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Maths-

General

Easy

Question

Domain of the function $f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of l n invisible function application c o t to the power of negative 1 end exponent invisible function application x end root end fraction$ is

$(c o t 1, \infty)$
$R - {c o t 1}$
$(- \infty_{4} 0) \cup (0, c o t 1)$
$(- \infty, c o t 1)$

The correct answer is: $left parenthesis negative infinity comma c o t invisible function application 1 right parenthesis$

$table row cell l n invisible function application open parentheses cot to the power of negative 1 end exponent invisible function application x close parentheses greater than 0 end cell row cell c o t to the power of negative 1 end exponent invisible function application x greater than 1 end cell row cell x less than c o t invisible function application 1 end cell row cell therefore text end text text d end text text o end text text m end text text a end text text i end text text n end text text end text left parenthesis negative infinity comma c o t invisible function application 1 right parenthesis end cell end table$

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If $f colon left parenthesis 0 comma pi right parenthesis rightwards arrow R$ defined by $f open parentheses x close parentheses equals stretchy sum from k equals 1 to n of open square brackets 1 plus sin invisible function application k x close square brackets comma$ where [x] denotes the integral part of x, then range of f(x) is

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An ellipse has foci at (9, 20) and (49, 55) in the xy-plane and is tangent to the x axis. The length of its major axis is :

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Three metal ions x⁺², y⁺², z⁺² are identify in qualitative analysis. Nitrates of x⁺², y⁺², z⁺² dissolve in three seprate test tubes and gives following observation.
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vi) x ⁺² gives no ppt with dil NH₄OH
Select correct about xCO₃ , y CO₃ , z CO₃ -

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i) All solution produce carbonate precipitate with (NH₄)₂CO₃
ii) Only one produce white ppt on addition of NaCl.
iii) Out of 3 cations two produce sulphide ppt.
iv) Sulphide of y⁺² is not produce by H₂S/H⁺but produce when H₂S is passed in basic medium.
v) Only y⁺² produce soluble sulphate
vi) x ⁺² gives no ppt with dil NH₄OH
Select correct about xCO₃ , y CO₃ , z CO₃ -

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