A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is
3x + 2y = 6xy
3x + 2y = 6
2x + 3y = xy
3x + 2y = xy
D.
3x + 2y = xy
Let the equation of line be
(i)
(a) passes through the fixed point (2,3)
.... (ii)
P(a, 0), Q(0, b), O(0, 0), Let R(h, k),
Midpoint of OR is (h/2, k/2)
Midpoint of PQ is (a/2, b/2)
⇒h =a, k = b... (iii)
From (ii) & (iii)
Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 12 + 2.22 + 32 + 2.42 + 52 + 2.62 + .....
If B – 2A = 100λ, then λis equal to
496
232
248
464
If the system of linear equations
x + ky + 3z = 0
3x + ky – 2z = 0
2x + 4y – 3z = 0
has a non-zero solution (x,y,z), then xz/y2 is equal to
30
-10
10
-30
Let S = {t ∈ R: f(x) = |x-π|.(e|x| - 1) sin |x| is not differentiable at t}. Then the set S is equal to
{0,π}
{0}
{π}
Let S = { x ∈ R : x ≥ 0 and Then S:
Contains exactly four elements
Is an empty set
Contains exactly one element
Contains exactly two elements