321. If X * Y = X² + Y² – XY then 11 * 13 is

1. 1. 117

   
   
   

   2. 147

   
   
   

   3. 290

   
   
   

   4. 433

   
   
   

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1. View Hint View Answer Discuss in Forum

   X ★ ★ Y = X² + Y² – XY
   ∴  11 ★ ★ 13 = 11² + 13² – 11 × 13
   = 121 + 169 – 143 = 147

   Correct Option: B

   X ★ ★ Y = X² + Y² – XY
   ∴  11 ★ ★ 13 = 11² + 13² – 11 × 13
   = 121 + 169 – 143 = 147

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322. If 9√x = √12 + √147 , then x = ?

1. 1. 2

   
   
   

   2. 3

   
   
   

   3. 4

   
   
   

   4. 5

   
   
   

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1. View Hint View Answer Discuss in Forum

   9√x = √3 × 2 × 2 + √3 × 7 × 7
   ⇒  9√x = 2√3 + 7√3 = 9√3
   ∴  x = 3

   Correct Option: B

   9√x = √3 × 2 × 2 + √3 × 7 × 7
   ⇒  9√x = 2√3 + 7√3 = 9√3
   ∴  x = 3

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323. If x * y = (x + 3)² (y –1), then the value of 5 * 4 is

1. 1. 192

   
   
   

   2. 182

   
   
   

   3. 180

   
   
   

   4. 172

   
   
   

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1. View Hint View Answer Discuss in Forum

   x ★ y = (x + 3)² (y – 1)
   ∴  5 ★ 4 = (5 + 3)² (4 – 1)
   = 64 × 3 = 192

   Correct Option: A

   x ★ y = (x + 3)² (y – 1)
   ∴  5 ★ 4 = (5 + 3)² (4 – 1)
   = 64 × 3 = 192

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324. If   √0.03 × 0.3a = 0.3 × 0.3 × √b,   value of	a	is
     	b

1. 1. 0.009

   
   
   

   2. 0.03

   
   
   

   3. 0.9

   
   
   

   4. 0.08

   
   
   

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1. View Hint View Answer Discuss in Forum

   √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

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325. If a * b = a^b , then the value of 5 * 3 is

1. 1. 125

   
   
   

   2. 243

   
   
   

   3. 53

   
   
   

   4. 15

   
   
   

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1. View Hint View Answer Discuss in Forum

   a * b = a^bb
   ∴  5 * 3 = 5³ = 5 × 5 × 5 = 125

   Correct Option: A

   a * b = a^bb
   ∴  5 * 3 = 5³ = 5 × 5 × 5 = 125

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