Finish Test
0 of 23 questions completed
Questions:
 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
Information
 Most Important Multiple Choice Questions
 Online Algebra Exercise with Correct Answer Key and Solutions
 Useful for all Competitive Exams
You have already completed the quiz before. Hence you can not start it again.
Test 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 23 questions answered correctly
Time has elapsed
You have reached 0 of 0 points, (0)
Categories
 Not categorized 0%
 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 Answered
 Review

Question 1 of 23
1. Question
If 2x + 3y = 78 and 3x + 2y = 72, what is the value of x + y?
Hint
2x + 3y = 78 …(i)
3x + 2y = 72 …(ii)
From equations (i) and (ii),
x = 12, y = 18
∴ x + y = 12 + 18 = 30

Question 2 of 23
2. Question
If x + y =18 and xy = 72, what is the value of (x)² + (y)²
Hint
x + y = 18
⇒ (x + y)² = 18² = 324
⇒ x² + y² + 2xy = 324
⇒ x² + y² = 324 – 2xy
⇒ x² + y² = 324 – 2(72)
⇒ x² + y² = 324 – 144 = 180

Question 3 of 23
3. Question
If 3x + 5y = 44 and 10x–2y=16, what is the value of x?
Hint
3x + 5y = 44 …(i)
10x – 2y = 16 …(ii)
By equation (i) × 2 + equation (ii) × 5
we have,
6x + 10y + 50x – 10y = 88 + 80
or 56x = 168
∴ x = = 3

Question 4 of 23
4. Question
If 3^{4x2} = 729, then the value of X is
Hint
729 = 9³ = 3⁶, Now 4X – 2 = 6 ⇒ X = 2.

Question 5 of 23
5. Question
If 2^{x+4} – 2^{x+2} = 3 then x is equal to
Hint
2^{x + 4} – 2^{x + 2} = 3
⇒ 2^{x + 2} (2² – 1) = 3
⇒ 2^{x + 2} = 2⁰
∴ x + 2 = 0 ⇒ x = –2

Question 6 of 23
6. Question
If 4^{x} = 5^{y} = 20^{z} then z is (x, y, z ≠ 0)
Hint
4 × 5 = 20z/x × 20z/y = 20z/x + z/y = 20
i.e. 1 = z/x + z/y
i.e. z = xy/(x + y)

Question 7 of 23
7. Question
If , then x is
Hint
We have,
⇒
⇒
⇒
⇒ x =

Question 8 of 23
8. Question
If x^{abc} = x^{a}x^{b}x^{c} and x are all positive integers, then a² + b² + c² =?
Hint
x^{abc} = x^{a}x^{b}x^{c}
⇒ x^{abc} = x^{a + b + c}
⇒ abc = a + b + c.
This happens for positive integer value of a, b, c, only when a, b, c take value of 1, 2 & 3.
Hence, a² + b² + c² = 1² + 2² + 3² = 1 + 4 + 9 = 14.

Question 9 of 23
9. Question
The pure form of the surd is
Hint

Question 10 of 23
10. Question
A student was asked to solve the fraction and his answer was ¼. By how much was his answer wrong?
Hint
∴ Required answer

Question 11 of 23
11. Question
A man plants 15376 apple trees in his garden and arranges them so that there are as many rows as there are apples trees in each row. The number of rows is:
Hint
∴ Number of rows = 124.

Question 12 of 23
12. Question
Number of prime factors in is
Hint
=
=
=
=
Hence, the number of prime factors = (2 + 3 + 2) = 7

Question 13 of 23
13. Question
The difference between two numbers is 3 and the difference of their squares is 63. Find the greater number.
Hint
Let the larger and smaller numbers be x and y respectively.
Then, x – y = 3 …(i)
and, x² – y² = 63
⇒ (x + y) (x – y) = 63
…(ii)
From equation (i) and (ii), x = 12

Question 14 of 23
14. Question
How much less is ⅘ of 1150 from ⅚ of 1248?
Hint
= 1040 – 920 = 120

Question 15 of 23
15. Question
The fourth root of 28 + 16is:
Hint
=
= =
= =
= = + 1

Question 16 of 23
16. Question
Find the value of x^{a} + y^{b}, if a^{y} = 19683, where y is a multiple of a and b^{x} = 1024, where b is a factor of x. a, b, x and y being positive integers:
Hint
a^{y} = 19683
⇒ 3⁹ = 27³ = (19683)¹ = 19683
As y is a multiple of a, a = 3, y = 9, b^{x} = 1024
⇒ 2¹⁰ = 4⁵ = 32² = (1024)¹ = 1024
As b is a factor of x, b = 2, x = 10
Now, x^{a} + y^{b}
⇒ 10³ + 9² = 1000 + 81 = 1081.

Question 17 of 23
17. Question
What is the difference in the sum of squares and the difference of squares of n and a whenand the sum the of a and n is 12.
Hint
Given, a + n = 12 ⇒ n = 12 – a
∴ Given expression becomes
= 2^{12 – a} . 3^{12 – a}
By comparing, power of 3, we get a + 2 = 12 – a ⇒ a = 5 and n = 7
∴ Required answer = (a² + n²) – (n² – a²) = (49 + 25) – (49 – 25) = 50

Question 18 of 23
18. Question
If mx^{m} – nx^{n} = 0, then what is the value of + terms of x^{n}?
Hint
mx^{m} = nx^{n}
∴ x^{m} =
∴ Given
=
= = .

Question 19 of 23
19. Question
Three of the following four parts are exactly equal. Which parts is not equal to the other three?
Hint
Check all options one by one.
(a)
(b) + (15.2 × 4) = 100
(c) (15 × 8) – (5 × 4) = 100
(d) (76 × 1.5) – (5.5 × 2.6) = 99.7

Question 20 of 23
20. Question
Three of the following four parts are exactly equal. Which parts is not equal to the other three?
Hint
All others are equal to 100. But option (c) gives a value equal to 98.

Question 21 of 23
21. Question
Three of the following four parts are exactly equal. Which parts is not equal to the other three?
Hint
Others equal 5650.

Question 22 of 23
22. Question
Three of the following four parts are exactly equal. Which parts is not equal to the other three?
Hint
Except it, others are equal to 550.

Question 23 of 23
23. Question
Three of the following four parts are exactly equal. Which parts is not equal to the other three?
Hint
Other parts are equal to 300.