Match the statements/expressions given in Column I with the values given in Column II. Column I (A) The number of solutions of the equation $$xe^{\sin x}-\cos x=0$$ in the interval $\left(0,\frac{\pi}{2}\right)$ (B) Value(s) of $k$ for which the planes $kx+4y+z=0,4x+ky+2z=0$ and $2x+2y+z=0$ intersect in a straight line (C) Value(s) of $k$ for which $$|x-1|+|x-2|+|x+1|+|x+2|=4k$$ has integer solution(s) (D) If $$y^{\prime}=y+1\text{ and }y(0)=1$$ then value(s) of $y(\ln2)$ Column II (p) 1 (q) 2 (r) 3 (s) 4 (t) 5
A-(p), B-(q,s), C-(p,q,r,s,t), D-(r)
Match the statements/expressions given in Column I with the values given in Column II.
\textbf{Column I}\\
(A) The number of solutions of the equation
$$xe^{\sin x}-\cos x=0$$
in the interval $\left(0,\frac{\pi}{2}\right)$\\
(B) Value(s) of $k$ for which the planes $kx+4y+z=0,4x+ky+2z=0$ and $2x+2y+z=0$ intersect in a straight line\\
(C) Value(s) of $k$ for which
$$|x-1|+|x-2|+|x+1|+|x+2|=4k$$
has integer solution(s)\\
(D) If
$$y^{\prime}=y+1\text{ and }y(0)=1$$
then value(s) of $y(\ln2)$
\textbf{Column II}\\
(p) 1\\
(q) 2\\
(r) 3\\
(s) 4\\
(t) 5