# Materials for sensors

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Instructions
For the following questions answer them individually
Question 1
If xy = 56 and x
2
+ y
2
= 113
, then what will be the value of (x + y)?
A 29
B 21
C 36
D 15
Explanation:
Given : (x
2
+ y
2
) = 113 and xy = 56
Using (x + y)
2
= x2 + y2 + 2xy
=> (x + y)
2
= 113 + (2 × 56)
=> (x + y)
2
= 113 + 112 = 225
=> (x + y) = 225 = 15
=> Ans - (D)
Question 2
If a + b = 11 and a
2
+ b
2
= 61, then value of ab is
A 12
B 96
C 24
D 30
Explanation:
Given : (a + b) = 11 and a
2
+ b
2
= 61
Using (a + b)
2
= a
2
+ b
2
+ 2ab
=> (11)
2
= 61 + (2 × ab)
=> 2ab = 121 − 61 = 60
60
=> ab =
2
= 30
=> Ans - (D)
Question 3
If 4(2x -4) - 2 > 3x - 1 ≥ 4x -7, then x can take which of the following values?

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A 7
B 6
C 2
D 0
Explanation:
Expression 1 : 4(2x -4) - 2 > 3x - 1
=> 8x 16 − 2 > 3x 1
=> 8x 3x > 1 + 18
=> x >
Expression 2 : 3x - 1 ≥ 4x -7
=> 4x 3x ≤ −1 + 7
=> x
≤ 6
-----------(ii)
17 Combining
inequalities (i) and (ii), we get : 5 < x
≤ 6
The only value that x can take among the options = 6
=> Ans - (B)
Question 4
Factors of 48x
3
8x
2
93x 45 are
A (4x + 3)(4x - 3)(3x - 5)
(4x - 3)(4x - 3)(3x
B
- 5)
(4x + 3)(4x + 3)(3x
C
- 5)
D (4x - 3)(4x + 3)(3x + 5)
Explanation:
(A) : (4x + 3)(4x - 3)(3x - 5)
= (16x
2
12x + 12x 9)(3x 5)
= (16x
2
9)(3x 5)
= 48x
3
80x
2
27x + 45
(B) : (4x - 3)(4x - 3)(3x - 5)

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Instructions For the following questions answer them individually Question 1 If xy = 56 and x2 + y2 = 113, then what will be the value of (x + y)? A 29 B 21 C 36 D 15 Answer: D Explanation: Given : (x2 + y2) = 113 and xy = 56 Using (x + y)2 = x2 + y2 + 2xy => (x + y)2 = 113 + (2 × 56) => (x + y)2 = 113 + 112 = 225 => (x + y) = 225 = 15 => Ans - (D) Question 2 If a + b = 11 and a2 + b2 = 61, then value of ab is A 12 B 96 C 24 D 30 Answer: D Explanation: Given : (a + b) = 11 and a2 + b2 = 61 Using (a + b)2 = a2 + b2 + 2ab => (11)2 = 61 + (2 × ab) => 2ab = 121 − 61 = 60 60 => ab = 2 = 30 => Ans - (D) Question 3 If 4(2x -4) - 2 > 3x - 1 ≥ 4x -7, then x can take which of the following values? A 7 B 6 C 2 D 0 Answer: B Explanation: Expression 1 : 4(2x -4) - 2 > 3x - 1 => 8x − 16 − 2 > 3x − 1 => 8x − 3x > −1 + 18 => x > Expression 2 : 3x - 1 ≥ 4x -7 => 4x − 3x ≤ −1 + 7 => x ≤ 6 -----------(ii) 17 Combining inequalities (i) and (ii), we get : 5 < x ≤ 6 The only value that x can take among the options = 6 => Ans - (B) Question 4 Factors of 48x3 − 8x2 − 93x − 45 are A (4x + 3)(4x - 3)(3x - 5) (4x - 3)(4x - 3)(3x B - 5) (4x + 3)(4x + 3)(3x C - 5) D (4x - 3)(4x + 3)(3x + 5) Answer: C Explanation: (A) : (4x + 3)(4x - 3)(3x - 5) = (16x2 − 12x + 12x − 9)(3x − 5) = (16x2 − 9)(3x − 5) = 48x3 − 80x2 − 27x + 45 (B) : (4x - 3)(4x - 3)(3x - 5) = (16x2 − 24x + 9)(3x − 5) = 48x3 − 80x2 − 72x2 + 120x + 27x − ...
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