Answer:
Option C
Explanation:
Concept involved
The given equation contains algebraic and trigonometric function called transcendal equation . To solve transcendal equations we should always plot the graph for LHS and RHS
Here, x2=xsinx+cosx
Let f(x)= x2 and g(x) = x sin x+cos x

we know the graph for f(x)= x2
To plot , g(x) = x sinx+cos x
g'(x) = x cos x+sinx-sinx
g'(x)= x cos x .....(i)
g"(x) =- x sinx +cos x ......(ii)
put g'(x)=0
⇒ x cos x=0
∴ x=0,π2,3π2,5π2,7π2,....
at x=0, 3π2,7π2,....f"(x) >0
∴ minimum
at x= π2,5π2,9π2,.... f"(x)<0
minimum

∴ f(x) and g(x) are shown as

∴ Number of solutions are 2.