Find the least value of `n` such that `(n-2)x^2+8x+n+4>0,AAx in R ,w h e r en in Ndot`

The number of terms in the expansion of (a+b+c)^n ,w h e r en in Ndot

Find the value of int_(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denote the greatest function and fractional parts of x , respectively.

If 9^7+7^9 is divisible b 2^n , then find the greatest value of n ,w h e r en in Ndot

Show that 2^(4n+4)-15n-16 ,w h e r en in N is divisible by 225.

f(x)=e^x-e^(-x)-2sinx-2/3x^3dot Then the least value of n for which (d^n)/(dx^n)f(x)(""|)_(x=0)i snon z e roi s (a) 5 (b) 6 (c) 7 (d) 8

Fill in the blanks If 2+isqrt(3) is a root of the equation x^2+p x+q=0,w h e r epa n dq are real, then (p ,q)=(______,_____) .

If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e r en in N , then value of a is n b. n-1 c. n+1 d. none of these

If cos^3xsin2x=sum_(r=0)^n a_xsin(r x),AAx in R then

If f(x) is continuous function AAx in R and the range of f(x)i s(2,sqrt(26))a n dg(x)=[(f(x))/c] is continuous AAx in R , then find the least positive integral value of c , where [dot] denotes the greatest integer function.

If the value of the definite integral int_0^1 "^(207)C_7x^(200)(1-x)^7dx is equal to 1/k ,w h e r ek in N , then the value of k/(26) is____