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  • Question
  • If a 2 + 1 = a, then the value of a 12 + a 6 + 1 is?


  • Options
  • A. 2
  • B. 3
  • C. -3
  • D. 1

  • Correct Answer


  • Explanation

    a2 + 1 = a
    ? a + 1/a = 1
    On squaring both sides, we get
    a2 + 1/a2 + 2 = 1
    On cubing both sides, we get
    (a2 + 1/a2)3 = (-1)3
    ? a6 + 1/a6 + 3a2 x 1/a2 (a2 + 1/a2) = -1
    ? a6 + 1/a6 + 3 x (-1) = -1
    Now, a6 + 1/a6 + 1 = 3
    As, a12 + a6 + 1 can be written as a6 + 1/a6 + 1
    ? a12 + a6 + 1 = 3


  • Simplification problems


    Search Results


    • 1. 
      If a 2 + b 2 = 234 and ab = 108, find the value of a + b / a - b .?

    • Options
    • A. 10
    • B. 8
    • C. 5
    • D. 4
    • Discuss
    • 2. 
      ? 132 + 28 / 4 - (3)3 + 107 = (?) 2

    • Options
    • A. 2
    • B. 16
    • C. 256
    • D. 4
    • Discuss
    • 3. 
      Ravi earns twice as much in January as in each of the other months. What part of his annual earnings he earns in that month?

    • Options
    • A. 2/13
    • B. 1/10
    • C. 5/7
    • D. 1/5
    • Discuss
    • 4. 
      In a family, the father took 1/4 of the cake and he had 3 times as much as others had. The total number of family members is?

    • Options
    • A. 3
    • B. 7
    • C. 10
    • D. 12
    • Discuss
    • 5. 
      The highest score in an innings was 3/11 of the total and the next highest was 3/11 of the remainder. If the scores differed by 9, then the total score is?

    • Options
    • A. 99
    • B. 110
    • C. 121
    • D. 132
    • Discuss
    • 6. 
      If a, b and c are non-zero, a + 1/b = 1 and b + 1/c = 1, then the value of abc is?

    • Options
    • A. -3
    • B. 1
    • C. -1
    • D. 3
    • Discuss
    • 7. 
      If a + b + c = 0, then the value of [(a + b)/c + (b + c)/a + (c + a)/b] x [a/(b + c) + b/(c + a) + c/(a + b)] is?

    • Options
    • A. 9
    • B. 0
    • C. 8
    • D. -3
    • Discuss
    • 8. 
      If a + b + c = 14 and a 2 + b 2 + c 2 = 96, then (ab + bc + ca) =?

    • Options
    • A. 51
    • B. 55
    • C. 50
    • D. 65
    • Discuss
    • 9. 
      [5 - [3/4 + {2 1/ 2 - (1/2 + 1/6 - 1/7)}]] / 2 =?

    • Options
    • A. 123/168
    • B. 223/168
    • C. 323/168
    • D. 423/168
    • Discuss
    • 10. 
      [0.5 x 0.5 x 0.5 + 0.2 x 0.2 x 0.2 + 0.3 x 0.3 x 0.3 - 3 x 0.5 x 0.3 x 0.2 ] / [0.5 x 0.5 + 0.2 x 0.2 + 0.3 x 0.3 - 0.5 x 0.2 - 0.2 x 0.3- 0.5 x 0.3] =?

    • Options
    • A. 1
    • B. 0.6
    • C. 0.4
    • D. 0.03
    • Discuss


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