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`

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

In a right-angled isosceles triangle, the ratio of the circumradius and inradius is 2(sqrt(2)+1):1 (b) (sqrt(2)+1):1 2:1 (d) sqrt(2):1

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)

Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is (A) 1-sqrt(2/3) (B) sqrt(3/2) -1 (C) 1+sqrt(2/3) (D) sqrt(3/2)+1

In a triangle, the lengths of the two larger sides are 10 and 9, respectively. If the angles are in A.P., then the length of the third side can be (a) 5-sqrt(6) (b) 3sqrt(3) (c) 5 (d) 5+sqrt(6)

The value 4^(5log_(4sqrt(2))(3-sqrt(6))-6log_8(sqrt(3)-sqrt(2))) is

Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) at their points of intersection is (5sqrt(3))/2 (b) (3sqrt(5))/2 (5sqrt(3))/4 (d) (3sqrt(5))/4

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

In an equilateral triangle, three coins of radii 1 unit each are kept so that they touch each other and also the sides of the triangle. The area of the triangle is (fig) 4:2sqrt(3) (b) 6+4sqrt(3) 12+(7sqrt(3))/4 (d) 3+(7sqrt(3))/4