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Question

Number of solution(s) of the equation x25x sgn(x29)+6=0 is
(Here, sgn denotes the signum function)

A
0
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B
2
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C
3
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D
1
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Solution

The correct option is D 1
We know that
sgn x=1 x>00 x=01 x<0

(i) x29>0
i.e., x(,3)(3,)
Then x25x+6=0
(x2)(x3)=0x=2,3
No solution as x(,3)(3,)

(ii) x29=0
i.e., x=3,3
Then x2+6=0
No real roots.

(iii) x29<0
i.e., x(3,3)
Then x2+5x+6=0
(x+2)(x+3)=0x=2 [x(3,3)]

x=2 is the only solution.
Hence, only one solution is possible.

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