171. A teacher wants to arrange his students in an equal number of rows and columns. If there are 1369 students, the number of students in the last row are

1. 1. 37

   
   
   

   2. 33

   
   
   

   3. 63

   
   
   

   4. 47

   
   
   

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1. View Hint View Answer Discuss in Forum

   Number of students in the last row = √1369 = 37
   

   Correct Option: A

   Number of students in the last row = √1369 = 37
   

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172. If   √0.05 × 0.5 × a = 0.5 × 0.05 × √b, then a/b is equal to

1. 1. 0.0025

   
   
   

   2. 0.025

   
   
   

   3. 0.25

   
   
   

   4. 0.00025;

   
   
   

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1. View Hint View Answer Discuss in Forum

   √0.05 × 0.5 × a
   = 0.5 × 0.05 × √b
   On squaring both sides,
   0.05 × 0.5 × a = 0.5 × 0.5 × 0.05 × 0.05 × b
   ⇒  a = 0.5 × 0.05b
   

   ⇒	a	= 0.5 × 0.05 = 0.025
   	b

   Correct Option: B

   √0.05 × 0.5 × a
   = 0.5 × 0.05 × √b
   On squaring both sides,
   0.05 × 0.5 × a = 0.5 × 0.5 × 0.05 × 0.05 × b
   ⇒  a = 0.5 × 0.05b
   

   ⇒	a	= 0.5 × 0.05 = 0.025
   	b

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173. The simplified value of	3√2	−	4√3	+	√6	is
     	√3 + √6		√6 + √2		√3 + √2

1. 1. √2

   
   
   

   2. 1/√2

   
   
   

   3. √3 − √2

   
   
   

   4. 0

   
   
   

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1. View Hint View Answer Discuss in Forum

   3√2

   √6 + √3

   
   

   =	3√2(√6 − √3)
   	(√6 + √3)(√6 − √3)

   
   

   =	3√2(√6 − √3)
   	6 − 3

   
   = √2(√6 − √3)
   = √12 − √6
   = 2 √3 − √6
   

   4√3

   √6 + √2

   
   

   =	4√3(√6 − √2)
   	(√6 + √2)(√6 − √2)

   
   

   =	4√3(√6 − √2)
   	6 − 2

   
   = √3(√6 − √2)
   = √18 − √6
   = 3√2 − √6
   

   √6

   √3 + √2

   
   

   =	√6(√3 − √2)
   	(√3 + √2)(√3 − √2)

   
   

   =	√18 − √12
   	3 − 2

   
   = 3√2 − 2√3
   ∴  Expression
   = 2√3 − √6 − (3√2 − √6) + 3√2 − 2√3
   = 2√3 − √6 − 3√2 + √6 + 3√2 − 2√3 = 0

   Correct Option: D

   3√2

   √6 + √3

   
   

   =	3√2(√6 − √3)
   	(√6 + √3)(√6 − √3)

   
   

   =	3√2(√6 − √3)
   	6 − 3

   
   = √2(√6 − √3)
   = √12 − √6
   = 2 √3 − √6
   

   4√3

   √6 + √2

   
   

   =	4√3(√6 − √2)
   	(√6 + √2)(√6 − √2)

   
   

   =	4√3(√6 − √2)
   	6 − 2

   
   = √3(√6 − √2)
   = √18 − √6
   = 3√2 − √6
   

   √6

   √3 + √2

   
   

   =	√6(√3 − √2)
   	(√3 + √2)(√3 − √2)

   
   

   =	√18 − √12
   	3 − 2

   
   = 3√2 − 2√3
   ∴  Expression
   = 2√3 − √6 − (3√2 − √6) + 3√2 − 2√3
   = 2√3 − √6 − 3√2 + √6 + 3√2 − 2√3 = 0

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174. The value of √10⁻⁶ × 0.25 is

1. 1. 0.0025

   
   
   

   2. 0.0005

   
   
   

   3. 0.25

   
   
   

   4. 0.50

   
   
   

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1. View Hint View Answer Discuss in Forum

   Expression =√10⁻⁶ × 0.25
   

   √	0.25	=	√	25
   	106			106 × 102

   
   

   √	0.25	=	5
   	108		104

   
   = 0.0005

   Correct Option: B

   Expression =√10⁻⁶ × 0.25
   

   √	0.25	=	√	25
   	106			106 × 102

   
   

   √	0.25	=	5
   	108		104

   
   = 0.0005

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175. A tourist spends daily as many rupees as the number of days of his total tour. If his total expenses were ₹ 361, then how many days did his tour last ?

1. 1. 17 days

   
   
   

   2. 19 days

   
   
   

   3. 21 days

   
   
   

   4. 31 days

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the number of days of tour be x.
   ∴  Total expenditure = x²
   ∴  x² = 361 ⇒ x = √361 = 19

   Correct Option: B

   Let the number of days of tour be x.
   ∴  Total expenditure = x²
   ∴  x² = 361 ⇒ x = √361 = 19

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