Among the following metal carbonyls, the C-O bond order is lowest in
The function f(x)=2∣x∣+∣x+2∣=∣∣x∣2∣−2∣x∣∣has a local minimum or a local maximum at x=−2 (b) −32 (c) 2 (d) 32
Word of length 10 are formed using the letters A,B,C,D,E,F,G,H,I,J. Let xbe the number of such words where no letter is repeated; and let ybe the number of such words where exactly one letter is repeated twice and no other letter is repeated. The, 9xy=
Let f:(0,∞)R be given by f(x)=∫x1xte−(t+t1)dt, then (a)f(x) is monotonically increasing on [1,∞)(b)f(x) is monotonically decreasing on (0,1)(c)f(2x) is an odd function of x on R
If g(x)=∫sinxsin(2x)sin−1(t)dt,then: (a)gprime(2π)=−2π (b) gprime(−2π)=−2π (c)gprime(−2π)=2π (d) gprime(2π)=2π
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 _______.
The common tangents to the circle x2+y2=2 and the parabola y2=8x touch the circle at P,Q andthe parabola at R,S. Then area of quadrilateral PQRS is
A box B1, contains 1 white ball, 3 red balls and 2 black balls. Another box B2, contains 2 white balls, 3 red balls and 4 black balls. A third box B3, contains 3 white balls, 4 red balls and 5 black balls.