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Unit 2

Unit-2:


(a) Number system
(b) Elementary algebra
(c) H.C.F. and L.C.M.
(d) Fractions and decimal fractions
(e) Logarithms


Q1. The sum of digits of a two digit number is 10. If the digit are reversed the number is decreased by 18. find the number.

(a) 49 (b) 23 (c) 64 (d) 54

Solution.
(c) 64

let the two digit numbers is 10x + y

x + y = 10 ---------1

10x + y - (10y + x) = 18

10x - 10y - (x - y) = 18

x - y = 2 ----------2

on solving equation 1 and 2, we get

x = 6 , y = 4
Solution

Q2. 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

Q3. Find the prime factors in the product 42 x 94 x 77 .

(a) 21 (b) 10 (c) 19 (d) 20

Solution.
= (22)2 x (32)4 x 77

= 24 x 38 x 77

= 4 + 8 + 7

= 19
Solution

Q4. Find the value of
(x-y)2/(y-z)(z-x)
+
(y-z)2/(x-y)(z-a)
+
(x-z)2/(x-y)(y-z)


(a) 7 (b) 3 (c) 2 (d) 6

Solution.
(x-y)3/(x-y)(y-z)(z-x)
+
(y-z)3/(y-z)(x-y)(z-x)
+
(x-z)3 /(x-z)(x-y)(y-z)


(x-y)3+ (y-z)3 + (x-z)3/ (x-y)(y-z)(z-x)
=
3(x-y)(y-z)(z-x)/ (x-y)(y-z)(z-x)


= 3

Note : a3 + b3 + c3 = 3abc
if a + b + c = 0
Solution

Q5. What should be added to 8x3 + 12x2 - 4x - 4 = 0 to make exactly divisible by x - 2.

(a) 40 (b) -100 (c) 90 (d) 100

Solution.
f(2) = 8(x)3 + 12(2)2 - 4(2) - 4

= 100

so put -100 so that f(2) = 0
Solution

Q6. Product of two numbers is 4107, and HCF is 37. so find the largest number.

(a) 211 (b) 111 (c) 140 (d) 191

Solution.
HCF (37) divides both the numbers exactly , so we can write

37x . 37y = 4107

xy = 3 (x and y both are prime numbers)

x = 1, y = 3 or y = 1, x = 3

largest number is 37 x 3 = 111
Solution

Q7. Find the smallest fraction which when multiplied to 2/5 x 10/24 x 7/5 x 3/8 gives a whole number.

(a) 3/10 (b) 2/3 (c) 7/80 (d) 80/7

Solution.
(d) 80/7
Simplifying 2/5 x 10/24 x 7/5 x 3/8

= 2/12 x 21/40

= 7/(20 x 4) = 7/80
Solution

Q8. Numerator of a fraction increased by 20% and denominator increased by 25%, then resultant fraction is 3/5 find the original fraction .

(a) 5/8 (b) 8/5 (c) 2/5 (d) 3/8

Solution.
Let original fraction is x/y

(120% of x)/(125% of y) = 3/5

x/y = (3 x 125)/(5 x 120)

= 375/600

= 5/8
Solution

Q9. Find the value of log20(1)20

(a) 0 (b) 3 (c) 2 (d) 1

Solution.
120 = 1

log 1 = 0
Solution

Q10. Evaluate 2log 3 + log(1/9)

(a) 3 (b) 0 (c) 1 (d) 2

Solution.
= log 32 + log 1 - log 9

= log 9 + log 1 - log 9

= log 1

= 0
Solution