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1

IIT-JEE 1992

Let $$\alpha \,,\,\beta$$ be the roots of the equation (x - a) (x - b) = c, $$c \ne 0$$. Then the roots of the equation $$(x - \alpha \,)\,(x - \beta ) + c = 0$$ are
A
a, c
B
b, c
C
a, b
D
a + c, b + c
2

IIT-JEE 1991

The product of $$n$$ positive numbers is unity. Then their sum is
A
a positive integer
B
divisible by $$n$$
C
equal to $$n + {1 \over n}$$
D
never less than $$n$$
3

IIT-JEE 1990

The number of solutions of the equation sin$${(e)^x} = {5^x} + {5^{ - x}}$$ is
A
0
B
1
C
2
D
Infinitely many
4

IIT-JEE 1987

If $$a,\,b,\,c,\,d$$ and p are distinct real numbers such that $$\left( {{a^2} + {b^2} + {c^2}} \right){p^2} - 2\left( {ab + bc + cd} \right)p + \left( {{b^2} + {c^2} + {d^2}} \right) \le 0$$\$
then $$a,\,b,\,c,\,d$$
A
are in A. P.
B
are in G P.
C
are in H. P.
D
satisfy $$ab = cd$$

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