Upon treatment with ammonical H2s, the metal ion that precipitates as a sulfide is
The option(s) with the values of a and L that satisfy the following equation is (are) ∫0πet(sin6at+cos4at)dt∫04πet(sin6at+cos4at)dt=L
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?
Let f:[−21,2]→R and g:[−21,2]→R be functions defined by f(x)=[x2−3] and g(x)=∣x∣f(x)+∣4x−7∣f(x), where [y] denotes the greatest integer less than or equal to y for y∈R. Then,
Let Pbe a point in the first octant, whose image Qin the plane x+y=3(that is, the line segment PQis perpendicular to the plane x+y=3and the mid-point of PQlies in the plane x+y=3)lies on the z-axis. Let the distance of Pfrom the x-axis be 5. If Ris the image of Pin the xy-plane, then the length of PRis _______.
If 2x−y+1=0 is a tangent to the hyperbola a2x2−16y2=1 then which of the following CANNOT be sides of a right angled triangle? (a)a,4,2 (b) a,4,1(c)2a,4,1 (d) 2a,8,1
A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation 3x+y−6=0 and the point D is (3 sqrt3/2, 3/2). Further, it is given that the origin and the centre of C are on the same side of the line PQ. (1)The equation of circle C is (2)Points E and F are given by (3)Equation of the sides QR, RP are