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Simplifications


  • 1. Find the value of 1/(3+1/(3+1/(3-1/3))) 
A.) 3/10
B.) 10/3
C.) 27/89
D.) 89/27

Answer: Option 'C'

1/[3 + (1/(3+1/(3 - 1/3)))] 
=> 1/[3 + 1/(3 + 1/(8/3))] 
=> 1/[3 + 1/(3 + 3/8)] 
=> 1/[3 + 8/27] 
=> 1/(89/27) 
=> 27/89

  • 2. Find the value of
A.) 3½ 99;
B.) 34/99
C.) 2.131313
D.) 3.141414

Answer: Option 'D'


6/9 + 7/9 + 9/9 + 69/99 
2/3 + 7/9 + 1 + 69/99 
(66 + 77 + 99 + 69)/99 
311/99 => 3.141414

  • 3. Find the value of
    ((0.1)3 + (0.6)3 + (0.7)3 − (0.3)(0.6)(0.7))/((0.1)2 + (0.6)2 + (0.7)2 − 0.006 − 0.42 − 0.07)
A.) 14/10
B.) 1.35
C.) 13/10
D.) 0

Answer: Option 'A'

((0.1)3 + (0.6)3 + (0.7)3 − (0.3)(0.6)(0.7))/((0.1)2 + (0.6)2 + (0.7)2 − 0.006 − 0.42 − 0.07)
=> (0.1 + 0.6 + 0.7)3/(0.1 + 0.6 + 0.7)2
=> 0.1 + 0.6 + 0.7 => 1.4 = 14/10

  • 4. Solve(0.76 × 0.76 × 0.76 − 0.008)/(0.76 × 0.76 + 0.76 × 0.2 + 0.04) 
A.) 0.56
B.) 0.65
C.) 0.54
D.) 0.45

Answer: Option 'A'

0.56

  • 5. Find the value of × in the following 
    (1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7) 
A.) 4
B.) 3
C.) 3.6
D.) 3.06

Answer: Option 'C'

3.6

  • 6. Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100) 
A.) 1/50
B.) 1/25
C.) 1/20
D.) 1/40

Answer: Option 'C'

(2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20

  • 7. Find the value of (875 233/899) × 899 
A.) 786588
B.) 786858
C.) 786885
D.) 786885

Answer: Option 'B'

(875 233/899) × 899 
(786625 + 233)/899 × 899 
786858/899 × 899 
786858

  • 8. Find the value of 3/11 × [(1 + 1/3) (1 + 1/4) …………. (1 + 1/120)] is 
A.) 121
B.) 11
C.) 10.6
D.) 7.82

Answer: Option 'B'

3/11 × [(1 + 1/3) (1 + 1/4) ....... (1 + 1/120)] 
3/11 × [4/3 + 5/4 × ........ 121/120] 
3/11 × 4/3 × 5/4 × .... 121/120 
121/11 = 11.

  • 9. If 13 + 23 + 33 +......+ 103 = 516 then the value of 23 + 43 + 63 + ..... + 203 is
A.) 1013
B.) 1032
C.) 516
D.) 900

Answer: Option 'B'

2(13 + 23 + 33 + ---------- + 103)
2 × 516 = 1032

  • 10. If 13 + 23 + ..... + 93 = 1025 then the value of (0.07)3 + (0.14)3 + (0.21)3 + ..... +(0.63)3 Is close to
A.) 0.351575
B.) 0.251575
C.) 2.515575
D.) 3.51575

Answer: Option 'A'

0.351575



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