If a and b be positive integers such that a2 - b2 = 19, then the value of a is
19
20
9
10
If a and b are two odd positive integers, by which of the following integers is (a4 - b4) always divisible?
3
6
8
12
C.
8
a4 - b4 = (a - b) (a + b) (a2 + b2), where a and b are odd positive integers.
If two positive integers are odd, then their sum, difference and sum of their squares always even.
∴ (a - b) (a + b) and (a2 + b2) are divisible by 2.
Hence (a - b) (a + b) x (a2 + b2) = a4 - b4 is always divisible by 23 = 8.
A drum of kerosene is full. When 30 L of kerosene is drawn from it, it remains full. The capacity of the drum is
120 L
135 L
150 L
180 L
By what least number should 675 be multiplied so as to obtain a perfect cube number?
3
5
24
40
Two numbers are in the ratio 3 : 4. Their LCM is 84. The greater number is
21
24
28
84