The number of rectangles that can be obtained by joining four of the twelves verties of a 12-sides regular polygon is -

Correct Answer - C When 4 points are selected, we get one intersecting point. So, probability is `(.^(n)C_(4))/(.^((.^(n)C_(2)-n))C_(2))`

Correct Answer - 1,2,3,4 The equation of the lines joining the origin to the points of intersection of the given lines is `3x^(2)+mxy-4x(2x+y)+(2x+y)^(2)=0` (by homogenization) or `x^(2)=mxy-y^(2)=0` which are perpendicular for...

We have A = set all rectangles in the same plane B = set all squares in the same plane C = set all parellegrams in the same plane. Since...

Correct Answer - A The point are such that one of the points is the orthocenter of the triangle formed by other three points. When the vertices of a triangle lie...

Correct Answer - `1 muT`

Let a be the radius of the circle. Then, `S_(1)` = Area of regular polygon of `n` sides inscribed in the circle `= (1)/(2) na^(2) sin ((2pi)/(n)) = na^(2) sin.(pi)/(n)...

Correct Answer - B Let a and b the roots of `x^(2) -7 x + 8 = 0` Then `a + b = 7, ab = 8` Also, `C = 60^(@)`...

Correct Answer - C `(c )` We have `pi-(2pi)/(n)=(5pi)/(6)` `implies (pi)/(6)=(2pi)/(n)` `impliesn=12` `:.` Number of diagonals `="^(10)C_(2)-12=54`

Correct Answer - `d=(n(n-3))/(2)`

Correct Answer - Rina