Let the numbers 2, b, c be in an A.P. and A = . If det(A) [2, 16], then c lies in the interval :
[4, 6]
(2 + 23/4, 4)
[2, 3)
[3, 2 + 23/4]
Let f : [- 1, 3] R be defined as f(x) = where [t] denotes the greatest integer less than or equal to t. Then, f is discontinuous at :
only three points
only one point
only two points
four or more points
Let f(x) = ax(a > 0) be written as f(x) = f1(x) + f2(x), where f1(x) is an even function and f2(x) is an odd function. Then f1(x + y) + f1(x – y) equals :
2f1(x)f1(y)
2f1(x + y)f1(x - y)
2f1(x + y)f2(x - y)
2f1(x)f2(y)
Given that the slope of the tangent to a curve y = y(x) at any point (x, y) is . If the curve passes through the centre of the circle x2 + y2 - 2x - 2y = 0, then its equation is :
Two vertical poles of heights, 20 m and 80 m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the Lines joining the top of each pole to the foot of the other, from this horizontal plane is :
12
18
15
16
D.
16