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Maths-

General

Easy

Question

If [x] stands for the greatest integer less or equal to x, then in order than the set of equations x – 3y = 4 ; 5x + y = 2 ; [2 $pi$ ]x – [e]y = [2a] may be consistent, then ‘a’ should lie in -

$[3, \frac{7}{2})$
$(3, \frac{7}{3})$
$(3, \frac{7}{3}]$
None of these

The correct answer is: $open square brackets 3 comma fraction numerator 7 over denominator 2 end fraction close parentheses$

On solving x – 3y = 4 and 5x + y = 2, we get x = $fraction numerator 5 over denominator 8 end fraction$ , y = – $fraction numerator 9 over denominator 8 end fraction$ . As [2 $pi$ ] = 6 and [e] = 2.
So that the three equations are consistence if
This gives 6 $less or equal than$ 2a < 7 or 3 $less or equal than$ a < $fraction numerator 7 over denominator 2 end fraction$ .
Hence (A) is correct answer.

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chemistry-General

Let A = $open square brackets table row 2 3 row cell negative 1 end cell 5 end table close square brackets$ if A^–1 = xA + yI₂ then x and y are respectively -

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parallel

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ii) AB = I₂ $rightwards double arrow$ A = B^–1
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Then

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ii) AB = I₂ $rightwards double arrow$ A = B^–1
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Then

Statement-I :If $x equals cos space theta left parenthesis 1 plus sin space theta right parenthesis plus sin space theta left parenthesis 1 minus cos space theta right parenthesis$ and $y equals cos space theta left parenthesis 1 plus cos space theta right parenthesis minus sin space theta left parenthesis 1 minus sin space theta right parenthesis$ then $x plus y less or equal than 3$
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Statement-III : $sin space open parentheses pi over n close parentheses plus sin space open parentheses fraction numerator 3 pi over denominator n end fraction close parentheses plus sin space open parentheses fraction numerator 5 pi over denominator n end fraction close parentheses plus midline horizontal ellipsis plus n text terms end text equals 0$

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Statement-III : $sin space open parentheses pi over n close parentheses plus sin space open parentheses fraction numerator 3 pi over denominator n end fraction close parentheses plus sin space open parentheses fraction numerator 5 pi over denominator n end fraction close parentheses plus midline horizontal ellipsis plus n text terms end text equals 0$

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chemistry-General

parallel

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