Question 17

Which of the following cannot be true for a polyhedron?
(a) V = 4, F = 4, E = 6
(a) V = 6, F = 8, E = 12
(a) V = 20, F = 12, E = 30
(a) V = 4, F = 6, E = 6

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Solution

We know that, Euler's formula for any polyhedron is F + V - E = 2
where, F = faces, V = vertices and E = edges
(a) V = 4, F = 4 and E = 6
LHS = F + V - E
= 4 + 4 - 6
= 8 - 6 = 2
= RHS

(b) V = 6, F = 8 and E = 12
LHS = F + V - E
= 8 + 6 -12
= 14 - 12 = 2
= RHS

(c) V = 20, F = 12 and E = 30
LHS = F + V - E
=12 + 20 - 30
= 32 - 30 = 2
= RHS

(d) V = 4, F = 6 and E = 6
LHS = F + V - E
= 6 + 4 - 6
= 10 - 6 = 4 $\neq$ RHS

$∴$ Option (d) is not true for a polyhedron.

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Q. Question 17

Which of the following cannot be true for a polyhedron?
(a) V = 4, F = 4, E = 6
(a) V = 6, F = 8, E = 12
(a) V = 20, F = 12, E = 30
(a) V = 4, F = 6, E = 6

Q. Question 72

Check whether a polyhedron can have V = 12, E = 6 and F = 8.

Q. On the basis of following

E^{\circ}

values, the strongest oxidising agent is:

[F e (C N)_{4}]^{4^{-}} \to [F e (C N)_{6}]^{3 -} + e^{-}

\begin{matrix} E^{\circ} = - 0.35 V F e^{2 +} \to F e^{3 +} + e^{-} & E^{\circ} = - 0.77 V \end{matrix}

$2 V O + 3 F e_{2} O_{3} \to 6 F e O + V_{2} O_{5}$ .
If we start with 2 g of $V O$ and 6 g of $F e_{2} O_{3}$ , is the limiting reagent. [V = 48 g] [Fe = 56 g]

The variable coefficients d, e, f and g are considered for balancing the chemical equation. Relationships between these variable are constructed by balancing the atoms of each element on either side of the reaction. Which of the following are correct?

(Note: Coefficients should be natural numbers.)

(i) 2d= f, d = 3g and e= f + 2g

(ii) 2d = f, 3d = g and 2e = 2f + g

(iii) d = f2, 2d = g and e = 2f + 2g

(iv)d = 1, e = 3.5, f = 4 and g = 6

(v) d = 2, e = 7, f = 4 and g = 6

(vi) d = 2, e = 7, f = 3 and g = 4

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Question 17 Which of the following cannot be true for a polyhedron? (a) V = 4, F = 4, E = 6 (a) V = 6, F = 8, E = 12 (a) V = 20, F = 12, E = 30 (a) V = 4, F = 6, E = 6

Question 17

Which of the following cannot be true for a polyhedron?
(a) V = 4, F = 4, E = 6
(a) V = 6, F = 8, E = 12
(a) V = 20, F = 12, E = 30
(a) V = 4, F = 6, E = 6