Solve for x : |(x,a,b),(a,x,b),(a,b,x)| = 0

Find the number of solutions to cos x = (x)/(10), x gt 0.

The number of real solutions of the (log)_(0. 5)(x)=|x| is (a) 1 (b) 2 (c) 0 (d) none of these

Find the particular solution of a^(2)y(dy)/(dx)+b^(2)x=0,"given "y=(b)/(sqrt2),"when" x=(a)/(sqrt2)

|{:(x,a,a),(a,x,b),(b,b,x):}|=0

The solution of (dy)/(dx)=(a x+h)/(b y+k) represent a parabola when (a) (a) a=0,b!=0 (b) a!=0,b!=0 (c) b=0,a!=0 (d) a=0,b in R

The number of real solutions of the (log)_(0. 5)|x|=2|x| is (a) 1 (b) 2 (c) 0 (d) none of these

The product of all values of t , for which the system of equations (a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0 has non-trivial solution, is (a) |[a, -c, -b], [-c, b, -a], [-b, -a, c]| (b) |[a, b, c], [b, c, a], [c, a, b]| (c) |[a, c, b], [b, a, c], [c, b, a]| (d) |[a, a+b, b+c], [b, b+c, c+a], [c, c+a, a+b]|

y=ae^(-1/x)+b is a solution of dy/dx=y/x^2 ,then (a) ainR (b) b=0 (c) b=1 (d) a takes finite number of values

f(x)=|a x-b|+c|x|AAx in (-oo,oo), where a >0, b >0,c > 0. Find the condition if f(x) attains the minimum value only at one point.