296. (113² + 115² + 117² – 113 × 115 – 115 × 117 – 117 × 113) is equal to

1. 1. 0

   
   
   

   2. 4

   
   
   

   3. 8

   
   
   

   4. 12

   
   
   

---

1. View Hint View Answer Discuss in Forum

   a² + b² + c² – ab – bc – ac
   

   =	1	(2a2 + 2b2 + 2c2 – 2ab – 2bc – 2ac)
   	2

   
   

   =	1	[(a − b)2 + (b − c)2 + (c − a)2 ]
   	2

   
   

   =	1	[(113 − 115)2 + (115 − 117)2 + (117 − 113)2 ]
   	2

   
   Where, a = 113, b = 115, c = 117.
   

   =	1	[( − 2)2 + (− 2)2 + 42 ]
   	2

   
   

   =	1	(4 + 4 + 16)
   	2

   
   

   =	1	× 24 = 12
   	2

   Correct Option: D

   a² + b² + c² – ab – bc – ac
   

   =	1	(2a2 + 2b2 + 2c2 – 2ab – 2bc – 2ac)
   	2

   
   

   =	1	[(a − b)2 + (b − c)2 + (c − a)2 ]
   	2

   
   

   =	1	[(113 − 115)2 + (115 − 117)2 + (117 − 113)2 ]
   	2

   
   Where, a = 113, b = 115, c = 117.
   

   =	1	[( − 2)2 + (− 2)2 + 42 ]
   	2

   
   

   =	1	(4 + 4 + 16)
   	2

   
   

   =	1	× 24 = 12
   	2

---

297. The value of the following is :	0.2 × 0.02 × 0.002 × 32
     	0.4 × 0.04 × 0.004 × 16

1. 1. 0.20

   
   
   

   2. 0.50

   
   
   

   3. 0.40

   
   
   

   4. 0.25

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Expression =	0.2 × 0.02 × 0.002 × 32
   	0.4 × 0.04 × 0.004 × 16

   
   

   =	32	=	1	= 0.25
   	2 × 2 × 2 × 16		4

   Correct Option: D

   Expression =	0.2 × 0.02 × 0.002 × 32
   	0.4 × 0.04 × 0.004 × 16

   
   

   =	32	=	1	= 0.25
   	2 × 2 × 2 × 16		4

---

---

298. If ‘+’ means ‘÷’, ‘×’, means ‘–’, ‘÷’ means ‘×’ and ‘–’ means ‘+’, what will be the value of the following expression ? 9 + 3 ÷ 4 – 8 × 2 = ?

1. 1. 6	1
      	4

   
   
   

   2. 6	3
      	4

   
   
   

   3. − 1	3
      	4

   
   
   

   4. 18

   
   
   

---

1. View Hint View Answer Discuss in Forum

   ? = 9 + 3 ÷ 4 – 8 × 2
   After respective substitutions,
   ? = 9 ÷ 3 × 4 + 8 – 2
   

   =	9	× 4 + 8 − 2
   	3

   
   = 20 – 2 = 18

   Correct Option: D

   ? = 9 + 3 ÷ 4 – 8 × 2
   After respective substitutions,
   ? = 9 ÷ 3 × 4 + 8 – 2
   

   =	9	× 4 + 8 − 2
   	3

   
   = 20 – 2 = 18

---

299. The value of

     is

1. 1. 15

      17

   
   
   

   2. 13

      17

   
   
   

   3. 15

      19

   
   
   

   4. 13

      19

   
   
   

   5. None of these

   
   
   

---

1. View Hint View Answer Discuss in Forum

   
   

   = 3 ÷		3 ÷	60
   			13

   
   

   = 3 ÷		3 × 13
   		60

   
   

   = 3 ÷	13	= 3 ×	20	=	60
   	20		13		13

   Correct Option: E

   
   

   = 3 ÷		3 ÷	60
   			13

   
   

   = 3 ÷		3 × 13
   		60

   
   

   = 3 ÷	13	= 3 ×	20	=	60
   	20		13		13

---

---

300. If x [–2 {–4 (–a)}] +5 [–2 {–2 (–a)}] = 4a, then x =

1. 1. –2

   
   
   

   2. –3

   
   
   

   3. –4

   
   
   

   4. –5

   
   
   

---

1. View Hint View Answer Discuss in Forum

   x [– 2 {– 4 (– a)}] + 5 [– 2 { – 2 (– a)} ] = 4 a
   ⇒  x × (– 8 a) + 5 × (– 4 a) = 4 a
   ⇒  x × (– 2) + 5 × (– 1) = 1
   ⇒  2 x + 5 = – 1
   ⇒  2 x = – 5 – 1 = – 6
   

   ⇒  x =	−6	= −3
   	2

   Correct Option: C

   x [– 2 {– 4 (– a)}] + 5 [– 2 { – 2 (– a)} ] = 4 a
   ⇒  x × (– 8 a) + 5 × (– 4 a) = 4 a
   ⇒  x × (– 2) + 5 × (– 1) = 1
   ⇒  2 x + 5 = – 1
   ⇒  2 x = – 5 – 1 = – 6
   

   ⇒  x =	−6	= −3
   	2

---