(A) Used to prepare primary amines
(B) Amides are treated with bromine in aqueous solution.
(C) NaOH is used in this reaction.
(D) HCI is used in this reaction
Choose the correct answer from the options given below:

C and Z in the species-area relationship log S = log C + Z log A represents: