4. The solution set of the inequality sinx 3 cosx 0 is U (en 1) 2 (3n +1) (A) (c) U 6n a, (3n 1) 1) (D) none of these

If ""^n C_3+ ""^n C_4 > ""^(n+1)C_3 , then a. n >6 b. n >7 c. n d. none of these

Determine the first four terms of the sequence defined by, u_(1) = -3, u_(n) = (1)/(n-1). u_(n-1) for n ge 2 . Also find the series of first five terms of the sequence.

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

("lim")_(xvec0)(sinx^n)/((sinx)^m),(m

("lim")_(xvec0)(sinx^n)/((sinx)^m),(m

If ^n C_3+^n C_4>^(n+1)C_3 , then a. n >6 b. n >7 c. n<6 d. none of these

If ^n C_3+^n C_4>^(n+1)C_3 , then a. n >6 b. n >7 c. n<6 d. none of these

If ^n C_3+^n C_4>^(n+1)C_3 , then a. n >6 b. n >7 c. n<6 d. none of these

The function u_(n) takes on the following values : u_(1) = ( 1)/( 4) , u_(2) = ( 1)/( 4) + ( 1)/( 10)"…....." u_(n) =(1)/( 3+1) + ( 1)/( 3^(2) + 1)+"…........." (1)/( 3^(n) + 1)"…........." Prove that underset( n rarr oo) ( "lim") u_(a) lt (1)/(2)