A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the tune, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?
Suppose that p,qandr are three non-coplanar vectors in R3. Let the components of a vector s along p,qandr be 4, 3 and 5, respectively. If the components of this vector s along (−p+q+r),(p−q+r)and(−p−q+r) are x, y and z, respectively, then the value of 2x+y+z is
Let Obe the origin, and OX,OY,OZbe three unit vectors in the direction of the sides QR, RP, PQ, respectively of a triangle PQR.∣OX×OY∣=s∈(P+R) (b) sin2R(c)sin(Q+R)(d) sin(P+Q)˙
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
A circle S passes through the point (0, 1) and is orthogonal to the circles (x−1)2+y2=16 and x2+y2=1. Then (A) radius of S is 8 (B) radius of S is 7 (C) center of S is (-7,1) (D) center of S is (-8,1)
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
The coefficients of three consecutive terms of (1+x)n+5are in the ratio 5:10:14. Then n=___________.