Model 1 Simplification using VBODMAS Practice Questions Answers Test with Solutions & More Shortcuts

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: (a)

Using Rule 2,

$1/{5×6} + 1/{6×7} + 1/{7×8} + 1/{8×9} + 1/{9×10} + 1/{10×11}$

= $1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 +1/9 - 1/10 +1/10 - 1/11 +1/11$

= $1/5 - 1/11 ={11 - 5}/55 = 6/55$

Answer: (b)

Using Rule 1,

Expression

= $9 - 11/9 of {36/11} ÷ {36/7} of 7/9$

= $9 - 11/9 × {36/11} ÷ {36/7} × 7/9$

= 9 - 4 ÷ 4

= $9 - 4 × 1/4$ = 9 - 1 = 8