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Question

Match the following by appropriately matching the lists based on the information given in Column 1 and Column 2
Column 1:Column 2:EquationNumberof rootsa. x2tanx=1,x[0,2π] p. 5b. 2cosx=|sinx|,x[0,2π] q. 2c. If f(x) is a polynomial of degree 5 with real coefficients such thatf(|x|)=0 has 8 real roots, then the number of roots of f(x)=0 is/arer. 3d. 7|x|(5|x|)=1 s. 4

Then which of the following is correct ?

A
as, br, cp, dq
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B
aq, bs, cp, ds
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C
aq, bs, cp, dr
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D
ap, br, cq, ds
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Solution

The correct option is B aq, bs, cp, ds
a.
y=tanx=1x2


From the graph, it is clear that it will have two real roots.

b.
y=2cosx and y=|sinx|


From the graph, two curves meet at four points for x[0,2π]. So the equation 2cosx=|sinx| has four solutions.

c.
Given that f(|x|)=0 has 8 real roots or f(x)=0 has four positive roots.
Since, f(x) is a polynomial of degree 5, f(x) can not have even number of real roots.
Hence, f(x) has all the five roots real and one root is negative.

d.
7|x|(|5|x||)=1
or |5|x||=7|x|
Draw the graph of y=7|x| and y=|5|x||


Hence, the number of roots is 4.

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