If the 7th tern in the binomial expansion of `(3/((84)^(1/3)) +sqrt(3) ln x )^9, x gt 0` is equal to 729 then x can be (A) `e^2` (B) `e` (C)`e/2` (D) `2e`

If the 6th term in the expansion of (1/(x^(8/3))+x^2(log)_(10)x)^8 is 5600, then x equals 1 b. (log)_e 10 c. 10 d. x does not exist

If the 6 th term in the expansion of ((1)/(x^((8)/(3)))+x^(2)log_(10)x)^(8) is 5600, then x equals 1 b.log_(e)10 c.10 d.x does not exist

The minimum value of x\ (log)_e x is equal to e (b) 1//e (c) -1//e (d) 2e (e) e

(lim)_(xvec0)("log"(e^x^2+2sqrt(x)))/(t a nsqrt(x)) is equal to 0 b. 1 c. 2 d. e^2

(lim)_(xvec0)("log"(e^x^2+2sqrt(x)))/(t a nsqrt(x)) is equal to 0 b. 1 c. 2 d. e^2

If (x^2+y^2)dy=xydx and y(1)=1 . If y(x_0)=e then x_0 is equal to (A) sqrt(2)e (B) sqrt(3)e (C) 2e (D) e

lim _( x to 0) [ (2 ^(x) -1)/( sqrt (1 + ) x-1 )] is equal to: a) log _(e) 2 b) log _(e) sqrt2 c) log _(e) 4 d) 1/2

the value of x , for which the 6th term in the expansions of [2^(log_2) (sqrt(9^((x-1)+7)))+1/(2^(1/5)(log)_2(3^(x-1)+1))]^7i s84 , is equal to a. 4 b. 3 c. 2 d. 1

lim_(x->oo)n^2(x^(1/n)-x^(1/((n+1)))),x >0 , is equal to (a)0 (b) e^x (c) (log)_e x (d) none of these