311. If	a	+	b	+	c	= 1   then
     	b + c		c + a		a + b

     a2	+	b2	+	c2	= ?
     b + c		c + a		a + b

1. 1. 1

   
   
   

   2. –1

   
   
   

   3. 0

   
   
   

   4. 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   a	= 1 −	b	−	c
   b + c		c + a		a + b

   
   

   ∴	a2	= a −	ab	−	ac
   	b + c		c + a		a + b

   
   

   b	= 1 −	a	−	c
   a + c		b + c		a + b

   
   

   ∴	b2	= b −	ab	−	bc
   	a + c		b + c		a + b

   
   

   a	= 1 −	a	−	b
   a + b		b + c		c + a

   
   

   ∴	c2	= c −	ac	−	bc
   	a + c		b + c		c + a

   
   

   ∴	a2	+	b2	+	c2
   	b + c		a + c		a + b

   
   

   = a + b + c –

   ab

   +

   bc

   –

   ac

   +

   bc

   –

   ab

   +

   ac

   c + a

   c + a

   a + b

   a + b

   b + c

   b + c

   
   

   = a + b + c – b		a + c		– c		a + b		– a		b + c
   		c + a				a + b				b + c

   
   = a + b + c – b – c – a = 0

   Correct Option: C

   a	= 1 −	b	−	c
   b + c		c + a		a + b

   
   

   ∴	a2	= a −	ab	−	ac
   	b + c		c + a		a + b

   
   

   b	= 1 −	a	−	c
   a + c		b + c		a + b

   
   

   ∴	b2	= b −	ab	−	bc
   	a + c		b + c		a + b

   
   

   a	= 1 −	a	−	b
   a + b		b + c		c + a

   
   

   ∴	c2	= c −	ac	−	bc
   	a + c		b + c		c + a

   
   

   ∴	a2	+	b2	+	c2
   	b + c		a + c		a + b

   
   

   = a + b + c –

   ab

   +

   bc

   –

   ac

   +

   bc

   –

   ab

   +

   ac

   c + a

   c + a

   a + b

   a + b

   b + c

   b + c

   
   

   = a + b + c – b		a + c		– c		a + b		– a		b + c
   		c + a				a + b				b + c

   
   = a + b + c – b – c – a = 0

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312. If a + b + c + d = 4 then the value of

     1	+	1	+	1	+	1	is
     (1 − a)(1 − b)(1 − c)		(1 − b)(1 − c)(1 − d)		(1 − c)(1 − d)(1 − a)		(1 − d)(1 − a)(1 − b)

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 4

   
   
   

   4. 1+ abcd

   
   
   

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1. View Hint View Answer Discuss in Forum

   a + b + c + d = 4
   ⇒  4 – a – b – c – d = 0    ...(i)
   Expression
   

   =	1	+	1	+	1	+	1
   	(1 − a)(1 − b)(1 − c)		(1 − b)(1 − c)(1 − d)		(1 − c)(1 − d)(1 − a)		(1 − d)(1 − a)(1 − b)

   
   

   =	(1 − d) + (1 − a) + (1 − b) + (1 − c)
   	(1 − a)(1 − b)(1 − c)(1 − d)

   
   

   =	4 − a − b − c − d	= 0
   	(1 − a)(1 − b)(1 − c)(1 − d)

   Correct Option: A

   a + b + c + d = 4
   ⇒  4 – a – b – c – d = 0    ...(i)
   Expression
   

   =	1	+	1	+	1	+	1
   	(1 − a)(1 − b)(1 − c)		(1 − b)(1 − c)(1 − d)		(1 − c)(1 − d)(1 − a)		(1 − d)(1 − a)(1 − b)

   
   

   =	(1 − d) + (1 − a) + (1 − b) + (1 − c)
   	(1 − a)(1 − b)(1 − c)(1 − d)

   
   

   =	4 − a − b − c − d	= 0
   	(1 − a)(1 − b)(1 − c)(1 − d)

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313. If   a +	1	= 1 and b +	1	= 1, then the value of c +	1	is
     	b		c		a

1. 1. 0

   
   
   

   2. 2

   
   
   

   3. 1

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   a +	1	= 1
   	b

   
   

   ⇒  a = 1 –	1	=	b − 1
   	b		b

   
   

   ⇒	1	=	b
   	a		b − 1

   
   

   Again,  b +	1	= 1
   	c

   
   

   ⇒	1	= 1 – b
   	c

   
   

   ⇒  c =	1
   	1 – b

   
   

   ∴  c +	1	=	1	+	b
   	a		1 – b		b − 1

   
   

   =	1	−	b	=	1 – b	= 1
   	1 – b		1 – b		1 – b

   Correct Option: C

   a +	1	= 1
   	b

   
   

   ⇒  a = 1 –	1	=	b − 1
   	b		b

   
   

   ⇒	1	=	b
   	a		b − 1

   
   

   Again,  b +	1	= 1
   	c

   
   

   ⇒	1	= 1 – b
   	c

   
   

   ⇒  c =	1
   	1 – b

   
   

   ∴  c +	1	=	1	+	b
   	a		1 – b		b − 1

   
   

   =	1	−	b	=	1 – b	= 1
   	1 – b		1 – b		1 – b

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314. The simplified form of (x + (3)² + (x – 1)² is

1. 1. (x² + 2x + 5)

   
   
   

   2. 2(x² + 2x + 5)

   
   
   

   3. (x² – 2x + 5)

   
   
   

   4. 2(x² – 2x + 5)

   
   
   

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1. View Hint View Answer Discuss in Forum

   x + (3)² + (x – 1)²
   = x² + 2 × x × 3 + 3² + x² – 2 × x × 1 + 1²
   = x² + 6x + 9 + x² – 2x + 1
   = 2x² + 4x + 10 = 2(x² + 2x + 5)

   Correct Option: B

   x + (3)² + (x – 1)²
   = x² + 2 × x × 3 + 3² + x² – 2 × x × 1 + 1²
   = x² + 6x + 9 + x² – 2x + 1
   = 2x² + 4x + 10 = 2(x² + 2x + 5)

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315. If a – b = 11 and ab = 24, then the value of (a² + b²) is

1. 1. 169

   
   
   

   2. 37

   
   
   

   3. 73

   
   
   

   4. 48

   
   
   

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1. View Hint View Answer Discuss in Forum

   a – b = 11 and ab = 24
   ∴  (a – b)² = 11²
   ⇒  a² + b² – 2ab = 121
   ⇒  a² + b² – 2 × 24 = 121
   ⇒  a² + b² = 121 + 48 = 169

   Correct Option: A

   a – b = 11 and ab = 24
   ∴  (a – b)² = 11²
   ⇒  a² + b² – 2ab = 121
   ⇒  a² + b² – 2 × 24 = 121
   ⇒  a² + b² = 121 + 48 = 169

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