Job Roles

Let the two consecutive odd integers be (2x + 1) and (2x + 3)

Then,

(2x + 3)² - (2x + 1)²

= (2x + 3 + 2x + 1) (2x + 3 - 2x - 1)

= (4x + 4)(2)
= 8 (x + 1), which is always divisible by 8

Two digit numbers: The two digits can be 2 and 9: Two possibilities 29 and 92.

Three-digit numbers: The three digits can be 1, 2 and 9 => 3! Or 6 possibilities.

We cannot have three digits as (3, 3, 2) as the digits have to be distinct.

We cannot have numbers with 4 digits or more without repeating the digits.

So, there are totally 8 numbers.

Given,

 5sinx + 12cosx ≥ -r 

⇒13513sin x + 1213cos x ≥ -rcosx) ≥ -r 

513= cosA => sinA =1213

=> 13(sinx cosA + sinA cosx) ≥ -r

=> 13(sin(x + A)) ≥ -r

we know that , -1 ≤ sin (angle) ≤ 1

=> 13sin (x + A) ≥ -13 ⇒rmin =13 

Given length of iron rod =7 mts and  and diameter of rod = 2 cms 

=> r = 1/100 mts

Therefore,  Volume of one rod = πr2h cu. m =  227×11002×7cu. m = 115000 cu. m

Given volume of iron = 0.88 cu. m 

Therefore, Number of rods = 0.88×500011 = 400.

Let the side of the square be x. Then, its diagonal = 2x.  

Radius of incircle = x/2  and radius of circumcircle =2x2 .

Therefore, required ratio = πx24:πx22 = 14:12=1:2

Given that container has 50 litres of milk.

 After replacing 8 litres of milk with water for three times, milk contained in the container is:

 ⇒501-8503

⇒50×4250×4250×4250  = 29.63 litres.

Given that 3x-y=27, 3x+y=243

⇒3x-y =33 , 3x+y=35

 => x-y=3, x+y=5

 => x = 4

Amount to be paid = Rs.100+200×5×1100+100×5×1100= Rs. 115.