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(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
|
Faizan Khan 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
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
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.
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
|
Nikita Singh 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.)
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
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.
- 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)
|
Dia Mehta 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
|
Kavya Saxena 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
(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?
(6)6.5 × (36)4.5 ÷ (216)4.5 = (6)?
a)
1
b)
2
c)
4
d)
6
|
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
= (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
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
|
Gajendra Jain answered |
To find the number of digits multiply 128 with log2 and then add 1.
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.
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 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.
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 = 0.3010 and log 3 = 0.4771, What is the value of log51024?- a)4.31
- b)3.88
- c)3.91
- d)2.97
Correct answer is option 'A'. Can you explain this answer?
If log 2 = 0.3010 and log 3 = 0.4771, What is the value of log51024?
a)
4.31
b)
3.88
c)
3.91
d)
2.97
|
|
Gowri Chakraborty answered |
log 5 1024= log1024/log5 = log ( 2^10)/log(10/2)=10log(2)/log10−log2
=10*0.3010/1−0.3010 = 3.01/0.699 = 3010/699 = 4.31
10222 ÷ 10220 = ?- a)10
- b)100
- c)1000
- d)10000
Correct answer is option 'B'. Can you explain this answer?
10222 ÷ 10220 = ?
a)
10
b)
100
c)
1000
d)
10000
|
Sagar Sharma answered |
10222 is a positive integer.
(0.04)-2.5 = ?- a)125
- b)2
- c)4
- d)6
Correct answer is option 'C'. Can you explain this answer?
(0.04)-2.5 = ?
a)
125
b)
2
c)
4
d)
6
|
|
Moumita Das answered |
Ans.
Option (c)
(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?
(25)7.5 x (5)2.5 ÷ (125)1.5 = 5?
a)
8.5
b)
13
c)
16
d)
17.5
|
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
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.
⇒ 515 x 52.5 / 54.5 = 5x
⇒ 5x = 5(15 + 2.5 - 4.5)
⇒ 5x = 513
∴ x = 13.
- a)
- b)1
- c)2
- d)
Correct answer is option 'C'. Can you explain this answer?
a)
b)
1
c)
2
d)
|
|
Aarav Sharma answered |
To solve the equation (a / b)x - 1 = (b / a)x - 3, we can start by simplifying both sides of the equation.
Step 1: Simplify the left side of the equation
(a / b)x - 1 = (b / a)x - 3
Multiply both sides of the equation by b to eliminate the fraction:
a^x - b = (b^2 / a)x - 3b
Step 2: Simplify the right side of the equation
(b / a)x - 3 = (b^2 / a)x - 3
Multiply both sides of the equation by a to eliminate the fraction:
ab^x - 3a = b^2x - 3a
Step 3: Combine like terms
a^x - b = ab^x - 3a
Rearrange the terms:
a^x - ab^x = b - 3a
Step 4: Factor out common terms
a^x(1 - b) = b - 3a
Step 5: Divide both sides of the equation by (1 - b)
a^x = (b - 3a) / (1 - b)
Step 6: Simplify the right side of the equation
a^x = (-3a + b) / (b - 1)
Step 7: Take the logarithm of both sides of the equation
log(a^x) = log((-3a + b) / (b - 1))
Step 8: Apply logarithmic properties
x log(a) = log((-3a + b) / (b - 1))
Step 9: Divide both sides of the equation by log(a)
x = log((-3a + b) / (b - 1)) / log(a)
At this point, we have obtained an expression for x in terms of a and b. To determine the specific value of x, we need to know the values of a and b. Without this information, we cannot calculate the exact value of x.
However, if we are given values for a and b, we can substitute them into the equation to find the value of x. In this case, the correct answer is option C, but we need to know the specific values of a and b to confirm this.
Step 1: Simplify the left side of the equation
(a / b)x - 1 = (b / a)x - 3
Multiply both sides of the equation by b to eliminate the fraction:
a^x - b = (b^2 / a)x - 3b
Step 2: Simplify the right side of the equation
(b / a)x - 3 = (b^2 / a)x - 3
Multiply both sides of the equation by a to eliminate the fraction:
ab^x - 3a = b^2x - 3a
Step 3: Combine like terms
a^x - b = ab^x - 3a
Rearrange the terms:
a^x - ab^x = b - 3a
Step 4: Factor out common terms
a^x(1 - b) = b - 3a
Step 5: Divide both sides of the equation by (1 - b)
a^x = (b - 3a) / (1 - b)
Step 6: Simplify the right side of the equation
a^x = (-3a + b) / (b - 1)
Step 7: Take the logarithm of both sides of the equation
log(a^x) = log((-3a + b) / (b - 1))
Step 8: Apply logarithmic properties
x log(a) = log((-3a + b) / (b - 1))
Step 9: Divide both sides of the equation by log(a)
x = log((-3a + b) / (b - 1)) / log(a)
At this point, we have obtained an expression for x in terms of a and b. To determine the specific value of x, we need to know the values of a and b. Without this information, we cannot calculate the exact value of x.
However, if we are given values for a and b, we can substitute them into the equation to find the value of x. In this case, the correct answer is option C, but we need to know the specific values of a and b to confirm this.
If log(64)= 1.806, log(16) = ?- a) 1.204
- b)0.903
- c)1.806
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
If log(64)= 1.806, log(16) = ?
a)
1.204
b)
0.903
c)
1.806
d)
None of these
|
|
Gowri Chakraborty answered |
log(64)= 1.806
=> log(4^3) = 1.806
=> 3log(4) = 1.806
⇒log(4) = 1.806/3
log(16) = log (4^2) = 2log(4) = 2*1.806/3 = 2*0.062 = 1.204
if 6m = 46656, What is the value of 6m-2- a)36
- b)7776
- c)216
- d)1296
Correct answer is option 'D'. Can you explain this answer?
if 6m = 46656, What is the value of 6m-2
a)
36
b)
7776
c)
216
d)
1296
|
|
Sagar Sharma answered |
Given: 6m = 46656
To find: The value of 6m - 2a
Solution:
We are given that 6m = 46656. We can solve this equation to find the value of m.
Dividing both sides of the equation by 6:
6m/6 = 46656/6
m = 7776
Now, we need to find the value of 6m - 2a.
Substituting the value of m in the equation:
6m - 2a = 6(7776) - 2a
Simplifying the equation:
6(7776) - 2a = 46656 - 2a
46656 - 2a = 46656 - 2a
46656 - 2a = 46656 - 2a
We can see that the equation is balanced on both sides and there are no variables left.
The value of 6m - 2a is equal to 46656.
Therefore, the correct answer is option D) 1296.
To find: The value of 6m - 2a
Solution:
We are given that 6m = 46656. We can solve this equation to find the value of m.
Dividing both sides of the equation by 6:
6m/6 = 46656/6
m = 7776
Now, we need to find the value of 6m - 2a.
Substituting the value of m in the equation:
6m - 2a = 6(7776) - 2a
Simplifying the equation:
6(7776) - 2a = 46656 - 2a
46656 - 2a = 46656 - 2a
46656 - 2a = 46656 - 2a
We can see that the equation is balanced on both sides and there are no variables left.
The value of 6m - 2a is equal to 46656.
Therefore, the correct answer is option D) 1296.
Chapter doubts & questions for Surds, Indices and Logarithms - CSAT Preparation 2025 is part of UPSC CSE exam preparation. The chapters have been prepared according to the UPSC CSE exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for UPSC CSE 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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