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All questions of Indices & Surds for JAMB Exam

(256)0.16 x (256)0.09 = ?
  • a)
    4
  • b)
    16
  • c)
    64
  • d)
    256.25
Correct answer is option 'A'. Can you explain this answer?

Naroj Boda answered
 (256)0.16 x (256)0.09 = (256)(0.16 + 0.09)
= (256)0.25
= (256)(25 / 100)
= (256)(1 / 4)
= (44)(1 / 4)
= 44(1 / 4)
= 41
= 4

If 3(x - y) = 27 and 3(x + y) = 243, then x is equal to:
  • a)
    0
  • b)
    2
  • c)
    4
  • d)
    6
Correct answer is option 'C'. Can you explain this answer?

Yash Patel answered
 3x - y = 27 = 33    ⇔    x - y = 3 ....(i)
⇒ 3x + y = 243 = 35    ⇔    x + y = 5 ....(ii)
On solving (i) and (ii), we get x = 4.

1/(1 + x(b - a) + x(c - a)) + 1/(1 + x(a - b) + x(c - b)) + 1/(1 + x(b - c) +x(a - c) ) = ?
  • a)
    0
  • b)
    1
  • c)
    xa - b - c
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Rhea Reddy answered
Given Exp: 
1/(1 + xb / xa + xc / xa) + 1/(1 + xa / xb + xc / xb) + 1/(1 + xb / xc +xa / xc)
= xa/(xa + xb + xc ) + xb/(xa + xb + xc ) + xc/(xa + xb + xc )
= (xa + xb + xc ) / (xa + xb + xc )
= 1.

(6)6.5 × (36)4.5 ÷ (216)4.5 = (6)?
  • a)
    1
  • b)
    2
  • c)
    4
  • d)
    6
Correct answer is option 'B'. Can you explain this answer?

Uday Nambiar answered
(6)6.5 × (36)4.5 ÷ (216)4.5

= (6)6.5 × [(6)2]4.5 ÷ [(6)3]4.5

= (6)6.5 × (6)9 ÷ (6)13.5

= (6)(6.5 + 9 - 13.5) 

= (6)2

(25)7.5 x (5)2.5 ÷ (125)1.5 = 5?
  • a)
    8.5
  • b)
    13
  • c)
    16
  • d)
    17.5
Correct answer is option 'B'. Can you explain this answer?

Alok Verma answered
Let (25)7.5 x (5)2.5 ÷ (125)1.5 = 5x.
Then, (52)7.5 x 52.5 / (53) 1.5 = 5x
⇒ (52)7.5 x 52.5 / (5)3 x 1.5 = 5x
⇒ 515 x 52.5 / 54.5 = 5x
⇒ 5x = 5(15 + 2.5 - 4.5)
⇒ 5x = 513
∴ x = 13.

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