Let `{t_n}` be a sequence of integers in G.P. in which `t_4: t_6=1:4 and t_2+t_5=216.` Then `t_1` is (a).`12` (b). `14` (c). `16` (d). none of these

If in G.P ., t_5:t_3=7:9 then t_9:t_5 is

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) none of these

If u=x^2+y^2 and x=s+3t, y=2s-t, then (d^2u)/(ds^2) is (a) 5/2 t (b) 20t^8 (c) 5/(16t^6) (d) none of these

If A is an orthogonal matrix then A^(-1) equals a. A^T b. A c. A^2 d. none of these

In triangle A B C ,/_A=30^0,H is the orthocenter and D is the midpoint of B C . Segment H D is produced to T such that H D=D T The length A T is equal to (a). 2B C (b). 3B C (c). 4/2B C (d). none of these

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.

t 1 and  t 2 are two points on the parabola y^2 =4ax . If the focal chord joining them coincides with the normal chord, then  (a) t1(t1+t2)+2=0 (b) t1+t2=0 (c) t1*t2=-1 (d) none of these     

In a G.P. T_10 = 9 and T_4.= 4 , T_7 will be

The following geometric arrays suggest a sequence of numbers. (a) Find the next three terms . (b) Find the 100^(th) term . (c) Find the n^(th) term . The dots here arranged in such a way that they form a rectangle. Here T_1 =2 , T_2 = 6 , T_3 = 12 , T_4 = 20 and so on. Cay you guess what T_5 is ? What about T_6 ? What about T_n ? Make a conjecture about T_n .

Let t_(r) be the rth term of an A.P. If t_(2), t_(8) and t_(32) are in G.P., then find the common ratio of the G.P.