If `1+a+a^2+a^3+a^4+........+a^n=(1+a)(1+a^2)(1+a^4)` then n is equal to ``
(a) 3` `
(b) 5` `
(c) 7` `
(d) 9``

lim_(n->oo)(n(2n+1)^2)/((n+2)(n^2+3n-1)) is equal to (a)0 (b) 2 (c) 4 (d) oo

If n=pi/(4alpha), then tan alpha tan 2alpha tan 3 alpha ... tan(2n-1)alpha is equal to (a) 1 (b) 1/2 (c) 2 (d) 1/3

If sum_(r=0)^(n){("^(n)C_(r-1))/('^(n)C_(r )+^(n)C_(r-1))}^(3)=(25)/(24) , then n is equal to (a) 3 (b) 4 (c) 5 (d) 6

In triangle A B C , if sinAcosB=1/4 and 3t a n A=t a n B ,t h e ncot^2A is equal to (a)2 (b) 3 (c) 4 (d) 5.

If the value of "^(n)C_(0)+2*^(n)C_(1)+3*^(n)C_(2)+...+(n+1)*^(n)C_(n)=576 , then n is (a) 7 (b) 5 (c) 6 (d) 9

If A-B=pi//4 , then (1+t a n A)(1-t a n B) is equal to 2 b. 1 c. 0 d. 3

In triangle A B C , if sinAcosB=1/4a n d3t a n A=t a n B ,t h e ncot^2A is equal to 2 (b) 3 (c) 4 (d) 5.

Let a_(1),a_(2),a_(3)"……." be an arithmetic progression and b_(1), b_(2), b_(3), "……." be a geometric progression sequence c_(1),c_(2),c_(3,"…." is such that c_(n)= a_(n) + b_(n) AA n in N . Suppose c_(1) = 1, c_(2) = 4, c_(3) = 15 and c_(4) = 2 . The value of sum of sum_(i = 1)^(20) a_(i) is equal to "(a) 480 (b) 770 (c) 960 (d) 1040"

In triangle A B C , if r_1=2r_2=3r_3, then a : b is equal to 5/4 (b) 4/5 (c) 7/4 (d) 4/7

If ^(n+1)C_3=2.^nC_2, then n= (A) 3 (B) 4 (C) 5 (D) 6