1

IIT-JEE 1988

MCQ (Single Correct Answer)
Sum of the first n terms of the series $${1 \over 2} + {3 \over 4} + {7 \over 8} + {{15} \over {16}} + ............$$ is equal to
A
$${2^n} - n - 1$$
B
$$1 - {2^{ - n}}$$
C
$$n + {2^{ - n}} - 1$$
D
$${2^n} + 1$$
2

IIT-JEE 1985

MCQ (Single Correct Answer)
If $$a,\,b,\,c$$ are in GP., then the equations $$\,\,\alpha {x^2} + 2bx + c = 0$$ and $$d{x^2} + 2ex + f = 0$$ have a common root if $${d \over a},\,{e \over b},{f \over c}$$ are in ________.
A
A.P.
B
GP.
C
H.P.
D
none of these
3

IIT-JEE 1983

MCQ (Single Correct Answer)
The rational number, which equals the number $$2\overline {357} $$ with recurring decimal is
A
$${{2355} \over {1001}}$$
B
$${{2379} \over {997}}$$
C
$${{2355} \over {999}}$$
D
none of these
4

IIT-JEE 1982

MCQ (Single Correct Answer)
If $$x,\,y$$ and $$z$$ are $$pth$$, $$qth$$ and $$rth$$ terms respectively of an A.P. and also of a G.P., then $${x^{y - z}}\,{y^{z - x}}\,{z^{x - y}}$$ is equal to :
A
$$xyz$$
B
$$0$$
C
$$1$$
D
None of these

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