Since 2, 3, 7, 11 are prime numbers and the given expression is
2¹⁰ x 3¹⁰ x 7¹⁷ x 11²⁷

Correct Option: B

Since 2, 3, 7, 11 are prime numbers and the given expression is
2¹⁰ x 3¹⁰ x 7¹⁷ x 11²⁷

So the number of prime factors in the given expression is (10 + 10 + 17 + 27 ) = 64.

L. C .M of 9, 11, 13 is 1287
On dividing 1294 by 1287, the remainder is 7 .

Correct Option: B

L. C .M of 9, 11, 13 is 1287
On dividing 1294 by 1287, the remainder is 7 .

∴ 1 must be subtracted from 1294, so that 1293 when divided by 9, 11, 13 leaves in each case the same remainder 6 .

L.C.M of 5, 6 , 7, 8 is 840
So, the number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2

Correct Option: B

L.C.M of 5, 6 , 7, 8 is 840
So, the number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2

∴ Required number = (840 x 2 + 3 ) = 1683

Required number = H.C.F of (1657 - 6) and (2037 - 5)
= H.C.F of 1651 and 2032

Correct Option: A

Required number = H.C.F of (1657 - 6) and (2037 - 5)
= H.C.F of 1651 and 2032
= 127

LCM of 5, 10, 15, 20, 25 and 30 is 300. So, the bell will toll together after every 300s (5min).

Correct Option: C

LCM of 5, 10, 15, 20, 25 and 30 is 300. So, the bell will toll together after every 300s (5min).
So, the number of times they toll together = 60/5 + 1=13