356. (53 × 87 + 159 × 21 + 106 × 25) is equal to

1. 1. 16000

   
   
   

   2. 1060

   
   
   

   3. 10600

   
   
   

   4. 60100

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Expression
   = (53 × 87 +159 ×21 + 106 × 25)
   = 53 (87 +3 ×21 + 2 × 25)
   = 53 (87 + 63 + 50)
   = 53 × 200 = 10600

   Correct Option: C

   Expression
   = (53 × 87 +159 ×21 + 106 × 25)
   = 53 (87 +3 ×21 + 2 × 25)
   = 53 (87 + 63 + 50)
   = 53 × 200 = 10600

---

357. 	1	+	1	+	1	+	1	+	1	+	1		is equal to :
     	3.5		5.7		7.9		9.11		11.13		13.15

1. 1. 2

      45

   
   
   

   2. 4

      45

   
   
   

   3. 7

      45

   
   
   

   4. 2

      15

   
   
   

---

1. View Hint View Answer Discuss in Forum

   =		1	+	1	+	1	+	1	+	1	+	1
   		3.5		5.7		7.9		9.11		11.13		13.15

   
   

   =	1		1	+	1	+	1	+	1	+	1	+	1
   	2		3.5		5.7		7.9		9.11		11.13		13.15

   
   

   =	1		1	+	1	+	1	+	1	+	1	+	1	+	1	+	1	+	1	+	1	+	1	+	1
   	2		3		5		5		7		7		9		9		11		11		13		13		15

   
   

   =	1		1	−	1		=	1		5 − 1
   	2		3		15			2		15

   
   

   =	1	×	4	=	2
   	2		15		15

   
   
   Second Method :
   

   =	1	+	1	+	1	+	1	+	1	+	1
   	3.5		5.7		7.9		9.11		11.13		13.15

   
   Here, n = 3 and r = 6
   

   =	1		1	−	1
   	2		n		n + 2r

   
   

   =	1		1	−	1
   	2		3		3 + 2 × 6

   
   

   =	1		1	−	1
   	2		3		15

   
   

   =	1		5 − 1		=	2
   	2		15			15

   Correct Option: D

   =		1	+	1	+	1	+	1	+	1	+	1
   		3.5		5.7		7.9		9.11		11.13		13.15

   
   

   =	1		1	+	1	+	1	+	1	+	1	+	1
   	2		3.5		5.7		7.9		9.11		11.13		13.15

   
   

   =	1		1	+	1	+	1	+	1	+	1	+	1	+	1	+	1	+	1	+	1	+	1	+	1
   	2		3		5		5		7		7		9		9		11		11		13		13		15

   
   

   =	1		1	−	1		=	1		5 − 1
   	2		3		15			2		15

   
   

   =	1	×	4	=	2
   	2		15		15

   
   
   Second Method :
   

   =	1	+	1	+	1	+	1	+	1	+	1
   	3.5		5.7		7.9		9.11		11.13		13.15

   
   Here, n = 3 and r = 6
   

   =	1		1	−	1
   	2		n		n + 2r

   
   

   =	1		1	−	1
   	2		3		3 + 2 × 6

   
   

   =	1		1	−	1
   	2		3		15

   
   

   =	1		5 − 1		=	2
   	2		15			15

---

---

358. (256)^0.16 × (16)^0.18 is equal to

1. 1. 4

   
   
   

   2. 16

   
   
   

   3. 64

   
   
   

   4. 256.25

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Expression
   = (256)^0.16 × (16)^0.18
   = (2⁸)^0.16 × (2⁴)^0.18
   = (2)^{8 × 0.16} × (2)4 × 0.18
   = (2)^1.28 × (2)^0.72 = (2)^{1.28 + 0.72}
   =(2)² = 4

   Correct Option: A

   Expression
   = (256)^0.16 × (16)^0.18
   = (2⁸)^0.16 × (2⁴)^0.18
   = (2)^{8 × 0.16} × (2)4 × 0.18
   = (2)^1.28 × (2)^0.72 = (2)^{1.28 + 0.72}
   =(2)² = 4

---

359. The value of	3√	0.2 × 0.2 × 0.2 + 0.4 × 0.4 × 0.4	is
     		0.4 × 0.4 × 0.4 + 0.8 × 0.8 × 0.8

1. 1. 0.5

   
   
   

   2. 0.25

   
   
   

   3. 0.75

   
   
   

   4. 0.125

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let 0.2 = a and 0.04 = b
   ⇒  0.4 = 2a and 0.08 = 2b
   

   ∴  Expression =	3√	a × a × a + b × b × b
   		2a × 2a × 2a + 2b × 2b × 2b

   
   

   =	3√	a3 + b3
   		8a3 + 8b3

   
   

   =	3√	1
   		8

   
   

   =	1	= 0.5
   	2

   Correct Option: A

   Let 0.2 = a and 0.04 = b
   ⇒  0.4 = 2a and 0.08 = 2b
   

   ∴  Expression =	3√	a × a × a + b × b × b
   		2a × 2a × 2a + 2b × 2b × 2b

   
   

   =	3√	a3 + b3
   		8a3 + 8b3

   
   

   =	3√	1
   		8

   
   

   =	1	= 0.5
   	2

---

---

360. (0 . 05 × 5 – 0 . 005 × 5) equals

1. 1. 2.250

   
   
   

   2. 0.225

   
   
   

   3. 0.0225

   
   
   

   4. 0.275

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Expression
   = 0.05 × 5 – 0.005 × 5
   = 0.25 – 0.025 = 0.225

   Correct Option: B

   Expression
   = 0.05 × 5 – 0.005 × 5
   = 0.25 – 0.025 = 0.225

---