[" 7.The number of solutions of "],[qquad [sin^(-1)(1+b+b^(2)+....oo)+cos^(-1)(a-(a^(2))/(3)+(a^(3))/(9)+...,oo)=(pi)/(2)],[1)1,2)2,3)3,4" ) "oo]]

Number of ordered pairs (a,b) for which sin^(-1)(1+b+b^(2)+...oo)+cos^(-1)(a-(a^(2))/(3)+(a^(4))/(9)+...oo)=(pi)/(2) is (A) 0(B)4(C)9(D) Infinite

The number of solution of x^(log_(x)(x+3)^(2))=16 is 0 (b) 1(c)2(d)oo

The number of solution of x^(log)x(x+3)^2=16 is a)0 (b) 1 (c) 2 (d) oo

Number of ordered pairs (a,b) for which sin^(-1)(1+b+b^2+..oo)+cos^(-1)(a-a^2/3+a^4/9+..oo)=pi/2 is (A) 0 (B) 4 (C) 9 (D) Infinite

The number of real solutions of tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^2+x+1)=pi//2 a)0 b)1 c)2 d) oo

If sin^(-1)(a-(a^(2))/3+(a^(3))/9+…..)+cos^(-1)(1+b+b^(2)=……..)=(pi)/2 then

The number of real solution of the equation sin^(-1) (sum_(i=1)^(oo) x^(i +1) -x sum_(i=1)^(oo) ((x)/(2))^(i)) = (pi)/(2) - cos^(-1) (sum_(i=1)^(oo) (-(x)/(2))^(i) - sum_(i=1)^(oo) (-x)^(i)) lying in the interval (-(1)/(2), (1)/(2)) is ______. (Here, the inverse trigonometric function sin^(-1) x and cos^(-1) x assume values in [-(pi)/(2), (pi)/(2)] and [0, pi] respectively)

The number of real solution of the equation sin^(-1) (sum_(i=1)^(oo) x^(i +1) -x sum_(i=1)^(oo) ((x)/(2))^(i)) = (pi)/(2) - cos^(-1) (sum_(i=1)^(oo) (-(x)/(2))^(i) - sum_(i=1)^(oo) (-x)^(i)) lying in the interval (-(1)/(2), (1)/(2)) is ______. (Here, the inverse trigonometric function sin^(-1) x and cos^(-1) x assume values in [-(pi)/(2), (pi)/(2)] and [0, pi] respectively)