Maths-
General
Easy

Question

x to the power of log subscript 5 invisible function application x end exponent greater than 5 implies

  1. x element of left parenthesis 0 comma straight infinity right parenthesis    
  2. x element of left parenthesis 0 comma 1 divided by 5 right parenthesis union left parenthesis 5 comma straight infinity right parenthesis    
  3. x element of left parenthesis 1 comma straight infinity right parenthesis    
  4. x element of left parenthesis 1 comma 2 right parenthesis    

The correct answer is: x element of left parenthesis 0 comma 1 divided by 5 right parenthesis union left parenthesis 5 comma straight infinity right parenthesis

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log4 (2x2 + x + 1) – log2 (2x – 1) less or equal than – tan fraction numerator 7 pi over denominator 4 end fraction

log4 (2x2 + x + 1) – log2 (2x – 1) less or equal than – tan fraction numerator 7 pi over denominator 4 end fraction

maths-General
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maths-

The solution set of the inequation log1/3 (x2 + x + 1) + 1 > 0 is

The solution set of the inequation log1/3 (x2 + x + 1) + 1 > 0 is

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If open parentheses a to the power of log subscript b end subscript invisible function application x end exponent close parentheses to the power of 2 end exponent–5x to the power of log subscript b end subscript invisible function application a end exponent + 6 = 0 where a > 0, b > 0 & ab not equal to 1. Then the value of x is equal to

If open parentheses a to the power of log subscript b end subscript invisible function application x end exponent close parentheses to the power of 2 end exponent–5x to the power of log subscript b end subscript invisible function application a end exponent + 6 = 0 where a > 0, b > 0 & ab not equal to 1. Then the value of x is equal to

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parallel
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maths-

No. of ordered pair satisfying simultaneously the system of equation 2 to the power of square root of x end exponent. 2 to the power of square root of y end exponent= 256 & log10square root of x y end root – log10 1.5 = 1 is.

No. of ordered pair satisfying simultaneously the system of equation 2 to the power of square root of x end exponent. 2 to the power of square root of y end exponent= 256 & log10square root of x y end root – log10 1.5 = 1 is.

maths-General
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maths-

If x to the power of left square bracket log subscript 3 end subscript invisible function application x to the power of 2 end exponent plus left parenthesis log subscript 3 end subscript invisible function application x right parenthesis to the power of 2 end exponent minus 10 right square bracket end exponent= 1/x2, then x =

If x to the power of left square bracket log subscript 3 end subscript invisible function application x to the power of 2 end exponent plus left parenthesis log subscript 3 end subscript invisible function application x right parenthesis to the power of 2 end exponent minus 10 right square bracket end exponent= 1/x2, then x =

maths-General
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If xn > xn–1 >...> x2 > x1 > 1 then the value of log subscript straight x subscript 1 end subscript invisible function application log subscript straight x subscript 2 end subscript invisible function application log subscript straight x subscript 3 end subscript invisible function application horizontal ellipsis log subscript straight x subscript straight n end subscript invisible function application x subscript nblank to the power of x subscript n minus 1 end subscript superscript up right diagonal ellipsis to the power of x subscript 1 end exponent end superscript end exponentis equal to-

log subscript x subscript 1 end subscript end subscript invisible function application blanklog subscript x subscript 3 end subscript end subscript invisible function application blank...log subscript x subscript n minus 1 end subscript end subscript invisible function application blank open parentheses x subscript n minus 1 end subscript to the power of x subscript n minus 2 end subscript superscript. to the power of. to the power of. x subscript 1 end subscript end exponent end exponent end superscript end exponent log subscript x subscript n end subscript end subscript invisible function application x subscript n end subscript close parentheses
= log subscript x subscript 1 end subscript end subscript invisible function application x subscript 1 end subscript= 1

If xn > xn–1 >...> x2 > x1 > 1 then the value of log subscript straight x subscript 1 end subscript invisible function application log subscript straight x subscript 2 end subscript invisible function application log subscript straight x subscript 3 end subscript invisible function application horizontal ellipsis log subscript straight x subscript straight n end subscript invisible function application x subscript nblank to the power of x subscript n minus 1 end subscript superscript up right diagonal ellipsis to the power of x subscript 1 end exponent end superscript end exponentis equal to-

maths-General
log subscript x subscript 1 end subscript end subscript invisible function application blanklog subscript x subscript 3 end subscript end subscript invisible function application blank...log subscript x subscript n minus 1 end subscript end subscript invisible function application blank open parentheses x subscript n minus 1 end subscript to the power of x subscript n minus 2 end subscript superscript. to the power of. to the power of. x subscript 1 end subscript end exponent end exponent end superscript end exponent log subscript x subscript n end subscript end subscript invisible function application x subscript n end subscript close parentheses
= log subscript x subscript 1 end subscript end subscript invisible function application x subscript 1 end subscript= 1
parallel
General
maths-

The expression logp where p greater or equal than 2 comma p element of N semicolon n element of N when simplified is.

The expression logp where p greater or equal than 2 comma p element of N semicolon n element of N when simplified is.

maths-General
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maths-

Let N=open parentheses open parentheses square root of 7 close parentheses to the power of fraction numerator 2 over denominator log subscript 25 end subscript invisible function application 7 end fraction end exponent minus 12 5 to the power of log subscript 25 end subscript invisible function application 6 end exponent close parentheses Then log2N has the value –

Let N=open parentheses open parentheses square root of 7 close parentheses to the power of fraction numerator 2 over denominator log subscript 25 end subscript invisible function application 7 end fraction end exponent minus 12 5 to the power of log subscript 25 end subscript invisible function application 6 end exponent close parentheses Then log2N has the value –

maths-General
General
maths-

If a2 + 4b2 = 12ab, then log (a + 2b) =

If a2 + 4b2 = 12ab, then log (a + 2b) =

maths-General
parallel
General
maths-

Given that logpx = α and logqx = β, then value of logp/q x equals-

Given that logpx = α and logqx = β, then value of logp/q x equals-

maths-General
General
Maths-

If f(x) is the primitive of fraction numerator sin invisible function application root index 3 of x end root log invisible function application left parenthesis 1 plus 3 x right parenthesis over denominator left parenthesis tan to the power of – 1 end exponent invisible function application square root of x right parenthesis to the power of 2 end exponent left parenthesis e to the power of root index 3 of x end root end exponent – 1 right parenthesis end fraction (x not equal to 0), then stack l i m with x rightwards arrow 0 below f ' (x) is -

 f(x) = not stretchy integral fraction numerator sin invisible function application x to the power of 1 divided by 3 end exponent log invisible function application left parenthesis 1 plus 3 x right parenthesis over denominator left parenthesis tan to the power of – 1 end exponent invisible function application square root of x right parenthesis to the power of 2 end exponent left parenthesis e to the power of x to the power of 1 divided by 3 end exponent end exponent – 1 right parenthesis end fraction
stack l i m with x rightwards arrow 0 below f'(x)
stack l i m with x rightwards arrow 0 below fraction numerator open parentheses fraction numerator sin invisible function application x to the power of 1 divided by 3 end exponent over denominator x to the power of 1 divided by 3 end exponent end fraction close parentheses x to the power of 1 divided by 3 end exponent open square brackets fraction numerator cos invisible function application left parenthesis 1 plus 3 x right parenthesis over denominator 3 x end fraction close square brackets left parenthesis 3 x right parenthesis over denominator open parentheses fraction numerator tan to the power of – 1 end exponent invisible function application square root of x over denominator square root of x end fraction close parentheses to the power of 2 end exponent. x. open parentheses fraction numerator e to the power of x to the power of 1 divided by 3 end exponent end exponent – 1 over denominator x to the power of 1 divided by 3 end exponent end fraction close parentheses. x to the power of 1 divided by 3 end exponent end fraction
= 3

If f(x) is the primitive of fraction numerator sin invisible function application root index 3 of x end root log invisible function application left parenthesis 1 plus 3 x right parenthesis over denominator left parenthesis tan to the power of – 1 end exponent invisible function application square root of x right parenthesis to the power of 2 end exponent left parenthesis e to the power of root index 3 of x end root end exponent – 1 right parenthesis end fraction (x not equal to 0), then stack l i m with x rightwards arrow 0 below f ' (x) is -

Maths-General
 f(x) = not stretchy integral fraction numerator sin invisible function application x to the power of 1 divided by 3 end exponent log invisible function application left parenthesis 1 plus 3 x right parenthesis over denominator left parenthesis tan to the power of – 1 end exponent invisible function application square root of x right parenthesis to the power of 2 end exponent left parenthesis e to the power of x to the power of 1 divided by 3 end exponent end exponent – 1 right parenthesis end fraction
stack l i m with x rightwards arrow 0 below f'(x)
stack l i m with x rightwards arrow 0 below fraction numerator open parentheses fraction numerator sin invisible function application x to the power of 1 divided by 3 end exponent over denominator x to the power of 1 divided by 3 end exponent end fraction close parentheses x to the power of 1 divided by 3 end exponent open square brackets fraction numerator cos invisible function application left parenthesis 1 plus 3 x right parenthesis over denominator 3 x end fraction close square brackets left parenthesis 3 x right parenthesis over denominator open parentheses fraction numerator tan to the power of – 1 end exponent invisible function application square root of x over denominator square root of x end fraction close parentheses to the power of 2 end exponent. x. open parentheses fraction numerator e to the power of x to the power of 1 divided by 3 end exponent end exponent – 1 over denominator x to the power of 1 divided by 3 end exponent end fraction close parentheses. x to the power of 1 divided by 3 end exponent end fraction
= 3
General
Maths-

If f(x) is the primitive of fraction numerator sin invisible function application root index 3 of x end root log invisible function application left parenthesis 1 plus 3 x right parenthesis over denominator left parenthesis tan to the power of negative 1 end exponent invisible function application square root of x right parenthesis to the power of 2 end exponent left parenthesis e to the power of root index 3 of x end root end exponent minus 1 right parenthesis end fraction(x not equal to 0), then stack l i m with x rightwards arrow 0 below f ´ left parenthesis x right parenthesis is-

f(x) = not stretchy integral fraction numerator sin invisible function application x to the power of 1 divided by 3 end exponent log invisible function application left parenthesis 1 plus 3 x right parenthesis d x over denominator left parenthesis tan to the power of negative 1 end exponent invisible function application square root of x right parenthesis to the power of 2 end exponent left parenthesis e to the power of 5 x to the power of 1 divided by 3 end exponent end exponent minus 1 right parenthesis end fraction
stack l i m with x rightwards arrow 0 below f ´ left parenthesis x right parenthesis = fraction numerator sin invisible function application x to the power of 1 divided by 3 end exponent log invisible function application left parenthesis 1 plus 3 x right parenthesis over denominator left parenthesis tan to the power of negative 1 end exponent invisible function application square root of x right parenthesis to the power of 2 end exponent left parenthesis e to the power of 5 x to the power of 1 divided by 3 end exponent end exponent minus 1 right parenthesis end fraction
= fraction numerator x to the power of 1 divided by 3 end exponent fraction numerator sin invisible function application x to the power of 1 divided by 3 end exponent over denominator x to the power of 1 divided by 3 end exponent end fraction. fraction numerator log invisible function application left parenthesis 1 plus 3 x right parenthesis over denominator 3 x end fraction.3 x over denominator x. open parentheses fraction numerator tan to the power of negative 1 end exponent invisible function application square root of x over denominator square root of x end fraction close parentheses to the power of 2 end exponent open parentheses fraction numerator e to the power of 5 x to the power of 1 divided by 3 end exponent end exponent minus 1 over denominator 5 x to the power of 1 divided by 3 end exponent end fraction close parentheses.5 x to the power of 1 divided by 3 end exponent end fraction
= fraction numerator 1.1.3 over denominator 1.1.5 end fraction equals 3/5

If f(x) is the primitive of fraction numerator sin invisible function application root index 3 of x end root log invisible function application left parenthesis 1 plus 3 x right parenthesis over denominator left parenthesis tan to the power of negative 1 end exponent invisible function application square root of x right parenthesis to the power of 2 end exponent left parenthesis e to the power of root index 3 of x end root end exponent minus 1 right parenthesis end fraction(x not equal to 0), then stack l i m with x rightwards arrow 0 below f ´ left parenthesis x right parenthesis is-

Maths-General
f(x) = not stretchy integral fraction numerator sin invisible function application x to the power of 1 divided by 3 end exponent log invisible function application left parenthesis 1 plus 3 x right parenthesis d x over denominator left parenthesis tan to the power of negative 1 end exponent invisible function application square root of x right parenthesis to the power of 2 end exponent left parenthesis e to the power of 5 x to the power of 1 divided by 3 end exponent end exponent minus 1 right parenthesis end fraction
stack l i m with x rightwards arrow 0 below f ´ left parenthesis x right parenthesis = fraction numerator sin invisible function application x to the power of 1 divided by 3 end exponent log invisible function application left parenthesis 1 plus 3 x right parenthesis over denominator left parenthesis tan to the power of negative 1 end exponent invisible function application square root of x right parenthesis to the power of 2 end exponent left parenthesis e to the power of 5 x to the power of 1 divided by 3 end exponent end exponent minus 1 right parenthesis end fraction
= fraction numerator x to the power of 1 divided by 3 end exponent fraction numerator sin invisible function application x to the power of 1 divided by 3 end exponent over denominator x to the power of 1 divided by 3 end exponent end fraction. fraction numerator log invisible function application left parenthesis 1 plus 3 x right parenthesis over denominator 3 x end fraction.3 x over denominator x. open parentheses fraction numerator tan to the power of negative 1 end exponent invisible function application square root of x over denominator square root of x end fraction close parentheses to the power of 2 end exponent open parentheses fraction numerator e to the power of 5 x to the power of 1 divided by 3 end exponent end exponent minus 1 over denominator 5 x to the power of 1 divided by 3 end exponent end fraction close parentheses.5 x to the power of 1 divided by 3 end exponent end fraction
= fraction numerator 1.1.3 over denominator 1.1.5 end fraction equals 3/5
parallel
General
maths-

If f left parenthesis x right parenthesis equals open vertical bar table row cell s i n invisible function application x end cell cell s i n invisible function application a end cell cell s i n invisible function application b end cell row cell c o s invisible function application x end cell cell c o s invisible function application a end cell cell c o s invisible function application b end cell row cell t a n invisible function application x end cell cell t a n invisible function application a end cell cell t a n invisible function application b end cell end table close vertical bar where 0 less than a less than b less than fraction numerator pi over denominator 2 end fraction hen the equation f(x) = 0 has, in the interval (a, b)

If f left parenthesis x right parenthesis equals open vertical bar table row cell s i n invisible function application x end cell cell s i n invisible function application a end cell cell s i n invisible function application b end cell row cell c o s invisible function application x end cell cell c o s invisible function application a end cell cell c o s invisible function application b end cell row cell t a n invisible function application x end cell cell t a n invisible function application a end cell cell t a n invisible function application b end cell end table close vertical bar where 0 less than a less than b less than fraction numerator pi over denominator 2 end fraction hen the equation f(x) = 0 has, in the interval (a, b)

maths-General
General
physics-

The velocity-time graph of a particle moving along a straight line is shown in figure. The displacement of the body in 5s is

Displacement (in magnitude)
equals fraction numerator 1 over denominator 2 end fraction open parentheses 3 cross times 2 minus fraction numerator 1 over denominator 2 end fraction cross times 1 cross times 2 plus 1 cross times 1 close parenthesesm=3m

The velocity-time graph of a particle moving along a straight line is shown in figure. The displacement of the body in 5s is

physics-General
Displacement (in magnitude)
equals fraction numerator 1 over denominator 2 end fraction open parentheses 3 cross times 2 minus fraction numerator 1 over denominator 2 end fraction cross times 1 cross times 2 plus 1 cross times 1 close parenthesesm=3m
General
maths-

Let f x( ) and g x( ) are defined and differentiable for x greater or equal than x subscript 0 end subscript and f open parentheses x subscript 0 close parentheses equals g open parentheses x subscript 0 close parentheses comma f to the power of ´ left parenthesis x right parenthesis greater than straight g to the power of straight prime left parenthesis x right parenthesis text  for  end text x greater than x subscript 0 then

ϕ left parenthesis x right parenthesis equals f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis text  where  end text x element of open square brackets x subscript 0 end subscript comma b close square brackets by c element of open parentheses x subscript 0 end subscript comma b close parentheses contains as member
ϕ to the power of ´ end exponent left parenthesis c right parenthesis equals fraction numerator ϕ left parenthesis b right parenthesis minus ϕ open parentheses x subscript 0 end subscript close parentheses over denominator b minus x subscript 0 end subscript end fraction greater than 0
therefore f left parenthesis x right parenthesis greater than g left parenthesis x right parenthesis text  for  end text x equals b

Let f x( ) and g x( ) are defined and differentiable for x greater or equal than x subscript 0 end subscript and f open parentheses x subscript 0 close parentheses equals g open parentheses x subscript 0 close parentheses comma f to the power of ´ left parenthesis x right parenthesis greater than straight g to the power of straight prime left parenthesis x right parenthesis text  for  end text x greater than x subscript 0 then

maths-General
ϕ left parenthesis x right parenthesis equals f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis text  where  end text x element of open square brackets x subscript 0 end subscript comma b close square brackets by c element of open parentheses x subscript 0 end subscript comma b close parentheses contains as member
ϕ to the power of ´ end exponent left parenthesis c right parenthesis equals fraction numerator ϕ left parenthesis b right parenthesis minus ϕ open parentheses x subscript 0 end subscript close parentheses over denominator b minus x subscript 0 end subscript end fraction greater than 0
therefore f left parenthesis x right parenthesis greater than g left parenthesis x right parenthesis text  for  end text x equals b
parallel

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