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Question Number 23968 Answers: 0 Comments: 3

Prove that n and 2n−1 are coprime.

$${Prove}\:{that}\:{n}\:{and}\:\mathrm{2}{n}−\mathrm{1}\:{are}\:{coprime}. \\ $$

Question Number 23972 Answers: 0 Comments: 0

∫_0 ^(90) ((sin^2 x)/(sin^4 x+cos^4 x))dx

$$\int_{\mathrm{0}} ^{\mathrm{90}} \frac{\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{sin}\:^{\mathrm{4}} {x}+\mathrm{cos}\:^{\mathrm{4}} {x}}{dx} \\ $$

Question Number 23953 Answers: 0 Comments: 4

find the nth term of the sequence 4, 9, 16, 45, 76 please help

$${find}\:{the}\:{nth}\:{term}\:{of}\:{the}\:{sequence} \\ $$$$\mathrm{4},\:\mathrm{9},\:\mathrm{16},\:\mathrm{45},\:\mathrm{76} \\ $$$$ \\ $$$${please}\:{help} \\ $$

Question Number 23940 Answers: 0 Comments: 2

When the gas is ideal and process is isothermal, then (1) P_1 V_1 = P_2 V_2 (2) ΔU = 0 (3) ΔW = 0 (4) ΔH_1 = ΔH_2

$$\mathrm{When}\:\mathrm{the}\:\mathrm{gas}\:\mathrm{is}\:\mathrm{ideal}\:\mathrm{and}\:\mathrm{process}\:\mathrm{is} \\ $$$$\mathrm{isothermal},\:\mathrm{then} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{P}_{\mathrm{1}} \mathrm{V}_{\mathrm{1}} \:=\:\mathrm{P}_{\mathrm{2}} \mathrm{V}_{\mathrm{2}} \\ $$$$\left(\mathrm{2}\right)\:\Delta\mathrm{U}\:=\:\mathrm{0} \\ $$$$\left(\mathrm{3}\right)\:\Delta\mathrm{W}\:=\:\mathrm{0} \\ $$$$\left(\mathrm{4}\right)\:\Delta\mathrm{H}_{\mathrm{1}} \:=\:\Delta\mathrm{H}_{\mathrm{2}} \\ $$

Question Number 23939 Answers: 0 Comments: 0

In a school of 500 students,150 played hockey 250 played football,120 played table tennis and 100 played one of the three games.If 50 played both hockey and football,how many played table tennis only?pls show workings with diagram

$${In}\:{a}\:{school}\:{of}\:\mathrm{500}\:{students},\mathrm{150}\:{played}\:{hockey} \\ $$$$\mathrm{250}\:{played}\:{football},\mathrm{120}\:{played}\:{table}\:{tennis}\:{and} \\ $$$$\mathrm{100}\:{played}\:{one}\:{of}\:{the}\:{three}\:{games}.{If}\:\mathrm{50}\: \\ $$$${played}\:{both}\:{hockey}\:{and}\:{football},{how}\:{many} \\ $$$${played}\:{table}\:{tennis}\:{only}?{pls}\:{show}\:{workings}\:{with} \\ $$$${diagram} \\ $$$$ \\ $$

Question Number 23937 Answers: 1 Comments: 1

Question Number 23928 Answers: 0 Comments: 4

Find^n C_1 − (1/2)^n C_2 + (1/3)^n C_3 − .... + (−1)^(n−1) (1/n) ∙^n C_n .

$$\mathrm{Find}\:^{{n}} {C}_{\mathrm{1}} \:−\:\frac{\mathrm{1}}{\mathrm{2}}\:^{{n}} {C}_{\mathrm{2}} \:+\:\frac{\mathrm{1}}{\mathrm{3}}\:^{{n}} {C}_{\mathrm{3}} \:−\:....\:+ \\ $$$$\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \frac{\mathrm{1}}{{n}}\:\centerdot\:^{{n}} {C}_{{n}} . \\ $$

Question Number 23932 Answers: 1 Comments: 0

A cord is wound around the circumference of a bicycle wheel (without tyre) of diameter 1 m. A mass of 2 kg is tied at the end of the cord and it is allowed to fall from rest. The weight falls 2 m in 4 s. The axle of the wheel is horizontal and the wheel rotates with its plane vertical. If g = 10 ms^(−2) , what is the angular acceleration of the wheel?

$$\mathrm{A}\:\mathrm{cord}\:\mathrm{is}\:\mathrm{wound}\:\mathrm{around}\:\mathrm{the}\:\mathrm{circumference} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{bicycle}\:\mathrm{wheel}\:\left(\mathrm{without}\:\mathrm{tyre}\right)\:\mathrm{of} \\ $$$$\mathrm{diameter}\:\mathrm{1}\:\mathrm{m}.\:\mathrm{A}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{2}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{tied}\:\mathrm{at} \\ $$$$\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cord}\:\mathrm{and}\:\mathrm{it}\:\mathrm{is}\:\mathrm{allowed}\:\mathrm{to} \\ $$$$\mathrm{fall}\:\mathrm{from}\:\mathrm{rest}.\:\mathrm{The}\:\mathrm{weight}\:\mathrm{falls}\:\mathrm{2}\:\mathrm{m}\:\mathrm{in}\:\mathrm{4} \\ $$$$\mathrm{s}.\:\mathrm{The}\:\mathrm{axle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{wheel}\:\mathrm{is}\:\mathrm{horizontal} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{wheel}\:\mathrm{rotates}\:\mathrm{with}\:\mathrm{its}\:\mathrm{plane} \\ $$$$\mathrm{vertical}.\:\mathrm{If}\:\mathrm{g}\:=\:\mathrm{10}\:\mathrm{ms}^{−\mathrm{2}} ,\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{angular}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{wheel}? \\ $$

Question Number 23922 Answers: 1 Comments: 0

if f(x)=2^x show that f(x+3)−f(x−1)=((15)/2)f(x)

$$\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{2}^{\boldsymbol{\mathrm{x}}} \\ $$$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}+\mathrm{3}\right)−\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}−\mathrm{1}\right)=\frac{\mathrm{15}}{\mathrm{2}}\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right) \\ $$

Question Number 23920 Answers: 1 Comments: 1

Question Number 23981 Answers: 1 Comments: 0

Amount of heat required to change 1 g ice at 0°C to 1 g steam at 100°C is (1) 616 cal (2) 12 kcal (3) 717 cal (4) none of these.

$$\mathrm{Amount}\:\mathrm{of}\:\mathrm{heat}\:\mathrm{required}\:\mathrm{to}\:\mathrm{change}\:\mathrm{1}\:{g} \\ $$$$\mathrm{ice}\:\mathrm{at}\:\mathrm{0}°\mathrm{C}\:\mathrm{to}\:\mathrm{1}\:{g}\:\mathrm{steam}\:\mathrm{at}\:\mathrm{100}°\mathrm{C}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{616}\:\mathrm{cal} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{12}\:\mathrm{kcal} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{717}\:\mathrm{cal} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{none}\:\mathrm{of}\:\mathrm{these}. \\ $$

Question Number 23925 Answers: 0 Comments: 0

Question Number 23900 Answers: 0 Comments: 0

Question Number 23897 Answers: 1 Comments: 3

Question Number 23891 Answers: 0 Comments: 3

Question Number 23883 Answers: 0 Comments: 0

plz anyone answer the question 23870 .plz plz plz.....

$${plz}\:{anyone}\:\:\:{answer}\:{the}\:{question}\:\mathrm{23870}\:.{plz}\:{plz}\:{plz}..... \\ $$

Question Number 23871 Answers: 0 Comments: 0

Let ABC be a triangle and B′ be the reflection of B in the line CA and C′ be reflection of C in the line AB. Prove that ΔABC′ ≅ ΔACB′ ≅ ΔABC.

$$\mathrm{Let}\:{ABC}\:\mathrm{be}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{and}\:{B}'\:\mathrm{be}\:\mathrm{the} \\ $$$$\mathrm{reflection}\:\mathrm{of}\:{B}\:\mathrm{in}\:\mathrm{the}\:\mathrm{line}\:{CA}\:\mathrm{and}\:{C}'\:\mathrm{be} \\ $$$$\mathrm{reflection}\:\mathrm{of}\:{C}\:\mathrm{in}\:\mathrm{the}\:\mathrm{line}\:{AB}.\:\mathrm{Prove} \\ $$$$\mathrm{that}\:\Delta{ABC}'\:\cong\:\Delta{ACB}'\:\cong\:\Delta{ABC}. \\ $$

Question Number 23870 Answers: 0 Comments: 0

Find a vector function F whose graph is the the line of intersection of the plane 4x−2y+z=3 and x+y−3y=1

$${Find}\:{a}\:{vector}\:{function}\:{F}\:\:{whose}\:{graph}\:{is}\:{the} \\ $$$${the}\:{line}\:{of}\:{intersection}\:{of}\:{the}\:{plane}\: \\ $$$$\mathrm{4}{x}−\mathrm{2}{y}+{z}=\mathrm{3}\:{and}\:{x}+{y}−\mathrm{3}{y}=\mathrm{1} \\ $$

Question Number 23884 Answers: 1 Comments: 0

If C_r stands for^n C_r = ((n!)/(r! n − r!)) and Σ_(r=1) ^n r.C_r ^2 = λ for n ≥ 2, then λ is divisible by (1) 3 (n − 1) (2) n + 1 (3) n (2n − 1) (4) n^2 + 1

$$\mathrm{If}\:{C}_{{r}} \:\mathrm{stands}\:\mathrm{for}\:^{{n}} {C}_{{r}} \:=\:\frac{{n}!}{{r}!\:{n}\:−\:{r}!}\:\mathrm{and} \\ $$$$\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}{r}.{C}_{{r}} ^{\mathrm{2}} \:=\:\lambda\:\mathrm{for}\:{n}\:\geqslant\:\mathrm{2},\:\mathrm{then}\:\lambda\:\mathrm{is}\:\mathrm{divisible} \\ $$$$\mathrm{by} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{3}\:\left({n}\:−\:\mathrm{1}\right) \\ $$$$\left(\mathrm{2}\right)\:{n}\:+\:\mathrm{1} \\ $$$$\left(\mathrm{3}\right)\:{n}\:\left(\mathrm{2}{n}\:−\:\mathrm{1}\right) \\ $$$$\left(\mathrm{4}\right)\:{n}^{\mathrm{2}} \:+\:\mathrm{1} \\ $$

Question Number 23865 Answers: 0 Comments: 7

A man of mass m, standing at the bottom of the staircase of height L climbs it and stands at its top. (1) Work done by all forces on man is equal to the rise in potential energy mgL. (2) Work done by all forces on man is zero. (3) Work done by the gravitational force on man is mgL. (4) The reaction force from a step does not do work because the point of application of the force does not move while the force exists.

$$\mathrm{A}\:\mathrm{man}\:\mathrm{of}\:\mathrm{mass}\:{m},\:\mathrm{standing}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{bottom}\:\mathrm{of}\:\mathrm{the}\:\mathrm{staircase}\:\mathrm{of}\:\mathrm{height}\:{L} \\ $$$$\mathrm{climbs}\:\mathrm{it}\:\mathrm{and}\:\mathrm{stands}\:\mathrm{at}\:\mathrm{its}\:\mathrm{top}. \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Work}\:\mathrm{done}\:\mathrm{by}\:\mathrm{all}\:\mathrm{forces}\:\mathrm{on}\:\mathrm{man}\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{rise}\:\mathrm{in}\:\mathrm{potential}\:\mathrm{energy} \\ $$$${mgL}. \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Work}\:\mathrm{done}\:\mathrm{by}\:{all}\:\mathrm{forces}\:\mathrm{on}\:\mathrm{man}\:\mathrm{is} \\ $$$$\mathrm{zero}. \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Work}\:\mathrm{done}\:\mathrm{by}\:\mathrm{the}\:\mathrm{gravitational} \\ $$$$\mathrm{force}\:\mathrm{on}\:\mathrm{man}\:\mathrm{is}\:{mgL}. \\ $$$$\left(\mathrm{4}\right)\:\mathrm{The}\:\mathrm{reaction}\:\mathrm{force}\:\mathrm{from}\:\mathrm{a}\:\mathrm{step}\:\mathrm{does} \\ $$$$\mathrm{not}\:\mathrm{do}\:\mathrm{work}\:\mathrm{because}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of} \\ $$$$\mathrm{application}\:\mathrm{of}\:\mathrm{the}\:\mathrm{force}\:\mathrm{does}\:\mathrm{not}\:\mathrm{move} \\ $$$$\mathrm{while}\:\mathrm{the}\:\mathrm{force}\:\mathrm{exists}. \\ $$

Question Number 23863 Answers: 0 Comments: 0

From the following data, calculate the enthalpy change for the combustion of cyclopropane at 298 K. The enthalpy of formation of CO_2 (g), H_2 O (l) and propene (g) are −393.5, −285.8 and 20.42 kJ mol^(−1) respectively. The enthalpy of isomerisation of cyclopropane to propene is −33 kJ mol^(−1) .

$$\mathrm{From}\:\mathrm{the}\:\mathrm{following}\:\mathrm{data},\:\mathrm{calculate}\:\mathrm{the} \\ $$$$\mathrm{enthalpy}\:\mathrm{change}\:\mathrm{for}\:\mathrm{the}\:\mathrm{combustion}\:\mathrm{of} \\ $$$$\mathrm{cyclopropane}\:\mathrm{at}\:\mathrm{298}\:\mathrm{K}.\:\mathrm{The}\:\mathrm{enthalpy} \\ $$$$\mathrm{of}\:\mathrm{formation}\:\mathrm{of}\:\mathrm{CO}_{\mathrm{2}} \:\left({g}\right),\:\mathrm{H}_{\mathrm{2}} \mathrm{O}\:\left({l}\right)\:\mathrm{and} \\ $$$$\mathrm{propene}\:\left({g}\right)\:\mathrm{are}\:−\mathrm{393}.\mathrm{5},\:−\mathrm{285}.\mathrm{8}\:\mathrm{and} \\ $$$$\mathrm{20}.\mathrm{42}\:\mathrm{kJ}\:\mathrm{mol}^{−\mathrm{1}} \:\mathrm{respectively}.\:\mathrm{The} \\ $$$$\mathrm{enthalpy}\:\mathrm{of}\:\mathrm{isomerisation}\:\mathrm{of}\:\mathrm{cyclopropane} \\ $$$$\mathrm{to}\:\mathrm{propene}\:\mathrm{is}\:−\mathrm{33}\:\mathrm{kJ}\:\mathrm{mol}^{−\mathrm{1}} . \\ $$

Question Number 23856 Answers: 0 Comments: 4

The value of (C_0 + C_1 )(C_1 + C_2 ).... (C_(n−1) + C_n ) is (1) (((n + 1)^n )/(n!)) ∙ C_1 C_2 .....C_n (2) (((n − 1)^n )/(n!)) ∙ C_1 C_2 .....C_n (3) (((n)^n )/((n + 1)!)) ∙ C_1 C_2 .....C_n (4) (((n)^n )/(n!)) ∙ C_1 C_2 .....C_n

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\left({C}_{\mathrm{0}} \:+\:{C}_{\mathrm{1}} \right)\left({C}_{\mathrm{1}} \:+\:{C}_{\mathrm{2}} \right).... \\ $$$$\left({C}_{{n}−\mathrm{1}} \:+\:{C}_{{n}} \right)\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\frac{\left({n}\:+\:\mathrm{1}\right)^{{n}} }{{n}!}\:\centerdot\:{C}_{\mathrm{1}} {C}_{\mathrm{2}} .....{C}_{{n}} \\ $$$$\left(\mathrm{2}\right)\:\frac{\left({n}\:−\:\mathrm{1}\right)^{{n}} }{{n}!}\:\centerdot\:{C}_{\mathrm{1}} {C}_{\mathrm{2}} .....{C}_{{n}} \\ $$$$\left(\mathrm{3}\right)\:\frac{\left({n}\right)^{{n}} }{\left({n}\:+\:\mathrm{1}\right)!}\:\centerdot\:{C}_{\mathrm{1}} {C}_{\mathrm{2}} .....{C}_{{n}} \\ $$$$\left(\mathrm{4}\right)\:\frac{\left({n}\right)^{{n}} }{{n}!}\:\centerdot\:{C}_{\mathrm{1}} {C}_{\mathrm{2}} .....{C}_{{n}} \\ $$

Question Number 23864 Answers: 1 Comments: 0

One mole of steam is condensed at 100°C, the water is cooled to 0°C and frozen to ice. Which of the following statements are correct, given heat of vapourization and fusion are 540 cal/ gm and 80 cal/gm? (average heat capacity of liquid water = 1 cal gm^(−1) degree^(−1) ) (1) Entropy change during the condensation of steam is −26.06 cal/°C (2) Entropy change during cooling of water from 100°C to 0°C is −5.62 cal/°C (3) Entropy change during freezing of water at 0°C is −5.27 cal/°C (4) Total entropy change is −36.95 cal/°C

$$\mathrm{One}\:\mathrm{mole}\:\mathrm{of}\:\mathrm{steam}\:\mathrm{is}\:\mathrm{condensed}\:\mathrm{at} \\ $$$$\mathrm{100}°\mathrm{C},\:\mathrm{the}\:\mathrm{water}\:\mathrm{is}\:\mathrm{cooled}\:\mathrm{to}\:\mathrm{0}°\mathrm{C}\:\mathrm{and} \\ $$$$\mathrm{frozen}\:\mathrm{to}\:\mathrm{ice}.\:\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{statements}\:\mathrm{are}\:\mathrm{correct},\:\mathrm{given}\:\mathrm{heat}\:\mathrm{of} \\ $$$$\mathrm{vapourization}\:\mathrm{and}\:\mathrm{fusion}\:\mathrm{are}\:\mathrm{540}\:\mathrm{cal}/ \\ $$$$\mathrm{gm}\:\mathrm{and}\:\mathrm{80}\:\mathrm{cal}/\mathrm{gm}?\:\left(\mathrm{average}\:\mathrm{heat}\right. \\ $$$$\mathrm{capacity}\:\mathrm{of}\:\mathrm{liquid}\:\mathrm{water}\:=\:\mathrm{1}\:\mathrm{cal}\:\mathrm{gm}^{−\mathrm{1}} \\ $$$$\left.\mathrm{degree}^{−\mathrm{1}} \right) \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Entropy}\:\mathrm{change}\:\mathrm{during}\:\mathrm{the} \\ $$$$\mathrm{condensation}\:\mathrm{of}\:\mathrm{steam}\:\mathrm{is}\:−\mathrm{26}.\mathrm{06}\:\mathrm{cal}/°\mathrm{C} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Entropy}\:\mathrm{change}\:\mathrm{during}\:\mathrm{cooling}\:\mathrm{of} \\ $$$$\mathrm{water}\:\mathrm{from}\:\mathrm{100}°\mathrm{C}\:\mathrm{to}\:\mathrm{0}°\mathrm{C}\:\mathrm{is}\:−\mathrm{5}.\mathrm{62}\:\mathrm{cal}/°\mathrm{C} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Entropy}\:\mathrm{change}\:\mathrm{during}\:\mathrm{freezing}\:\mathrm{of} \\ $$$$\mathrm{water}\:\mathrm{at}\:\mathrm{0}°\mathrm{C}\:\mathrm{is}\:−\mathrm{5}.\mathrm{27}\:\mathrm{cal}/°\mathrm{C} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{Total}\:\mathrm{entropy}\:\mathrm{change}\:\mathrm{is}\:−\mathrm{36}.\mathrm{95} \\ $$$$\mathrm{cal}/°\mathrm{C} \\ $$

Question Number 23851 Answers: 0 Comments: 0

Solve sin(83) − cos(17) in surd form

$$\mathrm{Solve}\:\:\:\:\:\:\mathrm{sin}\left(\mathrm{83}\right)\:−\:\mathrm{cos}\left(\mathrm{17}\right)\:\:\:\:\:\:\mathrm{in}\:\mathrm{surd}\:\mathrm{form} \\ $$

Question Number 23849 Answers: 2 Comments: 0

∫((x^6 +1)/(x^4 +1))dx

$$\int\frac{{x}^{\mathrm{6}} +\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}{dx} \\ $$

Question Number 23833 Answers: 1 Comments: 3

f(x^2 + x) + 2f(x^2 − 3x + 2) = 9x^2 − 15x then what is the value of f(10) ?

$${f}\left({x}^{\mathrm{2}} \:+\:{x}\right)\:+\:\mathrm{2}{f}\left({x}^{\mathrm{2}} \:−\:\mathrm{3}{x}\:+\:\mathrm{2}\right)\:=\:\mathrm{9}{x}^{\mathrm{2}} \:−\:\mathrm{15}{x} \\ $$$$\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{f}\left(\mathrm{10}\right)\:? \\ $$

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