Equations and Inequations Questions and Answers updated daily – Aptitude

Equations and Inequations Questions: Solved 316 Equations and Inequations Questions and answers section with explanation for various online exam preparation, various interviews, Aptitude Category online test. Category Questions section with detailed description, explanation will help you to master the topic.

Equations and Inequations Questions

301. Given that |x+3| < 2, then find the possible values of x, which satisfies the condition?




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Correct Ans:-5 < x < -1
Explanation:
|x+3| < 2
-2 < x+3 < 2
-3-2 < x < 2-3
-5 < x < -1
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302. Given that |x - 2| < 3, then which of the following options satisifies the given conditions ? 




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Correct Ans:-1
Explanation:
Given that |x-2| < 3
-3 < x-2 < 3
Add 2 to all sides, we get
2-3 < x -2 + 2 < 3 + 2
-1 < x < 5

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303. Evaluate the expression for x3+6x2+12x+9, when x = -2  




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Correct Ans:1
Explanation:
Given
(x+2)3=x3+6x2+12x + 8
x3+6x2+12x + 9 = (x3+6x2+12x + 8 )+1 = (x+2)3+1
By sub, x=-2 we get (-2+2)2+1 = 0+1 = 1
Therefore x = 1.
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304. Evaluate the expression x^3 - 7x^2 + 14x -8 when x = 4 




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Correct Ans:0
Explanation:
Subs x = 4 in the eqn x^3 - 7x^2 + 14x -8
=> 4^3 – 7 (4^2) + 14 * 4 – 8
=> 64 – 7 * 16 + 56 – 8
=> 64 – 112 + 56 – 8
=> 0
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305. Evaluate the expression x^3 - 7x^2 + 14x - 8, when x = 1 




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Correct Ans:0
Explanation:
Subs x = 1 in the eqn x^3 - 7x^2 + 14x – 8
=> (1)^3 - 7(1^2) + 14(1) – 8
= 1 – 7 + 14 – 8
= 0
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306. Evaluate the expression: x^2 - 5x + 6 when x = 4




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Correct Ans:2
Explanation:
Subs x = 4 in the given eqn, x^2 - 5x + 6
=> (4)^2 – (5 * 4) + 6
= 16 – 20 + 6
= 2
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307. Evaluate the expression x3 - 5x2 + 6x when x = 3




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Correct Ans:0
Explanation:
Substitutex = 3 in the given eqn: x3 - 5x2 + 6x
=> (3)^3 - 5 * (3)^2 + 6 * (3)
=> 27 - 45 +18
=> 0
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308. Evaluate the expression x^3 - 3x^2 + 3x - 10 , when x = 1 




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Correct Ans:None of the above
Explanation:
x^3 - 3x^2 + 3x - 10 , when x = 1
=
(1) ^ 3 - 3 (1) ^ 2 - 10
= 1 - 3 - 10
= - 13 + 1
= 12.
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309. If 432 is added to some number the answer we obtained is 2132, find that number. 




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Correct Ans:463
Explanation:
432 = 1849,
Let x be that number then 1849 + x = 2312
=> x = 2312 - 1849
=>x = 463
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310. If x + y = 24 and xy= 100, What is the value of x2 + y2 = ?. 




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Correct Ans:376
Explanation:
( x + y)2 = x2+y2+2xy ---->(1)
=> 242 = x2 + y2 + 2(100)
=> 242 = 576

substituting both the values (576 , 200) in eqn(1)

=> x2+y2
= 576 -200
= 376.
Thus the value ofx2+ y2= 376.
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311. In a group of ducks and buffaloes, the total number of legs are 24 more than twice the number of heads. Find the number of buffaloes.  




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Correct Ans:12
Explanation:
Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y
= 2 (x + y) + 24
=> 2x = 24
=> x = 12.
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312. What will be the value of the expression x^3 - 3x^2 + 3x - 1, if we substitute x = 1?




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Correct Ans:0
Explanation:
Given expression:x^3 - 3x^2 + 3x - 1

On substituting x = 1, we get,
13 - 3(12) + 3(1) -1
= 1 - 3 + 3 - 1
= 0
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313. Which of the following values will not satisfy the equation x3 - 6x2 + 11x - 6 = 0 




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Correct Ans:x=4
Explanation:
Given
x3- 6x2+ 11x - 6 = 0
Substituting x = 1, we get
=> (1) ^ 3 - 6 (1) ^ 2 + 11 (1) - 6 = 0
=> 1 - 6 + 11 - 6
=> 11 - 11
=>0
When x = 2
=> ( 2) ^ 3 - 6 ( 2) ^ 2 + 11 ( 2) - 6 = 0
=> 8 - 24 + 22 - 6 = 0
=> 8 - 2 - 6 = 0
=> 8 - 8
=> 0
When x = 3
=> ( 3) ^ 3 - 6 ( 3) ^ 2 + 11 ( 3) - 6 = 0
=> 27 - 54 + 33 -6 = 0
=> - 27 + 33 - 6 = 0
=> -33 + 33
=> 0
When x = 4
=> ( 4) ^ 3 - 6 ( 4) ^ 2 + 11 ( 4) - 6 = 0
=> 64 - 96 + 44 - 6 = 0
=> -32 + 44 - 6 = 0
=> -38 + 44
=> 6
Thus 4 gives us value so it doesnot satsify the condition.
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314. If 432 is added to some number the answer we obtained is 2132, find that number 




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Correct Ans:463
Explanation:
432 = 1849, Let x be that number then 1849 + x = 2312 => x = 2312 ? 1849 x = 463
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315. If x + y = 24 and xy= 100, What is the value of x2 + y2 = ?




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Correct Ans:376
Explanation:
( x + y)2 = x2+y2+2xy => 242 = x2 + y2 + 2(100) x2+y2 = 576 ? 200 = 376
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316. In a group of ducks and buffaloes, the total number of legs are 24 more than twice the number of heads. Find the number of buffaloes.




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Correct Ans:12
Explanation:
Let the number of buffaloes be x and the number of ducks be y => 4x + 2y = 2 (x + y) + 24 => 2x = 24 => x = 12
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