326. The simplified value of
     

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 1

      3

   
   
   

   4. 1

      9

   
   
   

---

1. View Hint View Answer Discuss in Forum

   The given expression
   

   Correct Option: A

   The given expression
   

---

327. The value of 1 ÷ [1 + 1 ÷ {1 + 1 ÷ (1 + 1 ÷ 2)}] is

1. 1. 1

   
   
   

   2. 5

      8

   
   
   

   3. 2

   
   
   

   4. 1

      2

   
   
   

---

1. View Hint View Answer Discuss in Forum

   

   Correct Option: B

   

---

---

328. If   I =	3	÷	5	, II = 3 ÷ [(4 ÷ 5) ÷ 6],
     	4		6

     
     III = [3 ÷ (4 ÷ 5)] ÷ 6, IV = 3 ÷ 4 (5 ÷ 6) then

1. 1. I and II are equal

   
   
   

   2. I and IV are equal

   
   
   

   3. I and III are equal

   
   
   

   4. All are equal

   
   
   

---

1. View Hint View Answer Discuss in Forum

   I. =	3	×	6	=	9
   	4		5		10

   
   

   II. = 3 ÷		4	×	1		= 3 ÷	2	=	45
   		5		6			15		2

   
   

   III. =		3 ÷	4		÷ 6 =	15	÷ 6 =	5
   			5			4		8

   
   

   IV. = 3 ÷ 4 ×	5	= 3 ÷	10	=	9
   	6		3		10

   
   Obviously, (I) and (IV) are equal

   Correct Option: B

   I. =	3	×	6	=	9
   	4		5		10

   
   

   II. = 3 ÷		4	×	1		= 3 ÷	2	=	45
   		5		6			15		2

   
   

   III. =		3 ÷	4		÷ 6 =	15	÷ 6 =	5
   			5			4		8

   
   

   IV. = 3 ÷ 4 ×	5	= 3 ÷	10	=	9
   	6		3		10

   
   Obviously, (I) and (IV) are equal

---

329. 1	+	1	+	1	+	1	+	1	+	1	= ?
     30		42		56		72		90		110

1. 1. √2	2
      	27

   
   
   

   2. 1

      9

   
   
   

   3. 5

      27

   
   
   

   4. 6

      55

   
   
   

---

1. View Hint View Answer Discuss in Forum

   1	+	1	+	1	+	1	+	1	+	1
   5 × 6		6 × 7		7 × 8		8 × 9		9 × 10		10 × 11

   
   

   =	1	−	1	+	1	−	1	+	1	−	1	+	1	−	1	+	1	−	1	+	1	−	1
   	5		6		6		7		7		8		8		9		9		10		10		11

   
   

   =	1	−	1	=	11 − 5	=	6
   	5		11		55		55

   Correct Option: D

   1	+	1	+	1	+	1	+	1	+	1
   5 × 6		6 × 7		7 × 8		8 × 9		9 × 10		10 × 11

   
   

   =	1	−	1	+	1	−	1	+	1	−	1	+	1	−	1	+	1	−	1	+	1	−	1
   	5		6		6		7		7		8		8		9		9		10		10		11

   
   

   =	1	−	1	=	11 − 5	=	6
   	5		11		55		55

---

---

330. The value of
     

     0.1 × 0.1 × 0.1 + 0.2 ×0.2 × 0.2 + 0.3 × 0.3 × 0.3 − 3 × 0.1 × 0.2 × 0.3

     0.1 × 0.1 + 0.2 × 0.2 + 0.3 × 0.3 − 0.1 × 0.2 − 0.2 × 0.3 − 0.3 × 0.1

     is

1. 1. 0.006

   
   
   

   2. 0.6

   
   
   

   3. 0

   
   
   

   4. 0.2

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Using (x) of Basic Formulae
   Let 0.1 = a, 0.2 = b and 0.3 = c
   Then, we have,
   

   a × a × a + b × b × b + c × c × c − 3abc

   a × a + b × b + c × c − ab − bc − ac

   
   

   =	a3 + b3 + c3 − 3abc
   	a2 + b2 + c2 − ab − bc − ac

   
   = a + b + c
   = 0.1 + 0.2 + 0.3 = 0.6

   Correct Option: B

   Using (x) of Basic Formulae
   Let 0.1 = a, 0.2 = b and 0.3 = c
   Then, we have,
   

   a × a × a + b × b × b + c × c × c − 3abc

   a × a + b × b + c × c − ab − bc − ac

   
   

   =	a3 + b3 + c3 − 3abc
   	a2 + b2 + c2 − ab − bc − ac

   
   = a + b + c
   = 0.1 + 0.2 + 0.3 = 0.6

---