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Statement 1: The slope of the tangent at any point P on a parabola, whose axis is the axis of x and vertex is at the origin, is inversely proportional to the ordinate of the point P.
Statement 2: The system of parabolas y2 = 4ax satisfies a differential equation of degree 1 and order 1.
If Z1 ≠ 0 and Z2 be two complex numbers such that Z2 / Z1 is a purely imaginary number, then is equal
If each of the lines 5x + 8y = 13 and 4x – y = 3 contains a diameter of the circle x2 + y2 – 2(a2 – 7a + 11) x – 2 (a2 – 6a + 6) y + b3 + 1 = 0, then:
If a, b, c are sides of a scalene triangle, then the value of
Let a1,a2,a3,....a1,a2,a3,.... be an A.P. such that
Statement 1: The equation x log x = 2 – x is satisfied by at least one value of x lying between 1 and 2.
Statement 2: The function f (x) = x log x is an increasing function in [1, 2] and g(x) = 2 – x is decreasing function in [1, 2] and the graphs represented by these functions intersect at a point in [1, 2].
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