Model 1 Simplification using VBODMAS Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

Using Rule 1,

$8{1/2} - [3{1/4} ÷(1{1/4} - 1/2(1{1/2} - 1/ 3 - {1/6}))]$

$17/2 - [{13/4} ÷({5/4} - 1/2({3/2} - 1/ 3 - {1/6}))]$

$17/2 - [{13/4} ÷({5/4} - 1/2({9 - 2 - 1}/6))]$

$17/2 - [{13/4} ÷({5/4} - 1/2 × {6/6})]$

$17/2 - [{13/4} ÷({5/4} - 1/2)]$

$17/2 - [{13/4} ÷({5 - 2}/4)]$

$17/2 - [{13/4} ÷ {3/4}]$

$17/2 - [{13/4} × 4/3] = 17/2 - 13/3$

= ${51 - 26}/6 = 25/6 = 4{1/6}$

Answer: (d)

Using (x) of Basic Formulae

Let 0.1 = a, 0.2 = b and 0.3 = c

Then, we have,

${a×a×a+b×b×b+c×c×c-3abc}/{a×a+b×b+c×c - ab - bc - ac}$

= ${a^3+b^3+c^3 - 3abc}/{a^2+b^2+c^2 - ab -bc - ac}$

= a + b + c

= 0.1 + 0.2 + 0.3 = 0.6

Answer: (d)

Using Rule 1,

I. = $3/4 × 6/5 = 9/10$

II. = 3 ÷ $[4/5 × 1/6] = 3 ÷ {2/15} = 45/2$

III. = $[3 ÷ {4/5}] ÷ 6 = {15/4} ÷ 6 = 5/8$

IV. =$3 ÷ {4} × 5/6 = 3 ÷ {10/3} = 9/10$

Obviously, (I) and (IV) are equal

Answer: (c)

${3{1/4} - 4/5 of {5/6}}/{4{1/3} ÷ {1/5} - (3/10 + 21{1/5})} - (1{2/3} of 1{1/2})$

Using Rule 1,

= ${{13/4} - {5/6} × {4/5}}/{{13/3} ÷ {1/5} - (3/10 + {106/5})} - ({3/2} × {5/3})$

= ${13/4 - 2/3}/{{13 × 5}/3 - ({3+212}/10)} - 5/2$

= ${{39 - 8}/12}/{{65/3} - {215/10}} - 5/2$

= ${31/12}/{{650 - 645}/30} - 5/2$

= $31/12 × 30/5 - 5/2$

= $31/2 - 5/2 = {31 - 5}/2 = 26/2 = 13$

Answer: (b)

Using Rule 1,

$5/{15/8 × 4/3} × {21/10}/{7/2} of {5/4}$

=$5 × 2/5 × 21/10 × 2/7 × 5/4$

=$3/2 = 1{1}/2$

Answer: (d)

$[3{1/4} ÷ (1{1/4} - 1/2(2{1/2} - \ov{1/4 - 1/6}))] ÷ (1/2 of 4{1/3})$

Using Rule 1,

= $[{13/4} ÷ ({5/4} - 1/2({5/2} - {3 - 2}/12))] ÷ {13/6}$

= $[{13/4} ÷ ({5/4} - 1/2({5/2} - 1/12))] ÷ {13/6}$

= $[{13/4} ÷ ({5/4} - 1/2({30 - 1}/12))] ÷ {13/6}$

= $[{13/4} ÷ ({5/4} - 1/2 × 29/12)] ÷ {13/6}$

= $[{13/4} ÷ ({30 - 29}/24)] ÷ {13/6}$

= $[{13/4} ÷ {1/24}] ÷ {13/6}$

$[{13/4} × 24] ÷ {13/6}$

= $13 × 6 × 6/13 = 36$