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Maths-

General

Easy

Question

If the lines joining the origin to the points of intersection of the line 3y = mx + 3 and the curve $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 1$ are at right angle, then value of m + 3 is equal to

5
6
1
0

The correct answer is: 0

$table row cell O P equals fraction numerator 1 over denominator square root of 2 end fraction end cell row cell rightwards double arrow open vertical bar fraction numerator 0 minus 0 plus 3 over denominator square root of 9 plus m to the power of 2 end exponent end root end fraction close vertical bar equals fraction numerator 1 over denominator square root of 2 end fraction end cell end table$
$table row cell rightwards double arrow 9 plus m to the power of 2 end exponent equals 18 end cell row cell rightwards double arrow m to the power of 2 end exponent equals 9 rightwards double arrow m equals plus-or-minus 3 end cell row cell rightwards double arrow m plus 3 equals 60 end cell end table$

Related Questions to study

If, for a positive integer n, the quadratic equation $x left parenthesis x plus 1 right parenthesis plus left parenthesis x plus 1 right parenthesis left parenthesis x plus 2 right parenthesis plus horizontal ellipsis plus left parenthesis x plus stack n minus 1 with bar on top right parenthesis left parenthesis x plus n right parenthesis equals 10 n$ has two consecutive integral solutions, then n is equal to

If, for a positive integer n, the quadratic equation $x left parenthesis x plus 1 right parenthesis plus left parenthesis x plus 1 right parenthesis left parenthesis x plus 2 right parenthesis plus horizontal ellipsis plus left parenthesis x plus stack n minus 1 with bar on top right parenthesis left parenthesis x plus n right parenthesis equals 10 n$ has two consecutive integral solutions, then n is equal to

If n is even, then in the expansion of $open parentheses 1 plus fraction numerator x to the power of 2 end exponent over denominator 2 factorial end fraction plus fraction numerator x to the power of 4 end exponent over denominator 4 factorial end fraction plus midline horizontal ellipsis close parentheses to the power of 2 end exponent$ , the coefficient of $x to the power of n end exponent text is end text$

If n is even, then in the expansion of $open parentheses 1 plus fraction numerator x to the power of 2 end exponent over denominator 2 factorial end fraction plus fraction numerator x to the power of 4 end exponent over denominator 4 factorial end fraction plus midline horizontal ellipsis close parentheses to the power of 2 end exponent$ , the coefficient of $x to the power of n end exponent text is end text$

The sum to n terms of the series $6 times 9 plus 12 times 21 plus 20 times 37 plus 30 times 57 plus 42 times 81 plus midline horizontal ellipsis$ is

The sum to n terms of the series $6 times 9 plus 12 times 21 plus 20 times 37 plus 30 times 57 plus 42 times 81 plus midline horizontal ellipsis$ is

parallel

$text If end text 0 less than alpha less than fraction numerator pi over denominator 2 end fraction text and end text f left parenthesis alpha right parenthesis equals pi to the power of sec to the power of 2 end exponent invisible function application alpha end exponent c o s to the power of 2 end exponent invisible function application alpha plus pi to the power of cosec to the power of 3 end exponent invisible function application alpha end exponent s i n to the power of 2 end exponent invisible function application alpha comma text end text$ then

$text If end text 0 less than alpha less than fraction numerator pi over denominator 2 end fraction text and end text f left parenthesis alpha right parenthesis equals pi to the power of sec to the power of 2 end exponent invisible function application alpha end exponent c o s to the power of 2 end exponent invisible function application alpha plus pi to the power of cosec to the power of 3 end exponent invisible function application alpha end exponent s i n to the power of 2 end exponent invisible function application alpha comma text end text$ then

When Cl₂ is passed into moist slaked like, compound formed is:

When Cl₂ is passed into moist slaked like, compound formed is:

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In zone - refining method the molten zone

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On igniting Fe₂O₃ at 1400°C, the product obtained is:

On igniting Fe₂O₃ at 1400°C, the product obtained is:

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AgCl on fusion with Na₂CO₃ form

AgCl on fusion with Na₂CO₃ form

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As the reaction is increased from T₁ to T₂

As the reaction is increased from T₁ to T₂

Chemistry-General

The conjugate base of H₃⁺O is

The conjugate base of H₃⁺O is

Chemistry-General

1 cc of 0.1M HCl is added to 999 cc solution of 0.1M NaCl. The pH of the resulting solution will be

1 cc of 0.1M HCl is added to 999 cc solution of 0.1M NaCl. The pH of the resulting solution will be

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parallel

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The hydrogen ion concentration of 0.2N CH₃COOH which is 40% dissociated is

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A gaseous reaction A₂(g) ¾¾→ B(g) + $fraction numerator 1 over denominator 2 end fraction$ C(g) Shows increase in pressure from 100mm to 120 mm in 5 minutes. The rate of disappearance of A₂ is

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For a chemical reaction 2X + Y $⟶$ Z, the rate of appearance of Z is 0.05 mol L^–1 per min. The rate of disappearance of X will be

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