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Maths-

General

Easy

Question

The maximum value of $open parentheses c o s invisible function application alpha subscript 1 end subscript close parentheses open parentheses c o s invisible function application alpha subscript 2 end subscript close parentheses horizontal ellipsis horizontal ellipsis. open parentheses c o s invisible function application alpha subscript n end subscript close parentheses$ under the restriction
$0 less or equal than alpha subscript 1 end subscript comma alpha subscript 2 end subscript horizontal ellipsis horizontal ellipsis horizontal ellipsis subscript n end subscript less or equal than fraction numerator pi over denominator 2 end fraction & c o t invisible function application alpha subscript 1 end subscript times c o t invisible function application alpha subscript 2 end subscript horizontal ellipsis horizontal ellipsis c o t invisible function application alpha subscript n end subscript equals 1$ is

$\frac{1}{2^{n / 2}}$
$\frac{1}{2^{n}}$
$\frac{1}{2^{n + 1}}$
1

The correct answer is: $fraction numerator 1 over denominator 2 to the power of n divided by 2 end exponent end fraction$

Related Questions to study

The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6. Then the other two are

The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6. Then the other two are

$text If end text x subscript 1 end subscript comma x subscript 2 end subscript comma x subscript 3 end subscript$ are three non zero real numbers such that $open parentheses x subscript 1 end subscript superscript 2 end superscript plus x subscript 2 end subscript superscript 2 end superscript close parentheses open parentheses x subscript 2 end subscript superscript 2 end superscript plus x subscript 3 end subscript superscript 2 end superscript close parentheses less or equal than open parentheses x subscript 1 end subscript x subscript 2 end subscript plus x subscript 2 end subscript x subscript 3 end subscript close parentheses to the power of 2 end exponent blank text then the G.M. of end text x subscript 1 end subscript comma x subscript 2 end subscript comma x subscript 3 end subscript text is end text$

$text If end text x subscript 1 end subscript comma x subscript 2 end subscript comma x subscript 3 end subscript$ are three non zero real numbers such that $open parentheses x subscript 1 end subscript superscript 2 end superscript plus x subscript 2 end subscript superscript 2 end superscript close parentheses open parentheses x subscript 2 end subscript superscript 2 end superscript plus x subscript 3 end subscript superscript 2 end superscript close parentheses less or equal than open parentheses x subscript 1 end subscript x subscript 2 end subscript plus x subscript 2 end subscript x subscript 3 end subscript close parentheses to the power of 2 end exponent blank text then the G.M. of end text x subscript 1 end subscript comma x subscript 2 end subscript comma x subscript 3 end subscript text is end text$

When 10 is subtracted from all the observations, the mean is reduced to 60% of its value. If 5 is added to all the observations, then the mean will be

Hence, the new mean is 30.

When 10 is subtracted from all the observations, the mean is reduced to 60% of its value. If 5 is added to all the observations, then the mean will be

Hence, the new mean is 30.

parallel

If mean deviation through median is 15 and median is 450, then coefficient of mean deviation is

Hence, the coefficient of Mean Deviation is 1/30.

If mean deviation through median is 15 and median is 450, then coefficient of mean deviation is

Hence, the coefficient of Mean Deviation is 1/30.

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The standard deviation of the data given by Variate (x) 0 1 2 3. . . . . n Frequency (f) $blank to the power of n end exponent C subscript 0 end subscript blank to the power of n end exponent C subscript 1 end subscript blank to the power of n end exponent C subscript 2 end subscript blank to the power of n end exponent C subscript 3 end subscript midline horizontal ellipsis times blank to the power of n end exponent C subscript n end subscript$

If the standard deviation of 0,1,2,3…..9 is K, then the standard deviation of 10,11,12,13…. 19 is

If the standard deviation of 0,1,2,3…..9 is K, then the standard deviation of 10,11,12,13…. 19 is

parallel

When 15 was subtracted from each of the seven observations the following number resulted : -3,0,-2,4,6,1,1. The mean of the distribution is

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The standard deviation of a variable x is $sigma$ . The standard deviation of the variable $fraction numerator a x plus b over denominator c end fraction$ where a, b, c are constants is ...

The standard deviation of a variable x is $sigma$ . The standard deviation of the variable $fraction numerator a x plus b over denominator c end fraction$ where a, b, c are constants is ...

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If $text end text n element of N text and end text 0 less or equal than theta less than pi text end text$ then the value of $stretchy integral subscript 0 end subscript superscript n pi plus theta end superscript vertical line s i n invisible function application x vertical line$ dx is equal to

parallel

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$stretchy integral subscript 0 end subscript superscript pi divided by 2 end superscript fraction numerator s i n to the power of 2 end exponent invisible function application 9 x over denominator sin invisible function application x end fraction d x equals$

$stretchy integral subscript 0 end subscript superscript pi divided by 2 end superscript fraction numerator s i n to the power of 2 end exponent invisible function application 9 x over denominator sin invisible function application x end fraction d x equals$

A square ABCD is inscribed in a circle of radius 4. A point P moves inside the circle such that $d left parenthesis P comma A B right parenthesis less or equal than$ min(d(P,BC),d(P,DA)) where d(P,AB) is the distance of a point P from line AB. The area of region covered by the moving point P is (sq units)

A square ABCD is inscribed in a circle of radius 4. A point P moves inside the circle such that $d left parenthesis P comma A B right parenthesis less or equal than$ min(d(P,BC),d(P,DA)) where d(P,AB) is the distance of a point P from line AB. The area of region covered by the moving point P is (sq units)

parallel

If $text end text I subscript n end subscript equals stretchy integral subscript 0 end subscript superscript infinity end superscript e to the power of negative x end exponent left parenthesis s i n invisible function application x right parenthesis to the power of n end exponent d x comma n greater than 1$ then the value of $fraction numerator 101 I subscript 10 end subscript over denominator I subscript 8 end subscript end fraction$ is equal to ____

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2k-mol of an ideal diatomic gas is enclosed in a vertical cylinder fitted with a piston and spring as shown in the figure. Initially the spring is compressed by 5 cm and then the electric heater starts supplying energy to the gas at constant rate of 100 J/S and due to conduction through walls of cylinder and radiation, 20 J/S has been lost to surroundings ( Take K=1000 N/m, $g equals 10 blank m divided by s to the power of 2 end exponent$ atomospheric pressure, $P subscript o end subscript equals 10 to the power of 5 end exponent blank N divided by m to the power of 2 end exponent$ , cross section area of piston $A subscript o end subscript equals 50 blank c m to the power of 2 end exponent$ , mass of piston m=1 kg R=8.3kj mol k) Answer the given question based on this information.

The initial pressure of the gas is

2k-mol of an ideal diatomic gas is enclosed in a vertical cylinder fitted with a piston and spring as shown in the figure. Initially the spring is compressed by 5 cm and then the electric heater starts supplying energy to the gas at constant rate of 100 J/S and due to conduction through walls of cylinder and radiation, 20 J/S has been lost to surroundings ( Take K=1000 N/m, $g equals 10 blank m divided by s to the power of 2 end exponent$ atomospheric pressure, $P subscript o end subscript equals 10 to the power of 5 end exponent blank N divided by m to the power of 2 end exponent$ , cross section area of piston $A subscript o end subscript equals 50 blank c m to the power of 2 end exponent$ , mass of piston m=1 kg R=8.3kj mol k) Answer the given question based on this information.

The initial pressure of the gas is

Physics-General

A system is taken from state ' i ' to the state 'f' along the path 'iaf', it is found that $capital delta Q equals 50 capital delta W$ =20 cal. Along the path 'ibf'. $capital delta Q equals 36$ cal.

If $capital delta W equals negative 13 c a l$ for curved path 'fi', what is the ' $capital delta Q to the power of ´ end exponent$ for this path ?

A system is taken from state ' i ' to the state 'f' along the path 'iaf', it is found that $capital delta Q equals 50 capital delta W$ =20 cal. Along the path 'ibf'. $capital delta Q equals 36$ cal.

If $capital delta W equals negative 13 c a l$ for curved path 'fi', what is the ' $capital delta Q to the power of ´ end exponent$ for this path ?

Physics-General

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