If `(y+3)/(2y+5)=sin^2x+2cosx+1,` then the value of `y` lies in the interval `(-oo,-8/3)` (b) `(-(12)/5,oo)` `(-8/3,-(12)/5)` (d) `(-8/3,oo)`

Let f(x)=inte^x(x-1)(x-2)dxdot Then f decreases in the interval (a) (-oo,-2) (b) -2,-1) (c) (1,2) (d) (2,+oo)

Find the values of 1/x for the following values of x (2,5) (b ) [-5 ,-1] ( c) ( 3, oo) (d) (-3,oo) ( e) (-oo , 4)

If cos^2x-(c-1)cosx+2cgeq6 for every x in R , then the true set of values of c is (2,oo) (b) (4,oo) (c) (-oo,-2) (d) (-oo,-4)

sinx+cosx=y^2-y+a has no value of x for any value of y if a belongs to (0,""sqrt(3)) (b) (-""sqrt(3),0) (-oo,-""sqrt(3)) (d) (""sqrt(3),oo)

The value of a for which the function f(x)=(4a-3)(x+log5)+2(a-7)cotx/2sin^2x/2 does not possess critical points is (a) (-oo,-4/3) (b) (-oo,-1) (c) [1,oo) (d) (2,oo)

Let f(x) be a quadratic expression such that f(-1)+f(2)=0 . If one root of f(x)=0 is 3 , then the other root of f(x)=0 lies in (A) (-oo,-3) (B) (-3,oo) (C) (0,5) (D) (5,oo)

If the intercepts made by the line y=mx by lines x=2 and x=5 is less than 5, then the range of values of m is a. (-oo,-4/3)uu(4/3,oo) b. (-4/3,4/3) c. (-3/4,4/3) d. none of these

If y=(x^4-x^2+1)/(x^2+sqrt(3)x+1)a n d(dy)/(dx)=a x+b , then the value of a+b is (a) cot(pi/8) (b) cot(pi/12) (c) tan((5pi)/12) (d) tan((5pi)/8)

If (y^2-5y+3)(x ^2+x+1)<2x for all x in R , then find the interval in which y lies.

Perpendiculars are drawn from points on the line (x+2)/2=(y+1)/(-1)=z/3 to the plane x + y + z=3 The feet of perpendiculars lie on the line (a) x/5=(y-1)/8=(z-2)/(-13) (b) x/2=(y-1)/3=(z-2)/(-5) (c) x/4=(y-1)/3=(z-2)/(-7) (d) x/2=(y-1)/(-7)=(z-2)/5