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Maths-

General

Easy

Question

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

$\frac{1}{2}$ (log a + log b – log 2)
log a/2 + log b/2 + log 2
$\frac{1}{2}$ (log a + log b + 4 log 2)
$\frac{1}{2}$ (log a – log b + 4log 2)

The correct answer is: $fraction numerator 1 over denominator 2 end fraction$ (log a + log b + 4 log 2)

Related Questions to study

Given that log_px = α and log_qx = β, then value of log_p_/q x equals-

Given that log_px = α and log_qx = β, then value of log_p_/q x equals-

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 -

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

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

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 -

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

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

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-

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

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-

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

parallel

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)

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 parentheses

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 parentheses

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

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

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

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

In the given figure, if POQ is a diameter of the circle and PR = QR, then RPQ is

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In the given figure, find the values of ‘x’ and ‘y’

In the given figure, find the values of ‘x’ and ‘y’

PQRS is a cyclic quadrilateral and PQ is the diameter of the circle. If QPR= ° 35 , then the value of PSR is

PQRS is a cyclic quadrilateral and PQ is the diameter of the circle. If QPR= ° 35 , then the value of PSR is

parallel

Find the value of ‘x’ in the given figure

Find the value of ‘x’ in the given figure

In the given figure, find PR

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parallel

If TP and TQ are the two tangents to a circle with centre ‘O’ such that then $text end text text PTO end text$ , is

If TP and TQ are the two tangents to a circle with centre ‘O’ such that then $text end text text PTO end text$ , is

Consider a rubber ball freely falling from a height $h equals 4.9 blank m$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time will be

h equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent comma blank

v equals negative g t

and after the collision,

v equals g t

(straight line)
Collision is perfectly elastic then ball reaches to same height again and again with same velocity

Consider a rubber ball freely falling from a height $h equals 4.9 blank m$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time will be

physics-General

h equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent comma blank

v equals negative g t

and after the collision,

v equals g t

(straight line)
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For upward motion
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equals negative open parentheses g plus a close parentheses

And for downward motion
Effective acceleration

equals left parenthesis g minus a right parenthesis

But both are constants. So the slope of speed-time graph will be constant

A ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball during its flight if the air resistance is not ignored

physics-General

For upward motion
Effective acceleration

equals negative open parentheses g plus a close parentheses

And for downward motion
Effective acceleration

equals left parenthesis g minus a right parenthesis

But both are constants. So the slope of speed-time graph will be constant

parallel

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