Maths-
General
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Question

Assertion: open vertical bar table row cell cos invisible function application left parenthesis theta plus alpha right parenthesis end cell cell cos invisible function application left parenthesis theta plus beta right parenthesis end cell cell cos invisible function application left parenthesis theta plus gamma right parenthesis end cell row cell sin invisible function application left parenthesis theta plus alpha right parenthesis end cell cell sin invisible function application left parenthesis theta plus beta right parenthesis end cell cell sin invisible function application left parenthesis theta plus gamma right parenthesis end cell row cell sin invisible function application left parenthesis beta minus gamma right parenthesis end cell cell sin invisible function application left parenthesis gamma minus alpha right parenthesis end cell cell sin invisible function application left parenthesis alpha minus beta right parenthesis end cell end table close vertical baris independent of theta
Reason: If f(theta) = c, then f(theta) is independent of theta.

  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).

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Statement-1 : The function f(x) = |x3| is differentiable at x = 0
Statement-2 : at x = 0, f to the power of straight prime(x) = 0

Statement-1 : The function f(x) = |x3| is differentiable at x = 0
Statement-2 : at x = 0, f to the power of straight prime(x) = 0

Maths-General
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Maths-

Statement-1 : The function y = sin–1 (cos x) is not differentiable at x equals n pi comma n element of Z is particular at x = pi

Statement-2 : fraction numerator d y over denominator d x end fraction=fraction numerator negative sin invisible function application x over denominator vertical line sin invisible function application x vertical line end fraction so the function is not differentiable at the points where sin x = 0.

Statement-1 : The function y = sin–1 (cos x) is not differentiable at x equals n pi comma n element of Z is particular at x = pi

Statement-2 : fraction numerator d y over denominator d x end fraction=fraction numerator negative sin invisible function application x over denominator vertical line sin invisible function application x vertical line end fraction so the function is not differentiable at the points where sin x = 0.

Maths-General
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Maths-

Statement-1 : fleft parenthesis x right parenthesis equals x to the power of n end exponent s i n invisible function application open parentheses fraction numerator 1 over denominator x end fraction close parentheses semicolon x not equal to 0 equals 0 semicolon x equals 0 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 : fleft parenthesis x right parenthesis equals x to the power of n end exponent s i n invisible function application open parentheses fraction numerator 1 over denominator x end fraction close parentheses semicolon x not equal to 0 equals 0 semicolon x equals 0 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
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General
Maths-

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

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

Maths-General
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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
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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
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
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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
General
Chemistry-

Extraction of zinc from zinc blende is achieved by-

Extraction of zinc from zinc blende is achieved by-

Chemistry-General
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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
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Which statement is not correct for Kohlrausch law?

Which statement is not correct for Kohlrausch law?

Chemistry-General
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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
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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 –

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