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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
(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
 | Raj Mehta answered |
Understanding the Equation
To solve the equation 3^(x) - 3^(x-1) = 18, we need to first simplify it.
Rearranging the Terms
1. Notice that 3^(x-1) can be rewritten as 3^x / 3.
2. Hence, the equation can be transformed to:
- 3^(x) - (3^(x)/3) = 18
Finding a Common Denominator
3. To combine the terms on the left side:
- Multiply the first term by 3:
- (3 * 3^(x)) / 3 - (3^(x)/3) = 18
- This simplifies to:
- (3 * 3^(x) - 3^(x)) / 3 = 18
Simplifying Further
4. Now, factor out 3^(x):
- (3^(x)(3 - 1)) / 3 = 18
- This further simplifies to:
- (2 * 3^(x)) / 3 = 18
Isolating 3^(x)
5. Multiply both sides by 3 to eliminate the denominator:
- 2 * 3^(x) = 54
6. Now, divide by 2:
- 3^(x) = 27
Finding the Value of x
7. Recognize that 27 can be rewritten as 3^3:
- So, 3^(x) = 3^3
8. Therefore, equating the exponents gives:
- x = 3
Conclusion
Hence, the value of x is 3, which corresponds to option 'C'.
To solve the equation 3^(x) - 3^(x-1) = 18, we need to first simplify it.
Rearranging the Terms
1. Notice that 3^(x-1) can be rewritten as 3^x / 3.
2. Hence, the equation can be transformed to:
- 3^(x) - (3^(x)/3) = 18
Finding a Common Denominator
3. To combine the terms on the left side:
- Multiply the first term by 3:
- (3 * 3^(x)) / 3 - (3^(x)/3) = 18
- This simplifies to:
- (3 * 3^(x) - 3^(x)) / 3 = 18
Simplifying Further
4. Now, factor out 3^(x):
- (3^(x)(3 - 1)) / 3 = 18
- This further simplifies to:
- (2 * 3^(x)) / 3 = 18
Isolating 3^(x)
5. Multiply both sides by 3 to eliminate the denominator:
- 2 * 3^(x) = 54
6. Now, divide by 2:
- 3^(x) = 27
Finding the Value of x
7. Recognize that 27 can be rewritten as 3^3:
- So, 3^(x) = 3^3
8. Therefore, equating the exponents gives:
- x = 3
Conclusion
Hence, the value of x is 3, which corresponds to option 'C'.
[(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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