Explanation

A number divisible by 7, 11 and 13:

= LCM of 7, 11 and 13

= 1001

A number which is multiple of 1001 is of the form:

Xyz xyz …….. (digits repeating)

Answer: 624624

Explanation

Common ratio r = 2.

Sum of 10 terms = 3 × (2¹⁰ - 1) = 3069

Explanation

Each pair (2,5), (4,7), (17,6) has no common factor other than 1.

Hence, they are co-prime (relatively prime) numbers.

Explanation

Total ways = (12 2) = 66; same color ways = 10 + 6 + 3 = 19

Different color ways = 66 - 19 = 47; so probability = 47/66.

Explanation

From DRAIN → ^!#*@, we get the mapping: D→^, R→!, A→#, I→*, N→@.

Encode NARD as N(@) A(#) R(!) D(^) → @#!^.

Explanation

For 123 → 13², the first and last digits 1 and 3 form 13, then squared gives 169.

Apply same rule to 235 → first and last digits 2 and 5 form 25, squared gives 625.

Explanation

The word CHORD has 5 distinct letters: C-H-O-R-D.

When taking all the letters together, the number of ways to arrange them is equal to the number of permutations of 5 items, which is calculated as:

5! = 5 × 4 × 3 × 2 × 1 = 120

Explanation

• Atoms of the same element with different numbers of neutrons are called isotopes.
• Atoms of the same element have the same number of protons and electrons but different numbers of neutrons.

Explanation

Syed Ameer Ali established the London Muslim League in 1908.

In 1909, Syed Ameer Ali became the first Indian to sit as a member of the Judicial Committee of the Privy Council on which he would serve till his death in 1928.

Explanation