Maths Quiz (Algebra) for KVS/NVS and CTET Exams_00.1
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Maths Quiz (Algebra) for KVS/NVS and CTET Exams

Maths Quiz (Algebra) for KVS/NVS and CTET Exams_40.1

Q1. If a, b, c are real numbers and a + b + c = 0 then the value of a^3+b^3+c^3 is 
(a) 1
(b) ab^2+bc^2+ca^2
(c) 0
(d) 3abc 

Q2. If x-(1/x)=1/2 then the value of 4x^2+(4/x^2) 
(a) 7
(b) -7
(c) 9
(d) -9 

Q3. If x^13+(1/x^13) =2 then the value of x^7+(1/x^7 )  is  
(a) 2
(b) 3
(c) 4
(d) None of these 

Q4. If 2a-(3/a)=-1 then a^3+4a^2-6a+1= ? 
(a) 3
(b) 4
(c) 0
(d) -3 

Q5. If x+(2/x)=3 then the value of x^3-x^2-4x+4 is  
(a) 2
(b) 3
(c) 4
(d) 0

Q6. If 3^(x-y)=27 and 3^(x+y)=243, then the value of x is  
(a) 0
(b) 2
(c) 4
(d) 6

Q7. If x+(1/x)=3 then the value of x^3+(1/x^3 ) is 
(a) 20
(b) 18
(c) 16
(d) 24

Q8. If x = 12 and y = 4 then the value of (x+y)^(x/y)  is  
(a) 4096
(b) 3066
(c) 3616
(d) 4226

Q9. If y=(x+3)^2 then the value of (-2x-6)^2 equals to  
(a) -4y^2
(b) -2y^2
(c) 4y
(d) 2y

Q10. If x+(1/x)=2, then x-(1/x) is equals to  
(a) 3
(b) 2
(c) 1
(d) 0

Solutions

S1. Ans.(d)
Sol. a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca) 
a^3+b^3+c^3-3abc=0 (∴a+b+c=0) 
a^3+b^3+c^3=3abc 
Maths Quiz (Algebra) for KVS/NVS and CTET Exams_50.1
S4. Ans.(c)
Sol. 2a-(3/a)=-1
2a^2-3=-a 
2a^2+a-3=0 
2a^2+3a-2a-3=0 
(a-1)(2a+3)=0 
a=1 a=-3/2 
∴a^3+4a^2-6a+1=1+4-6+1=0 

S5. Ans.(d)
Sol. x+(2/x)=3 
x^2+2=3x 
x^2-3x+2=0 
x^2-2x-x+2=0 
(x-2)(x-1)=0 
x = 1 or x = 2 
By putting x=1=(1)^3-1^2-4×1+4 =0
By putting x=2=(2)^3-2^2-4×2+4 =0

S6. Ans.(c)
Sol. ∴3^(x-y)=27
Or, 3^(x-y)=3^3
x – y = 3 …(i) 
∴3^(x+y)=243  
3^(x+y)=3^5   
Or, x + y = 5 …(ii)
By adding the equation (i) and (ii) 
x-y=3 
x+y=5 
2x=8 
x=8/2=4 

Maths Quiz (Algebra) for KVS/NVS and CTET Exams_60.1
S8. Ans.(a)
Sol. (12+4)^(12/4) 
=(16)^3=4096 

S9. Ans.(c)
Sol. y=(x+3)^2 
∴(-2x-6)^2=[-2(x+3)]^2 
=4(x+3)^2 
= 4y 

Maths Quiz (Algebra) for KVS/NVS and CTET Exams_70.1
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