Let L denote the line in the xy-plane with x and y intercepts as 3 respectively. Then the image of the point (– 1, – 4) in the line is :
If the normal at an end of latus rectum of an ellipse passes through an extremity of the minor axis, the eccentricity e of the ellipse satisfies :
The set of all real values for which the function
has exactly one maxima and exactly one minima, is
For an integer n, if n is even, then n3 – 1 is odd
For an integer n, if n is even, then n3 – 1 is even.
For an integer n, if n3 – 1 is not even, then n is not odd
For an integer n, if n is odd, then n3 – 1 is even.
The centre of the circle passing through the point (0, 1) and touching the parabola y = x2 at the point (2, 4) is:
The angle of elevation of the summit of a mountain from a point on the ground is 45º. After climbing up one km towards the summitat an inclination of 30º from the ground, the angle of elevation of the summit is found to be 60º. Then the height (in km) of the summit from the ground is
C.