`f(x)=(x-8)^4(x-9)^5,0lt=xlt=10 ,` monotonically decreases in `((76)/(9, 10)]` (b) `((8, 76)/9)` `(0,8)` (d) `((76)/9, 10)`

intx^(8)(1+x^(9))^(5)dx :

If f(x)=k x^3-9x^2+9x+3 monotonically increasing in R , then (a) k<3 (b) klt=2 (c) kgeq3 (d) none of these

If z=sec^(-1)(x+1/x)+sec^(-1)(y+1/y), where x y<0, then the possible values of z is (a) (8pi)/(10) (b) (7pi)/(10) (c) (9pi)/(10) (d) (21pi)/(20)

Let f(x)=|x^2-3x-4|,-1lt=xlt=4 Then f(x) is monotonically increasing in [-1,3/2] f(x) monotonically decreasing in (3/2,4) the maximum value of f(x)i s(25)/4 the minimum value of f(x) is 0

(10x^(9) + 10^(x) log , 10)/(10^(x)+ x^(10))

If (1)/(8!)+(1)/(9!)=(x)/(10!) , find x.

A point on the parabola y^2=18 x at which the ordinate increases at twice the rate of the abscissa is (a)(2,6) (b) (2,-6) (c) (9/8,-9/2) (d) (9/8,9/2)

The function f(x) = sin ^(4)x+ cos ^(4)x increases, if (A) 0 lt x lt (pi)/(8) (B) (pi)/(4) lt x lt (3pi)/(8) (C) ( 3pi)/(8) lt x lt (5pi)/(8) (D) ( 5pi)/(8) lt x lt(3pi)/(4)

(4)/(x)+(3)/(y)=1,(8)/(x)-(9)/(y)=7

If (-6,-4),(3,5),(-2,1) are the vertices of a parallelogram, then the remaining vertex can be (a) (0,-1) (b) 7,9) (c) (-1,0) (d) (-11 ,-8)