Ncert Solutions Maths class 12th

Let the focal chord PQ of the parabola y² = 4x make an angle of 60° with the positive x-axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the y-axis at the point (0, a), then 5a² is equal to:

Let the vertices Q and R of the triangle PQR lie on the line (x+3)/5 = (y-1)/2 = (z+4)/3, QR = 5 and the coordinates of the point P be (0,2,3). If the area of the triangle PQR is m/n, then :

Let E? denote the complement of an event E. Let E?, E?, and E? be any pairwise independent events with P(E?)>0 and P(E?∩E?∩E?)=0. Then P(E?∩E?/E?) is equal to

The largest n ∈ N such that 3ⁿ divides 50! is:

Let f: (-1, ∞) → R be defined by f(0) = 1 and f(x) = (1/x)log?(1+x), x≠0. Then the function f:

A plane passing through the point (3,1,1) contains two lines whose direction ratios are 1, -2, 2 and 2, 3, -1 respectively. If this plane also passes through the point (α, -3, 5), then α is equal to

Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is:

The plane passing through the points (1,2,1), (2,1,2) and parallel to the line, 2x = 3y, z = 1 also passes through the point: