`10 m ^(2) - 31m - 132=0`

If sin A + cos A = m and sin^3 A + cos^3A=n , then (1) m^3-3m + n = 0 (2) n^3-3n + 2m=0 (3) m^3-3m + 2n = 0 (4) m^3 + 3m + 2n = 0

If the lines mx+ ( 2m + 3)y+ m + 6=0 and (2m+1) x + (m-1) y+m-9=0 intersects on Y-axis then m=…....

You measure two quantities as A = 1.0 m +-0.2 m, B = 2.0 m +- 0.2 m . We should report correct value for sqrt(AB) as

Two moving coil meters M_1 and M_2 have the following particulars : R_1 = 10 Omega , N_1 = 30 A_1 = 3.6 xx 10^(-3) m^2 , B_1 = 0.25 T R_2 = 14Omega , N_2 = 42 A_2 = 1.8 xx 10^(-3) m^2 , B_2 = 0.50 T (The spring constants are identical for the two meters). Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M_2 and M_1 .

Figure shows a composite rod of cross-sectional area 10^(-4) m^(2) made by joining three rods AB, BC and CD of different materials end to end. The composite rod is suspended vertically and an object of 10 kg is hung by it. L _(AB) =0.1 m, _(BC) =0.2 m and L _(CD) =0.15 m. Calculate displacement of B,C and D Y_(AB) =2.5 xx 10 ^(10) Pa, Y_(BC) = 4 xx 10 ^(10) Pa and Y_(CD) = 1 xx 10 ^(10) Pa.

The pressure in monoatomic gas increases linearly from =4xx10^(5) Nm^(-2) to 8xx10^(+5) Nm^(-2) when its volume increases from 0.2m^(3) to 0.5m^(3) . Calculate . (i) Work done by the gas , (ii) Increase in the internal energy, (iii) Amount of heat supplied, (iv) Molar heat capacity of the gas R= 8.31J mol^(-1) K^(-1)

Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A. P. and the ratio of 7^(th) and (m - 1)^(th) numbers is 5 : 9. Find the value of m.

In an atom, an electron is moving with a speed of 600 m//s with an accuracy of 0.005% . Certainty with which the position of the electron can be localized is : ( h = 6.6 xx 10^(-34) kg m^2 s^(-1) , mass of electron (e_m) = 9. 1 xx10^(-31) kg) .