[" Let "S" be the set of all "alpha in R" such that "t],[" equation,"cos2x+alpha sin x=2 alpha-7" has a "]

Let S be the set of all alpha in R such that the equation, cos 2x + alpha sin x = 2alpha -7 has a solution. The S, is equal to

Let S be the set of all non-zero numbers alpha such that the quadratic equation alpha x^(2)-x+alpha=0 has two distinct real roots x_(1), and x_(2) satisfying the inequality |x_(1)-x_(2)|<1 which of the following intervals is(are) a subset of S?

int(cos2x-cos2 alpha)/(sin x-sin alpha)dx=

If the equation cos2x+alpha sin x=2 alpha-7 has a solution.Then range of alpha is

There are two sets of parallel lines, their equations being x cos alpha+y sin alpha=p and x sin alpha- y cos alpha=p , p=1,2,3,….n and alpha in (0,pi//2) . If the number of rectangles formed by these two sets of lines is 225 , then the value of n is equals to

Let lambda and alpha be real. Let S denote the set of all values of lambda for which the system of linear equations lambda x+ (sin alpha) y + (cos alpha)z = 0 , x + (cos alpha) y + (sin alpha) z = 0 , -x + (sin alpha) y - (cos alpha) z = 0 has a non trivial solution then S contains a) (-1,1) b) [-sqrt2,-1] c) [1,sqrt2] d) [-sqrt2,sqrt2]

Let lambda "and" alpha be real. Let S denote the set of all values of lambda for which the system of linear equations lambda x+(sinalpha)y+(cos alpha)z=0 x+(cos alpha) y+(sin alpha) z=0 -x+ (sin alpha) y-(cos alpha) z=0 has a non- trivial solution then S contains

Let lambda "and" alpha be real. Let S denote the set of all values of lambda for which the system of linear equations lambda x+(sinalpha)y+(cos alpha)z=0 x+(cos alpha) y+(sin alpha) z=0 -x+ (sin alpha) y-(cos alpha) z=0 has a non- trivial solution then S contains