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1

### 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
2

### 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 $$ab = cd$$
3

### IIT-JEE 1986

If $$a,\,b$$ and $$c$$ are distinct positive numbers, then the expression
$$\left( {b + c - a} \right)\left( {c + a - b} \right)\left( {a + b - c} \right) - abc$$ is
A
positive
B
negative
C
non-positive
D
non-negative
4

### IIT-JEE 1985

If $${\log _{0.3}}\,(x\, - \,1) < {\log _{0.09}}(x - 1)$$, then x lies in the interval-
A
$$(2,\infty )$$
B
(1, 2)
C
(- 2, - 1)
D
none of these

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NEET

Class 12