What is the next number in the series 5, 10, 26, 50, 122, ……
5, 10, 26, 50, 122, …
(2)^{2} + 1, (3)^{2 }+ 1, (5)^{2} + 1,
(7)^{2} + 1, (11)^{2} + 1, (13)^{2} + 1
∴ Next number = (13)^{2} + 1 = 170
A number is divisible by 63 if it is divisible by:
63 = 7 × 9
∴ If a number is divisible by 63, then it should be divisible by both 7 and 9.
What is the sum of first 15 natural numbers?
Sum of first ‘n’ natural numbers =
∴ Sum of first 15 natural numbers
= 15 × 8 = 120
7,835 + 2b1 = 8126, then the value of b will be :
Let ‘x’ be the carry, resulting from sum of b and 3.
8 + 2 + x = 11 ⇒ x = 1
∴ 3 + b = 12
⇒ b = 9
What is the sum of first 20 odd numbers?
Sum of ‘n’ odd natural numbers (first)= n^{2}
∴ Sum of first 20 odd natural numbers = (20)^{2}
= 400
, the value of ‘a’ will be :
182 × 22 = 4004
∴ a = 4
What will be the last digit of 7^{333} ?
7^{1 }= 7
7^{2} = 49
7^{3 }= 343
7^{4} = 2401
7^{5} = 16807
∴ After leaving 43 exponents 7^{n} repeats its unit digit.
∴ 7^{4n} has 1 as its units place digit.
∴ 7^{332} has 1 as units place digit.
∴ 7^{333} has 7 as its units place digit.
Which of the following numbers is divisible by 11?
1221, 10·1221 = 99, 99 can be divided by 11, hence 1221 is divisible by 11.
the value of (x + y) will be :
When 8 and 7 are added, 1 is carry.
∴ x = 7 + 1 + 1 = 9
The carry of sum (5 + y) should be 1.
∴ 5 + y = 13
⇒ y = 8
∴ x + y = 17
, the value of (ab) will be : (1 ≤ a, b ≤ 9)
⇒ a^{2} + a^{2} = 8
⇒ 2a^{2} = 8
⇒ a = 2, b = 4
∴ a × b = 8
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