Number System
Question
Q1.
Find the least number by which 19404 must be multiplied or divided so as to make it a perfect square ?
Solution.
19404 = 2x2x3x3x7x7x11 = 22 x 32 x 72 x 11
Thus, if the number is multiplied or divided
by 11 the resultant number will be a perfect square. Therefore, required number is 11.
Solution
Q2.
If a number is as much greater than 31 as it is less than 75, then the number is.
(a)106 (b)44 (c)74 (d) 53
Solution.
If the number be x , then
x - 31 = 75 - x
= 2x = 75 + 31 = 106
x = 53
Solution
Q3.
Two number 902 and 607 is divided by a third number and leave the same remainder in both cases . find the two digit divisor which leave
the same remainder.
(a) 59 (b) 65 (c) 34 (d) 95
Solution.
(a) 59
Difference of 902 and 607 is 295
295 = 5 x 59
Solution
Q4.
Find the unit digit in the product of 771 x 663 x 365 .
(a) 6 (b) 1 (c) 4 (d) 5
Solution.
(c) 4
771 = 74 x 17 + 3 = 1 x 343 = ----------3
663 = 64 x 15 + 3 = 6 x 216 = ---------6
365 = 34 x 16 + 3 = 1 x 3 = ---------3
= (---3)(--6)(---3)
= (-- 54)
Solution
Q5.
The (3/5)th of the square of a number is 126.15, find the number.
(a) 16.5 (b) 14.5 (c) 14 (d) 19
Solution.
let the number is x
x2 (3/5) = 126.15
x2 = 210.25
x = 14.5
Solution
Q6.
If 13 + 23 + 33 + --------- + 103, so find the value of 4 + 32 + 108 + -------- + 4000.
(a) 12,800 (b) 11,000 (c) 12,050 (d) 12,100
Solution.
= 4(1 + 8 + 27 + ------- + 1000)
= 4(13 + 23 + 33 + -------- + 103)
= 4(3025)
= 12,100
Solution
Q7.
If (a - 1)2 + (b + 2)2 + (c + 1)2 = 0, Then the value of 2a - 3b + 7c is.
(a)12 (b)3 (c)11 (d)1
Solution.
(a - 1)2 + (b + 2)2 + (c + 1)2 = 0
a - 1 = 0, a = 1
b + 2 = 0, b = -2
c + 1 = 0,
c = -1
2a -3b + 7c
2 - 3(-2)+ 7(-1)
2 + 6 - 7 = 1
Solution
Q8.
The value of 0.65 x 0.65 + 0.35 x 0.35 + 0.70 x 0.65 is.
(a)1.75 (b)1.00 (c)1.65 (d)1.55
Solution.
Expression = 0.65 x 0.65 + 0.35 x 0.35 + 2 x 0.35 x 0.65
=(0.65 + 0.35)2
= (1)2=1
{a2+b2+2ab = (a + b)2}
Solution
Q9.
{(21)2-1} is divisible by which number?
(a)6 (b)7 (c)8 (d)9
Solution.
(8)
Note:As we know that n2 - 1 is divisible by 8, if n is an odd positive integer.
Solution
Q10.
If 3x+3 + 7 = 250, then x is equal to.
(a)5 (b)3 (c)2 (d)1
Solution.
3x+3 + 7 = 250
3x+3 = 243
3x+3 = 35
x+3 = 5
x = 2
Solution
