Unit-2:
(a) Number system
(b) Elementary algebra
(c) H.C.F. and L.C.M.
(d) Fractions and decimal fractions
(e) Logarithms
Q1.
If the numerator of a fraction be increased by 6% and its denominator decreased by 2% the value of fraction becomes 6/7, find the original
fraction .
(a) 2/3 (b) 1/2 (c) 41/19 (d) 42/53
Solution.
So let original fraction is x/y
as per question =
106% of x/ 98% of y
=
6/ 7
x/ y
=
42/ 53
Solution
Q2.
Find the number of different divisors of 72 besides unity.
(a) 10 (b) 12 (c) 9 (d) 15
Solution.
Note : Find the prime factors of the number and increase the exponent of each factor by 1, then multiply.
72 = 2 x 2 x 2 x 3 x 3
= 23 . 32
(3 + 1)(2 + 1) = 12
Solution
Q3.
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
Q4.
Find the multiple of expression 72n - 33n .
(a) 10 (b) 12 (c) 27 (d) 22
Solution.
(d) 22
xn - an = is exactly divisible by (x-a)
= (49)n - (27)n
Solution
Q5.
If a = b = c, then find the value of
(a+b+c)2/ 3(a2+b2+c2)
(a) 1 (b) 2 (c) 3 (d) 4
Solution.
(3a)2/3(3a2) = (9a2)/(9a2) = 1
Solution
Q6.
what is the greatest number that will divide 38,45 and 52 and will leave as remember 2,3 and 4 respectively.
(a) 2 (b) 3 (c) 4 (d) 6
Solution.
In this case we have to find HCF, as HCF will divide exactly (38 - 2)(45 - 3) and (52 - 4).
Prime factors of 36 = 22
x 32
42 = 21 x 31 x 71 , 48 = 24 x 31
HCF = 2 x 3 = 6
Solution
Q7.
In the lowest form of a fraction, denominator and numerator are prime number to each other.
(a) Yes (b) No (c) Can't say
Solution.
(a) Yes
Solution
Q8.
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
Q9.
A fraction becomes 4/7, when its denominator increased by 10% and numerator decreased by 10% respectively . find the original fraction.
(a) 61/78 (b) 1/3 (c) 44/81 (d) 4/9
Solution.
(90% of x)/(110% of y) = 4/7
90x/110y = 4/9
x/y = (4 x 110)/(9 x 90)
= 44/81
Solution
Q10.
Which one is correct .
(a) Logarithm is not defined for negative number.
(b) log 1 = 1
(c) log22 = 2
(d) lognn = (log n/log m)
Solution.
(a) Logarithm is not defined for negative number.
Solution
