In triangle `A B C` , if angle `c` is 90 and the area of triangle is 30 sq.units,then minimum possible value of hypotenuse c is equal to (a)`30sqrt(2)` (b) `60sqrt(2)` (c) `120sqrt(2)` (d) `2sqrt(30)`

The value of (lim)_(xvecoo)(tan^(-1)x))) is equal to (a)-1 (b) pi/2 (c) -1/(sqrt(2)) (d) 1/(sqrt(2))

One angle of an isosceles triangle is 120^0 and the radius of its incircle is sqrt(3)dot Then the area of the triangle in sq. units is (a) 7+12sqrt(3) (b) 12-7sqrt(3) (c) 12+7sqrt(3) (d) 4pi

In a triangle ABC if 2a=sqrt(3)b+c , then possible relation is

d/(dx)(cos^(-1)sqrt(cosx)) is equal to (a) 1/2sqrt(1+s e cx) (b) sqrt(1+secx) (c) -1/2sqrt(1+secx) (d) -sqrt(1+secx)

A right triangle has perimeter of length 7 and hypotenuse of length 3. If theta is the larger non-right angle in the triangle, then the value of costhetae q u a ldot (sqrt(6)-sqrt(2))/4 (b) (4+sqrt(2))/6 (4-sqrt(2))/3 (d) (4-sqrt(2))/6

A rectangle is inscribed in an equilateral triangle of side length 2a units. The maximum area of this rectangle can be sqrt(3)a^2 (b) (sqrt(3)a^2)/4 a^2 (d) (sqrt(3)a^2)/2

If asinx+bcos(x+theta)+bcos(x-theta)=d , then the minimum value of |costheta| is equal to (a) 1/(2|b|)sqrt(d^2-a^2) (b) 1/(2|a|)sqrt(d^2-a^2) (c) 1/(2|d|)sqrt(d^2-a^2) (d) none of these

The area of a triangle A B C is equal to (a^2+b^2-c^2) , where a, b and c are the sides of the triangle. The value of tan C equals

In a triangle ABC, angleA =60^o ,angleC =30^o ,b=2sqrt3,c=2 then a is: