The velocity, acceleration and force in two systems of units are related as under:
(i) `v'=(alpha^(2))/(beta)v`
(ii) `a'=(alphabeta)a`
(iii) `F'=((1)/(alphabeta))F`
All the primed symbols belong to one system and unprimed ones belong to the other system. Here `alpha and beta` are dimensionless constants. Which of the following is/are correct?

The units (U) of velocity acceleration and force in two systems are related as under: (a) U'_(V) = (alpha^(2))/(beta)U_(V) , (b) U'_(a) = (alpha beta)U_(a) (c) U'_(F) = [(1)/(alpha beta)]U_(F) All the primed symbols (U) belong to one system and unprimed ones (U) belong to the other systems. alpha and beta are dimensionless constants. How momentum units of the two systems are related?

Potential energy of a system of particles is U(alpha)/(3r^(3))-(beta)/(2r^(2)), where r is distance between the particles. Here alpha and beta are positive constants. Which of the following are correct for the system?

In two systems of relations among velocity , acceleration , and force are , respectively , v_(2) = (alpha^(2))/( beta) v_(1) , a_(2) = alpha beta a_(1), and F_(2) = (F_(1))/( alpha beta) . If alpha and beta are constants , then make relations among mass , length , and time in two systems.

Study the following information carefully and answer the questions given below: P, Q, R, S, T, V and W are travelling in three different vehicles, There are at least two passengers in each vehicle I, II & III—and only one of them is a male. There are two engineers, two doctors and three teachers among them. (i) R is a lady doctor and she does not travel with the pair of sisters, P and V. (ii) , a male engineer, travels with only W, a teacher in vehicle I. (iii) S is a male doctor. (iv) Two persons belonging to the same profession do not travel in the same vehicle. (v) P is not an engineer and travels in vehicle II. Which of the following is not correct?

Suppose two students are trying to make a new measurement system so that they can use it like a code measurement. Instead of taking 1 kg, 1 m 1 s, as the basic unit they took unit of mass as alpha kg, the unit of length as beta m and the unit of tme as gamma s. They called the new system as ACME. Column I represents the units of the physical quantities, Column II represents the ACME units and Column III represents the CGS units of the physical quantities. Which of the following represents the correct combination for a physical quantity known as rate of energy?

Let the coefficient of the middle term of the binomial expansion of (1+x)^(2n) be alpha and those of two middle terms of the binomial expansion of (1+x)^(2n-1) "be" beta and gamma . Which one of the following relations is correct ?

The angle of elevation of the top of a tower EF (F being the foot of the tower) as seen from a point A which is on the same level as F, is alpha . On advancing towards the foot of the tower the angle of elevation of the top of the tower as seen from a point B such that AB=x , is beta . If BF=y, h is the height of the tower and alpha + beta = (pi)/(2) , then which one of the following is correct?

Consider the following relations among the angles alpha,beta and gamma made by a vector with the coordinate axes I. cos^2alpha+cos2beta+cos2gamma=-1 II. sin^2alpha+sin^2beta+sin^2gamma=1 Which of the above is/are correct?