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

281. If x^2 -7x + 10 < 0, then which of the following option satisfy the inequation ?

Correct Ans:Both (a) and (b)
Explanation:
x^2 -7x + 10
=> x^2 - 5x -2x + 10 = 0
=> x( x - 5) - 2 ( x -5) = 0
=> ( x - 2) ( x - 5) = 0
Thus x => 2 , 5
=>( x- 2 ) = 0
=> x = 2
=> ( x - 5) = 0
=> x = 5
=> x = 2 , 5

Thus both a & b gives value of x.
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282. If x + 1/x = 21, then find the value of x^2 + 1/x^2 = ?

Correct Ans:439
Explanation:
Given x + (1 / x) = 21
Squaring on both sides, we get
=> [x + (1 / x)]^2 = 21 * 21
By Formula: (a + b)^2 = a^2 + b^2 + 2ab
=> x^2 + (1/x)^2 + 2 * x * (1/x) = 441
=> x^2 + (1/x)^2 + 2 = 441
=> x^2 + (1/x)^2 = 441 - 2
=> x^2 + 1/x^2 = 439
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283. Which of the following values satisify the condition x^2 - 5x + 6 < 0

Correct Ans:2, -3
Explanation:
x^ 2 - 5x + 6 = 0
= x^2 - 2x -3x + 6 = 0
= x( x -2) + 3 ( x - 2)
= (x + 3) + ( x - 2 ) = 0
=>(x + 3) = 0
=> x = -3
=> ( x - 2 ) = 0
=> x = 2
=> x = 2 , -3
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284. Find the solution for the equation x^2 - 49x + 600 = 0

Correct Ans:x = 25
Explanation:
On solving this eqn by using the formula for the eqn: ax2+bx+c= 0
=> X = [-b ± sqrt(b^2 – 4ac)] / 2a
Given equation: x^2 - 49x + 600 = 0
Here a = 1, b = -49, c = 600
=> X = [49 ± sqrt (49^2 – 4*1*600)] / 2
= [49 ± sqrt (2401 – 2400)] / 2
= [49 ± sqrt (1)] / 2
= (49 ± 1) / 2
= (49 + 1) / 2, (49 - 1) / 2
= 50 / 2, 48/ 2
=> X = 25, 24
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285. Sum of two digits in a given two digit number is 7. The number formed by reversing the digits exceed the original number by 27. Find the original number.

Correct Ans:25
Explanation:
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286. Given x^2 - 16 < 0, then which of the following options are true?

Correct Ans:x < 4
Explanation:
x^2 - 16 < 0
=> x^2 < 16
=> x < sqrt(16)
=> x < ± 4
=> -4 < x < +4
Thus among given options, x < 4 is the correct answer.
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287. Find the possible values of x which satisfies the equation x^2 - 4 < 0

Correct Ans:either (a) or (c)
Explanation:
Given, x^2 - 4 < 0
=> x^2 < 4
=> x < sqrt(4)
=> x <± 2
=> -2 < x < 2
=> x > -2
OR x < 2
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288. Given | x - 7 | < 1 , then find the values what x can take?

Correct Ans:6 < x < 8
Explanation:
Given | x - 7 | < 1
=> -1 < x-7 < 1
=> -1 + 7 < x < 1 + 7
=> 6 < x < 8
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289. Find the value obtained when we substitute x=8 in the equation x^2 - 13x + 42

Correct Ans:2
Explanation:
Given equation, x^2 - 13 x + 42
Sub x= 8, we get 8^2 - 13(8) + 42 = 64 - 104 + 42 = 106 - 104 = 2
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290. Which of the following options are possibly the solution for the equations x^2 - 26 x + 120 = 0

Correct Ans:None of the above
Explanation:
x^2 - 26 x + 120 = 0
x ^ 2 + 4 x - 30 x = 0
x ^ 2 + 4x - 30 x = 0
x ( x + 4 ) - 30 ( x + 4 ) = 0
( x - 30 ) ( x + 4) = 0
x = 30 , x = -4.
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291. In a group of cows and hens, the number of legs are 14 more than twice the number of heads. Find the number of cows.

Correct Ans:7
Explanation:
Let the number of cows be C and the number of hens be H.
Given, Number of legs = 14 + Number of heads
We know that, Cow has 4 legs, whereas Hen has 2 legs
=> 4C + 2H = 14 + 2(C + H)
=> 4C + 2H = 14 + 2C + 2H
=> 4C – 2C + 2H – 2H = 14
=> 2C = 14
=> C = 7
Therefore, the number of Cows = 7
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292. In a group of cows and hens, the number of legs are 12 more than twice the number of heads. Find the number of cows

Correct Ans:6
Explanation:
Let the number of cows be x and the number of hens by y,
Then, 4x + 2y = 2(x+y) + 12
Solving the above equations,we get number of cows = 6
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293. A student got twice as many sums wrong as he got right. If he attempted 48 sums in all, how many did he solve correctly ?

Correct Ans:16
Explanation:

Suppose the boy got x sums right and 2x sums wrong.
Then, x + 2x = 48
3x = 48
x = 16.

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294. A student got twice as many sums wrong as he got right. If he attempted 75 sums in all, how many did he solve correctly?

Correct Ans:25
Explanation:

Suppose the boy got "x"sums right.
Given,A student got twice as many sums wrong as he got right
=> He got "2x" sums wrong.

Given,he attempted 75 sums in all
=> Right sums + wrong sums = 75 sums
=> x + 2x = 75
=> 3x = 75
=> x = 75 / 3
=> x = 25

Therefore,the boy got "25"sums right.

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295. Given expression x^3 -3x^2 + 2x, evaluate for x= 2 ?

Correct Ans:0
Explanation:
x^3 - 3x^2 + 2x
Sub, x = 2, we get
2^3 - 3(2^2) + 2(2) = 8 - 12 + 4 = 0
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296. If x=2, then find the value of x^3  - 3x^2 +3x-6

Correct Ans:-4
Explanation:
x^3 - 3x^2 + 3x --6
Substituting x=2
=> 2^3 - 3(2^2) + 3(2) - 6
= 8 - 12 + 6 - 6
= -4
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297. If x + (1/x) = 3, then what will be the value of  x2 + (1/x2) = ?

Correct Ans:7
Explanation:
Given x + (1 / x) = 3
Squaring on both sides, we get
=> [x + (1 / x)]^2 = 3 * 3
By Formula: (a + b)^2 = a^2 + b^2 + 2ab
=> x^2 + (1/x)^2 + 2 * x * (1/x) = 9
=> x^2 + (1/x)^2 + 2 = 9
=> x^2 + (1/x)^2 = 9 - 2
=> x^2 + 1/x^2 = 7
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298. Given that |x-2| < 6, then find which of the following possible values x can take?

Correct Ans:-4 <  x < 8
Explanation:
Given |x-2| < 6
=> -6 < x - 2 < 6
=> -6 + 2 < x < 6 + 2
=> -4 < x < 8
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299. Given that |x-2| < 3, then find which of the following possible values x can take?

Correct Ans:-1 <  x < 5
Explanation:
Given |x-2| < 3
=> -3 < x - 2 < 3
=> -3 + 2 < x < 3 + 2=> -1 < x < 5
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300. Given that |x-2| < 7, then find which of the following possible values x can take ?

Correct Ans:-5 <  x < 9
Explanation:
Given |x-2| < 7
=> -7 < x - 2 < 7
=> -7 + 2 < x < 7 + 2=> -5 < x < 9
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