logo

CuriousTab

CuriousTab

Discussion


Home Aptitude Simplification Comments

  • Question
  • If a 2 + b 2 = 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
    ? a2 + 1/a2 = -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 also be written as a6 + 1/a6 + 1
    ? a12 + a6 + 1 = 3


  • Simplification problems


    Search Results


    • 1. 
      (2.247) 3 + (1.730) 3 + (1.023) 3 -3 x 2.247 x 1.730 x 1.023 / [(2.247) 2 + (1.730) 2 + (1.023) 2 - 2.247 x 1.730 - 1.730 x 1.023 - 2.247 x 1.023] =?

    • Options
    • A. 1.730
    • B. 4
    • C. 5
    • D. 5.247
    • Discuss
    • 2. 
      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
    • 3. 
      City A has a population of 136000 which is decreasing at the rate of 2400 per year , City B has a population of 84000 which is increasing at the rate of 1600 per year . In how many years will the population of two cities become equal ?

    • Options
    • A. 15
    • B. 18
    • C. 13
    • D. 19
    • Discuss
    • 4. 
      A fruit seller has a crate of apple containing 1 bruised apple for every 40 apples in the crate, If 3 out of every 4 bruised apples are considered unsaleable and there are 9 unsaleable apples in the crate, then how many apples are there in the crate?

    • Options
    • A. 500
    • B. 390
    • C. 632
    • D. 480
    • Discuss
    • 5. 
      Mr. Sahni employed a worker for a certain work to be done in some days. He pays ?20 to the worker for each working day and the payment is reduced by ? 3 for each non-working day of the worker. For how many days the worker does remain absent from work if at the end of 120 days, he gets ? 560 as total remuneration?

    • Options
    • A. 80
    • B. 60
    • C. 70
    • D. 40
    • Discuss
    • 6. 
      If a * b = a + b + a / b, Then the value of 12 * 4 is

    • Options
    • A. 48
    • B. 19
    • C. 20
    • D. 21
    • Discuss
    • 7. 
      (4 x 4 x 4 x 4 x 4 x 4) 5 x (4 x 4 x 4 ) 8 ÷ (4) 3 = (64) ?

    • Options
    • A. 17
    • B. 10
    • C. 16
    • D. 11
    • Discuss
    • 8. 
      3x + 2y = 12 and xy = 6, them the value of 9x2 + 4y2 is?

    • Options
    • A. 76
    • B. 80
    • C. 72
    • D. 74
    • Discuss
    • 9. 
      If x + 1/x = 3, then x5 + 1/x5 is equal to?

    • Options
    • A. 123
    • B. 83
    • C. 92
    • D. 112
    • Discuss
    • 10. 
      If x + 1/x = 2, then what is value of x - 1/x ?

    • Options
    • A. 0
    • B. 1
    • C. 2
    • D. -2
    • Discuss


    Comments

    There are no comments.

Enter a new Comment