`A_0, A_1 ,A_2, A_3, A_4, A_5` be a regular hexagon inscribed in a circle of unit radius ,then the product of `(A_0A_1*A_0A_2*A_0A_4` is equal to

Regular pentagons are inscribed in two circles of radius 5 and 2 units respectively. The ratio of their areas is

If the area of the circle is A_1 and the area of the regular pentagon inscribed in the circle is A_2, then find the ratio (A_1)/(A_2)dot

Let A_1 A_2 A_3 A_4 A_5 A_6 A_1 be a regular hexagon. Write the x-components of the vectors representeed by the six sides taken in order. Use the fact that the resultant of these six vectors is zero, to prove that cos0+cospi/3+cos(2pi)/3+cos(4pi)/3+cos(5pi)/3=0 Use the known cosine values of verify the result. .

Let A_1,A_2,....A_n be the vertices of an n-sided regular polygon such that , 1/(A_1A_2)=1/(A_1A_3)+1/(A_1A_4) . Find the value of n.

If cos4x=a_0+a_1cos^2x+a^2cos^4x is true for all values of x in R , then the value of 5a_0+a_1+a_2 is_______

If a_1,a_2, a_3, a_4 be the coefficient of four consecutive terms in the expansion of (1+x)^n , then prove that: (a_1)/(a_1+a_2)+(a_3)/(a_3+a_4)=(2a_2)/(a_2+a_3)dot

Find the centre and radius of the circle 3x^(2)+(a+1)y^(2)+6x-9y+a+4=0 .

Statement 1: if A={2,4,6,},B{1,5,3}w h e r eAa n dB are the events of numbers occurring on a dice, then P(A)+P(B)=1. Statement 2: A_1, A_2, A_3, A_n are all mutually exclusive events, then P(A_1)+P(A_2)++P(A_n)=1.

Let vec r_1, vec r_2, vec r_3, , vec r_n be the position vectors of points P_1,P_2, P_3 ,P_n relative to the origin Odot If the vector equation a_1 vec r_1+a_2 vec r_2++a_n vec r_n=0 hold, then a similar equation will also hold w.r.t. to any other origin provided a. a_1+a_2+dot+a_n=n b. a_1+a_2+dot+a_n=1 c. a_1+a_2+dot+a_n=0 d. a_1=a_2=a_3dot+a_n=0

If the product of n matrices [[1,n][0, 1] [[1, 2],[ 0 , 1]] [[1 , 3],[ 0, 1]][[1, n],[ 0 , 1]] is equal to the matrix [[1, 378], [0 , 1]] then the value of n is equal to