Solve the following initial value problem: `(d r)/(dt)=\ -r t ,\ r(0) = r_0`

Which of the following can have negative value ? A. chi B. mu_(r) C. mu_(0) D. mu_(r) and chi both

Differentiate the following w.r.t.x

A soap bubble of radius 'r' and surface tension 'T' is given a potential of 'V' volt. If the new radiys 'R' of the bubble is related to its initial radius by equation. P_(0)[R^(3) - r^(3)] + [lambda T [R^(2) - r^(2)] - epsilon_(0) V^(2)R//2 = 0 , where P_(0) is the atmospheric pressure. Then find lambda

A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate (dB)/(dt) . Loop 1 of radius R gt r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in figure. Then, the emf generated is Zero in loop 1 and zero in loop 2 − d B d t π r 2 in loop 1 and − d B d t π 2 in loop 2 − d B d t π R 2 in loop 1 and zero in loop 2 − d B d t π r 2 in loop 1 and zero in loop 2

The inversion of a sugar follows first order rate equation which can be followed by noting the change in the rotation of the plane of polarization of light in the polarimeter. If r_(oo), r_(f) and r_(0) are the rotations at t = oo, t = t , and t = 0 , then the first order reaction can be written as (a) k = (1)/(t)log.(r_(1)-r_(oo))/(r_(o) -r_(oo)) (b) k = (1)/(t)ln.(r_(0)-r_(oo))/(r_(t)-r_(o)) (c) k = (1)/(t)ln.(r_(oo)-r_(o))/(r_(oo)-r_(t)) (d) k = (1)/(t)ln.(r_(oo)-r_(t))/(r_(oo)-r_(0))

A soap bubble of radius r and surface tension T is given a potential V. Show that the new radius R of the bubble is related with the initial radius by the equation P(R^(3) -r^(3)) +4T (R^(2)-r^(2)) = (in_(0)V^(2)R)/(2) where P is the atmospheric pressure.

If S be the surface area of V be the volume of a sphere of radius r. Then (dv)/(dt) = (r)/(k) (ds)/(dt) . Value of k is

Current density in a cylindrical wire of radius R is given as J={(J_(0)((x)/(R )-1)" for "0lex lt (R )/(2)),(J_(0)(x)/(R )" for "(R )/(2)le x le R):} . If the current flowing in the wire is (k)/(12)piJ_(0)R^(2) , find the value of k.

Find the value of sum_(r=0)^(oo) tan^(-1) ((1)/(1 + r + r^(2)))

The incorrect statement is (A) p →q is logically equivalent to ~p ∨ q. (B) If the truth-values of p, q r are T, F, T respectively, then the truth value of (p ∨ q) ∧ (q ∨ r) is T. (C) ~(p ∨ q ∨ r) = ~p ∧ ~q ∧ ~r (D) The truth-value of p ~ (p ∧ q) is always T