431. If   p × q = p + q +	p	, the value of 8 × 2 is :
     	q

1. 1. 6

   
   
   

   2. 10

   
   
   

   3. 14

   
   
   

   4. 16

   
   
   

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1. View Hint View Answer Discuss in Forum

   p × q = p + q +	p
   	q

   
   

   ∴  8 × 2 = 8 + 2 +	8
   	2

   
   =10 + 4 = 14

   Correct Option: C

   p × q = p + q +	p
   	q

   
   

   ∴  8 × 2 = 8 + 2 +	8
   	2

   
   =10 + 4 = 14

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432. If a * b = 2a – 3b + ab, then 3 * 5 + 5 * 3 is equal to :

1. 1. 22

   
   
   

   2. 24

   
   
   

   3. 26

   
   
   

   4. 28

   
   
   

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1. View Hint View Answer Discuss in Forum

   a * b = 2a – 3b + ab
   ⇒  3 * 5 = 2 × 3 – 3 × 5 + 3 × 5 = 6
   5 * 3 = 2 × 5 – 3 × 3 + 3 × 5
   = 10 – 9 + 15 = 16
   Therefore, 3 * 5 + 5 *3
   = 6 + 16 = 22

   Correct Option: A

   a * b = 2a – 3b + ab
   ⇒  3 * 5 = 2 × 3 – 3 × 5 + 3 × 5 = 6
   5 * 3 = 2 × 5 – 3 × 3 + 3 × 5
   = 10 – 9 + 15 = 16
   Therefore, 3 * 5 + 5 *3
   = 6 + 16 = 22

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433. If p(x + y)² = 5 and q(x - y)² = 3 , then the simplified value of p² (x + y)² + 4pq xy – q² (x - y)² is :
     

1. 1. – (p + q)
      

   
   
   

   2. 2 (p + q)
      

   
   
   

   3. p + q
      

   
   
   

   4. –2 (p + q)

   
   
   

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1. View Hint View Answer Discuss in Forum

   p(x + y)² = 5
   

   ⇒ (x + y)2 =	5
   	p

   
   

   ⇒ q(x - y)2 = 3 ⇒ (x - y)2 =	3
   	q

   
   

   ∴ (x + y)2 - (x - y)2 =	5	-	3
   	p		q

   
   

   ⇒ 4xy =	5	-	3	=	5q - 3p
   	p		q		pq

   
   

   ∴ p2 (x + y)2 + 4pq xy – q2 (x - y)2 = p2 .	5	+ pq.	(5q - 3p)	- q2 .	3
   	p		pq		q

   
   p² (x + y)² + 4pq xy – q² (x - y)² = 5p + 5q – 3p – 3q = 2p + 2q

   Correct Option: B

   p(x + y)² = 5
   

   ⇒ (x + y)2 =	5
   	p

   
   

   ⇒ q(x - y)2 = 3 ⇒ (x - y)2 =	3
   	q

   
   

   ∴ (x + y)2 - (x - y)2 =	5	-	3
   	p		q

   
   

   ⇒ 4xy =	5	-	3	=	5q - 3p
   	p		q		pq

   
   

   ∴ p2 (x + y)2 + 4pq xy – q2 (x - y)2 = p2 .	5	+ pq.	(5q - 3p)	- q2 .	3
   	p		pq		q

   
   p² (x + y)² + 4pq xy – q² (x - y)² = 5p + 5q – 3p – 3q = 2p + 2q

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434. If x = ³√7 + 3 then the vlaue of x³ - 9x² + 27x - 34 is :
     

1. 1. 0
      

   
   
   

   2. 1
      

   
   
   

   3. 2
      

   
   
   

   4. –1

   
   
   

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1. View Hint View Answer Discuss in Forum

   x = ³√7 + 3
   ⇒ x - 3 = ³√7
   On cubing both sides ,
   (x - 3)³ = (³√7)³
   ⇒ x³ - 3.x².3 + 3.x.(3)² - (3)³ = 7
   ⇒ x³ - 9x² + 27x - 27 = 7
   ⇒ x³ - 9x² + 27x - 34 = 0

   Correct Option: A

   x = ³√7 + 3
   ⇒ x - 3 = ³√7
   On cubing both sides ,
   (x - 3)³ = (³√7)³
   ⇒ x³ - 3.x².3 + 3.x.(3)² - (3)³ = 7
   ⇒ x³ - 9x² + 27x - 27 = 7
   ⇒ x³ - 9x² + 27x - 34 = 0

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435. If c +	1	= 3 , then the value of (c - 3)7 +	1	is
     	c		c7

     
     

1. 1. 2
      

   
   
   

   2. 0
      

   
   
   

   3. 3
      

   
   
   

   4. 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   c +	1	= 3
   	c

   
   

   ⇒ c - 3 = -	1
   	c

   
   

   ∴ (c - 3)7 +	1	=		-	1		7	+	1
   	c7				c				c7

   
   

   Required answer = -	1	+	1	= 0
   	c7		c7

   
   

   Correct Option: B

   c +	1	= 3
   	c

   
   

   ⇒ c - 3 = -	1
   	c

   
   

   ∴ (c - 3)7 +	1	=		-	1		7	+	1
   	c7				c				c7

   
   

   Required answer = -	1	+	1	= 0
   	c7		c7

   
   

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