436. If a +	1	= 3 then a3 +	1	+ 1 is
     	a		a3

     
     

1. 1. 27
      

   
   
   

   2. 24
      

   
   
   

   3. 19
      

   
   
   

   4. 25

   
   
   

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1. View Hint View Answer Discuss in Forum

   a +	1	= 3
   	a

   
   On cubing both sides,
   

   ⇒		a +	1		3	= 33 = 27
   			a

   
   

   ⇒ a3 +	1	+ 3 × a ×	1		a +	1		= 27
   	a3		a			a

   
   

   ⇒ a3 +	1	+ 3 × 3 = 27
   	a3

   
   

   ⇒ a3 +	1	= 27 - 9 = 18
   	a3

   
   

   ∴ a3 +	1	+ 1 = 18 + 1 = 19
   	a3

   Correct Option: C

   a +	1	= 3
   	a

   
   On cubing both sides,
   

   ⇒		a +	1		3	= 33 = 27
   			a

   
   

   ⇒ a3 +	1	+ 3 × a ×	1		a +	1		= 27
   	a3		a			a

   
   

   ⇒ a3 +	1	+ 3 × 3 = 27
   	a3

   
   

   ⇒ a3 +	1	= 27 - 9 = 18
   	a3

   
   

   ∴ a3 +	1	+ 1 = 18 + 1 = 19
   	a3

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437. 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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438. If √2^x = 256 , then the value of x is

1. 1. 14

   
   
   

   2. 16

   
   
   

   3. 18

   
   
   

   4. 20

   
   
   

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1. View Hint View Answer Discuss in Forum

   √2^x = 256
   ⇒ 2^x/2 = 2⁸
   

   ⇒	x	= 8 ⇒ x = 16
   	2

   Correct Option: B

   √2^x = 256
   ⇒ 2^x/2 = 2⁸
   

   ⇒	x	= 8 ⇒ x = 16
   	2

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439. If (√5)⁷ ÷ (√5)⁵ = 5^p, then the value of p is

1. 1. 5

   
   
   

   2. 2

   
   
   

   3. 3

      2

   
   
   

   4. 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   (√5)7	= 5p
   (√5)5

   
   ⇒ (√5)^{7 − 5} = 5^p
   ⇒  (√5)² = 5^p
   ⇒  5¹ = 5^p ⇒ p = 1

   Correct Option: D

   (√5)7	= 5p
   (√5)5

   
   ⇒ (√5)^{7 − 5} = 5^p
   ⇒  (√5)² = 5^p
   ⇒  5¹ = 5^p ⇒ p = 1

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440. If a   b = 2a + 3b – ab, then the value of (3 5 + 5 3) is

1. 1. 10

   
   
   

   2. 6

   
   
   

   3. 4

   
   
   

   4. 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given that
   a ★ b = 2a + 3b – ab
   ∴  3 ★ 5 + 5 ★ 3
   = (2 × 3 + 3 × 5 – 3 × 5) + (5 × 2 + 3 × 3 – 5 × 3)
   = (6 + 15 – 15) + (10 + 9 – 15)
   = 6 + 4 = 10
   

   Correct Option: A

   Given that
   a ★ b = 2a + 3b – ab
   ∴  3 ★ 5 + 5 ★ 3
   = (2 × 3 + 3 × 5 – 3 × 5) + (5 × 2 + 3 × 3 – 5 × 3)
   = (6 + 15 – 15) + (10 + 9 – 15)
   = 6 + 4 = 10
   

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