451. The expression x⁴ – 2x² + k will be a perfect square when the value of k is

1. 1. 2

   
   
   

   2. 1

   
   
   

   3. –1

   
   
   

   4. –2

   
   
   

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1. View Hint View Answer Discuss in Forum

   (a – b)² = a² –2ab + b²
   x⁴ – 2x² + k = (x²)² – 2.x² .1+ k
   ∴  k = (1)² = 1

   Correct Option: B

   (a – b)² = a² –2ab + b²
   x⁴ – 2x² + k = (x²)² – 2.x² .1+ k
   ∴  k = (1)² = 1

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452. If 2^{x + 3} = 32, then the value of 3^x+1 is equal to

1. 1. 27

   
   
   

   2. 81

   
   
   

   3. 72

   
   
   

   4. 9

   
   
   

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1. View Hint View Answer Discuss in Forum

   2^{x + 3} = 32 = 2⁵
   ⇒  x + 3 = 5 ⇒ x = 5 – 3 = 2
   ∴  3^{x + 1} = 3³ = 27

   Correct Option: A

   2^{x + 3} = 32 = 2⁵
   ⇒  x + 3 = 5 ⇒ x = 5 – 3 = 2
   ∴  3^{x + 1} = 3³ = 27

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453. If	x	=	3	, the value of	6	+	y − x	is :
     	y		4		7		y + x

1. 1. 1

   
   
   

   2. 2

      7

   
   
   

   3. 3

      7

   
   
   

   4. 1	3
      	7

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given,	x	=	3
   	y		4

   
   

   Now,	6	+	y − x
   	7		y + x

   
   

   = (6/7) +	1 −	x
   		y
   	1 +	x
   		y

   
   [Dividing N^r and D^r by y]
   

   = (6/7) +	1 −	3
   		4
   	1 +	3
   		4

   
   

   =	6	+	4 − 3
   	7		4 + 3

   
   

   =	6	+	1	= 1
   	7		7

   Correct Option: A

   Given,	x	=	3
   	y		4

   
   

   Now,	6	+	y − x
   	7		y + x

   
   

   = (6/7) +	1 −	x
   		y
   	1 +	x
   		y

   
   [Dividing N^r and D^r by y]
   

   = (6/7) +	1 −	3
   		4
   	1 +	3
   		4

   
   

   =	6	+	4 − 3
   	7		4 + 3

   
   

   =	6	+	1	= 1
   	7		7

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454. If   n +	2	n +	1	n +	1	n = 97 then the value of n is
     	3		2		7

1. 1. 40

   
   
   

   2. 42

   
   
   

   3. 44

   
   
   

   4. 46

   
   
   

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1. View Hint View Answer Discuss in Forum

   n +	2n	+	n	+	n	= 97
   	3		2		7

   
   

   ⇒	42n + 28n + 21n + 6n	= 97
   	42

   
   

   ⇒	97n	= 97 ⇒ n =	97 × 42	= 42
   	42		97

   
   ∴  n = 42

   Correct Option: B

   n +	2n	+	n	+	n	= 97
   	3		2		7

   
   

   ⇒	42n + 28n + 21n + 6n	= 97
   	42

   
   

   ⇒	97n	= 97 ⇒ n =	97 × 42	= 42
   	42		97

   
   ∴  n = 42

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455. If 5^√x + 12^√x = 13^√x , then x is equal to

1. 1. 25

      4

   
   
   

   2. 4

   
   
   

   3. 9

   
   
   

   4. 16

   
   
   

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1. View Hint View Answer Discuss in Forum

   5^√x + 12^√x = 13^√x
   We know that 5² + 12² + 13²
   [Pythagorean Triplet]
   ∴ √x = 2 ⇒ x = 2² = 4

   Correct Option: B

   5^√x + 12^√x = 13^√x
   We know that 5² + 12² + 13²
   [Pythagorean Triplet]
   ∴ √x = 2 ⇒ x = 2² = 4

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