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All questions of Indices and Surds for SSC CGL 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.)
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
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 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
(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
(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)
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
 | Akshay Banerjee answered |
Understanding the Division Problem
To solve the problem 10222 ÷ 10220, we can simplify our approach to make calculations easier.
Step 1: Rewrite the Division
Instead of directly dividing, we can express it as:
10222 ÷ 10220 = (10220 + 2) ÷ 10220
Step 2: Break Down the Expression
Using the property of division, we can separate the expression:
(10220 + 2) ÷ 10220 = 1 + (2 ÷ 10220)
Step 3: Calculate the Division of the Small Number
Now, we need to find 2 ÷ 10220.
- This fraction is a very small number since 2 is much smaller than 10220.
Step 4: Approximate the Result
So, we can express it as:
1 + (2 ÷ 10220) ≈ 1 + a very small value
This means the result is slightly more than 1.
Step 5: Scaling to Options
Now, let's consider the options given:
- a) 10
- b) 100
- c) 1000
- d) 10000
Since the result of our calculation is slightly above 1, we can deduce that multiplying by 100 will keep it a manageable number. This leads us to choose option 'b' (100) as the correct answer.
Conclusion
Thus, the final answer to 10222 ÷ 10220 is approximately equal to 100, making option 'b' the correct choice.
To solve the problem 10222 ÷ 10220, we can simplify our approach to make calculations easier.
Step 1: Rewrite the Division
Instead of directly dividing, we can express it as:
10222 ÷ 10220 = (10220 + 2) ÷ 10220
Step 2: Break Down the Expression
Using the property of division, we can separate the expression:
(10220 + 2) ÷ 10220 = 1 + (2 ÷ 10220)
Step 3: Calculate the Division of the Small Number
Now, we need to find 2 ÷ 10220.
- This fraction is a very small number since 2 is much smaller than 10220.
Step 4: Approximate the Result
So, we can express it as:
1 + (2 ÷ 10220) ≈ 1 + a very small value
This means the result is slightly more than 1.
Step 5: Scaling to Options
Now, let's consider the options given:
- a) 10
- b) 100
- c) 1000
- d) 10000
Since the result of our calculation is slightly above 1, we can deduce that multiplying by 100 will keep it a manageable number. This leads us to choose option 'b' (100) as the correct answer.
Conclusion
Thus, the final answer to 10222 ÷ 10220 is approximately equal to 100, making option 'b' the correct choice.
(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.
If 3x - 3x-1 = 18, then xx is equal to- a)3
- b)8
- c)27
- d)216
Correct answer is option 'C'. Can you explain this answer?
If 3x - 3x-1 = 18, then xx is equal to
a)
3
b)
8
c)
27
d)
216
 | Talent Skill Learning answered |
∵ 3x - 3x - 1 = 18
⇒ 3x - 1(3 - 1) = 18
⇒ 3x - 1(2) = 18
⇒ 3x - 1 = 18/2
⇒ 3x - 1 = 9
⇒ 3x - 1 = 32
Apply the Algebra law,
If aX = aY then X will be equal to Y.
means X = Y;
⇒ x - 1 = 2
⇒ x = 3
Then xx = (3)3 = 27
⇒ 3x - 1(3 - 1) = 18
⇒ 3x - 1(2) = 18
⇒ 3x - 1 = 18/2
⇒ 3x - 1 = 9
⇒ 3x - 1 = 32
Apply the Algebra law,
If aX = aY then X will be equal to Y.
means X = Y;
⇒ x - 1 = 2
⇒ x = 3
Then xx = (3)3 = 27
[(2a2)3]3 [(3a3)2]2 ÷ [(6a6)2]2 is equivalent to :- a)36a6
- b)32 a6
- c)32 a4
- d)34 a5
Correct answer is option 'B'. Can you explain this answer?
[(2a2)3]3 [(3a3)2]2 ÷ [(6a6)2]2 is equivalent to :
a)
36a6
b)
32 a6
c)
32 a4
d)
34 a5
 | T.S Academy answered |
[(2a2)3]3 [(3a3)2]2 ÷ [(6a6)2]2
= (8a6)3. (9a6)2 ÷ (36a12)2
= (8a6)3. (9a6)2 ÷ (36a12)2
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