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Types of Linear Programing Problems

If z1≠ -z2 ...

Question

If $z_{1} \neq - z_{2}$ and $| z_{1} + z_{2} | = | (\frac{1}{z_{1}}) + (\frac{1}{z_{2}}) |$ then
Statement 1: $z_{1} z_{2}$ is unimodular.
Statement 2: Both $z_{1}$ and $z_{2}$ are unimodular.

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

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Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.

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Statement 1 is true and Statement 2 is false.

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Statement 1 is false and Statement 2 is true.

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Solution

The correct option is C Statement 1 is true and Statement 2 is false.

$| z_{1} + z_{2} | = | \frac{z_{1} + z_{2}}{z_{1} z_{2}} | ⟹ | z_{1} + z_{2} | (1 - \frac{1}{| z_{1} z_{2} |}) = 0 s i n c e | z_{1} + z_{2} | \neq 0, s o, 1 = \frac{1}{| z_{1} z_{2} |} ⟹ | z_{1} z_{2} | = 1$
Hence the statement 1 is correct but statement 2 is not necessary

Suggest Corrections

Similar questions

1 :

x y + y z + z x = 1

x, y, z \in R^{+}

\frac{x}{1 + x^{2}} + \frac{y}{1 + y^{2}} + \frac{z}{1 + z^{2}} = \frac{2}{\sqrt{(1 + x^{2}) (1 + y^{2}) (1 + z^{2})}}

2 :

A B C

sin 2 A + sin 2 B + sin 2 C = 4 sin A sin B sin C

| z_{1} | = | z_{2} | = 1

z_{1} z_{2} \neq - 1.

A = \frac{z_{1} + z_{2}}{1 + z_{1} z_{2}},

(p \lor q) \land \sim p

\sim p \land q

Choose the correct option.

Statement $1 : (p \land \sim q) \land (\sim p \land q)$ is a fallacy.

Statement $2 : (p \Rightarrow q) \Leftrightarrow (\sim q \Rightarrow\sim p)$ is a tautology.

M n^{2 +}, C r^{3 +}, V^{3 +}

T i^{3 +}

V^{3 +}

(8)^{\frac{1}{2}} B M

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