Match each coordination compound in List-I with an appropriate pair of characteristics from List-II and select the correct answer using the code given below the lists.
Let Xbe the set consisting of the first 2018 terms of the arithmetic progression 1, 6, 11, ,¨and Ybe the set consisting of the first 2018 terms of the arithmetic progression 9, 16, 23, ¨. Then, the number of elements in the set X∪Yis _____.
Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively.Column I, Column 2, Column 3I, x2+y2=a, (i), my=m2x+a, (P), (m2a,m2a)II, x2+a2y2=a, (ii), y=mx+am2+1, (Q), (m2+1−ma,m2+1a)III, y2=4ax, (iii), y=mx+a2m2−1, (R), (a2m2+1−a2m,a2m2+11)IV, x2−a2y2=a2, (iv), y=mx+a2m2+1, (S), (a2m2+1−a2m,a2m2+1−1)If a tangent to a suitable conic (Column 1) is found to be y=x+8and its point of contact is (8,16), then which of the followingoptions is the only CORRECT combination?(III) (ii) (Q) (b) (II) (iv) (R)(I) (ii) (Q) (d) (III) (i) (P)
Three boys and two girls stand in a queue. The probability, that the number of boys ahead is at least one more than the number of girls ahead of her, is (A) 21 (B) 31 (C) 32 (D) 43
Â·If the normals of the parabola y2=4x drawn at the end points of its latus rectum are tangents to the circle (x−3)2(y+2)2=r2 , then the value of r2 is
Let f:R→Rand g:R→Rbe two non-constant differentiable functions. If fprime(x)=(e(f(x)−g(x)))gprime(x)for all x∈R, and f(1)=g(2)=1, then which of the following statement(s) is (are) TRUE?f(2)<1−(log)e2(b) f(2)>1−(log)e2(c) g(1)>1−(log)e2(d) g(1)<1−(log)e2