Quant Quiz " Algebra" for SSC CGL 2016

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Q1. If (a-3)^2+(b-4)^2+(c-9)^2 = 0, then the value of √(a+b+c) is: 
(a) –4
(b) 4
(c) ±4
(d) ±2

Q2. If x^2-3x+1=0, then the value of x^3+1/x^3  is  
(a) 9
(b) 18
(c) 27
(d) 1

Q3. If x=3+2√2, then the value of (√x-1/√x) is:
(a) 1
(b) 2
(c) 2√2
(d) 3√3

Q4. If a = 23 and b = – 29 then the value of 25a^2+40ab+16b^2 is: 
(a) 1
(b) –1
(c) 0
(d) 2
 

Q5. If x=4ab/(a + b) , (a≠b), the value of (x + 2a)/(x - 2a)+(x + 2b)/(x - 2b) is 
(a) a
(b) b
(c) 2ab
(d) 2

Q6. If x=b+c-2a, y=c+a-2b, z=a+b-2c, then the value of x^2+y^2-z^2+2xy is  
(a) 0
(b) a + b + c
(c) a – b + c
(d) a + b – c

Q7. If the sum of a/b and its reciprocal is 1 and a≠0, b≠0, then the value of a^3+b^3 is  
(a) 2
(b) –1
(c) 0
(d) 1


(a) 0
(b) 1
(c) 2
(d) 3

Q9. If x-y=(x + y)/7=xy/4, the numerical value of xy is  
(a) 4/3
(b) 3/4
(c) 1/4
(d) 1/3

(a) 0
(b) 1
(c) –1
(d) 72

ANSWERS:

Q1. If (a-3)^2+(b-4)^2+(c-9)^2 = 0, then the value of √(a+b+c) is: 
(a) –4
(b) 4
(c) ±4
(d) ±2
S1. Ans.(c)
Sol. 
(a-3)^2+(b-4)^2+(c-9)^2=0
⇒ a-3=0
⇒ a=3
⇒ b – 4 = 0
⇒ b = 4 and c – 9 = 0
⇒ c = 9
∴ √(a+b+c)=√(3+4+ 9)=√16=± 4

Q2. If x^2-3x+1=0, then the value of x^3+1/x^3  is  
(a) 9
(b) 18
(c) 27
(d) 1

Q3. If x=3+2√2, then the value of (√x-1/√x) is:
(a) 1
(b) 2
(c) 2√2
(d) 3√3

Q4. If a = 23 and b = – 29 then the value of 25a^2+40ab+16b^2 is: 
(a) 1
(b) –1
(c) 0
(d) 2
 S4. Ans.(a) 

Sol. 

 25a^2+40ab+16ab^2 =(5a+4b)^2 =(5×23-29×4)^2 =(115-116)^2=1   

Q5. If x=4ab/(a + b) , (a≠b), the value of (x + 2a)/(x - 2a)+(x + 2b)/(x - 2b) is 
(a) a
(b) b
(c) 2ab
(d) 2

Q6. If x=b+c-2a, y=c+a-2b, z=a+b-2c, then the value of x^2+y^2-z^2+2xy is  
(a) 0
(b) a + b + c
(c) a – b + c
(d) a + b – c

Q7. If the sum of a/b and its reciprocal is 1 and a≠0, b≠0, then the value of a^3+b^3 is  
(a) 2
(b) –1
(c) 0
(d) 1

(a) 0
(b) 1
(c) 2
(d) 3

Q9. If x-y=(x + y)/7=xy/4, the numerical value of xy is  
(a) 4/3
(b) 3/4
(c) 1/4
(d) 1/3

(a) 0

(b) 1
(c) –1
(d) 72