Algebra
- What should be added to 8 (3x – 4y) to obtain (18x – 18y) ?
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Required answer
= (18x – 18y) – 8 (3x – 4y)
= 18x – 18y – 24x + 32y
= 14y – 6xCorrect Option: C
Required answer
= (18x – 18y) – 8 (3x – 4y)
= 18x – 18y – 24x + 32y
= 14y – 6x
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x2 + 3x + 1 = 1 , then the value of x + 1 is : x2 − 3x + 1 2 x
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x2 + 3x + 1 = 1 x2 − 3x + 1 2
⇒ 2x2 + 6x + 2 = x2 – 3x + 1
⇒ 2x2 – x2 + 2 – 1 = – 6x – 3x
⇒ x2 + 1 = – 9x⇒ x2 + 1 = –9 x ⇒ x + 1 = –9 x Correct Option: B
x2 + 3x + 1 = 1 x2 − 3x + 1 2
⇒ 2x2 + 6x + 2 = x2 – 3x + 1
⇒ 2x2 – x2 + 2 – 1 = – 6x – 3x
⇒ x2 + 1 = – 9x⇒ x2 + 1 = –9 x ⇒ x + 1 = –9 x
- If (a + b)2 = 100 and (a – b) = 4, then ab equals to :
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4ab = (a + b)2 – (a – b)2
⇒ 4ab = 100 – (4)2 = 100 – 16
⇒ 4ab = 84⇒ ab = 84 = 21 4 Correct Option: C
4ab = (a + b)2 – (a – b)2
⇒ 4ab = 100 – (4)2 = 100 – 16
⇒ 4ab = 84⇒ ab = 84 = 21 4
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If 4x + 1 = 5, x ≠ 0, then the value of 5x is : x 4x2 + 10x + 1
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4x + 1 = 5 x Expression = 5x 4x2 + 1 + 10x = 5x x 4x + 1 + 10 x = 5 = 5 = 1 5 + 10 15 3 Correct Option: B
4x + 1 = 5 x Expression = 5x 4x2 + 1 + 10x = 5x x 4x + 1 + 10 x = 5 = 5 = 1 5 + 10 15 3
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If a + b + c = 1 , then the value of 1 − 2a 1 − 2b 1 − 2c 2 1 + 1 + 1 is : 1 − 2a 1 − 2b 1 − 2c
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a + b + c = 1 1 − 2a 1 − 2b 1 − 2c 2 ⇒ 2a + 2b + 2c = 2 = 1 1 − 2a 1 − 2b 1 − 2c 2 ⇒ 2a + 1 + 2b + 1 + 2c + 1 = 4 1 − 2a 1 − 2b 1 − 2c ⇒ 2a + 1 − 2a + 2b + 1 − 2b + 2c + 1 − 2c = 4 1 − 2a 1 − 2b 1 − 2c ⇒ 1 + 1 + 1 = 4 1 − 2a 1 − 2b 1 − 2c Correct Option: D
a + b + c = 1 1 − 2a 1 − 2b 1 − 2c 2 ⇒ 2a + 2b + 2c = 2 = 1 1 − 2a 1 − 2b 1 − 2c 2 ⇒ 2a + 1 + 2b + 1 + 2c + 1 = 4 1 − 2a 1 − 2b 1 − 2c ⇒ 2a + 1 − 2a + 2b + 1 − 2b + 2c + 1 − 2c = 4 1 − 2a 1 − 2b 1 − 2c ⇒ 1 + 1 + 1 = 4 1 − 2a 1 − 2b 1 − 2c