Question

1. Assertion –On dilution of anacid, the number of H+ions per unit volume in the solution decreases.

Reason–Dissociation of an acid in water gives H+ions

2. Assertion -Iron gets corroded in the moist air but copper is not.

Reason –Iron is more reactive than copper

3. Assertion –Green Ferrous sulphate crystals on heating, first turns white and on further heating leave reddish brown residue.

Reason –They turn white due to the loss of water of crystallization and reddish-brown residue of ferrous oxide.


a)Both A and R are true and R is the correct explanation of the A.

b)Both A and R are true and R is not the correct explanation of the A.

c)A is true, but R is false.

d)A is false, but R is true

Answer 1

Explanation:

Given:cot2θ+sinθ3+3=0

\sf\blue{To\:Find\::General\: Solution\:of\:this\: equation}ToFind:GeneralSolutionofthisequation

\sf\red{Solution\::}Solution:

\sf{\cot^{2}\theta\:+\:\frac{3}{\sin\theta}\:+\:3\:=\:0}cot2θ+sinθ3+3=0

We know that cot = cos/sin so put that value over here which will give you the following equation ,

\sf{\frac{\cos^2\theta}{\sin^2\theta}\:+\:\frac{3}{\sin\theta}\:+\:3\:=\:0}sin2θcos2θ+sinθ3+3=0

Now by using the first identity of trigonometry we get here ,

\sf{\cos^2\theta\:+\:\sin^2\theta\:=\:1}cos2θ+sin2θ=1

Or

\sf{\cos^2\theta\:=\:1-\:\sin^2\theta\:}cos2θ=1−sin2θ

Now use this value here ,

\sf{\frac{1\:-\:\sin^2\theta}{\sin^2\theta}\:+\:\frac{3}{\sin\theta}\:+\:3\:=\:0}sin2θ1−sin2θ+sinθ3+3=0

Now multiply LHS with sin²theta

\sf{1\:-\:\sin^2\theta\:+\:3\sin\theta\:+\:3\sin^2\theta\:=\:0}1−sin2θ+3sinθ+3sin2θ=0

\sf{1\:+\:+\:3\sin\theta\:+\:2\sin^2\theta\:=\:0}1++3sinθ+2sin2θ=0

We can write it as ,

\sf{2\sin^2\theta\:+\:2\sin\theta\:+\:\sin\theta\:+\:1\:=\:0}2sin2θ+2sinθ+sinθ+1=0

= (2 sin theta + 1 )( sin theta + 1 ) = 0

= sin theta = - 1/2 or - 1

\sf{\theta\:=\:n\pi\:+\:(-1)^n\:\frac{-\pi}{6}\:and\:\theta\:=\:n\pi\:+\:(-1)^n\:\frac{-\pi}{2}}θ=nπ+(−1)n6−πandθ

dont knoe the ans hope this helps ✌