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Maths-

General

Easy

Question

If k . $open square brackets table row cell negative 1 end cell 2 2 row 2 cell negative 1 end cell 2 row 2 2 cell negative 1 end cell end table close square brackets$ is an orthogonal matrix, then k is equal to-

1
1/2
1/3
None of these

The correct answer is: 1/3

Let A = k $open square brackets table row cell negative 1 end cell 2 2 row 2 cell negative 1 end cell 2 row 2 2 cell negative 1 end cell end table close square brackets$
Since A is orthogonal $therefore$ AA^T = I
k² $open square brackets table row 9 0 0 row 0 9 0 row 0 0 9 end table close square brackets$ = I $rightwards double arrow$ 9k²I = I $rightwards double arrow$ k² = $fraction numerator 1 over denominator 9 end fraction$ $rightwards double arrow$ k = ± $fraction numerator 1 over denominator 3 end fraction$

Related Questions to study

If A is square matrix such that A² = A, then |A| equals-

If A is square matrix such that A² = A, then |A| equals-

If the matrix A = $open square brackets table row 8 cell negative 6 end cell 2 row cell negative 6 end cell 7 cell negative 4 end cell row 2 cell negative 4 end cell lambda end table close square brackets$ is singular, then $lambda$ equal to:

If the matrix A = $open square brackets table row 8 cell negative 6 end cell 2 row cell negative 6 end cell 7 cell negative 4 end cell row 2 cell negative 4 end cell lambda end table close square brackets$ is singular, then $lambda$ equal to:

If A² = 8A + kI where A = $open square brackets table row 1 0 row cell negative 1 end cell 7 end table close square brackets$ then k is :

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If A = $open square brackets table row alpha 0 row 1 1 end table close square brackets$ and B = $open square brackets table row 1 0 row 5 1 end table close square brackets$ such that A² = B the $alpha$ n is :

Matrix M_r is defined as M_r= $open square brackets table row r cell r – 1 end cell row cell r – 1 end cell r end table close square brackets$ , r $element of$ N. Then det. (M₁) + det.(M₂) + ........... + det.(M₂₀₀₉) = ?

Matrix M_r is defined as M_r= $open square brackets table row r cell r – 1 end cell row cell r – 1 end cell r end table close square brackets$ , r $element of$ N. Then det. (M₁) + det.(M₂) + ........... + det.(M₂₀₀₉) = ?

if $open square brackets table row 1 2 3 row 3 1 2 row 2 3 1 end table close square brackets$ $open square brackets table row x row y row z end table close square brackets$ = $open square brackets table row cell 4 – 2 end cell row cell 0 – 6 end cell row cell – 12 end cell end table close square brackets$ $open square brackets table row 2 row 1 end table close square brackets$ then (x, y, z) is equal to -

if $open square brackets table row 1 2 3 row 3 1 2 row 2 3 1 end table close square brackets$ $open square brackets table row x row y row z end table close square brackets$ = $open square brackets table row cell 4 – 2 end cell row cell 0 – 6 end cell row cell – 12 end cell end table close square brackets$ $open square brackets table row 2 row 1 end table close square brackets$ then (x, y, z) is equal to -

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Which of the following is not a disproportionation reaction?
I) $NH subscript 4 NO subscript 3 not stretchy rightwards arrow with straight capital delta on top straight N subscript 2 straight O plus straight H subscript 2 straight O$
II) $straight P subscript 4 not stretchy rightwards arrow with straight capital delta on top PH subscript 3 plus HPO subscript 2 superscript ⊖$
III) $PCl subscript 5 not stretchy rightwards arrow with straight capital delta on top PCl subscript 3 plus Cl subscript 2$
IV) $IO subscript 3 superscript ⊖ plus straight I to the power of ⊖ not stretchy ⟶ straight I subscript 2$

Which of the following is not a disproportionation reaction?
I) $NH subscript 4 NO subscript 3 not stretchy rightwards arrow with straight capital delta on top straight N subscript 2 straight O plus straight H subscript 2 straight O$
II) $straight P subscript 4 not stretchy rightwards arrow with straight capital delta on top PH subscript 3 plus HPO subscript 2 superscript ⊖$
III) $PCl subscript 5 not stretchy rightwards arrow with straight capital delta on top PCl subscript 3 plus Cl subscript 2$
IV) $IO subscript 3 superscript ⊖ plus straight I to the power of ⊖ not stretchy ⟶ straight I subscript 2$

chemistry-General

Which is not true for ozone?

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chemistry-General

parallel

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parallel

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parallel

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