Dimensions of`epsilon_(0)` are
`M^(-1)L^(-3)T^(4)A^(2) `
`M^(0)L^(-3)T^(3)A^(3)`
`M^(-1)L^(-3)T^(3)A`
`M^(-1)L^(-3)TA^(2)`

Dimension of sqrt((in_(0))/(mu_(0))) are (A) [M L^(2) T^(-3) A^(-2)] (B) [M^(-1) L^(-2) T^(3) A^(2)] (C) [M^(2)L^(2)T^(-3) A^(2)] (D) [M^(-1) L^(2) T^(3) A^(2)]

If E and G respectively denote energy and gravitational constant,then (E)/(G) has the dimensions of: (1) [M^(2)][L^(-2)][T^(-1)] (2) [M^(2)][L^(-1)][T^(0)] (3) [M][L^(-1)][T^(0)] (4) [M][L^(0)][T^(0)]

Mathc list I with II and select the correct answer : {:((A)"spring constant",(1)M^(1)L^(2)T^(-2)),((B)"pascal",(2)M^(0)L^(0)T^(-1)),((C)"hertz",(3)M^(1)L^(0)T^(-2)),((D)"joule",(4)M^(1)L^(-1)T^(-2)):}

Given that in (alpha//pbeta )=alphaz//K_(B)theta where p is pressure, z is distance, K_(B) is Boltzmann constant and theta is temperature, the dimension of beta are (useful formula Energy =K_(B)xx temperature) (A) L^(0)M^(0)T^(0) " " (B)L^(1)M^(-1)T^(2) " " (C)L^(2)M^(0)T^(0)" "(D)L^(-1)M^(1)T^(-2)

Match the physical quantities with dimehnsions expressed in disarray. (i) Angular momentum (i) [M^(-1) L^3T^(-2)] (ii) Latent heat (ii) [M^1 L^3 T^(-3)A^(-2)] (iii) Specific heat (iii) [M^0 L^2 T^(-2)] (iv) Joule's mechanical equivalent of heat (iv) [M^0L^2 T^(-2)K^(-1)] (v) Resistivity (v) [M^0 L^) T^0] (vi) Gravitational Constant (vi) [M^1 L^2 T^(-1)]

Match the following: {:(," ""Column-I",," ""Column-II"),((a),F = A sin(B t) + (1)/(C ln (Dx)) "For above equation to be dimensionally correct",(p),[A] = [M^(1)L^(1)T^(-1)]","[B] = [M^(0)L^(0)T^(-1)]","[C] = [M^(0)L^(0)T^(-1)]),((b) ,"Pressure" = P + (1)/(2)rhov^(2) + gX ,(q),[A] = [M^(0)L^(1)T^(-1)]"," [B] = [M^(0)L^(0)T^(-1)]","[C] = [M^(0)L^(0)T^(-1)]","),((c),X = At+(v)/(B ln(Cr)),(r),[A] = [M^(1)L^(1)T^(-2)]","[B] = [M^(0)L^(0)T^(-1)]","[C] = [M^(-1)L^(0)T^(1)]),(,,(s),"Dimensionally incorrect""):} (Where F = force, P = pressure, rho = density, t = time, v = velocity, a = acceleration, X = displacement)

The physical quanitity the dimensions [M^(-2)L^(-3)T^(0)A^(2)] is

Statement-I : If x and y are the distance along x and y axes respectively then the dimensions of (d^(3)y)/(dx^(3)) is M^(0)L^(-2) T^(@) Statement-II : Dimensions of int_(a)^(b) ydx is M^(0)L^(2)T^(@)