If in triangle `A B C ,sumsinA/2=6/5a n dsumI I_1=9` (where `I_1,I_2a n dI_3` are excenters and `I` is incenter, then circumradius `R` is equal to `(15)/8` (b) `(15)/4` (c) `(15)/2` (d) `4/(12)`

If in a A B C , =a^2-(b-c)^2, then tanA is equal to 15//16 b. 8//15 c.8//17 d. 1//2

If I_(n)=int_(0)^((pi)/(4))tan^(n)xdx, where n is a positive integer,then I_(10)+I_(8) is equal to (A)(1)/(9)(B)(1)/(8) (C) (1)/(7)(D)9

If A=[(2,-1),(-1,2)] and i is the unit matrix of order 2, then A^2 is equal to (A) 4A-3I (B) 3A-4I (C) A-I (D) A+I

Let I_(n)=inttan^(n)xdx , n gt 1 . I_(4)+I_(6)=atan^(5)x+bx^(5)+C , where C is a constant of integration , then the ordered pair ( a , b) is equal to

If R_1 is the circumradius of the pedal triangle of a given triangle A B C ,a n dR_2 is the circumradius of the pedal triangle of the pedal triangle formed, and so on R_3,R_4 then the value of sum_(i=1)^ooR_i , where R (circumradius) of A B C is 5 is 8 (b) 10 (c) 12 (d) 15

If A is a nilpotent matrix of index 2, then for any positive integer n,A(I+A)^(n) is equal to A^(-1) b.A c.A^(n) d.I_(n)

For triangle ABC,R=(5)/(2) and r=1. Let I be the incenter of the triangle and D,E and F be the feet of the perpendiculars from I rarr BC,CA and AB, respectively. The value of (IDxIExIF)/(IAxIBxIC) is equal to (a) (5)/(2) (b) (5)/(4)(c)10(d)(1)/(5)

Let I_(n)=int tan^(n)xdx,(n>1). If I_(4)+I_(6)=a tan^(5)x+bx^(5)+C, where C is a constant of integration,then the ordered pair (a,b) is equal to :

Which one of the following is wrong? (9)/(4)+1.75=4( b) (9)/(5)+2.2=4(c)(6)/(5)+2.8=4(d)(3)/(2)+1.5=4

If I_n=int_0^(pi/4) tan^nx then lim_(nrarroo)n(I_n+I_(n-2)) equals (A) 1/2 (B) 1 (C) oo (D) 0