Maths-
General
Easy

Question

Statement-1 : f(x) = cos2x + cos3 open parentheses x plus fraction numerator pi over denominator 3 end fraction close parentheses– cos x cos3 open parentheses x plus fraction numerator pi over denominator 3 end fraction close parenthesesThen f‘(x) = 0
Statement-2 : Derivative of constant function is zero

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

The correct answer is: If both (A) and (R) are true but (R) is not the correct explanation of (A).

Related Questions to study

General
Maths-

Let f and g be real valued functions defined on interval (–1, 1) such that g to the power of ′′ left parenthesis x right parenthesis text  is continuous,  end text g left parenthesis 0 right parenthesis not equal to 0. g to the power of straight prime left parenthesis 0 right parenthesis equals 0 comma g to the power of ′′ left parenthesis 0 right parenthesis not equal to 0 comma straight & f left parenthesis x right parenthesis equals g(x)sin x
Statement-1 : stack l i m with x rightwards arrow 0 below [g(x) cot x –g(0) cosec x] =f to the power of ′′ (0)
Statement-2 : f to the power of straight prime(0) = g (0)

Let f and g be real valued functions defined on interval (–1, 1) such that g to the power of ′′ left parenthesis x right parenthesis text  is continuous,  end text g left parenthesis 0 right parenthesis not equal to 0. g to the power of straight prime left parenthesis 0 right parenthesis equals 0 comma g to the power of ′′ left parenthesis 0 right parenthesis not equal to 0 comma straight & f left parenthesis x right parenthesis equals g(x)sin x
Statement-1 : stack l i m with x rightwards arrow 0 below [g(x) cot x –g(0) cosec x] =f to the power of ′′ (0)
Statement-2 : f to the power of straight prime(0) = g (0)

Maths-General
General
Maths-

Statement-1 : If f(x) =fraction numerator left parenthesis e to the power of k x end exponent minus 1 right parenthesis sin invisible function application blank k x over denominator 4 x to the power of 2 end exponent end fraction (x not equal to 0) and f(0) = 9 is continuous at x = 0 then k = ± 6.
Statement-2 : For continuous function stack l i m with x rightwards arrow 0 belowf(x) = f(0)

Statement-1 : If f(x) =fraction numerator left parenthesis e to the power of k x end exponent minus 1 right parenthesis sin invisible function application blank k x over denominator 4 x to the power of 2 end exponent end fraction (x not equal to 0) and f(0) = 9 is continuous at x = 0 then k = ± 6.
Statement-2 : For continuous function stack l i m with x rightwards arrow 0 belowf(x) = f(0)

Maths-General
General
Maths-

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, xelement ofopen 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 ifstack l i m with x rightwards arrow a below f(x) = f(a)

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, xelement ofopen 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 ifstack l i m with x rightwards arrow a below f(x) = f(a)

Maths-General
parallel
General
Maths-

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 than2).
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 than2).
Statement 2 : For n greater or equal than 2, Right derivative = left derivative (for all real values of x).

Maths-General
General
Chemistry-

If H22 is mixed with Fe2+, which reaction is more likely:

If H22 is mixed with Fe2+, which reaction is more likely:

Chemistry-General
General
Chemistry-

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, Ecell 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, Ecell is:

Chemistry-General
parallel
General
Chemistry-

Extraction of zinc from zinc blende is achieved by-

Extraction of zinc from zinc blende is achieved by-

Chemistry-General
General
Chemistry-

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
General
Chemistry-

Which statement is not correct for Kohlrausch law?

Which statement is not correct for Kohlrausch law?

Chemistry-General
parallel
General
Chemistry-

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
General
Chemistry-

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
General
Chemistry-

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
General
Chemistry-

Metals can be prevented from rusting by –

Metals can be prevented from rusting by –

Chemistry-General
General
Chemistry-

The thermodynamic efficiency of cell is given by –

The thermodynamic efficiency of cell is given by –

Chemistry-General
General
Chemistry-

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
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