# Equations and Inequations Questions and Answers updated daily – Aptitude

128 Equations and Inequations Questions and answers section with explanation for various online exam preparation, various interviews, Aptitude Equations and Inequations online test. Equations and Inequations Questions with detailed description, explanation will help you to master the topic.

## Equations and Inequations Questions

1. If x^2 - 20 x + 75 < 0 then

Correct Ans:5 < x < 15
Explanation:
x^2 - 20 x + 75 < 0
=> (x – 15) (x – 5) < 0
=> x < 15, 5
=> 5 < x < 15

2. If |x-2| < 12 then

Correct Ans:-10 < x < 14
Explanation:
Given, |x-2| < 12
=> -12 < x -2 < 12
=> -12 + 2 < x < 12 + 2
=> -10 < x < 14

3. Evaluate the expression x^2 - 4x + 5 when x = 1.

Correct Ans:2
Explanation:
Subs x = 1 in the given expression: x^2 - 4x + 5
=> (1)^2 – 4(1) + 5
= 1 – 4 + 5
= 2

4. Evaluate: x^3 - 6x^2 + 11x - 7 when x = 2

Correct Ans:-1
Explanation:
Substitute x = 2 in the given eqn: x^3 - 6x^2 + 11x – 7
=> (2)^3 – 6*(2)^2 + 11*(2) – 7
= 8 – 24 + 22 – 7
= -1

5. Evaluate the expression x^3  + 3x^2 + 3x + 1, when x = 10

Correct Ans:1331
Explanation:
Subs x = 10 in the given eqn, x^3 + 3x^2 + 3x + 1
=> (10)^3 + 3 * (10^2) + (3 * 10) + 1
= 1000 + 300 + 30 + 1
= 1331

6. If x^2 - 10 x + 16 > 0 then which of the following option is correct?

Correct Ans:x > 8
Explanation:
Given, x^2 - 10 x + 16 > 0
=> (x -8) (x-2) > 0
=> X > 8 and x > 2

Substitute values randomly taken from the interval and mark that option which satisfies the question.
On substituting x = 7 (which is greater than 2) in the eqn:x^2 - 10 x + 16, we get, -5 as the answer which is not greater than "0".
On substituting x = 9 (which is greater than 8) in the eqn:x^2 - 10 x + 16, we get, 7 as the answer which is greater than "0".
Hence, the correct answer is x > 8.

7. If x^2 + x + 1 = 0 then the number of real solutions is

Correct Ans:0
Explanation:

8. If x^2 - 7x + 12 < 0 then find the solution of x ?

Correct Ans:3 < x < 4
Explanation:

9. Evaluate t^3 - 3t^2 + 3t - 2 when t = 4

Correct Ans:26
Explanation:

10. If x^2 - 2x + 1 < 0 then which of the following is true ?

Correct Ans:No solution
Explanation:

11. Compute 23^3 - 12^3 - 11^3

Correct Ans:9108
Explanation:

23^3 = 12167
12^3 = 1728
11^3= 1331

Now, 23^3 - 12^3 - 11^3= 12167 – 1728 – 1331
= 9108

12. Given that x + 1/x = 3 then evaluate x^3 + 1/x^3 = ?

Correct Ans:18
Explanation:

13. If x + 1 /x = 2 then evaluate x^23 + 1/x^32

Correct Ans:2
Explanation:
Given, x + (1 /x) = 2
=> (x^2 + 1) / x = 2
=> (x^2 + 1) = 2x
=> x^2 - 2x + 1 = 0
=> (x – 1) (x – 1) = 0
=> x = 1
Subs x = 1 in the eqn x^23 + 1/x^32
=> (1)^23 + (1/1^32)
= 1 + 1
= 2
Therefore, x^23 + 1/x^32 = 2

14. Evaluate x^2 - 27 x + 180 at x = 15

Correct Ans:0
Explanation:
Subs x = 15 in the given eqn x^2 - 27 x + 180
=> (15)^2 – 27*(15) + 180
=> 225 – 405 + 180
=> 405 – 405
=> 0
So, Ans is 0

15. Evaluate the expression x^3 + 3x +1 at x =2

Correct Ans:15
Explanation:
Subs x = 2 in the expression: x^3 + 3x +1
=> 2^3 + 3*2 + 1
=> 8 + 6 + 1
=> 15

16. The average of the linear factors of x^2 - 14x + 48 = 0  is

Correct Ans:x - 7
Explanation:
Given, x^2 – 14x + 48
=> x^2 –2 * (7) x + 48
=> x^2 –2 * (7) x + 48 + (7^2) - (7^2)
=> {x^2 –2 * (7) x + (7^2)} + 48 - 49
By the formula: (a^2 – 2ab – b^2) = (a – b)^2
=> (x – 7)^2 – 1
=> (x – 7)^2 – 1^2
By the formula: (a^2) – (b^2) = (a-b)(a+b)
=> (x – 7 + 1) (x – 7 – 1)
=> (x - 6) (x – 8)

The two linear factors are (x - 6) and (x – 8)
Average = (x – 6 + x – 8) / 2
= (2x -14)/2
= 2(x – 7) / 2
= (x – 7)
Therefore, Average = x – 7

17. If x^2 - 9 < 0 then which of the following options are true?

Correct Ans:-3 < x < 3
Explanation:
Given, x^2 - 9 < 0
=> x^2 < 9
=> x < sqrt(9)
=> x < ± 3
=> -3 < x < 3

18. If  |x - 1| < 11 then which of the following options are true?

Correct Ans:-10 <  x < 12
Explanation:

Given, | x - 1 | < 11
=> -11 < (x-1) < 11
=> (-11 + 1) < x < (11 + 1)
=> -10 < x < 12

19. Find the sum of the linear factors of x^2 - 12 x + 20

Correct Ans:2(x-6)
Explanation:

20. The sum of the linear factors of x^2 - 10 x+ 21 = 0 is

Correct Ans:2(x-5)
Explanation:
x^2 - 10x + 21
= x^2 - 2 (5x) + 21
= x^2 - 2 (5) x + 21
= x^2 - 2(5) x + 5^2 + 21 - 25
=x^2 -2(5)(x) + 5^2 - 4
= (x-5)^2 - 4
= (x-5)^2 - 2^2
= ( (x-5) - 2 ) x ((x-5) + 2)
= (x - 5 - 2) x (x - 5 + 2)
=(x-7) x (x-3)
The two linear factors are x - 3 and x - 7
Sum is x - 3 + x - 7 = 2x - 10 = 2(x-5)

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