If, v stands for velocity, L for length and T for time ,what is the value of x in the equation – `L = (vT)^x`?
a) 3
b) 2
c) 1
d) 0

If the roots of the equaion x^4-12 x^3+c x^2+dx+81=0 are positive then the value of c is The value of d is. Roots of the equation 2cx+d=0 is

If velocity v varies with time(t) as v=2t-3 , then the plot between v and t is represented by :

Two masses m_(1) and m_(2) concute a high spring of natural length l_(0) is compressed completely and tied by a string. This system while conving with a velocity v_(0) along +ve x-axis pass thorugh the origin at t = 0 , at this position the string sanps, Position of mass m_(1) at time t is given by the equation x_(1)t = v_(0)(A//1-cosomegat) . Calculate (i) position of the particle m_(2) as a funcation of time, (ii) l_(0) in terms of A.

A U-shaped conducting frame is placed in a magnetic field B in such a way that the plane of the frame is perpendicular to the field lines. A conducting rod is supported on the parallel arms of the frame, perpendicular to them and is given a velocity v_0 at time t = 0. Prove that the velocity of the rod at time t will be given by v_t=v_0 "exp" ((-B^2l^2)/(mR)t) .

The velocity fo a body depends on time according to equation, v= 2.0 + 0.1 t^2 . The body is undergoing.

If the velocity (V) , acceleration (A) , and force (F) are taken as fundamental quantities instead of mass (M) , length (L) , and time (T) , the dimensions of young's modulus (Y) would be

If t is a real number satisfying the equation 2t^3-9t^2+30-a=0, then find the values of the parameter a for which the equation x+1/x=t gives six real and distinct values of x .

In an imeganary experiment, the Young's modulus Y of a material is given by Y=( tau cos thetaT^(x))/(l^(3)) where tau is the torque, theta is the angle of twist, T is the time perod and l is the length of the wire. What is the value of x ?

The velocity - time graph of a particle in one dimensional motion is shown in figure. Which of the following formulae are correct for describing the motion of the particle over the time- interval t _(1) to t _(2) : (a) x (t _(2)) = x (t _(1)) +v (t _(2) - t _(1)) + ((1)/(2)) a (t _(2) - t _(1)) ^(2) (b) v (t_(2)) = v (t_(1)) + a (t _(1)))//(t_(2) -t _(1)) (C) v _("average")= (x (t _(2)) -x (t _(1)))//(t_(2) -t _(1)) (d) a _("average")= (v(t _(2)) - v (t _(1))) //(t_(2) -t _(1)) (e) x (t _(2))=x(t_(1)) + v _("average") (t _(2) - t _(1)) + ((1)/(2)) a _("average") (t _(2) -t _(1)) ^(2) (f) c (t _(2)) - c (t _(1)) = area under the v-t curve bonunded by the t -axis and the dotted line shown.

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alpha and beta .