Quizsummary
0 of 20 questions completed
Questions:
 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
Information
Number of Questions: 20
Time: 20 Minutes
Category: Aptitude
You must specify a number. 
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Results
0 of 20 questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 points, (0)
Average score 

Your score 

Categories
 Surds & indices 0%
Pos.  Name  Entered on  Points  Result 

Table is loading  
No data available  
 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 Answered
 Review

Question 1 of 20
1. Question
(17)^{3.5} x (17)^{?} = 17^{8}
Correct
Let (17)^{3.5} x (17)^{x} = 17^{8}.
Then, (17)^{3.5 + x} = 17^{8}.
3.5 + x = 8
x = (8 – 3.5)
x = 4.5
Incorrect
Let (17)^{3.5} x (17)^{x} = 17^{8}.
Then, (17)^{3.5 + x} = 17^{8}.
3.5 + x = 8
x = (8 – 3.5)
x = 4.5

Question 2 of 20
2. Question
If 3^{(x – y)} = 27 and 3^{(x + y)} = 243, then x is equal to:
Correct
3^{x – y} = 27 = 3^{3} x – y = 3 ….(i)
3^{x + y} = 243 = 3^{5} x + y = 5 ….(ii)
On solving (i) and (ii), we get x = 4.
Incorrect
3^{x – y} = 27 = 3^{3} x – y = 3 ….(i)
3^{x + y} = 243 = 3^{5} x + y = 5 ….(ii)
On solving (i) and (ii), we get x = 4.

Question 3 of 20
3. Question
(25)^{7.5} x (5)^{2.5} ÷ (125)^{1.5} = 5^{?}
Correct
Let (25)^{7.5} x (5)^{2.5} ÷ (125)^{1.5} = 5^{x}.
Then, (5^{2})^{7.5} x (5)^{2.5} = 5^{x} (5^{3})^{1.5} 5^{(2 x 7.5)} x 5^{2.5} = 5x 5^{(3 x 1.5)} 5^{15} x 5^{2.5} = 5^{x} 5^{4.5} 5^{x} = 5^{(15 + 2.5 – 4.5)}
5^{x} = 5^{13}
x = 13.
Incorrect
Let (25)^{7.5} x (5)^{2.5} ÷ (125)^{1.5} = 5^{x}.
Then, (5^{2})^{7.5} x (5)^{2.5} = 5^{x} (5^{3})^{1.5} 5^{(2 x 7.5)} x 5^{2.5} = 5x 5^{(3 x 1.5)} 5^{15} x 5^{2.5} = 5^{x} 5^{4.5} 5^{x} = 5^{(15 + 2.5 – 4.5)}
5^{x} = 5^{13}
x = 13.

Question 4 of 20
4. Question
If m and n are whole numbers such that mn = 121, the value of (m – 1)n + 1 is:
Correct
We know that 11^{2} = 121.
Putting m = 11 and n = 2, we get:
(m – 1)^{n + 1} = (11 – 1)^{(2 + 1)} = 10^{3} = 1000.
Incorrect
We know that 11^{2} = 121.
Putting m = 11 and n = 2, we get:
(m – 1)^{n + 1} = (11 – 1)^{(2 + 1)} = 10^{3} = 1000.

Question 5 of 20
5. Question
If = 3125, then the value of is:
Correct
= 3125
=
a = 5.Then =
=
= 25.
Incorrect
= 3125
=
a = 5.Then =
=
= 25.

Question 6 of 20
6. Question
36 × 36 × 36 × 36 = 6^{?}
Correct
36 × 36 × 36 × 36 = 6^{2} × 6^{2} × 6^{2} × 6^{2} = 6^{(2+2+2+2)} = 6^{8}
Incorrect
36 × 36 × 36 × 36 = 6^{2} × 6^{2} × 6^{2} × 6^{2} = 6^{(2+2+2+2)} = 6^{8}

Question 7 of 20
7. Question
If 3^{(n + 4)} – 3^{(n + 2)} = 8, What is the value of n?
Correct
3^{(n + 4)} – 3^{(n + 2)} = 8
3^{(n + 2 + 2)} – 3^{(n + 2)} = 8
3^{(n + 2)} × 3^{(2)} – 3^{(n + 2)} = 8
3^{(n + 2)}[3^{(2)} – 1] = 8
3^{(n + 2)} × 8 = 8
3^{(n + 2)} = 1
=> n + 2 = 0
=> n = 2
Incorrect
3^{(n + 4)} – 3^{(n + 2)} = 8
3^{(n + 2 + 2)} – 3^{(n + 2)} = 8
3^{(n + 2)} × 3^{(2)} – 3^{(n + 2)} = 8
3^{(n + 2)}[3^{(2)} – 1] = 8
3^{(n + 2)} × 8 = 8
3^{(n + 2)} = 1
=> n + 2 = 0
=> n = 2

Question 8 of 20
8. Question
49 * 49 * 49 * 49 = 7^{?}
Correct
49 * 49 * 49 * 49 = (7^{2} * 7^{2} * 7^{2} * 7^{2}) = 7^{(2+2+2+2)} = 7^{8}.
So, the correct answer is 8.Incorrect
49 * 49 * 49 * 49 = (7^{2} * 7^{2} * 7^{2} * 7^{2}) = 7^{(2+2+2+2)} = 7^{8}.
So, the correct answer is 8. 
Question 9 of 20
9. Question
The value of (8^{25} 8^{26}) is
Correct
8^{25} 8^{26} = [1/8^{25} – 1/8^{26}] = 7 * 8^{26}.
Incorrect
8^{25} 8^{26} = [1/8^{25} – 1/8^{26}] = 7 * 8^{26}.

Question 10 of 20
10. Question
If 2^{x1} + 2^{x+1} = 1280, then find the value of x.
Correct
2^{x1} + 2^{x+1} = 1280 ⇔ 2^{x1} (1+2^{2}) = 1280
⇔ 2^{x1} = 1280 / 5 = 256 = 2^{8}
⇔ x – 1 = 8 ⇔ x = 9.
Hence, x = 9.Incorrect
2^{x1} + 2^{x+1} = 1280 ⇔ 2^{x1} (1+2^{2}) = 1280
⇔ 2^{x1} = 1280 / 5 = 256 = 2^{8}
⇔ x – 1 = 8 ⇔ x = 9.
Hence, x = 9. 
Question 11 of 20
11. Question
What is the quotient when (x^{1} – 1) is divided by (x – 1) ?
Correct
x^{1} 1 /x1
(1/x)1/x1
(1 x)/x * 1/(x1) = 1/x
Hence, the required quotient is 1/x
Incorrect
x^{1} 1 /x1
(1/x)1/x1
(1 x)/x * 1/(x1) = 1/x
Hence, the required quotient is 1/x

Question 12 of 20
12. Question
Find the largest from among 4√6, √2 and ^{3}√4.
Correct
Given surds are of order 4, 2 and 3 respectively. Their L.C,M, is 12, Changing each to a surd of order 12, we get:
^{4}√6 = 6^{1/4} = 6^{((1/4)*(3/3))} = 6^{3/12} = (6^{3})^{1/12 } = (216)^{1/12.}
√2 = 2^{1/2} = 2^{((1/2)*(6/6))} = 2^{6/12} = (2^{6})^{1/12 } = (64)^{1/12}.
^{3}√4 = 4^{1/3} = 4^{((1/3)*(4/4))} = 4^{4/12 } = (4^{4})^{1/12} = (256)^{1/12}.
Clearly, (256)^{1/12} > (216)^{1/12 } > (64)^{1/12}
Largest one is (256)^{1/12}. i.e. ^{3}√4 .
Incorrect
Given surds are of order 4, 2 and 3 respectively. Their L.C,M, is 12, Changing each to a surd of order 12, we get:
^{4}√6 = 6^{1/4} = 6^{((1/4)*(3/3))} = 6^{3/12} = (6^{3})^{1/12 } = (216)^{1/12.}
√2 = 2^{1/2} = 2^{((1/2)*(6/6))} = 2^{6/12} = (2^{6})^{1/12 } = (64)^{1/12}.
^{3}√4 = 4^{1/3} = 4^{((1/3)*(4/4))} = 4^{4/12 } = (4^{4})^{1/12} = (256)^{1/12}.
Clearly, (256)^{1/12} > (216)^{1/12 } > (64)^{1/12}
Largest one is (256)^{1/12}. i.e. ^{3}√4 .

Question 13 of 20
13. Question
Simplify [(x^{a} / x^{b})^(a^{2}+b^{2}+ab)] * [(x^{b} / x^{c} )^ b^{2}+c^{2}+bc)] * [(x^{c}/x^{a})^(c^{2}+a^{2}+ca)]
Correct
Given Expression
= [{x^{(o }^{– b)}}^(a^{2} + b^{2} + ob)].[‘(x^{(b }^{– c)}}^ (b^{2} + c^{2} + bc)].[‘(x^{(c }^{– a)}}^(c^{2} + a^{2} + ca])
= [x^{(a }^{– b)(a2 + b2 + ab)} . x^{(b }^{– c) (b2 +c2+ bc)}.x^{(c}^{– a) (c2 + a2 + ca)}]
= [x^(a^{3}b^{3})].[x^(b^{3}e^{3})].[x^(c^{3}a^{3})] = x^(a^{3}b^{3}+b^{3}c^{3}+c^{3}a^{3}) = x^{0} = 1.
Incorrect
Given Expression
= [{x^{(o }^{– b)}}^(a^{2} + b^{2} + ob)].[‘(x^{(b }^{– c)}}^ (b^{2} + c^{2} + bc)].[‘(x^{(c }^{– a)}}^(c^{2} + a^{2} + ca])
= [x^{(a }^{– b)(a2 + b2 + ab)} . x^{(b }^{– c) (b2 +c2+ bc)}.x^{(c}^{– a) (c2 + a2 + ca)}]
= [x^(a^{3}b^{3})].[x^(b^{3}e^{3})].[x^(c^{3}a^{3})] = x^(a^{3}b^{3}+b^{3}c^{3}+c^{3}a^{3}) = x^{0} = 1.

Question 14 of 20
14. Question
If x= y^{a}, y=z^{b} and z=x^{c},then find the value of abc.
Correct
z^{1}= x^{c} =(y^{a})^{c} [since x= y^{a}]
=y^{(ac)} = (z^{b})^{ac} [since y=z^{b}]
=z^{b(ac)}= z^{abc}
\ abc = 1.
Incorrect
z^{1}= x^{c} =(y^{a})^{c} [since x= y^{a}]
=y^{(ac)} = (z^{b})^{ac} [since y=z^{b}]
=z^{b(ac)}= z^{abc}
\ abc = 1.

Question 15 of 20
15. Question
Find the value Of (2^{1/4}1)(2^{3/4}+2^{1/2}+2^{1/4}+1)
Correct
Putting 2^{1/4} = x, we get :
(2^{1/4}1) (2^{3/4}+2^{1/2}+2^{1/4}+1)=(x1)(x^{3}+x^{2}+x+1) , where x = 2^{1/4}
=(x1)[x^{2}(x+1)+(x+1)]
=(x1)(x+1)(x^{2}+1) = (x^{2}1)(x^{2}+1)
=(x^{4}1) = [(2^{1/4})^{4}1] = [2^{(1/4}*^{4)} –1] = (21) = 1.
Incorrect
Putting 2^{1/4} = x, we get :
(2^{1/4}1) (2^{3/4}+2^{1/2}+2^{1/4}+1)=(x1)(x^{3}+x^{2}+x+1) , where x = 2^{1/4}
=(x1)[x^{2}(x+1)+(x+1)]
=(x1)(x+1)(x^{2}+1) = (x^{2}1)(x^{2}+1)
=(x^{4}1) = [(2^{1/4})^{4}1] = [2^{(1/4}*^{4)} –1] = (21) = 1.

Question 16 of 20
16. Question
(256)0.16 x (256)0.09 = ?
Correct
(256)^{0.16} x (256)^{0.09} = (256)^{(0.16 + 0.09)}
= (256)^{0.25}
= (256)^{(25/100)}
= (256)^{(1/4)}
= (4^{4})^{(1/4)}
= 4^{4(1/4)}
= 4^{1}
= 4
Incorrect
(256)^{0.16} x (256)^{0.09} = (256)^{(0.16 + 0.09)}
= (256)^{0.25}
= (256)^{(25/100)}
= (256)^{(1/4)}
= (4^{4})^{(1/4)}
= 4^{4(1/4)}
= 4^{1}
= 4

Question 17 of 20
17. Question
Evaluate (0.04)^{1.5}× (0.125)^{4/3}– (^{1}/_{121})^{1/2}
Correct
Given expression = (0.2)^{3}×(0.5)^{4} – 11 = (0.2)^{3}×(0.5)^{3}.(0.5)^{1}11= (0.1)^{3}×(0.5)^{1}11 = 200011=1989Incorrect
Given expression = (0.2)^{3}×(0.5)^{4} – 11 = (0.2)^{3}×(0.5)^{3}.(0.5)^{1}11= (0.1)^{3}×(0.5)^{1}11 = 200011=1989 
Question 18 of 20
18. Question
If (64)^{2/3} × (256)^{1/2} = 4^{n }, then n= ?
Correct
(4^{3})^{2/3}×(4^{4})^{1/2} = 4^{n}
4^{2 }× 4^{2 }= 4^{n}, ⇒4^{0}⇒ n = 0Incorrect
(4^{3})^{2/3}×(4^{4})^{1/2} = 4^{n}
4^{2 }× 4^{2 }= 4^{n}, ⇒4^{0}⇒ n = 0 
Question 19 of 20
19. Question
(27)^{2}/_{3}=x then 3x is equal to
Correct
(27)^{2/3} = x ⇒ (3^{3})^{2/3} = x ⇒ 3^{2} = x ⇒ 3x = 2
Incorrect
(27)^{2/3} = x ⇒ (3^{3})^{2/3} = x ⇒ 3^{2} = x ⇒ 3x = 2

Question 20 of 20
20. Question
Express ^{2}/_{3} √32 as a pure surd .
Correct
^{2}/_{3 }√32 = √(^{2}/_{3})^{2}×32
=√^{128}/_{9} a pure surdIncorrect
^{2}/_{3 }√32 = √(^{2}/_{3})^{2}×32
=√^{128}/_{9} a pure surd