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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?
(256)0.16 x (256)0.09 = ?
a)
4
b)
16
c)
64
d)
256.25
 | 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
= (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?
If 3(x - y) = 27 and 3(x + y) = 243, then x is equal to:
a)
0
b)
2
c)
4
d)
6
 | 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.
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:- a)1.45
- b)1.88
- c)2.9
- d)3.7
Correct answer is option 'C'. Can you explain this answer?
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:
a)
1.45
b)
1.88
c)
2.9
d)
3.7
 | KS Coaching Center answered |
⇒ xz = y2 ⇔ 10(0.48 z) = 10(2 x 0.70) = 101.40
⇒ 0.48 z = 1.40
⇒ z = 140 / 48 = 35 / 12 = 2.9(approx.)
⇒ 0.48 z = 1.40
⇒ z = 140 / 48 = 35 / 12 = 2.9(approx.)
- a)- (1 + a)
- b)(1 + a)-1
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
a)
- (1 + a)
b)
(1 + a)-1
c)
d)
 | Wizius Careers answered |
⇒ - log10 (7 x 10)
⇒ - (log10 7 + log10 10)
⇒ - (a + 1)
⇒ - (log10 7 + log10 10)
⇒ - (a + 1)
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for "Surds and Indices" under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations. (17)3.5 x (17)? = 178- a)2.29
- b)2.75
- c)4.25
- d)4.5
Correct answer is option 'D'. Can you explain this answer?
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for "Surds and Indices" under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.
(17)3.5 x (17)? = 178
a)
2.29
b)
2.75
c)
4.25
d)
4.5
 | Divey Sethi answered |
Let (17)3.5 x (17)x = 178
Then, (17)3.5 + x = 178
∴ 3.5 + x = 8
⇒ x = (8 - 3.5)
⇒ x = 4.5
Then, (17)3.5 + x = 178
∴ 3.5 + x = 8
⇒ x = (8 - 3.5)
⇒ x = 4.5
If 5a = 3125, then the value of 5(a - 3) is:- a)25
- b)125
- c)625
- d)1625
Correct answer is option 'A'. Can you explain this answer?
If 5a = 3125, then the value of 5(a - 3) is:
a)
25
b)
125
c)
625
d)
1625
 | Ravi Singh answered |
⇒ 5a = 3125 ⇔ 5a = 55
⇒ a = 5.
∴ 5(a - 3) = 5(5 - 3) = 52 = 25.
⇒ a = 5.
∴ 5(a - 3) = 5(5 - 3) = 52 = 25.
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?
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
| | Rhea Reddy answered |
Given Exp:
1/(1 + xb / xa + xc / xa) + 1/(1 + xa / xb + xc / xb) + 1/(1 + xb / xc +xa / xc)
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.
= (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?
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
 | 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?
The value of is:
is:a)
0
b)
1
c)
5
d)
60
 | Shalini Patel answered |
Given expression = 1/log60 3 + 1/log60 4 + 1/log60 5
= log60 (3 x 4 x 5)
= log60 60
= 1.
= log60 (3 x 4 x 5)
= log60 60
= 1.
Which of the following statements is not correct?- a)log10 10 = 1
- b)log (2 + 3) = log (2 x 3)
- c)log10 1 = 0
- d)log (1 + 2 + 3) = log 1 + log 2 + log 3
Correct answer is option 'B'. Can you explain this answer?
Which of the following statements is not correct?
a)
log10 10 = 1
b)
log (2 + 3) = log (2 x 3)
c)
log10 1 = 0
d)
log (1 + 2 + 3) = log 1 + log 2 + log 3
 | Prince Chaudhary answered |
According to logarithm rule . option B is never correct
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?
If log 27 = 1.431, then the value of log 9 is:
a)
0.934
b)
0.945
c)
0.954
d)
0.958
 | Gowri Chakraborty answered |
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?
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
 | Cstoppers Instructors answered |
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
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?
if log 2 = 0.30103, the number of digits in 2128 is
a)
38
b)
39
c)
40
d)
41
 | 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
ie, its characteristic = 38
Hence, number of digits in 2128 = 38+1 = 39
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