Tiêu đề 6.BINOMIAL THEOREM.pdf ✅

(7.) If = − −  4 3 1:  n X n n N and Y n n = −  {9 1 : ( ) N , where N is the set of natural numbers, then X Y  is equal to [JEE (Main)-2014] (a.) x (b.) Y (c.) N (d.) Y X− (8.) If the coefficients of 3 x and 4 x in the expansion of ( ) 2 18 1 (1 2 ) + + − ax bx x in powers of x are both zero, then (a b, ) is equal to [JEE (Main)-2014] (a.) 272 14, 3       (b.) 272 16, 3       (c.) 251 16, 3       (d.) 251 14, 3       (9.) The sum of coefficients of integral powers of x in the binomial expansion of 50 (1 2 ) − x is [JEE (Main)-2015] (a.) ( ) 1 50 3 1 2 + (b.) ( ) 1 50 3 2 (c.) ( ) 1 50 3 1 2 − (d.) ( ) 1 50 2 1 2 + (10.) If the number of terms in the expansion of 2 2 4 1 , 0     − +    n x x x , is 28 , then the sum of the coefficients of all the terms in this expansion, is [JEE (Main)-2016] (a.) 2187 (b.) 243 (c.) 729 (d.) 64 (11.) The value of ( ) ( ) ( ) 21 10 21 10 21 10 1 1 2 2 3 3 C C C C C C − + − + − + ( ) ( ) 21 10 21 10 4 4 10 10 is C C C C − ++ − [JEE (Main)-2017] (a.) 21 10 2 2 − (b.) 20 9 2 2 − (c.) 20 10 2 2 − (d.) 21 11 2 2 − (12.) The sum of the co-efficients of all odd degree terms in the expansion of ( ) ( ) 5 5 3 3 x x x x x + − + − −  1 1 ,( 1) is [JEE (Main)-2018] (a.) -1 (b.) 0 (c.) 1 (d.) 2 (13.) If the fractional part of the number 403 2 15 is 15 k , then k is equal to [JEE (Main)- 2019] (a.) 8 (b.) 4 (c.) 6 (d.) 14 (14.) The coefficient of 4 t in the expansion of 3 6 1 1   −     − t t is [JEE (Main)-2019] (a.) 15 (b.) 14 (c.) 12 (d.) 10 (15.) If 3 20 20 1 1 20 20 1 21 = = −    =     + i i i i C k C C , then k equals [JEE (Main)-2019]

(24.) The sum of the co-efficients of all even degree terms in x in the expansion of ( ) 6 3 x x + − + 1 ( ) 6 3 x x x − −  1 ,( 1) is equal to : [JEE (Main)-2019] (a.) 24 (b.) 32 (c.) 26 (d.) 29 (25.) If the fourth term in the binomial expansion of 10 6 1 12 1 log 1 +     +   x x x is equal to 200 , and x 1 , then the value of x is : [JEE (Main)-2019] (a.) 10 (b.) 3 10 (c.) 100 (d.) 4 10 (26.) If the fourth term in the Binomial expansion of b 6 2 log ( 0)     +    x x x x is 7 20 8 , then a value of x is [JEE (Main)-2019] (a.) 3 8 (b.) 8 (c.) 2 8 − (d.) 2 8 (27.) If some three consecutive coefficients in the binomial expansion of ( 1) + n x in powers of x are in the ratio 2:15:70 , then the average of these three coefficients is [JEE (Main)-2019] (a.) 625 (b.) 964 (c.) 232 (d.) 227 (28.) If the coefficients of 2 x and 3 x are both zero, in the expansion of the expression ( ) 2 1+ + ax bx 15 (1 3 ) − x in powers of x , then the ordered pair (a b, ) is equal to : [JEE (Main)-2019] (a.) (−54,315) (b.) (28,861) (c.) (−21,714) (d.) 28,315 (29.) The smallest natural number n , such that the coefficient of x in the expansion of 2 3   1   +   n x x is 23 nC , is [JEE (Main)-2019] (a.) 58 (b.) 35 (c.) 38 (d.) 23 (30.) The coefficient of 18 x in the product (1+ x) ( ) 9 10 2 (1 ) 1 − + + x x x is [JEE (Main)- 2019] (a.) 84 (b.) -126 (c.) -84 (d.) 126 (31.) If ( ) ( ) ( ) 20 2 20 2 20 2 20 1 2 3 20 2 3 . 20 C C C C + + + + (2 )  = A , then the ordered pair ( A,  ) is equal to [JEE (Main)-2019] (a.) (420,19) (b.) (380,19) (c.) (420,18) (d.) (380,18)