Multiple Choice QuestionsFind the least number which when divided by 12, 18, 36 and 45 leaves the remainder 8, 14, 32 and 41 respectively.
176
180
178
178
a and b are irrational numbers such that a + b = q is a rational number, then a - b is
always rational
sometimes rational
always irrational
always irrational
The difference between the greatest and least five-digit numbers formed by the digits 2, 5,0, 6, 8 is (repetition of digits are not allowed)
69552
65925
65952
65952
A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is
220030
22030
1220
1220
When a number x is divided by a divisor it is seen that the divisor = 4 times the quotient = double the remainder. If the remainder is 80 then the value of x is
6480
9680
8460
8460
On dividing a certain number by 342 we get 47 as remainder. If the same number is divided by 18, what will be the remainder?
15
11
17
17
The sum of three numbers is 252. If the first number is thrice and the second and third number is two-third of the first, then the second number is
41
21
42
42
Three numbers are in Arithmetic Progression (AP) whose sum is 30 and the product is 910. Then the greatest number in the AP is
17
15
13
13
C.
13
Let three numbers in A.P. be a - d, a and a + d respectively.
According to the question,
(a - d) + (a) + (a + d) = 30
⇒ 3a = 30 ⇒ a = 30/3 = 10
Again, a (a - d) (a + d) = 910
⇒ 10 (10 - d) (10 + d) = 910
⇒ 100 - d2 = 91
⇒ d2 = 100 - 91 = 9
⇒ 
∴ Largest number = a + d = 10 + 3 = 13
The number which can be written in the form of n(n + 1) (n + 2) where n is a natural number, is
7
3
5
5
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