If `sinx+cosx=(sqrt(7))/2,` where `x in 1s t` quadrant, then `tanx/2` is equal to (a) `(3-sqrt(7))/3` (b) `(sqrt(7)-2)/3` (c) `(4-sqrt(7))/4` (d) none of these

If cosx=(2cosy-1)/(2-cosy), where x , y in (0,pi) then tan(x/2)cot(y/2) is equal to sqrt(2) (b) sqrt(3) (c) 1/(sqrt(2)) (d) 1/(sqrt(3))

If (sinx)/(siny)=1/2,(cosx)/(cosy)=3/2 , where x , y , in (0,pi/2), then the value of "tan"(x+y) is equal to (a) sqrt(13) (b) sqrt(14) (c) sqrt(17) (d) sqrt(15)

If tan^(-1)(a+x)/a+tan^(-1)(a-x)/a=pi/6,t h e nx^2= (a) 2sqrt(3)a (b) sqrt(3)a (c) 2sqrt(3)a^2 (d) none of these

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

The solution for x of the equation int_(sqrt(2))^x(dt)/(tsqrt(t^2-1))=pi/2 is pi (b) (sqrt(3))/2 (c) 2sqrt(2) (d) none of these

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

Which of the following is not the solution of (log)_3(x^2-2)<(log)_3(3/2|x|-1) is (a) (sqrt(2),2) (b) (-2,-sqrt(2)) (c) (-sqrt(2),2 (d) none of these

The value of ("lim")_(xto2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a) 1/(8sqrt(3)) (b) 1/(4sqrt(3)) (c) 0 (d) none of these

If the ellipse (x^2)/(a^2-7)+(y^2)/(13-5a)=1 is inscribed in a square of side length sqrt(2)a , then a is equal to (a) 6/5 (b) (-oo,-sqrt(7))uu(sqrt(7),(13)/5) (c) (-oo,-sqrt(7))uu((13)/5,sqrt(7),) (d)no such a exists

If A=[(sqrt(7), -3), (-sqrt(5), 2), (sqrt(3), -5)] then find the transpose of -A.