Algebra
- If 0.13 ÷ p2 = 13, then p is equal to
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0.13 ÷ p2 = 13
⇒ 0.13 = 13 p2 ⇒ p2 = 0.13 = 1 13 100 ⇒ p = 1 = 0.1 10 Correct Option: C
0.13 ÷ p2 = 13
⇒ 0.13 = 13 p2 ⇒ p2 = 0.13 = 1 13 100 ⇒ p = 1 = 0.1 10
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If a = b = c , then a + b + c is equal to 2 3 5 c
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a = b = c = k (let) 2 3 5 ∴ a + b + c = 2k + 3k + 5k c 5k = 10k = 2 5k Correct Option: A
a = b = c = k (let) 2 3 5 ∴ a + b + c = 2k + 3k + 5k c 5k = 10k = 2 5k
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If 7x = 1 , then the value of x is 343
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7x = 1 343 ⇒ 7x = 1 = 7−3 73
⇒ x = –3Correct Option: B
7x = 1 343 ⇒ 7x = 1 = 7−3 73
⇒ x = –3
- If a = 7, b = 5 and c = 3, then the value of a2 + b2 + c2 – ab – bc – ca is
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a2 + b2 + c2 – ab – bc – ca
= 1 [ (a − b)2 + (b − c)2 + (c − a)2] 2 = 1 [ (7 − 5)2 + (5 − 3)2 + (3 − 7)2] 2 = 1 [ 4 + 4 + 16] 2 = 1 × 24 = 12 2 Correct Option: A
a2 + b2 + c2 – ab – bc – ca
= 1 [ (a − b)2 + (b − c)2 + (c − a)2] 2 = 1 [ (7 − 5)2 + (5 − 3)2 + (3 − 7)2] 2 = 1 [ 4 + 4 + 16] 2 = 1 × 24 = 12 2
- If xx√x = (x√x)x , then x equals
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xx√x = (x√x)x
⇒ xx.x1/2 = (x×x1/2)x
⇒ xx1 + (1/2) = (x 1 + (1/2))x
xx3/2 = (x 3/2)x = x 3x/2⇒ x3/2 = 3x ⇒ x3/2 − 3x = 0 2 2 ⇒ x 
x1/2 − 3 
= 0 2 ⇒ x = 0 or 1 = 3 x2 2 ⇒ x = 3 2 = 9 2 4
x = 0 given indeterminate value.∴ x = 9 4 Correct Option: C
xx√x = (x√x)x
⇒ xx.x1/2 = (x×x1/2)x
⇒ xx1 + (1/2) = (x 1 + (1/2))x
xx3/2 = (x 3/2)x = x 3x/2⇒ x3/2 = 3x ⇒ x3/2 − 3x = 0 2 2 ⇒ x x1/2 − 3 = 0 2 ⇒ x = 0 or 1 = 3 x2 2 ⇒ x = 3 2 = 9 2 4
x = 0 given indeterminate value.∴ x = 9 4
