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Home Aptitude Surds and Indices Comments

  • Question
  • If m = 7 - 4?3, then (?m + 1/?m) =?


  • Options
  • A. 8
  • B. 3
  • C. 4
  • D. 9

  • Correct Answer


  • Explanation

    Given that ,
    m = 7 - 4?3
    Then I/m = 1/7 - 4?3......................(1)

    Now multiply and divide with 7 + 4?3 in Eq. (1)
    We will get,
    1/m = ( 1/7 - 4?3 ) x ( 7 + 4?3 / 7 + 4?3)
    ?1/m = ( 7 + 4?3 )/ ( 7 - 4?3 ) x ( 7 + 4?3
    ?1/m = ( 7 + 4?3 ) / ( 72 - ( 4?3)2 )
    ?1/m = ( 7 + 4?3 ) / ( 49 - 4 x 4 x 3 )
    ?1/m = ( 7 + 4?3 ) /49 - 48
    ?1/m = ( 7 + 4?3 ) / 1
    ?1/m = 7 + 4?3
    ? m + 1/m = 14
    ? ( m + 1/m ) + 2 = 14 + 2 = 16
    ? (?m + 1/?m)2 = ( m + 1/m )+ 2
    ? (?m + 1/?m)2 = 16
    ? (?m + 1/?m)2 = 42
    ? (?m + 1/?m) = 4


  • Surds and Indices problems


    Search Results


    • 1. 
      If m and n are natural numbers, the m?n

    • Options
    • A. always irrational
    • B. irrational unless n is the mth power of an integer
    • C. irrational unless m is the nthpower of an integer
    • D. irrational unless m and n are coprime
    • Discuss
    • 2. 
      if a = 2 + ?3, then what is the value of (a2 + a -2)?

    • Options
    • A. 12
    • B. 14
    • C. 16
    • D. 18
    • Discuss
    • 3. 
      1/1 + xb - a + xc - a + 1/1 + xa-b + xc - b + 1/1 + xb - c+ xa - c =?

    • Options
    • A. xa - b - c
    • B. 1
    • C. 0
    • D. 3
    • Discuss
    • 4. 
      If a = ?3/2, then ?1 + a + ?1 - a =?

    • Options
    • A. (2- ?3)
    • B. (2 + ?3)
    • C. ?3/2
    • D. ?3
    • Discuss
    • 5. 
      If (p/q)n - 1 = (q/p)n - 3, then the value of n is

    • Options
    • A. 1/2
    • B. 7/2
    • C. 1
    • D. 2
    • Discuss
    • 6. 
      If ?2n = 64 , what will be the value of n?

    • Options
    • A. 8
    • B. 4
    • C. 12
    • D. 16
    • Discuss
    • 7. 
      (100)0 is equivalent to :

    • Options
    • A. 0
    • B. 10
    • C. 1
    • D. 100
    • Discuss
    • 8. 
      The value of 6a3 b3 c2 ÷ 2ab2 c is :

    • Options
    • A. 3a 2 bc
    • B. 3a b 2 c
    • C. 3a 2 b 2 c 2
    • D. 3a 3 b3 c3
    • Discuss
    • 9. 
      (16)?3/4 + 2?3 + (8)?2/3 is equivalent to :

    • Options
    • A. 1 2
    • B. 3 2
    • C. 9 2
    • D. 5 4
    • Discuss
    • 10. 
      [(2a2)3]3 [(3a3)2]2 ÷ [(6a6)2]2 is equivalent to :

    • Options
    • A. 36a6
    • B. 32 a6
    • C. 32 a4
    • D. 34 a5
    • Discuss


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