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
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
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
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