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Question Number 23758 Answers: 1 Comments: 0

solve ∫tan^(−1) x ln (1+x^2 )dx

$${solve} \\ $$$$\int\mathrm{tan}^{−\mathrm{1}} {x}\:\mathrm{ln}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 23759 Answers: 0 Comments: 3

Question Number 23831 Answers: 0 Comments: 0

What is the answer for P(z=0.23)?

$${What}\:{is}\:{the}\:{answer}\:{for}\:{P}\left({z}=\mathrm{0}.\mathrm{23}\right)? \\ $$$$ \\ $$$$ \\ $$

Question Number 23830 Answers: 0 Comments: 2

∫sin(101x)sin^(99) xdx

$$\int\mathrm{sin}\left(\mathrm{101x}\right)\mathrm{sin}^{\mathrm{99}} \mathrm{xdx} \\ $$

Question Number 23752 Answers: 1 Comments: 0

∫_1 ^2 x^3 +1=?

$$\int_{\mathrm{1}} ^{\mathrm{2}} {x}^{\mathrm{3}} +\mathrm{1}=? \\ $$

Question Number 23785 Answers: 2 Comments: 0

A function f is define by f : → 3 − 2sinx, for 0 ≤ x ≤ 360 find the range of f

$$\mathrm{A}\:\mathrm{function}\:\mathrm{f}\:\mathrm{is}\:\mathrm{define}\:\mathrm{by}\:\:\mathrm{f}\::\:\rightarrow\:\mathrm{3}\:−\:\mathrm{2sinx},\:\:\mathrm{for}\:\:\mathrm{0}\:\leqslant\:\mathrm{x}\:\leqslant\:\mathrm{360} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\:\mathrm{f} \\ $$

Question Number 23748 Answers: 1 Comments: 1

Question Number 23741 Answers: 1 Comments: 0

(1+i)(2+i)

$$\left(\mathrm{1}+{i}\right)\left(\mathrm{2}+{i}\right) \\ $$

Question Number 23715 Answers: 0 Comments: 0

Why ΔS > 0 for the reaction 2HgO(s) → 2Hg(l) + O_2 (g)?

$$\mathrm{Why}\:\Delta\mathrm{S}\:>\:\mathrm{0}\:\mathrm{for}\:\mathrm{the}\:\mathrm{reaction} \\ $$$$\mathrm{2HgO}\left(\mathrm{s}\right)\:\rightarrow\:\mathrm{2Hg}\left({l}\right)\:+\:\mathrm{O}_{\mathrm{2}} \left(\mathrm{g}\right)? \\ $$

Question Number 23711 Answers: 1 Comments: 0

A certain ideal gas has C_(v, m) = a + bT, where a = 25 J/(mol. K) and b = 0.03 J(mol.K^2 ). Let 2 mole of this gas go from 300 K and 2 litre volume to 600 K and 4 litre. ΔS_(gas) is

$$\mathrm{A}\:\mathrm{certain}\:\mathrm{ideal}\:\mathrm{gas}\:\mathrm{has}\:\mathrm{C}_{\mathrm{v},\:\mathrm{m}} \:=\:\mathrm{a}\:+\:\mathrm{bT}, \\ $$$$\mathrm{where}\:\mathrm{a}\:=\:\mathrm{25}\:\mathrm{J}/\left(\mathrm{mol}.\:\mathrm{K}\right)\:\mathrm{and}\:\mathrm{b}\:=\:\mathrm{0}.\mathrm{03} \\ $$$$\mathrm{J}\left(\mathrm{mol}.\mathrm{K}^{\mathrm{2}} \right).\:\mathrm{Let}\:\mathrm{2}\:\mathrm{mole}\:\mathrm{of}\:\mathrm{this}\:\mathrm{gas}\:\mathrm{go} \\ $$$$\mathrm{from}\:\mathrm{300}\:\mathrm{K}\:\mathrm{and}\:\mathrm{2}\:\mathrm{litre}\:\mathrm{volume}\:\mathrm{to}\:\mathrm{600}\:\mathrm{K} \\ $$$$\mathrm{and}\:\mathrm{4}\:\mathrm{litre}.\:\Delta\mathrm{S}_{\mathrm{gas}} \:\mathrm{is} \\ $$

Question Number 23707 Answers: 1 Comments: 4

Two blocks A and B of mass 1 kg and 2 kg respectively are connected by a string, passing over a light frictionless pulley. Both the blocks are resting on a horizontal floor and the pulley is held such that string remains just taut. At time t = 0, a force F = 20t N, starts acting on the pulley along vertically upward direction. Calculate vertical displacement of the pulley upto the instant when B loses contact with the floor.

$$\mathrm{Two}\:\mathrm{blocks}\:{A}\:\mathrm{and}\:{B}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1}\:\mathrm{kg}\:\mathrm{and} \\ $$$$\mathrm{2}\:\mathrm{kg}\:\mathrm{respectively}\:\mathrm{are}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{a} \\ $$$$\mathrm{string},\:\mathrm{passing}\:\mathrm{over}\:\mathrm{a}\:\mathrm{light}\:\mathrm{frictionless} \\ $$$$\mathrm{pulley}.\:\mathrm{Both}\:\mathrm{the}\:\mathrm{blocks}\:\mathrm{are}\:\mathrm{resting}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{horizontal}\:\mathrm{floor}\:\mathrm{and}\:\mathrm{the}\:\mathrm{pulley}\:\mathrm{is}\:\mathrm{held} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{string}\:\mathrm{remains}\:\mathrm{just}\:\mathrm{taut}.\:\mathrm{At} \\ $$$$\mathrm{time}\:{t}\:=\:\mathrm{0},\:\mathrm{a}\:\mathrm{force}\:{F}\:=\:\mathrm{20}{t}\:\mathrm{N},\:\mathrm{starts} \\ $$$$\mathrm{acting}\:\mathrm{on}\:\mathrm{the}\:\mathrm{pulley}\:\mathrm{along}\:\mathrm{vertically} \\ $$$$\mathrm{upward}\:\mathrm{direction}.\:\mathrm{Calculate}\:\mathrm{vertical} \\ $$$$\mathrm{displacement}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pulley}\:\mathrm{upto}\:\mathrm{the} \\ $$$$\mathrm{instant}\:\mathrm{when}\:{B}\:\mathrm{loses}\:\mathrm{contact}\:\mathrm{with}\:\mathrm{the} \\ $$$$\mathrm{floor}. \\ $$

Question Number 24506 Answers: 0 Comments: 8

A spot light S rotates in a horizontal plane with a constant angular velocity of 0.1 rad/s. The spot of light P moves along the wall at a distance 3 m. What is the velocity of the spot P when θ = 45°?

$$\mathrm{A}\:\mathrm{spot}\:\mathrm{light}\:{S}\:\mathrm{rotates}\:\mathrm{in}\:\mathrm{a}\:\mathrm{horizontal} \\ $$$$\mathrm{plane}\:\mathrm{with}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{angular}\:\mathrm{velocity} \\ $$$$\mathrm{of}\:\mathrm{0}.\mathrm{1}\:\mathrm{rad}/\mathrm{s}.\:\mathrm{The}\:\mathrm{spot}\:\mathrm{of}\:\mathrm{light}\:{P}\:\mathrm{moves} \\ $$$$\mathrm{along}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{3}\:\mathrm{m}.\:\mathrm{What} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{spot}\:{P}\:\mathrm{when}\:\theta\:=\:\mathrm{45}°? \\ $$

Question Number 23700 Answers: 0 Comments: 3

If (1 − x^3 )^n = Σ_(r=0) ^n a_r x^r (1 − x)^(3n−2r) , then the value of a_r , where n ∈ N is (1)^n C_r ∙3^r (2)^n C_(3r) (3)^n C_(r−1) 2^(r−1) (4)^n C_r 2^r

$$\mathrm{If}\:\left(\mathrm{1}\:−\:{x}^{\mathrm{3}} \right)^{{n}} \:=\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}{a}_{{r}} {x}^{{r}} \left(\mathrm{1}\:−\:{x}\right)^{\mathrm{3}{n}−\mathrm{2}{r}} ,\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{a}_{{r}} ,\:\mathrm{where}\:{n}\:\in\:{N}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:^{{n}} {C}_{{r}} \centerdot\mathrm{3}^{{r}} \\ $$$$\left(\mathrm{2}\right)\:^{{n}} {C}_{\mathrm{3}{r}} \\ $$$$\left(\mathrm{3}\right)\:^{{n}} {C}_{{r}−\mathrm{1}} \mathrm{2}^{{r}−\mathrm{1}} \\ $$$$\left(\mathrm{4}\right)\:^{{n}} {C}_{{r}} \mathrm{2}^{{r}} \\ $$

Question Number 23694 Answers: 0 Comments: 0

Calculate the lattice enthalpy of MgBr_2 . Given that Enthalpy of formation of MgBr_2 = −524 kJ mol^(−1) Sublimation energy of Mg = +2187 kJ mol^(−1) Vaporisation energy of Br_2 (l) = +31 kJ mol^(−1) Dissociation energy of Br_2 (g) = +193 kJ mol^(−1) Electron gain enthalpy of Br = −331 kJ mol^(−1)

$${Calculate}\:{the}\:{lattice}\:{enthalpy}\:{of}\:{MgBr}_{\mathrm{2}} . \\ $$$${Given}\:{that} \\ $$$${Enthalpy}\:{of}\:{formation}\:{of}\:{MgBr}_{\mathrm{2}} \:=\:−\mathrm{524} \\ $$$${kJ}\:{mol}^{−\mathrm{1}} \\ $$$${Sublimation}\:{energy}\:{of}\:{Mg}\:=\:+\mathrm{2187} \\ $$$${kJ}\:{mol}^{−\mathrm{1}} \\ $$$${Vaporisation}\:{energy}\:{of}\:{Br}_{\mathrm{2}} \left({l}\right)\:=\:+\mathrm{31} \\ $$$${kJ}\:{mol}^{−\mathrm{1}} \\ $$$${Dissociation}\:{energy}\:{of}\:{Br}_{\mathrm{2}} \left({g}\right)\:=\:+\mathrm{193} \\ $$$${kJ}\:{mol}^{−\mathrm{1}} \\ $$$${Electron}\:{gain}\:{enthalpy}\:{of}\:{Br}\:=\:−\mathrm{331} \\ $$$${kJ}\:{mol}^{−\mathrm{1}} \\ $$

Question Number 23688 Answers: 1 Comments: 0

Question Number 23687 Answers: 1 Comments: 0

Solve for x, y and z x^2 − yz = 1 .......... (i) y^2 − xz = 4 .......... (i) z^2 − xy = 9 .......... (i)

$$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{x},\:\mathrm{y}\:\mathrm{and}\:\mathrm{z} \\ $$$$\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{yz}\:=\:\mathrm{1}\:\:\:\:\:\:..........\:\left(\mathrm{i}\right) \\ $$$$\mathrm{y}^{\mathrm{2}} \:−\:\mathrm{xz}\:=\:\mathrm{4}\:\:\:\:\:\:..........\:\left(\mathrm{i}\right) \\ $$$$\mathrm{z}^{\mathrm{2}} \:−\:\mathrm{xy}\:=\:\mathrm{9}\:\:\:\:\:\:..........\:\left(\mathrm{i}\right) \\ $$

Question Number 23686 Answers: 0 Comments: 0

A function f is defined by f : x → 3 − 2sin(x), for 0 ≤ x ≤ 360° find the range of f

$$\mathrm{A}\:\mathrm{function}\:\:\mathrm{f}\:\:\mathrm{is}\:\mathrm{defined}\:\mathrm{by}\:\:\mathrm{f}\::\:\mathrm{x}\:\rightarrow\:\mathrm{3}\:−\:\mathrm{2sin}\left(\mathrm{x}\right),\:\:\mathrm{for}\:\:\mathrm{0}\:\leqslant\:\mathrm{x}\:\leqslant\:\mathrm{360}° \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\:\mathrm{f} \\ $$

Question Number 23683 Answers: 0 Comments: 0

Question Number 23682 Answers: 0 Comments: 0

Question Number 23679 Answers: 2 Comments: 0

Question Number 23718 Answers: 0 Comments: 1

5(tan^2 x−cos^2 x)=2cosx+a then find then find the value of cos4x.???

$$\mathrm{5}\left(\mathrm{tan}^{\mathrm{2}} {x}−\mathrm{cos}^{\mathrm{2}} {x}\right)=\mathrm{2}{cosx}+{a}\:{then}\:{find} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}\:{cos}\mathrm{4}{x}.??? \\ $$

Question Number 23739 Answers: 0 Comments: 3

Question Number 23666 Answers: 2 Comments: 1

A uniform rope of length L and mass per unit λ having one end fixed with the ceiling is released from rest. Find the tension in the fixed end as a function of the distance travelled by the movable end.

$$\mathrm{A}\:\mathrm{uniform}\:\mathrm{rope}\:\mathrm{of}\:\mathrm{length}\:{L}\:\mathrm{and}\:\mathrm{mass} \\ $$$$\mathrm{per}\:\mathrm{unit}\:\lambda\:\mathrm{having}\:\mathrm{one}\:\mathrm{end}\:\mathrm{fixed}\:\mathrm{with} \\ $$$$\mathrm{the}\:\mathrm{ceiling}\:\mathrm{is}\:\mathrm{released}\:\mathrm{from}\:\mathrm{rest}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{tension}\:\mathrm{in}\:\mathrm{the}\:\mathrm{fixed}\:\mathrm{end}\:\mathrm{as}\:\mathrm{a}\:\mathrm{function} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{travelled}\:\mathrm{by}\:\mathrm{the}\:\mathrm{movable} \\ $$$$\mathrm{end}. \\ $$

Question Number 23677 Answers: 0 Comments: 0

solve lim_(x→inf+) ∫^(2(√x)) _(2sin(1/x)) ((2t^4 +1)/((t−3)(t^3 +3))) dt

$${solve} \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$$$\underset{{x}\rightarrow{inf}+} {\mathrm{li}{m}}\:\:\underset{\mathrm{2}{sin}\frac{\mathrm{1}}{{x}}} {\int}^{\mathrm{2}\sqrt{{x}}} \frac{\mathrm{2}{t}^{\mathrm{4}} +\mathrm{1}}{\left({t}−\mathrm{3}\right)\left({t}^{\mathrm{3}} +\mathrm{3}\right)}\:{dt} \\ $$

Question Number 23663 Answers: 1 Comments: 3

solve ∫^1_ _(−1) x^2 d(lnx)

$${solve} \\ $$$$ \\ $$$$\underset{−\mathrm{1}} {\int}^{\mathrm{1}_{} } {x}^{\mathrm{2}} {d}\left({lnx}\right) \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 23657 Answers: 0 Comments: 1

Mr.Ajfour ,which app do you use for making these diagrams?

$${Mr}.{Ajfour}\:,{which}\:{app}\:{do}\:{you} \\ $$$${use}\:{for}\:{making}\:{these}\:{diagrams}? \\ $$

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