Algebra
- If X * Y = X2 + Y2 – XY then 11 * 13 is
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X ★ ★ Y = X2 + Y2 – XY
∴ 11 ★ ★ 13 = 112 + 132 – 11 × 13
= 121 + 169 – 143 = 147Correct Option: B
X ★ ★ Y = X2 + Y2 – XY
∴ 11 ★ ★ 13 = 112 + 132 – 11 × 13
= 121 + 169 – 143 = 147
- If 9√x = √12 + √147 , then x = ?
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9√x = √3 × 2 × 2 + √3 × 7 × 7
⇒ 9√x = 2√3 + 7√3 = 9√3
∴ x = 3Correct Option: B
9√x = √3 × 2 × 2 + √3 × 7 × 7
⇒ 9√x = 2√3 + 7√3 = 9√3
∴ x = 3
- If x * y = (x + 3)2 (y –1), then the value of 5 * 4 is
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x ★ y = (x + 3)2 (y – 1)
∴ 5 ★ 4 = (5 + 3)2 (4 – 1)
= 64 × 3 = 192Correct Option: A
x ★ y = (x + 3)2 (y – 1)
∴ 5 ★ 4 = (5 + 3)2 (4 – 1)
= 64 × 3 = 192
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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
- 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