Govt. Exams
Entrance Exams
This question asks us to identify which number is a perfect square (a number that equals an integer multiplied by itself).
A perfect square is a number that can be expressed as n × n where n is an integer.
Test each option by finding if its square root is a whole number.
Only 169 has a whole number square root.
169 is a perfect square because 13 × 13 = 169, making the correct answer (B).
First five prime numbers are 2, 3, 5, 7, 11.
Product = 2 × 3 × 5 × 7 × 11 = 2310
If a number is divisible by both 3 and 5, and 3 and 5 are coprime (HCF=1), then the number must be divisible by their product: 3×5 = 15
Factors of 48: 1,2,3,4,6,8,12,16,24,48.
Factors of 64: 1,2,4,8,16,32,64.
Common factors: 1,2,4,8,16. HCF = 16
Check: 21=3×7 (not prime), 23 is only divisible by 1 and 23 (prime), 25=5×5 (not prime), 27=3×9 (not prime).
So 23 is the smallest prime greater than 20.
Sum of first n natural numbers = n(n+1)/2.
Here n=10, so sum = 10(11)/2 = 110/2 = 55
