The two circles x2 + y2 = ax and x2 + y2 = c2(c > 0) touch each other if
2|a| = c
|a| = c
a = 2c
a = 2c
If two tangents drawn from a point P to the parabola y2= 4x are at right angles, then the locus of P is
X = 1
2x +1 = 0
x = -1
x = -1
The radius of a circle, having minimum area, which touches the curve y = 4 – x2 and the lines, y = |x| is
Let y be an implicit function of x defined by x2x – 2xxcoty – 1 = 0. Then y′ (1) equals
-1
1
log 2
log 2
Given P(x) = x4+ ax3 + cx + d such that x = 0 is the only real root of P′ (x) = 0. If P(–1) < P(1),then in the interval [–1, 1].
P(–1) is the minimum and P(1) is the maximum of P
P(–1) is not minimum but P(1) is the maximum of P
P(–1) is the minimum but P(1) is not the maximum of P
P(–1) is the minimum but P(1) is not the maximum of P
Suppose the cube x3– px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?
The cubic has minima at and maxima at –
The cubic has minima at – and maxima at
The cubic has minima at both and-
The cubic has minima at both and-
The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is
(x – 2)y′2 = 25 – (y – 2)2
(y – 2)y′2 = 25 – (y – 2)2
(y – 2)2y′2= 25 – (y – 2)2
(y – 2)2y′2= 25 – (y – 2)2
The function f(x) = tan-1 (sinx + cosx) is an increasing function in
(π/4, π /2)
(–π/2, π /4)
(0, π /2)
(0, π /2)
The normal to the curve x = a(1 + cosθ), y = asinθ at ‘θ’ always passes through the fixed point
(a, 0)
(0, a)No
(0,0)
(0,0)