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Question Number 18847 Answers: 1 Comments: 0

In an equilateral triangle with usual notations the value of ((27r^2 R)/(r_1 r_2 r_3 )) is equal to

$$\mathrm{In}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{usual} \\ $$$$\mathrm{notations}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{27}{r}^{\mathrm{2}} {R}}{{r}_{\mathrm{1}} {r}_{\mathrm{2}} {r}_{\mathrm{3}} }\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 18846 Answers: 0 Comments: 0

There are two crystalline forms of PbO ; one is yellow and the other is red. The standard enthalpies of formation of these two forms are −217.3 and −219 kJ per mole respectively. Calculate the enthalpy change for the solid-solid phase transition. PbO (yellow) → PbO (red)

$$\mathrm{There}\:\mathrm{are}\:\mathrm{two}\:\mathrm{crystalline}\:\mathrm{forms}\:\mathrm{of}\:\mathrm{PbO}\:; \\ $$$$\mathrm{one}\:\mathrm{is}\:\mathrm{yellow}\:\mathrm{and}\:\mathrm{the}\:\mathrm{other}\:\mathrm{is}\:\mathrm{red}.\:\mathrm{The} \\ $$$$\mathrm{standard}\:\mathrm{enthalpies}\:\mathrm{of}\:\mathrm{formation}\:\mathrm{of} \\ $$$$\mathrm{these}\:\mathrm{two}\:\mathrm{forms}\:\mathrm{are}\:−\mathrm{217}.\mathrm{3}\:\mathrm{and}\:−\mathrm{219} \\ $$$$\mathrm{kJ}\:\mathrm{per}\:\mathrm{mole}\:\mathrm{respectively}.\:\mathrm{Calculate}\:\mathrm{the} \\ $$$$\mathrm{enthalpy}\:\mathrm{change}\:\mathrm{for}\:\mathrm{the}\:\mathrm{solid}-\mathrm{solid} \\ $$$$\mathrm{phase}\:\mathrm{transition}. \\ $$$$\mathrm{PbO}\:\left(\mathrm{yellow}\right)\:\rightarrow\:\mathrm{PbO}\:\left(\mathrm{red}\right) \\ $$

Question Number 18885 Answers: 0 Comments: 0

Question Number 18886 Answers: 0 Comments: 0

Question Number 18841 Answers: 1 Comments: 0

Question Number 18830 Answers: 1 Comments: 2

If sin 2x = a find the simplest expression for cos x

$$\mathrm{If}\:\mathrm{sin}\:\mathrm{2}{x}\:=\:{a} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{simplest}\:\mathrm{expression}\:\mathrm{for}\:\mathrm{cos}\:{x} \\ $$

Question Number 18827 Answers: 0 Comments: 3

Question Number 18851 Answers: 0 Comments: 0

Question Number 18823 Answers: 0 Comments: 2

If P≡(2,1) and A and B lie on x−axis and y=x respectively such that PA+PB+AB is minimum find A and B.

$$\mathrm{If}\:\mathrm{P}\equiv\left(\mathrm{2},\mathrm{1}\right)\:\mathrm{and}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{lie}\:\mathrm{on}\:\mathrm{x}−\mathrm{axis} \\ $$$$\mathrm{and}\:\mathrm{y}=\mathrm{x}\:\mathrm{respectively}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{PA}+\mathrm{PB}+\mathrm{AB}\:\mathrm{is}\:\mathrm{minimum}\:\mathrm{find} \\ $$$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}. \\ $$

Question Number 18818 Answers: 2 Comments: 0

Question Number 18808 Answers: 1 Comments: 0

((5+2(√5)))^(1/3) + ((5−2(√5)))^(1/3) =? help me

$$\sqrt[{\mathrm{3}}]{\mathrm{5}+\mathrm{2}\sqrt{\mathrm{5}}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{5}−\mathrm{2}\sqrt{\mathrm{5}}}\:=? \\ $$$$\boldsymbol{{help}}\:\boldsymbol{{me}} \\ $$

Question Number 18801 Answers: 0 Comments: 1

Question Number 18800 Answers: 0 Comments: 0

Solve: x sin(y)dx + x^2 + y cos(y)dy = 0, subject to y(1)

$$\mathrm{Solve}:\:\:\mathrm{x}\:\mathrm{sin}\left(\mathrm{y}\right)\mathrm{dx}\:+\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}\:\mathrm{cos}\left(\mathrm{y}\right)\mathrm{dy}\:=\:\mathrm{0},\:\:\mathrm{subject}\:\mathrm{to}\:\mathrm{y}\left(\mathrm{1}\right) \\ $$

Question Number 18799 Answers: 1 Comments: 0

Question Number 18798 Answers: 1 Comments: 0

Question Number 18797 Answers: 1 Comments: 0

If A, B, C are the angles of a triangle, then 2sin(A/2)cosec(B/2)sin(C/2) − sinAcot(B/2) − cos A is (1) Independent of A, B, C (2) Function of A, B, C (3) Function of A, B (4) Function of B, C

$$\mathrm{If}\:{A},\:{B},\:{C}\:\mathrm{are}\:\mathrm{the}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}, \\ $$$$\mathrm{then}\:\mathrm{2sin}\frac{{A}}{\mathrm{2}}\mathrm{cosec}\frac{{B}}{\mathrm{2}}\mathrm{sin}\frac{{C}}{\mathrm{2}}\:−\:\mathrm{sin}{A}\mathrm{cot}\frac{{B}}{\mathrm{2}} \\ $$$$−\:\mathrm{cos}\:{A}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Independent}\:\mathrm{of}\:{A},\:{B},\:{C} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Function}\:\mathrm{of}\:{A},\:{B},\:{C} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Function}\:\mathrm{of}\:{A},\:{B} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{Function}\:\mathrm{of}\:{B},\:{C} \\ $$

Question Number 18834 Answers: 1 Comments: 0

Question Number 18783 Answers: 1 Comments: 0

∫sin x

$$ \\ $$$$\int\mathrm{sin}\:{x} \\ $$

Question Number 18779 Answers: 0 Comments: 2

If (1/(2x))+(1/2)((1/(2x))+(1/2)((1/(2x))+(1/2)((1/(2x))+......=y what does x equals? a)1/2 b)2/4 c)1 d)1/4

$$\mathrm{If}\:\:\frac{\mathrm{1}}{\mathrm{2x}}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2x}}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2x}}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2x}}+......=\mathrm{y}\right.\right.\right. \\ $$$$\mathrm{what}\:\mathrm{does}\:\mathrm{x}\:\mathrm{equals}? \\ $$$$ \\ $$$$\left.\mathrm{a}\right)\mathrm{1}/\mathrm{2} \\ $$$$\left.\mathrm{b}\right)\mathrm{2}/\mathrm{4} \\ $$$$\left.\mathrm{c}\right)\mathrm{1} \\ $$$$\left.\mathrm{d}\right)\mathrm{1}/\mathrm{4} \\ $$

Question Number 18763 Answers: 0 Comments: 3

Question Number 18762 Answers: 1 Comments: 0

If (1+x)^n =C_0 +C_1 x+C_2 x^2 +...+C_n x^n , then C_1 ^2 +C_2 ^2 +....+C_n ^2 is equal to

$$\mathrm{If}\:\left(\mathrm{1}+{x}\right)^{{n}} ={C}_{\mathrm{0}} +{C}_{\mathrm{1}} {x}+{C}_{\mathrm{2}} {x}^{\mathrm{2}} +...+{C}_{{n}} {x}^{{n}} , \\ $$$$\mathrm{then}\:{C}_{\mathrm{1}} \:^{\mathrm{2}} +{C}_{\mathrm{2}} \:^{\mathrm{2}} +....+{C}_{{n}} \:^{\mathrm{2}} \:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 18761 Answers: 0 Comments: 1

If x ∈ R, then the expression 9^x −3^x +1 assumes

$$\mathrm{If}\:\:{x}\:\in\:{R},\:\:\:\mathrm{then}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{9}^{{x}} −\mathrm{3}^{{x}} +\mathrm{1} \\ $$$$\mathrm{assumes}\: \\ $$

Question Number 18760 Answers: 0 Comments: 1

If the coefficient of x^7 and x^8 in (2+(x/3))^n are equal then r is equal to

$$\mathrm{If}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{\mathrm{7}} \mathrm{and}\:{x}^{\mathrm{8}} \:\mathrm{in}\:\left(\mathrm{2}+\frac{{x}}{\mathrm{3}}\right)^{{n}} \\ $$$$\mathrm{are}\:\mathrm{equal}\:\mathrm{then}\:{r}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 18759 Answers: 2 Comments: 0

The coefficient of the middle term in the expansion of (1+x)^(2n) is

$$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{the}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+{x}\right)^{\mathrm{2}{n}} \:\mathrm{is} \\ $$

Question Number 18758 Answers: 1 Comments: 0

If the coefficient of r^(th) and (r+1)^(th) terms in the expansion of (3+7x)^(29) are equal, then r equals

$$\mathrm{If}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\:{r}^{\mathrm{th}} \:\mathrm{and}\:\left({r}+\mathrm{1}\right)^{\mathrm{th}} \:\mathrm{terms} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{3}+\mathrm{7}{x}\right)^{\mathrm{29}} \:\mathrm{are}\:\mathrm{equal}, \\ $$$$\mathrm{then}\:\:{r}\:\mathrm{equals} \\ $$

Question Number 18757 Answers: 0 Comments: 0

If a_1 , a_2 , a_3 , a_4 are the coefficient of any four four consecutive terms in the expansion of (1+x)^n , then (a_1 /(a_1 +a_2 )) + (a_3 /(a_3 +a_4 )) is equal to

$$\mathrm{If}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:{a}_{\mathrm{3}} ,\:{a}_{\mathrm{4}} \:\mathrm{are}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{any} \\ $$$$\mathrm{four}\:\mathrm{four}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\left(\mathrm{1}+{x}\right)^{{n}} ,\:\mathrm{then}\:\frac{{a}_{\mathrm{1}} }{{a}_{\mathrm{1}} +{a}_{\mathrm{2}} }\:+\:\frac{{a}_{\mathrm{3}} }{{a}_{\mathrm{3}} +{a}_{\mathrm{4}} }\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

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