Algebra MCQ Set 4

ALGEBRA MCQ SET 4

1. If a + b + c = 6 , a² + b² + c² = 14 and ab + bc + ca = 11 , then what is the value of a³ + b³ + c³ – 3abc ?

(a) 31

(b) 12

(c) 18

(d) 42

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Answer: C

2. If a + b + c = 15 and ab + bc + ca = 35 , then find the value of a³ + b³ + c³ – 3abc .

(a) 2100

(b) 1500

(c) 1200

(d) 1800

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Answer: D

3. If (a + b + c) = 20 , and a² + b² + c² = 152 , find the value of a³ + b³ + c³ – 3abc .

(a) 560

(b) 640

(c) 480

(d) 720

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Answer: A

4. If the sum of three numbers is 18 and the sum of their square is 36 , then find the difference between the sum of their cubes and three times of their product .

(a) 1449

(b) -1944

(c) -1494

(d) 4149

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Answer: B

5. If x = 110 , y = 111 , z = 112 , then find the value of x³ + y³ + z³ – 3xyz .

(a) 999

(b) 991

(c) 997

(d) 995

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Answer: A

6. If (a³ + b³ + c³ – 3abc) = 405 , and (a + b + c) = 15 , find the value of (a – b)² + (b – c)² + (c – a)² .

(a) 27

(b) 54

(c) 18

(d) 45

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Answer: B

7. If (5x + 1)³ + (x – 3)³ + 8(3x – 4)³ = 6(5x + 1) (x – 3) (3x – 4) , then x is equal to :

(a) 5/6

(b) 1/3

(c) 2/3

(d) 3/4

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 Answer: A

8. If ab + bc + ca = 8 a² + b² + c² = 20 , then possible value of 1/2(a + b + c) [(a – b)² + (b – c)² + (c – a)²] is :

(a) 72

(b) 56

(c) 84

(d) 80

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Answer: A

9. If p = 106 , q = 105 and r = 104 , then value of p² + q² + r² – pq – qr – rp is :

(a) 2

(b) 0

(c) 1

(d) 3

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Answer: C

10. If a² + b² = 148 and ab = 54 , then find the value of a + b/a – b .

(a) 8/√10

(b) 2/√10

(c) 8/√7

(d) 5/√3

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Answer: A