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
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
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
From a point P(λ,λ,λ), perpendicular PQ and PR are drawn respectively on the lines y=x,z=1 and y=−x,z=−1.If P is such that ∠QPR is a right angle, then the possible value(s) of λ is/(are)
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 _______.
There are five students S1, S2, S3, S4and S5in a music class and for them there are five seats R1, R2, R3, R4and R5arranged in a row, where initially the seat Riis allotted to the student Si, i=1, 2, 3, 4, 5. But, on the examination day, the five students are randomly allotted five seats.The probability that, on the examination day, the student S1gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her is403(b) 81(c) 407(d) 51