Consider a body of mass 1.0 at rest at the origin at time t=0. A force F=(αtl^+βJ^) is applied on the body, where α=1.0Ns−1andβ=1.0N. The torque acting on the body about the origin at time t=1.0s is τ . Which of the following statements is (are) true?
Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3,4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let xi be the number on the card drawn from the ith box, i = 1, 2, 3.The probability that x1+x2+x3 is odd isThe probability that x1,x2,x3 are in an aritmetic progression is
Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover cards numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done isa.264 b. 265 c. 53 d. 67
The total number of ways in which 5 balls of differert colours can be distributed among 3 persons so thai each person gets at least one ball is
The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has A. only purely imaginary roots B. all real roots C. two real and purely imaginary roots D. neither real nor purely imaginary roots
For a non-zero complex number z, let arg(z)denote theprincipal argument with π<arg(z)≤πThen, whichof the following statement(s) is (are) FALSE?arg(−1,−i)=4π,where i=−1(b) The function f:R→(−π,π],defined by f(t)=arg(−1+it)for all t∈R, iscontinuous at all points of R, where i=−1(c) For any two non-zero complex numbers z1and z2, arg(z2z1)−arg(z1)+arg(z2)is an integer multiple of 2π(d) For any three given distinct complex numbers z1, z2and z3, the locus of the point zsatisfying the condition arg((z−z3)(z2−z1)(z−z1)(z2−z3))=π, lies on a straight line
Let Xbe a set with exactly 5 elements and Ybe a set with exactly 7 elements. If αis the number of one-one function from Xto Yand βis the number of onto function from Yto X, then the value of 5!1(β−α)is _____.
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)