Algebra
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If 
then the value of x is
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Squaring both sides,1 + x = 169 9 9 ⇒ x = 169 − 1 = 160 9 9 9 ⇒ x = 160 × 9 = 160 9 Correct Option: B
Squaring both sides,1 + x = 169 9 9 ⇒ x = 169 − 1 = 160 9 9 9 ⇒ x = 160 × 9 = 160 9
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If 4√3 + 5√2 = a + b√6, then the values of a and b are respectively √48 + √18
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L.H.S. = 4√3 + 5√2 √48 + √18 = 4√3 + 5√2 4√3 + 3√2 = 4√3 + 5√2 × 4√3 − 3√2 4√3 + 3√2 4√3 − 3√2
(Rationalising the denominator)= 16 × 3 − 12 √6 + 20√6 −15 × 2 (4√3)2 − (3√2)2 = 48 + 8√6 − 30 48 − 18 = 18 + 8√6 = 9 + 4√6 30 15 15 = 3 + 4√6 5 15 Now, 3 + 4√6 = a + b√6 5 15 ∴ a = 3 and b = 4 5 15 Correct Option: D
L.H.S. = 4√3 + 5√2 √48 + √18 = 4√3 + 5√2 4√3 + 3√2 = 4√3 + 5√2 × 4√3 − 3√2 4√3 + 3√2 4√3 − 3√2
(Rationalising the denominator)= 16 × 3 − 12 √6 + 20√6 −15 × 2 (4√3)2 − (3√2)2 = 48 + 8√6 − 30 48 − 18 = 18 + 8√6 = 9 + 4√6 30 15 15 = 3 + 4√6 5 15 Now, 3 + 4√6 = a + b√6 5 15 ∴ a = 3 and b = 4 5 15
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If x + y = 2z then the value of x + z is x − z y − z
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x + y = 2z
⇒ x = 2z – y
⇒ x – z = 2z – y – z = z – y∴ x + z x − z y − z = x − z x − z z − y = x − z = x − z = 1 x − z x − z x − z Correct Option: A
x + y = 2z
⇒ x = 2z – y
⇒ x – z = 2z – y – z = z – y∴ x + z x − z y − z = x − z x − z z − y = x − z = x − z = 1 x − z x − z x − z
- If a * b = ab , then the value of 5 * 3 is
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a * b = abb
∴ 5 * 3 = 53 = 5 × 5 × 5 = 125Correct Option: A
a * b = abb
∴ 5 * 3 = 53 = 5 × 5 × 5 = 125
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If √0.03 × 0.3a = 0.3 × 0.3 × √b, value of a is b
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√0.03 × 0.3 × a
= 0.03 × 0.3 √b
On squaring,
0.03 × 0.3 × a = 0.09 × 0.09×b⇒ a = 0.09 × 0.09 = 0.9 b 0.03 × 0.3 Correct Option: C
√0.03 × 0.3 × a
= 0.03 × 0.3 √b
On squaring,
0.03 × 0.3 × a = 0.09 × 0.09×b⇒ a = 0.09 × 0.09 = 0.9 b 0.03 × 0.3
