If area of ` A B C()` and angle C are given and if the side `c` opposite to given angle is minimum, then `a=sqrt((2)/(sinC))` (b) `b=sqrt((2)/(sinC))` `a=sqrt((4)/(sinC))` (d) `b=sqrt((4)/(sinC))`

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)

In any triangle ABC prove that (a^(2)sin(B-C))/(sinA)+(b^(2)sin(C-A))/(sinB)+(c^(2)sin(A-B))/(sinC)=0

Let i=int_a^b(x^4-2x^2)dx for (a,b) which given integration is minimum (bgt0) (a) (sqrt2,-sqrt2) (b) (0,sqrt2) (c) (-sqrt2,sqrt2) (d) (sqrt2,0)

If the angle A ,Ba n dC of a triangle are in an arithmetic propression and if a , ba n dc denote the lengths of the sides opposite to A ,Ba n dC respectively, then the value of the expression a/csin2C+c/asin2A is 1/2 (b) (sqrt(3))/2 (c) 1 (d) sqrt(3)

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

If sin2theta=cos3theta"and"theta is an acute angle, then sintheta equal (a) (sqrt(5)-1)/4 (b) -((sqrt(5)-1)/4) (c) (sqrt(5)+1)/4 (d) (-sqrt(5)-1)/4

The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot Then (a) a=2sqrt(2) (b) a=1-sqrt(3) (c) a=-1+sqrt(3) (d) a=-4

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