If `|{:(x^(n),x^(x+2),x^(2n)),(1,x^(a),a),(x^(n+5),x^(a+6),x^(2n+5)):}|` =0 `forallx in "R where n" in` N, the value of a is

If |{:(x^(n),x^(n+2),x^(2n)),(1,x^(a),a),(x^(n+5),x^(a+6),x^(2n+5)):}| =0 forallx in "R where n" in N, the value of a is

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 I_(n)=int_(0)^(1)(1+x+x^(2)+....+x^(n-1))(1+3x+5x^(2)+....+(2n-3)x^(n-2)+(2n-1)x^(n-1))dx,n in N, then the value of sqrt(I_(9)) is

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of

Let f _(n) x+ f _(n) (y ) = (x ^(n)+y ^(n))/(x ^(n) y ^(n))AA x, y in R-{0}. where n in N and g (x) = max { f_(2) (x), f _(3) (x),(1)/(2)} AA x in R - {0} The number of values of x for which g(x) is non-differentiable (x in R - {0}):

If 5x^(3) +Mx+ N, M,N in R is divisible by x^(2) + x+1 , then the value of M +N is

If the 4 th term in the expansion of (a x + (1)/(x))^(n) is (5)/(2) , for all x in R then the values of a and n are respectively

If (1-x^(3))^(n)=underset(r=0)overset(n)(sum)a_(r)x^(r)(1-x)^(3n-2r) , then the value of a_(r) , where n in N is