Consider an electrochemical cell: A(s)∣∣An+(aq,2M)∣∣∣∣B2n+(aq,1M)∣∣B(s). The value of △Gθ for the cell reaction is twice that of △Gθ at 300 K. If the emf of the cell is zero, the △Gθ∈JK?1mol?1 of the cell reaction per mole of B formed at 300 K is ____. (Given: ln(2) = 0.7, (universal gas constant) =8.3JK?1mol?1. H, S and G are enthalpy, entropy and Gibbs energy, respectively.)
The function y=f(x) is the solution of the differential equation dxdy+x2−1xy=1−x2x4+2x in (−1,1) satisfying f(0)=0. Then ∫2323f(x)dx is
In R', consider the planes P1,y=0 and P2:x+z=1. Let P3, be a plane, different from P1, and P2, which passes through the intersection of P1, and P2. If the distance of the point (0,1,0) from P3, is 1 and the distance of a point (α,β,γ) from P3 is 2, then which of the following relation is (are) true ?
Consider the family of all circles whose centers lie on the straight line `y=x`. If this family of circles is represented by the differential equation `P y^(primeprime)+Q y^(prime)+1=0,`where `P ,Q`are functions of `x , y`and `y^(prime)(h e r ey^(prime)=(dy)/(dx),y^=(d^2y)/(dx^2)),`then which of the following statements is (are) true?(a)`P=y+x`(b)`P=y-x`(c)`P+Q=1-x+y+y^(prime)+(y^(prime))^2`(d)`P-Q=x+y-y^(prime)-(y^(prime))^2`
For a non-zero complex number z, let arg(z)denote theprincipal argument with π<arg(z)≤πThen, whichof the following statement(s) is (are) FALSE?arg(−1,−i)=4π,where i=−1(b) The function f:R→(−π,π],defined by f(t)=arg(−1+it)for all t∈R, iscontinuous at all points of R, where i=−1(c) For any two non-zero complex numbers z1and z2, arg(z2z1)−arg(z1)+arg(z2)is an integer multiple of 2π(d) For any three given distinct complex numbers z1, z2and z3, the locus of the point zsatisfying the condition arg((z−z3)(z2−z1)(z−z1)(z2−z3))=π, lies on a straight line
Let f[0,1]→R (the set of all real numbers be a function.Suppose the function f is twice differentiable, f(0)=f(1)=0,and satisfies f′(x)–2f′(x)+f(x)≤ex,x∈[0,1].Which of the following is true for 0<x<1?
Let PR=3i^+j^−2k^andSQ=i^−3j^−4k^determine diagonals of a parallelogram PQRS,andPT=i^+2j^+3k^be another vector. Then the volume of the parallelepiped determine by the vectors PT, PQand PSis5b. 20c. 10d. 30
Let Sbe the set of all column matrices [b1b2b3]such that b1,b2,b3∈Rand the system of equations (in real variable)−x+2y+5z=b12x−4y+3z=b2x−2y+2z=b3has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each [b1b2b3]∈S?(a) x+2y+3z=b1,4y+5z=b2and x+2y+6z=b3(b) x+y+3z=b1,5x+2y+6z=b2and −2x−y−3z=b3(c) −x+2y−5z=b1,2x−4y+10z=b2and x−2y+5z=b3(d) x+2y+5z=b1,2x+3z=b2and x+4y−5z=b3