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- Most Important Multiple Choice Questions
- Online Algebra Exercise with Correct Answer Key and Solutions
- Useful for all Competitive Exams
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- 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 34x-2 = 729, then the value of X is
Hint
729 = 9³ = 3⁶, Now 4X – 2 = 6 ⇒ X = 2.
- Question 5 of 23
5. Question
If 2x+4 – 2x+2 = 3 then x is equal to
Hint
2x + 4 – 2x + 2 = 3
⇒ 2x + 2 (2² – 1) = 3
⇒ 2x + 2 = 2⁰
∴ x + 2 = 0 ⇒ x = –2
- Question 6 of 23
6. Question
If 4x = 5y = 20z 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 isHint
We have,
⇒
⇒
⇒
⇒ x =
- Question 8 of 23
8. Question
If xabc = xaxbxc and x are all positive integers, then a² + b² + c² =?
Hint
xabc = xaxbxc
⇒ xabc = xa + 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
isHint
- 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
isHint
=
=
=
=
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 + 16
is:Hint
= 
=
= 
=
= 
=
= 
+ 1 - Question 16 of 23
16. Question
Find the value of xa + yb, if ay = 19683, where y is a multiple of a and bx = 1024, where b is a factor of x. a, b, x and y being positive integers:
Hint
ay = 19683
⇒ 3⁹ = 27³ = (19683)¹ = 19683
As y is a multiple of a, a = 3, y = 9, bx = 1024
⇒ 2¹⁰ = 4⁵ = 32² = (1024)¹ = 1024
As b is a factor of x, b = 2, x = 10
Now, xa + yb
⇒ 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 when
and the sum the of a and n is 12.Hint
Given, a + n = 12 ⇒ n = 12 – a
∴ Given expression becomes
= 212 – a . 312 – aBy 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 mxm – nxn = 0, then what is the value of
+ 
terms of xn?Hint
mxm = nxn
∴ xm =
∴ 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.