Match the following lists and then choose the correct code.

Options

A. `{:(a,b,c,d),(q,s,r,p):}`
B. `{:(a,b,c,d),(p,s,r,s):}`
C. `{:(a,b,c,d),(q,s,p,s):}`
D. `{:(a,b,c,d),(s,p,q,r):}`

Answer

C

Explanation

p. `y=tanx=(1)/(x^(2))`
From the graph, it is clear it will have two real roots.

q. See the graphs of `y=2^(cosx) and y=|sinx|.` Two curves meet at four points for ` x in [0, 2pi].`

So, the equation `2^(cosx)=|sinx|` has four solutions.
r. 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)` cannot have even number of real roots.
Hence, `f(x)` has all the five roots real and one root is negative.
s. `7^(|x|)(|5-|x|)=1.`
`or |5-|x||=7^(-|x|)`
Draw the graph of `y=7^(-|x|) and y=|5-|x||.`

From the graph, the number of roots is 4.