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1

### IIT-JEE 1983

Subjective
Find three numbers $$a,b,c$$ between $$2$$ and $$18$$ such that
(i) their sum is $$25$$
(ii) the numbers $$2,$$ $$a, b$$ are consecutive terms of an A.P. and
(iii) the numbers $$b,c,18$$ are consecutive terms of a G.P.

$$5, 8, 12$$
2

### IIT-JEE 1982

Subjective
Does there exist a geometric progression containing $$27, 8$$ and $$12$$ as three of its terms? If it exits, how many such progressions are possible ?

$$\Rightarrow$$ yes infinite
3

### IIT-JEE 1980

Subjective
The interior angles of a polygon are in arithmetic progression. The smallest angle is $${120^ \circ }$$, and the common difference is $${5^ \circ }$$, Find the number of sides of the polygon.

9
4

### IIT-JEE 1979

Subjective
The harmonic mean of two numbers is 4.Their arithmetic mean $$A$$ and the geometric mean $$G$$ satisfy the relation. $$2A + {G^2} = 27$$

$$3$$ and $$6$$ or $$6$$ and $$3$$

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