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Maths-

General

Easy

Question

If A = $open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets$ , then Aⁿ (where n $element of$ N) is

$[\begin{matrix} 3 n & - 4 n \\ n & - n \end{matrix}]$
$[\begin{matrix} n + 2 & 5 - n \\ n & - n \end{matrix}]$
$[\begin{matrix} 3^{n} & (- 4)^{n} \\ 1 & (- 1)^{n} \end{matrix}]$
None of these

The correct answer is: None of these

We have
A² = $open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets$ $open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets$ = $open square brackets table row 5 cell negative 8 end cell row 2 cell negative 3 end cell end table close square brackets$
For n = 2, none of (A) , (B) , (C) match with the actual answer.
Thus, answer is (D).

Related Questions to study

If A and B are two skew symmetric matrices of order n, then-

If A and B are two skew symmetric matrices of order n, then-

The correct order of acidic strength is:

The correct order of acidic strength is:

chemistry-General

Let E ( $alpha$ ) = $open square brackets table row cell cos to the power of 2 end exponent invisible function application alpha end cell cell cos invisible function application alpha sin invisible function application alpha end cell row cell cos invisible function application alpha sin invisible function application alpha end cell cell sin to the power of 2 end exponent invisible function application alpha end cell end table close square brackets$ . If $alpha$ and $beta$ differs by an odd multiple of $pi$ /2,then E( $alpha$ ) E( $beta$ ) is a -

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parallel

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parallel

If the matrix M_r is given by M_r = $open square brackets table row r cell r minus 1 end cell row cell r minus 1 end cell r end table close square brackets$ , r = 1, 2, 3 .... Then the value of det (M₁) + det(M₂) + .... + det (M₂₀₀₉) is

If the matrix M_r is given by M_r = $open square brackets table row r cell r minus 1 end cell row cell r minus 1 end cell r end table close square brackets$ , r = 1, 2, 3 .... Then the value of det (M₁) + det(M₂) + .... + det (M₂₀₀₉) is

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chemistry-General

parallel

For a general reaction given, below the value of solubility product can be given as :

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Which metal sulphides can be precipitated from a solution that is 0.01 M in Na⁺ , Zn²⁺, Pb²⁺ and Cu²⁺ and 0.10 M in H₂S at a pH of 1.0 ?

For a general reaction given, below the value of solubility product can be given as :

$K subscript s p end subscript equals left parenthesis x s right parenthesis to the power of X end exponent times left parenthesis y s right parenthesis to the power of y end exponent$ or $K subscript s p end subscript equals x to the power of x end exponent y to the power of y end exponent left parenthesis S right parenthesis to the power of x plus y end exponent$
Solubility product gives us not only an idea about the solubility of an electrolyte in a solvent but also helps in explaining concept of precipitation and calculation of H⁺ ion, OH^- ion. It is also useful in qualitative analysis for the identification and separation of basic radicals.
Which metal sulphides can be precipitated from a solution that is 0.01 M in Na⁺ , Zn²⁺, Pb²⁺ and Cu²⁺ and 0.10 M in H₂S at a pH of 1.0 ?

chemistry-General

A weak acid (or base) is titrated against a strong base (or acid), volume v of strong base (or acid) is plotted against pH of the solution. The weak protolyte i.e acid (or base) could be

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chemistry-General

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Let A = $open square brackets table row 0 cell 2 y end cell z row x y cell negative z end cell row x cell negative y end cell z end table close square brackets$ and A' . A = I, then the value of $x to the power of 2 end exponent plus y to the power of 2 end exponent plus z to the power of 2 end exponent$ is -

parallel

If A is a n rowed square matrix, A = [a_ij] where a_ij = $open square brackets fraction numerator i over denominator j end fraction close square brackets$ , [ ] denotes greatest integer, then det (A) =

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If A = $open square brackets table row 0 5 row 0 0 end table close square brackets$ and f(x) = 1 + x + x² + … + x¹⁶, then f(A) =

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Assertion : The expression n!(20 – n)! is minimum when n = 10.
Reason : $blank to the power of 2 straight m end exponent C subscript r$ is maximum when r = m.

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parallel

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