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Quiz: Surds And Indices

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Number of Questions: 25

Question: 16 -

If y3 = 0.008, y5 = ?

Options:

  1. 0.032

  2. 0.00032

  3. 0.0032

  4. 0.000032

    5. Answer:

    0.00032
    Solution:

    y5 = (0.2)5 = 0.00032.

Question: 17 -

Simplify: yp(q - r) . yq(r - p) . yr(p - q)

Options:

  1. y

  2. 1

  3. y2

  4. 0

    5. Answer:

    1
    Solution:

    yp(q - r) . yq(r - p) . yr(p - q) 

    = ypq - pr + qr - qp + rp - rq 
    = yp0 = 1.

Question: 18 -

Identify the greatest numbers: 450, 2100, 1625

Options:

  1. All are equal

  2. 1625

  3. 450

  4. 2100

    5. Answer:

    All are equal
    Solution:

    450 = (22)50 = 2100 => 1625 = (24)25 = 2100 

    Hence, 450, 2100 and 16425 are all equal.

Question: 19 -

[(√7 + √5) / ( (√7 - √5)] + [(√7 - √5) / (√7 + √5)] = ? 

Options:

  1. 12

  2. 6

  3. 18

  4. 14

    5. Answer:

    12
    Solution:

    [(√7 + √5) / ( (√7 - √5)] + [(√7 - √5) / (√7 + √5)] 

    = [(√7 + √5)2 + (√7 - √5)2] / (√7 + √5)(√7 - √5)
    [(√7 + √5)2 + (√7 - √5)2] / 2 = 12

Question: 20 -

Which of the following is the greatest?

Options:

  1. 51/2

  2. 61/5

  3. 41/4

  4. 37/10

    5. Answer:

    51/2
    Solution:

    5 > 4 and 1/2 > 1/4 

    51/2 > 41/4 
    41/4 cannot be the greatest. Hence 31/4 also cannot be the greatest. 
    37/10 = (37)1/10 = (2187)1/10 
    51/2 = 55/10 = (55)1/10 = (3125)1/10 
    61/5 = 62/10 = (62)1/10 = (36)1/10 
    As (3125)1/10 > (2187)1/10 > (36)1/10 , 51/2 is the greatest.