31.
Find the simplest value of
- (A) 3.8
- (B) 3.9
- (C) 4
- (D) 2.9
Solution:
$$\eqalign{ & \frac{{6.25 - 1.96}}{{1.1}} \cr & = \frac{{{{\left( {2.5} \right)}^2} - {{\left( {1.4} \right)}^2}}}{{\left( {1.1} \right)}} \cr & = \frac{{\left( {1.1} \right) \times 3.9}}{{\left( {1.1} \right)}} \cr & = 3.9{\text{ Answer}} \cr} $$
32.
The square root of
- (A) 250
- (B) 2500
- (C) 2000
- (D) 4000
Solution:
$$\eqalign{ & {\text{According to the question,}} \cr & \sqrt {\frac{{0.342 \times 0.684}}{{0.000342 \times 0.000171}}} \cr & = \sqrt {\frac{{342 \times 684 \times 1000000}}{{342 \times 171}}} \cr & = \sqrt {4 \times 1000000} \cr & = 2 \times 1000 \cr & = 2000 \cr} $$
33.
The difference of ÃÂÃÂ and its reciprocal is equal to = ?
- (A)
- (B)
- (C)
- (D) None of these
Solution:
$$\eqalign{ & {\text{Required differnce}} \cr & {\text{ = }}\frac{{19}}{{16}} - \frac{{16}}{{19}} = \frac{{{{19}^2} - {{16}^2}}}{{304}} \cr & = \frac{{\left( {19 + 16} \right)\left( {19 - 16} \right)}}{{304}} \cr & = \frac{{35 \times 3}}{{304}} \cr & = \frac{{105}}{{304}} \cr} $$
34.
- (A) ab = cd
- (B) ad = bc
- (C) ac = bd
- (D) a = b =c ≠ d
Solution:
$$\eqalign{ & {\text{According to question,}} \cr & \frac{{3a + 4b}}{{3a - 4b}}{\text{ = }}\frac{{3c + 4d}}{{3c - 4d}} \cr & \Rightarrow \frac{{3a}}{{4b}} = \frac{{3c}}{{4d}} \cr & \Rightarrow ad = bc \cr} $$
35.
The value of ÃÂÃÂ ÃÂÃÂ ÃÂÃÂ is:
Solution:
$$\eqalign{ & \frac{{1.6 \times 1.6 \times 1.6 - 0.6 \times 0.6 \times 0.6}}{{1.6 \times 1.6 + 1.6 \times 0.6 + 0.6 \times 0.6}} \cr & = \frac{{{{\left( {1.6} \right)}^3} - {{\left( {0.6} \right)}^3}}}{{{{\left( {1.6} \right)}^2} + 1.6 \times 0.6 + {{\left( {0.6} \right)}^2}}} \cr & = \frac{{\left( {1.6 - 0.6} \right)\left\{ {{{\left( {1.6} \right)}^2} + 1.6 \times 0.6 + {{\left( {0.6} \right)}^2}} \right\}}}{{{{\left( {1.6} \right)}^2} + 1.6 \times 0.6 + {{\left( {0.6} \right)}^2}}} \cr & = 1.6 - 0.6 \cr & = 1 \cr} $$
36.
If a - b = 3 and a2 + b2 = 29, find the value of ab.
- (A) 10
- (B) 12
- (C) 15
- (D) 18
Solution:
2ab = (a2 + b2) - (a - b)2 2ab = 29 - 9 2ab = 20 ∴ ab = 10
37.
ÃÂÃÂ ÃÂÃÂ ÃÂÃÂ is equal to = ?
Solution:
$$\eqalign{ & {\text{According to the question,}} \cr & \frac{{\root 3 \of 8 }}{{\sqrt {16} }} \div \sqrt {\frac{{100}}{{49}}} \times \root 3 \of {125} \, \cr & \Rightarrow \frac{2}{4} \div \frac{{10}}{7} \times 5 \cr & \Rightarrow \frac{2}{4} \times \frac{7}{{10}} \times 5 \cr & \Rightarrow \frac{7}{4} \cr & \Rightarrow 1\frac{3}{4} \cr} $$
38.
If of of a number is 35, then how much is of that number?
- (A) 612.5
- (B) 715
- (C) 624.5
- (D) 723.5
Solution:
$$\eqalign{ & x \times \frac{1}{4} \times \frac{1}{5} = 35 \cr & x = 35 \times 20 \cr & x = 700 \cr & 700 \times \frac{7}{8} = \frac{{4900}}{8} = 612.5 \cr} $$
39.
The value of ÃÂÃÂ ÃÂÃÂ is :
- (A) 164
- (B) 152
- (C) 189
- (D) 156
Solution:
$$\eqalign{ & \frac{{\root 3 \of { - 2744} \times \root 3 \of { - 216} }}{{\root 3 \of {\frac{{64}}{{729}}} }} \cr & = \frac{{\left( { - 14} \right) \times \left( { - 6} \right)}}{{\frac{4}{9}}} \cr & = \frac{{84}}{{\frac{4}{9}}} \cr & = 189 \cr} $$
40.
Given that ÃÂÃÂ is approximately equal to ÃÂÃÂ is nearly equal to =?
- (A) 0.544
- (B) 1.333
- (C) 1.633
- (D) 2.666
Solution:
$$\eqalign{ & {\text{According to question,}} \cr & \Rightarrow \sqrt {\frac{8}{3}} \cr & \Rightarrow \sqrt {\frac{{8 \times 3}}{{3 \times 3}}} \cr & \Rightarrow \sqrt {\frac{{24}}{9}} \cr & \Rightarrow \frac{{4.898}}{3} \cr & \Rightarrow 1.633 \cr} $$