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Surds, Indices and Logarithms MCQs for UPPSC (UP) Exam

It covers all Important Questions with answers on Surds, Indices and Logarithms for the UPPSC (UP) exam. The questions are based on important topics. Details about the questions:
  • Topic: Surds, Indices and Logarithms
  • Type of Questions: MCQs with solutions
  • Number of Questions: 33
  • You can attempt them on EduRev to score high in UPPSC (UP) 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.

  • a)
    - (1 + a)
  • b)
    (1 + a)-1
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?

Wizius Careers answered
⇒ - log10 (7 x 10)
⇒ - (log10 7 + log10 10)
⇒ - (a + 1)

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.

if log 2 = 0.30103 and log 3 = 0.4771, find the number of digits in (648)5.
  • a)
    15
  • b)
    14
  • c)
    13
  • d)
    12
Correct answer is option 'A'. Can you explain this answer?

Ishani Rane answered
log(648)^5 
= 5 log(648) 
= 5 log(81 x 8) 
= 5[log(81) + log(8)] 
=5 [log(34) + log(23)] 
=5[4log(3) + 3log(2)]
= 5[4 x 0.4771 + 3 x 0.30103] 
= 5(1.9084 + 0.90309) 
= 5 x 2.81149 
approx. = 14.05

ie, log(648)^5 = 14.05 (approx.)

ie, its characteristic = 14

Hence, number of digits in (648)5 = 14+1 = 15

 
The value of is:
 
  • a)
    0
  • b)
    1
  • c)
    5
  • d)
    60
Correct answer is option 'B'. Can you explain this answer?

Shalini Patel answered
Given expression = 1/log60 3 + 1/log60 4 + 1/log60 5
= log60 (3 x 4 x 5)
= log60 60
= 1.

If log 27 = 1.431, then the value of log 9 is:
  • a)
    0.934
  • b)
    0.945
  • c)
    0.954
  • d)
    0.958
Correct answer is option 'C'. Can you explain this answer?

Log 27 = 1.431

 log (33 ) = 1.431

 3 log 3 = 1.431

 log 3 = 0.477

 log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.

If m and n are whole numbers and mn = 196, what is the value of (m - 3)(n+1) ?
  • a)
    2744
  • b)
    1
  • c)
    121
  • d)
    1331
Correct answer is option 'D'. Can you explain this answer?

mn = 196

We know that 142 = 196

Hence we can take m = 14 and n = 2

(m - 3)(n+1) = (14 - 3)(2+1) = 113 = 1331

if log 2 = 0.30103, the number of digits in 2128 is
  • a)
    38
  • b)
    39
  • c)
    40
  • d)
    41
Correct answer is option 'B'. Can you explain this answer?

Milan Nair answered
log(2128) = 128log(2) = 128 × 0.30103 ≈ 38.4

ie, its characteristic = 38

Hence, number of digits in 2128 = 38+1 = 39

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