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Real Numbers

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is
(A) 10 (B) 100 (C) 504 (D) 2520

Real Numbers

The product of a non-zero rational and an irrational number is
(A) always irrational (B) always rational
(C) rational or irrational (D) one

Real Numbers

If two positive integers p and q can be expressed as

p = ab² and q = a³b; a, b being prime numbers, then LCM (p, q) is

(A) ab (B) a²b² (C) a³b²     (D) a³b³

Real Numbers

If two positive integers a and b are written as a = x³y² and b = xy³; x, y are prime numbers, then HCF (a, b) is

(A) xy (B) xy² (C) x³y³ (D) x²y²

Real Numbers

The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is
(A) 13 (B) 65
(C) 875 (D) 1750

Real Numbers

If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is
(A) 4 (B) 2
(C) 1 (D) 3

Real Numbers

n² – 1 is divisible by 8, if n is
(A) an integer (B) a natural number
(C) an odd integer (D) an even integer

Real Numbers

For some integer q, every odd integer is of the form
(A) q (B) q + 1
(C) 2q (D) 2q + 1

Real Numbers

For some integer m, every even integer is of the form
(A) m (B) m + 1
(C) 2m (D) 2m + 1

Real Numbers

Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy
(A) 1 < r < b (B) 0 < r ≤ b
(C) 0 ≤ r < b (D) 0 < r < b