Class 11th

Let N be the set of natural numbers and a relation R on N be defined by R = {(x,y) ∈ N*N : x³ - 3x²y – xy² + 3y³ = 0} . Then the relation R is :

Let a,b and c be three vectors such that a = b*(bxc). If magnitudes of the vectors a,b and c are √2, 1 and 2 respectively and the angle between b and c is θ(0<

10.0 ml of 0.05 M KMnO₄ solution was consumed in a titration with 10.0 mL of given oxalic acid dehydrate solution. The strength of given oxalic acid solution is _____ *10⁻² g/L. (Round off to the Nearest Integer).

When 400 mL of 0.2 M H₂SO₄ solution is mixed with 600 mL of of 0.1 M NaOH solution the increase in temperature of the final solution is _____ *10⁻² K. (Round off to the Nearest Integer).
[Use : H⁺(aq) + OH⁻(aq) → H₂O : ΔₙH = –57.1kJmol⁻¹
Specific heat of H₂O = 4.18JK⁻¹g⁻¹
Density of H₂O = 1.0gcm⁻³
Assume no change in volume of solution on mixing]

The total number of electrons in all bonding molecular orbitals of O₂⁻ is _____. (Round off to the Nearest Integer).

The dihedral angle in staggered from the Newman projection of 1,1,1,-Trichloro ethane is _____ degree. (Round off to the Nearest Integer).

The equilibrium constant for the reaction
A(s) ⇌ M(s) + ½ O₂(g)
ln Kp = 4. At equilibrium, the partial pressure of O₂ is _____ atm. (Round off to the Nearest Integer).

Certain fixed quantity of an ideal gas expands by adiabatic manner such that w_gas is equal to -25 kJ and ∆H_gas for the expansion is -75kJ. The ratio of C_p/C_v for this gas will be equal to:

Given that ∆c H° (combustion enthalpy) for Diamond is -834.8 kJ mole and ∆c H° for graphite is -832.8 kJ/mole, the value of ∆f H°(Diamond) i.e. [C(graphite) → C(diamond)] [in kJ/mole] is:

At critical condition of temperature and pressure for a real gas, what would be the value of 16 Z? Here, Z is its compressibility factor.