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Question Number 22515 Answers: 0 Comments: 0

In a quadrilateral ABCD, it is given that AB is parallel to CD and the diagonals AC and BD are perpendicular to each other. Show that (a) AD.BC ≥ AB.CD; (b) AD + BC ≥ AB + CD.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{quadrilateral}\:{ABCD},\:\mathrm{it}\:\mathrm{is}\:\mathrm{given} \\ $$$$\mathrm{that}\:{AB}\:\mathrm{is}\:\mathrm{parallel}\:\mathrm{to}\:{CD}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{diagonals}\:{AC}\:\mathrm{and}\:{BD}\:\mathrm{are}\:\mathrm{perpendicular} \\ $$$$\mathrm{to}\:\mathrm{each}\:\mathrm{other}. \\ $$$$\mathrm{Show}\:\mathrm{that} \\ $$$$\left(\mathrm{a}\right)\:{AD}.{BC}\:\geqslant\:{AB}.{CD}; \\ $$$$\left(\mathrm{b}\right)\:{AD}\:+\:{BC}\:\geqslant\:{AB}\:+\:{CD}. \\ $$

Question Number 22503 Answers: 1 Comments: 4

If (a + bx)^(−2) = (1/4) − 3x + ..., then (a, b) =

$$\mathrm{If}\:\left({a}\:+\:{bx}\right)^{−\mathrm{2}} \:=\:\frac{\mathrm{1}}{\mathrm{4}}\:−\:\mathrm{3}{x}\:+\:...,\:\mathrm{then}\:\left({a},\:{b}\right)\:= \\ $$

Question Number 22499 Answers: 1 Comments: 1

A cylinder of weight 200 N is supported on a smooth horizontal plane by a light cord AC and pulled with force of 400 N. The normal reaction at B is equal to

$$\mathrm{A}\:\mathrm{cylinder}\:\mathrm{of}\:\mathrm{weight}\:\mathrm{200}\:\mathrm{N}\:\mathrm{is}\:\mathrm{supported} \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{smooth}\:\mathrm{horizontal}\:\mathrm{plane}\:\mathrm{by}\:\mathrm{a}\:\mathrm{light} \\ $$$$\mathrm{cord}\:{AC}\:\mathrm{and}\:\mathrm{pulled}\:\mathrm{with}\:\mathrm{force}\:\mathrm{of}\:\mathrm{400}\:\mathrm{N}. \\ $$$$\mathrm{The}\:\mathrm{normal}\:\mathrm{reaction}\:\mathrm{at}\:{B}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 22492 Answers: 1 Comments: 1

A ball of mass 400 g travels horizontally along the ground and collides with a wall. The velocity-time graph below represents the motion of the ball for the first 1.2 seconds. The magnitude of average force between the ball and the wall is

$$\mathrm{A}\:\mathrm{ball}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{400}\:\mathrm{g}\:\mathrm{travels}\:\mathrm{horizontally} \\ $$$$\mathrm{along}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{and}\:\mathrm{collides}\:\mathrm{with}\:\mathrm{a} \\ $$$$\mathrm{wall}.\:\mathrm{The}\:\mathrm{velocity}-\mathrm{time}\:\mathrm{graph}\:\mathrm{below} \\ $$$$\mathrm{represents}\:\mathrm{the}\:\mathrm{motion}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{first}\:\mathrm{1}.\mathrm{2}\:\mathrm{seconds}. \\ $$$$\mathrm{The}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{average}\:\mathrm{force}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{ball}\:\mathrm{and}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{is} \\ $$

Question Number 22491 Answers: 1 Comments: 0

The coefficient of x^r in the expansion of (1 − 2x)^(−1/2) is (1) (((2r)!)/((r!)^2 )) (2) (((2r)!)/(2^r (r!)^2 )) (3) (((2r)!)/((r!)^2 2^(2r) )) (4) (((2r)!)/(2^r (r + 1)!(r − 1)!))

$$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{{r}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\mathrm{1}\:−\:\mathrm{2}{x}\right)^{−\mathrm{1}/\mathrm{2}} \:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\frac{\left(\mathrm{2}{r}\right)!}{\left({r}!\right)^{\mathrm{2}} } \\ $$$$\left(\mathrm{2}\right)\:\frac{\left(\mathrm{2}{r}\right)!}{\mathrm{2}^{{r}} \:\left({r}!\right)^{\mathrm{2}} } \\ $$$$\left(\mathrm{3}\right)\:\frac{\left(\mathrm{2}{r}\right)!}{\left({r}!\right)^{\mathrm{2}} \:\mathrm{2}^{\mathrm{2}{r}} } \\ $$$$\left(\mathrm{4}\right)\:\frac{\left(\mathrm{2}{r}\right)!}{\mathrm{2}^{{r}} \:\left({r}\:+\:\mathrm{1}\right)!\left({r}\:−\:\mathrm{1}\right)!} \\ $$

Question Number 22487 Answers: 1 Comments: 1

Question Number 22483 Answers: 0 Comments: 0

Predict the density of Cs from the density of the following elements K 0.86 g/cm^3 Ca 1.548 g/cm^3 Sc 2.991 g/cm^3 Rb 1.532 g/cm^3 Sr 2.68 g/cm^3 Y 4.34 g/cm^3 Cs ? Ba 3.51 g/cm^3 La 6.16 g/cm^3

$$\mathrm{Predict}\:\mathrm{the}\:\mathrm{density}\:\mathrm{of}\:\mathrm{Cs}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{density}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{elements} \\ $$$$\mathrm{K}\:\mathrm{0}.\mathrm{86}\:\mathrm{g}/\mathrm{cm}^{\mathrm{3}} \:\:\:\:\:\:\:\:\mathrm{Ca}\:\mathrm{1}.\mathrm{548}\:\mathrm{g}/\mathrm{cm}^{\mathrm{3}} \\ $$$$\mathrm{Sc}\:\mathrm{2}.\mathrm{991}\:\mathrm{g}/\mathrm{cm}^{\mathrm{3}} \:\:\:\:\:\mathrm{Rb}\:\mathrm{1}.\mathrm{532}\:\mathrm{g}/\mathrm{cm}^{\mathrm{3}} \\ $$$$\mathrm{Sr}\:\mathrm{2}.\mathrm{68}\:\mathrm{g}/\mathrm{cm}^{\mathrm{3}} \:\:\:\:\:\:\:\:\mathrm{Y}\:\mathrm{4}.\mathrm{34}\:\mathrm{g}/\mathrm{cm}^{\mathrm{3}} \\ $$$$\mathrm{Cs}\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Ba}\:\mathrm{3}.\mathrm{51}\:\mathrm{g}/\mathrm{cm}^{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{La}\:\mathrm{6}.\mathrm{16}\:\mathrm{g}/\mathrm{cm}^{\mathrm{3}} \\ $$

Question Number 22481 Answers: 1 Comments: 1

Question Number 22479 Answers: 0 Comments: 2

A ladder of mass m is leaning against a wall. It is in static equilibrium making an angle θ with the horizontal floor. The coefficient of friction between the wall and the ladder is μ_1 and that between the floor and the ladder is μ_2 . The normal reaction of the wall on the ladder is N_1 and that of the floor is N_2 . If the ladder is about to slip, then (1) μ_1 = 0, μ_2 ≠ 0 and N_2 tan θ = mg/2 (2) μ_1 ≠ 0, μ_2 = 0 and N_1 tan θ = mg/2 (3) μ_1 ≠ 0, μ_2 ≠ 0 and N_2 = ((mg)/(1 + μ_1 μ_2 )) (4) μ_1 = 0, μ_2 ≠ 0 and N_1 tan θ = ((mg)/2)

$$\mathrm{A}\:\mathrm{ladder}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{is}\:\mathrm{leaning}\:\mathrm{against}\:\mathrm{a} \\ $$$$\mathrm{wall}.\:\mathrm{It}\:\mathrm{is}\:\mathrm{in}\:\mathrm{static}\:\mathrm{equilibrium}\:\mathrm{making} \\ $$$$\mathrm{an}\:\mathrm{angle}\:\theta\:\mathrm{with}\:\mathrm{the}\:\mathrm{horizontal}\:\mathrm{floor}. \\ $$$$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{between}\:\mathrm{the} \\ $$$$\mathrm{wall}\:\mathrm{and}\:\mathrm{the}\:\mathrm{ladder}\:\mathrm{is}\:\mu_{\mathrm{1}} \:\mathrm{and}\:\mathrm{that} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{floor}\:\mathrm{and}\:\mathrm{the}\:\mathrm{ladder}\:\mathrm{is}\:\mu_{\mathrm{2}} . \\ $$$$\mathrm{The}\:\mathrm{normal}\:\mathrm{reaction}\:\mathrm{of}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{ladder}\:\mathrm{is}\:\mathrm{N}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{floor}\:\mathrm{is}\:\mathrm{N}_{\mathrm{2}} . \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{ladder}\:\mathrm{is}\:\mathrm{about}\:\mathrm{to}\:\mathrm{slip},\:\mathrm{then} \\ $$$$\left(\mathrm{1}\right)\:\mu_{\mathrm{1}} \:=\:\mathrm{0},\:\mu_{\mathrm{2}} \:\neq\:\mathrm{0}\:\mathrm{and}\:{N}_{\mathrm{2}} \:\mathrm{tan}\:\theta\:=\:{mg}/\mathrm{2} \\ $$$$\left(\mathrm{2}\right)\:\mu_{\mathrm{1}} \:\neq\:\mathrm{0},\:\mu_{\mathrm{2}} \:=\:\mathrm{0}\:\mathrm{and}\:{N}_{\mathrm{1}} \:\mathrm{tan}\:\theta\:=\:{mg}/\mathrm{2} \\ $$$$\left(\mathrm{3}\right)\:\mu_{\mathrm{1}} \:\neq\:\mathrm{0},\:\mu_{\mathrm{2}} \:\neq\:\mathrm{0}\:\mathrm{and}\:{N}_{\mathrm{2}} \:=\:\frac{{mg}}{\mathrm{1}\:+\:\mu_{\mathrm{1}} \mu_{\mathrm{2}} } \\ $$$$\left(\mathrm{4}\right)\:\mu_{\mathrm{1}} \:=\:\mathrm{0},\:\mu_{\mathrm{2}} \:\neq\:\mathrm{0}\:\mathrm{and}\:{N}_{\mathrm{1}} \:\mathrm{tan}\:\theta\:=\:\frac{{mg}}{\mathrm{2}} \\ $$

Question Number 22478 Answers: 0 Comments: 1

{ ((x+y^2 +z^3 =3)),((y+z^2 +x^3 =3)),((z+x^2 +z^3 =3)) :} trouver les solutions positives

$$\begin{cases}{{x}+{y}^{\mathrm{2}} +{z}^{\mathrm{3}} =\mathrm{3}}\\{{y}+{z}^{\mathrm{2}} +{x}^{\mathrm{3}} =\mathrm{3}}\\{{z}+{x}^{\mathrm{2}} +{z}^{\mathrm{3}} =\mathrm{3}}\end{cases} \\ $$$${trouver}\:{les}\:{solutions}\:{positives} \\ $$$$ \\ $$

Question Number 22696 Answers: 1 Comments: 5

A force F^→ = 2xj^∧ newton acts in a region where a particle moves anticlockwise in a square loop of 2 m in x-y plane. Calculate the total amount of work done. Is this force a conservative force or a non-conservative force?

$$\mathrm{A}\:\mathrm{force}\:\overset{\rightarrow} {{F}}\:=\:\mathrm{2}{x}\overset{\wedge} {{j}}\:\mathrm{newton}\:\mathrm{acts}\:\mathrm{in}\:\mathrm{a}\:\mathrm{region} \\ $$$$\mathrm{where}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{anticlockwise} \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{square}\:\mathrm{loop}\:\mathrm{of}\:\mathrm{2}\:\mathrm{m}\:\mathrm{in}\:{x}-{y}\:\mathrm{plane}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{total}\:\mathrm{amount}\:\mathrm{of}\:\mathrm{work} \\ $$$$\mathrm{done}.\:\mathrm{Is}\:\mathrm{this}\:\mathrm{force}\:\mathrm{a}\:\mathrm{conservative}\:\mathrm{force} \\ $$$$\mathrm{or}\:\mathrm{a}\:\mathrm{non}-\mathrm{conservative}\:\mathrm{force}? \\ $$

Question Number 22475 Answers: 0 Comments: 1

Question Number 22474 Answers: 0 Comments: 0

Let R = (5(√5) + 11)^(2n+1) and f = R − [R], then prove that Rf = 4^(2n+1) .

$$\mathrm{Let}\:{R}\:=\:\left(\mathrm{5}\sqrt{\mathrm{5}}\:+\:\mathrm{11}\right)^{\mathrm{2}{n}+\mathrm{1}} \:\mathrm{and}\:{f}\:=\:{R}\:−\:\left[{R}\right], \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:{Rf}\:=\:\mathrm{4}^{\mathrm{2}{n}+\mathrm{1}} . \\ $$

Question Number 22473 Answers: 0 Comments: 1

Question Number 22472 Answers: 0 Comments: 0

If x^x ∙y^y ∙z^z = x^y ∙y^z ∙z^x = x^z ∙y^x ∙z^y such that x, y and z are positive integers greater than 1, then which of the following cannot be true for any of the possible value of x, y and z? (1) xyz = 27 (2) xyz = 1728 (3) x + y + z = 32 (4) x + y + z = 12

$$\mathrm{If}\:{x}^{{x}} \centerdot{y}^{{y}} \centerdot{z}^{{z}} \:=\:{x}^{{y}} \centerdot{y}^{{z}} \centerdot{z}^{{x}} \:=\:{x}^{{z}} \centerdot{y}^{{x}} \centerdot{z}^{{y}} \:\mathrm{such} \\ $$$$\mathrm{that}\:{x},\:{y}\:\mathrm{and}\:{z}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\mathrm{greater}\:\mathrm{than}\:\mathrm{1},\:\mathrm{then}\:\mathrm{which}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{following}\:\mathrm{cannot}\:\mathrm{be}\:\mathrm{true}\:\mathrm{for}\:\mathrm{any}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:{x},\:{y}\:\mathrm{and}\:{z}? \\ $$$$\left(\mathrm{1}\right)\:{xyz}\:=\:\mathrm{27} \\ $$$$\left(\mathrm{2}\right)\:{xyz}\:=\:\mathrm{1728} \\ $$$$\left(\mathrm{3}\right)\:{x}\:+\:{y}\:+\:{z}\:=\:\mathrm{32} \\ $$$$\left(\mathrm{4}\right)\:{x}\:+\:{y}\:+\:{z}\:=\:\mathrm{12} \\ $$

Question Number 22470 Answers: 0 Comments: 0

If f(x)= determinant ((1,x,(x+1)),((2x),(x(x−1)),((x+1)x)),((3x(x−1)),(2(x−1)(x−2)),((x+1) x(x−1)))), then f(100) is equal to

$$\mathrm{If}\:{f}\left({x}\right)= \\ $$$$\begin{vmatrix}{\mathrm{1}}&{{x}}&{{x}+\mathrm{1}}\\{\mathrm{2}{x}}&{{x}\left({x}−\mathrm{1}\right)}&{\left({x}+\mathrm{1}\right){x}}\\{\mathrm{3}{x}\left({x}−\mathrm{1}\right)}&{\mathrm{2}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)}&{\left({x}+\mathrm{1}\right)\:{x}\left({x}−\mathrm{1}\right)}\end{vmatrix}, \\ $$$$\mathrm{then}\:{f}\left(\mathrm{100}\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 22468 Answers: 0 Comments: 0

If a_r is the coefficient of x^r in the expansion (1 + x + x^2 )^n , then a_1 − 2a_2 + 3a_3 − ....... 2na_(2n) =

$$\mathrm{If}\:{a}_{{r}} \:\mathrm{is}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{{r}} \:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\left(\mathrm{1}\:+\:{x}\:+\:{x}^{\mathrm{2}} \right)^{{n}} ,\:\mathrm{then} \\ $$$${a}_{\mathrm{1}} \:−\:\mathrm{2}{a}_{\mathrm{2}} \:+\:\mathrm{3}{a}_{\mathrm{3}} \:−\:.......\:\mathrm{2}{na}_{\mathrm{2}{n}} \:= \\ $$

Question Number 22463 Answers: 1 Comments: 0

Solve for real x: (1/([x])) + (1/([2x])) = (x) + (1/3), where [x] is the greatest integer less than or equal to x and (x) = x − [x], [e.g. [3.4] = 3 and (3.4) = 0.4].

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:{x}: \\ $$$$\frac{\mathrm{1}}{\left[{x}\right]}\:+\:\frac{\mathrm{1}}{\left[\mathrm{2}{x}\right]}\:=\:\left({x}\right)\:+\:\frac{\mathrm{1}}{\mathrm{3}}, \\ $$$$\mathrm{where}\:\left[{x}\right]\:\mathrm{is}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{less} \\ $$$$\mathrm{than}\:\mathrm{or}\:\mathrm{equal}\:\mathrm{to}\:{x}\:\mathrm{and}\:\left({x}\right)\:=\:{x}\:−\:\left[{x}\right], \\ $$$$\left[\mathrm{e}.\mathrm{g}.\:\left[\mathrm{3}.\mathrm{4}\right]\:=\:\mathrm{3}\:\mathrm{and}\:\left(\mathrm{3}.\mathrm{4}\right)\:=\:\mathrm{0}.\mathrm{4}\right]. \\ $$

Question Number 22457 Answers: 0 Comments: 1

Prove the inequality cos (sin x) > sin (cos x) .

$${Prove}\:{the}\:{inequality} \\ $$$$\:\:\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)\:>\:\mathrm{sin}\:\left(\mathrm{cos}\:{x}\right)\:. \\ $$

Question Number 22456 Answers: 1 Comments: 0

A long plank begins to move at t = 0 and accelerates along a straight track with a speed given by v = 2t^2 for 0 ≤ t ≤ 2. After 2 s, the plank continues to move at the constant speed acquired. A small block initially at rest on the plank begins to slip at t = 1 s and stops sliding at t = 3 s. Find the coefficient of static and kinetic friction between the block and the plank.

$$\mathrm{A}\:\mathrm{long}\:\mathrm{plank}\:\mathrm{begins}\:\mathrm{to}\:\mathrm{move}\:\mathrm{at}\:{t}\:=\:\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{accelerates}\:\mathrm{along}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{track} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{speed}\:\mathrm{given}\:\mathrm{by}\:{v}\:=\:\mathrm{2}{t}^{\mathrm{2}} \:\mathrm{for}\:\mathrm{0}\:\leqslant\:{t} \\ $$$$\leqslant\:\mathrm{2}.\:\mathrm{After}\:\mathrm{2}\:\mathrm{s},\:\mathrm{the}\:\mathrm{plank}\:\mathrm{continues}\:\mathrm{to} \\ $$$$\mathrm{move}\:\mathrm{at}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{speed}\:\mathrm{acquired}. \\ $$$$\mathrm{A}\:\mathrm{small}\:\mathrm{block}\:\mathrm{initially}\:\mathrm{at}\:\mathrm{rest}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{plank}\:\mathrm{begins}\:\mathrm{to}\:\mathrm{slip}\:\mathrm{at}\:{t}\:=\:\mathrm{1}\:\mathrm{s}\:\mathrm{and}\:\mathrm{stops} \\ $$$$\mathrm{sliding}\:\mathrm{at}\:{t}\:=\:\mathrm{3}\:\mathrm{s}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of} \\ $$$$\mathrm{static}\:\mathrm{and}\:\mathrm{kinetic}\:\mathrm{friction}\:\mathrm{between}\:\mathrm{the} \\ $$$$\mathrm{block}\:\mathrm{and}\:\mathrm{the}\:\mathrm{plank}. \\ $$

Question Number 29184 Answers: 1 Comments: 0

{ (((√(x^2 −4xy))+(√(y^2 +2xy+9))=10)),((x−y=7)) :} How many real roots of the equtions system?

$$\begin{cases}{\sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{\mathrm{xy}}}+\sqrt{\boldsymbol{\mathrm{y}}^{\mathrm{2}} +\mathrm{2}\boldsymbol{\mathrm{xy}}+\mathrm{9}}=\mathrm{10}}\\{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{y}}=\mathrm{7}}\end{cases} \\ $$$$\boldsymbol{\mathrm{How}}\:\boldsymbol{\mathrm{many}}\:\:\boldsymbol{\mathrm{real}}\:\boldsymbol{\mathrm{roots}}\:\boldsymbol{\mathrm{of}}\: \\ $$$$\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{equtions}}\:\boldsymbol{\mathrm{system}}? \\ $$

Question Number 22447 Answers: 1 Comments: 0

The standard heats of formation of at 298 K for CCl_4 (g), H_2 O(g), CO_2 (g) and HCl(g) are −25.5, −57.8, −94.1 and −22.1 kcal mol^(−1) respectively. Calculate Δ_r H^⊝ for the reaction CCl_4 (g) + 2H_2 O(g) → CO_2 (g) + 4HCl(g)

Question Number 22446 Answers: 0 Comments: 0

Select the species which has the smallest radius stating appropriate reason. K^+ , Sr^(2+) , Ar

$$\mathrm{Select}\:\mathrm{the}\:\mathrm{species}\:\mathrm{which}\:\mathrm{has}\:\mathrm{the}\:\mathrm{smallest} \\ $$$$\mathrm{radius}\:\mathrm{stating}\:\mathrm{appropriate}\:\mathrm{reason}. \\ $$$$\mathrm{K}^{+} ,\:\mathrm{Sr}^{\mathrm{2}+} ,\:\mathrm{Ar} \\ $$

Question Number 22437 Answers: 0 Comments: 11

A cubical block is held stationary against a rough wall by applying force ′F′ then incorrect statement among the following is (1) frictional force, f = Mg (2) f = N, N is normal reaction (3) F does not apply any torque (4) N does not apply any torque

$$\mathrm{A}\:\mathrm{cubical}\:\mathrm{block}\:\mathrm{is}\:\mathrm{held}\:\mathrm{stationary} \\ $$$$\mathrm{against}\:\mathrm{a}\:\mathrm{rough}\:\mathrm{wall}\:\mathrm{by}\:\mathrm{applying}\:\mathrm{force} \\ $$$$'\mathrm{F}'\:\mathrm{then}\:\boldsymbol{{incorrect}}\:\mathrm{statement}\:\mathrm{among} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{frictional}\:\mathrm{force},\:\mathrm{f}\:=\:\mathrm{Mg} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{f}\:=\:\mathrm{N},\:\mathrm{N}\:\mathrm{is}\:\mathrm{normal}\:\mathrm{reaction} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{F}\:\mathrm{does}\:\mathrm{not}\:\mathrm{apply}\:\mathrm{any}\:\mathrm{torque} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{N}\:\mathrm{does}\:\mathrm{not}\:\mathrm{apply}\:\mathrm{any}\:\mathrm{torque} \\ $$

Question Number 22435 Answers: 0 Comments: 0

C_0 ^(2n) C_n −C_1 ^(2n−2) C_n +C_2 ^(2n−4) C_n .... equals to

$${C}_{\mathrm{0}} \:^{\mathrm{2}{n}} {C}_{{n}} −{C}_{\mathrm{1}} \:^{\mathrm{2}{n}−\mathrm{2}} {C}_{{n}} +{C}_{\mathrm{2}} \:^{\mathrm{2}{n}−\mathrm{4}} {C}_{{n}} \:.... \\ $$$$\mathrm{equals}\:\mathrm{to} \\ $$

Question Number 22434 Answers: 1 Comments: 0

Im(2z+1)/(iz−1)=2

$$\boldsymbol{\mathrm{I}}\mathrm{m}\left(\mathrm{2z}+\mathrm{1}\right)/\left(\mathrm{iz}−\mathrm{1}\right)=\mathrm{2} \\ $$

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