Algebra
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If a = b , then value of 2a + 3b is 3 2 3a − 2b
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a = b ⇒ a = 3 3 2 b 2 ∴ 2a + 3b 3a − 2b = 2 × a + 3 b 3 × a − 2 b = 2 × 3 + 3 2 3 × 3 − 2 2 = 6 9 − 4 2 = 12 5 Correct Option: A
a = b ⇒ a = 3 3 2 b 2 ∴ 2a + 3b 3a − 2b = 2 × a + 3 b 3 × a − 2 b = 2 × 3 + 3 2 3 × 3 − 2 2 = 6 9 − 4 2 = 12 5
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If a = b = c then a + b + c is
equal to3 4 7 c
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a = b = c = k (let) 3 4 7
a = 3k, b = 4k, c = 7k∴ a + b + c = 3k + 4k + 7k c 7k = 14k = 2 7k Correct Option: C
a = b = c = k (let) 3 4 7
a = 3k, b = 4k, c = 7k∴ a + b + c = 3k + 4k + 7k c 7k = 14k = 2 7k
- If x y = 3x +2y, Then 2 3 + 3 4 is equal to
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∵ x * y = 3x + 2y
2 * 3 + 3 * 4
= 3 × 2 + 2 × 3 + 3 × 3 + 2 × 4
= 6 + 6 + 9 + 8 = 29Correct Option: B
∵ x * y = 3x + 2y
2 * 3 + 3 * 4
= 3 × 2 + 2 × 3 + 3 × 3 + 2 × 4
= 6 + 6 + 9 + 8 = 29
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If x = 7 − 4√3 , then the value of 
x + 1 
is : x
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x = 7 − 4√3
∴ 1 = 1 x 7 − 4√3 = 1(7 + 4√3) (7 + 4√3)(7 − 4√3) = 7 + 4√3 = 7 + 4√3 49 − 48 ∴ x + 1 x
= 7 − 4√3 + 7 + 4√3 = 14Correct Option: D
x = 7 − 4√3
∴ 1 = 1 x 7 − 4√3 = 1(7 + 4√3) (7 + 4√3)(7 − 4√3) = 7 + 4√3 = 7 + 4√3 49 − 48 ∴ x + 1 x
= 7 − 4√3 + 7 + 4√3 = 14
- If a * b = a + b + ab, then 3 * 4 – 2 * 3 is equal to :
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Given a * b = a + b + ab
∴ 3 * 4 – 2 * 3
= (3 + 4 + 3 × 4) – (2 + 3 + 2 × 3)
= (7 + 12) – (5 + 6) = 19 – 11 = 8Correct Option: B
Given a * b = a + b + ab
∴ 3 * 4 – 2 * 3
= (3 + 4 + 3 × 4) – (2 + 3 + 2 × 3)
= (7 + 12) – (5 + 6) = 19 – 11 = 8
