1. If x^2 - 20 x + 75 < 0 then
SHOW ANSWER
Correct Ans:5 < x < 15
Explanation:
x^2 - 20 x + 75 < 0
=> (x – 15) (x – 5) < 0
=> x < 15, 5
=> 5 < x < 15
SHOW ANSWER
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.
SHOW ANSWER
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
SHOW ANSWER
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
SHOW ANSWER
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?
SHOW ANSWER
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
SHOW ANSWER
Correct Ans:0
Explanation:
8. If x^2 - 7x + 12 < 0 then find the solution of x ?
SHOW ANSWER
Correct Ans:3 < x < 4
Explanation:
9. Evaluate t^3 - 3t^2 + 3t - 2 when t = 4
SHOW ANSWER
Correct Ans:26
Explanation:
10. If x^2 - 2x + 1 < 0 then which of the following is true ?
SHOW ANSWER
Correct Ans:No solution
Explanation:
11. Compute 23^3 - 12^3 - 11^3
SHOW ANSWER
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 = ?
SHOW ANSWER
Correct Ans:18
Explanation:
13. If x + 1 /x = 2 then evaluate x^23 + 1/x^32
SHOW ANSWER
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
SHOW ANSWER
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
SHOW ANSWER
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
SHOW ANSWER
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?
SHOW ANSWER
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?
SHOW ANSWER
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 value obtained when we substitute z = 3 in the equation z^2 - 5z + 10
SHOW ANSWER
Correct Ans:4
Explanation:
20. The sum of the linear factors of x^2 - 10 x+ 21 = 0 is
SHOW ANSWER
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)
Are you seeking for good platform for practicing Equations and Inequations questions in online. This is the right place. The time you spent in Fresherslive will be the most beneficial one for you.
Online Test on Equations and Inequations @ Fresherslive
This page provides important questions on Equations and Inequations along with correct answers and clear explanation, which will be very useful for various Interviews, Competitive examinations and Entrance tests. Here, Most of the Equations and Inequations questions are framed with Latest concepts, so that you may get updated through these Equations and Inequations Online tests. Equations and Inequations Online Test questions are granted from basic level to complex level.
Why To Practice Equations and Inequations Test questions Online @ Fresherslive?
Equations and Inequations questions are delivered with accurate answer. For solving each and every question, very lucid explanations are provided with diagrams wherever necessary.
Practice in advance of similar questions on Equations and Inequations may improve your performance in the real Exams and Interview.
Time Management for answering the Equations and Inequations questions quickly is foremost important for success in Competitive Exams and Placement Interviews.
Through Fresherslive Equations and Inequations questions and answers, you can acquire all the essential idea to solve any difficult questions on Equations and Inequations in short time and also in short cut method.
Winners are those who can use the simplest method for solving a question. So that they have enough time for solving all the questions in examination, correctly without any tense. Fresherslive provides most simplest methods to answer any tough questions. Practise through Fresherslive test series to ensure success in all competitive exams, entrance exams and placement tests.
Why Fresherslive For Equations and Inequations Online Test Preparation?
Most of the job seekers finding it hard to clear Equations and Inequations test or get stuck on any particular question, our Equations and Inequations test sections will help you to success in Exams as well as Interviews. To acquire clear understanding of Equations and Inequations, exercise these advanced Equations and Inequations questions with answers.
You're Welcome to use the Fresherslive Online Test at any time you want. Start your beginning, of anything you want by using our sample Equations and Inequations Online Test and create yourself a successful one. Fresherslive provides you a new opportunity to improve yourself. Take it and make use of it to the fullest. GOODLUCK for Your Bright Future.