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Maths-

General

Easy

Question

Statement-I : Let f(x) = $fraction numerator 1 minus tan invisible function application x over denominator 4 x minus pi end fraction$ , x $not equal to$ $fraction numerator pi over denominator 4 end fraction$ , x $element of$ $open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses$ . If f(x) is continuous in $open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses$ , Then f $open parentheses fraction numerator pi over denominator 4 end fraction close parentheses$ = $negative fraction numerator 1 over denominator 2 end fraction$ .
Statement-II : f(x) is continuous at x = a if $stack l i m with x rightwards arrow a below$ f(x) = f(a)

If both (A) and (R) are true, and (R) is the correct explanation of (A).
If both (A) and (R) are true but (R) is not the correct explanation of (A).
If (A) is true but (R) is false.
If (A) is false but (R) is true.

The correct answer is: If both (A) and (R) are true, and (R) is the correct explanation of (A).

Statement 1 : f(/4) = f(/4)
= $stack l i m with h rightwards arrow 0 below$ $fraction numerator left parenthesis 0 right parenthesis over denominator left parenthesis 0 right parenthesis end fraction$
= $stack l i m with h rightwards arrow 0 below$ – $fraction numerator sec to the power of 2 end exponent invisible function application left parenthesis pi divided by 4 plus h right parenthesis over denominator 4 end fraction$ = – 2/4 f(/4) = –1/2
Statement 2 : $stack l i m with x rightwards arrow a below$ f(x) = (a)  f(a +) = f(a –) = f(a)
Both are correct

Related Questions to study

Statement 1 : f(x) = xⁿ sin $open parentheses fraction numerator 1 over denominator x end fraction close parentheses$ is differentiable for all real values of x (n $greater or equal than$ 2).
Statement 2 : For n $greater or equal than$ 2, Right derivative = left derivative (for all real values of x).

Statement 1 : f(x) = xⁿ sin $open parentheses fraction numerator 1 over denominator x end fraction close parentheses$ is differentiable for all real values of x (n $greater or equal than$ 2).
Statement 2 : For n $greater or equal than$ 2, Right derivative = left derivative (for all real values of x).

If H₂O₂ is mixed with Fe²⁺, which reaction is more likely:

If H₂O₂ is mixed with Fe²⁺, which reaction is more likely:

Chemistry-General

For the following cell reaction $P b open parentheses s close parentheses plus H g subscript 2 end subscript S O subscript 4 end subscript open parentheses s close parentheses P b S O subscript 4 end subscript open parentheses s close parentheses plus 2 H g open parentheses l close parentheses E subscript text cell end text end subscript superscript ring operator end superscript equals 0.92 V comma$ $K subscript S p end subscript open parentheses P b S O subscript 4 end subscript close parentheses equals 2 cross times 10 to the power of negative 8 end exponent$ , $K subscript S p end subscript open parentheses H g S O subscript 4 end subscript close parentheses equals 1 cross times 10 to the power of negative 6 end exponent$ Hence, E_cell is:

For the following cell reaction $P b open parentheses s close parentheses plus H g subscript 2 end subscript S O subscript 4 end subscript open parentheses s close parentheses P b S O subscript 4 end subscript open parentheses s close parentheses plus 2 H g open parentheses l close parentheses E subscript text cell end text end subscript superscript ring operator end superscript equals 0.92 V comma$ $K subscript S p end subscript open parentheses P b S O subscript 4 end subscript close parentheses equals 2 cross times 10 to the power of negative 8 end exponent$ , $K subscript S p end subscript open parentheses H g S O subscript 4 end subscript close parentheses equals 1 cross times 10 to the power of negative 6 end exponent$ Hence, E_cell is:

Chemistry-General

parallel

Extraction of zinc from zinc blende is achieved by-

Extraction of zinc from zinc blende is achieved by-

Chemistry-General

When the sample of Cu with Zn impurity is to be purified by electrolysis, the appropriate electrodes are-
CathodeAnode

When the sample of Cu with Zn impurity is to be purified by electrolysis, the appropriate electrodes are-
CathodeAnode

Chemistry-General

Which statement is not correct for Kohlrausch law?

Which statement is not correct for Kohlrausch law?

Chemistry-General

parallel

The equivalent conductivity of 0.1 M weak acid is 100 times less than that at infinite dilution. The degree of dissociation of weak electrolyte at 0.1 M is –

The equivalent conductivity of 0.1 M weak acid is 100 times less than that at infinite dilution. The degree of dissociation of weak electrolyte at 0.1 M is –

Chemistry-General

3 faraday of electricity are passed through molten Al₂O₃, aqueous solution of CuSO₄ and molten NaCl taken in three different electrolytic cells. The amount of Al, Cu and Na deposited at the cathodes will be in the ratio of –

3 faraday of electricity are passed through molten Al₂O₃, aqueous solution of CuSO₄ and molten NaCl taken in three different electrolytic cells. The amount of Al, Cu and Na deposited at the cathodes will be in the ratio of –

Chemistry-General

Beryllium is placed above magnesium in the II group. Beryllium dust, therefore, when added to MgCl₂ solution will –

Beryllium is placed above magnesium in the II group. Beryllium dust, therefore, when added to MgCl₂ solution will –

Chemistry-General

parallel

Metals can be prevented from rusting by –

Metals can be prevented from rusting by –

Chemistry-General

The thermodynamic efficiency of cell is given by –

The thermodynamic efficiency of cell is given by –

Chemistry-General

The following facts are available $table row cell 2 X to the power of minus end exponent plus Y subscript 2 end subscript rightwards arrow 2 Y to the power of minus end exponent plus X subscript 2 end subscript end cell row cell 2 W to the power of minus end exponent plus Y subscript 2 end subscript rightwards arrow text end text text N end text text o end text text end text text r end text text e end text text a end text text c end text text t end text text i end text text o end text text n end text text end text end cell row cell 2 Z to the power of minus end exponent plus X subscript 2 end subscript rightwards arrow 2 X to the power of minus end exponent plus Z subscript 2 end subscript end cell end table$ Which of the following is correct?

The following facts are available $table row cell 2 X to the power of minus end exponent plus Y subscript 2 end subscript rightwards arrow 2 Y to the power of minus end exponent plus X subscript 2 end subscript end cell row cell 2 W to the power of minus end exponent plus Y subscript 2 end subscript rightwards arrow text end text text N end text text o end text text end text text r end text text e end text text a end text text c end text text t end text text i end text text o end text text n end text text end text end cell row cell 2 Z to the power of minus end exponent plus X subscript 2 end subscript rightwards arrow 2 X to the power of minus end exponent plus Z subscript 2 end subscript end cell end table$ Which of the following is correct?

Chemistry-General

parallel

A standard hydrogen electrode has zero electrode potential because:

A standard hydrogen electrode has zero electrode potential because:

Chemistry-General

Given that $E subscript F e to the power of 3 plus end exponent divided by F e to the power of 2 plus end exponent end subscript equals negative 0.36 V$ and $E subscript F e to the power of 2 plus end exponent divided by F e end subscript equals negative 0.439 V$ respectively. Therefore value of $E to the power of ring operator end exponent F e to the power of 3 plus end exponent comma F e to the power of 2 plus end exponent divided by P t$ is :

Given that $E subscript F e to the power of 3 plus end exponent divided by F e to the power of 2 plus end exponent end subscript equals negative 0.36 V$ and $E subscript F e to the power of 2 plus end exponent divided by F e end subscript equals negative 0.439 V$ respectively. Therefore value of $E to the power of ring operator end exponent F e to the power of 3 plus end exponent comma F e to the power of 2 plus end exponent divided by P t$ is :

Chemistry-General

Given that $E subscript H subscript 2 end subscript O open vertical bar H subscript 2 end subscript close vertical bar P t end subscript equals 0$ at 298 K. The pressure of H₂(g) would be –

Given that $E subscript H subscript 2 end subscript O open vertical bar H subscript 2 end subscript close vertical bar P t end subscript equals 0$ at 298 K. The pressure of H₂(g) would be –

Chemistry-General

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