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Solution:  In the given sequence all then numbers except 100 are perfect cubes of natural numbers. As , 8=23,27=33,64=43, 125=53,216=63,343=73 Than is correct answer = 100

Solution Let the length of the smallerline segment”= x cm.The length of larger line segment= (x+ 2) cm.According to the question,(x + 2)² – X² = 32⇒x²+4x+4-x²=32⇒4x=32-4=28x=28/4=7The required length= x+ 2 = 7 + 2 = 9 cm.

(1) 54036 (2) 50436 (3) 34056 (4) 65043 Solution: (4) A number will be exactly divisible by 18 if it is divisible by 2 and 9 both.Clearly 65043 is not divisible by 2.= Required number = 65043

Solution Total age of 14 girls + 1 teacher = 15 x 15 = 225 yrs. Average age of 14 girls = 14 yrs.:. Total age of 14 girls= 14 x 14 = 196 yrs.:. Teacher’s age= 225 – 196 = 29 yrs.

Solution- [latexpage] \[ Sum of First 60 numbers = \frac{60(60+1)|2}= 60*61= 1830This number is divisble by 61 \] Thus Answer is option – 4