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Question Number 24417 Answers: 1 Comments: 0

The time taken by a train l metres long running at x km/h to pass a man who is running at y km/h in the direction opposite to that of the train = The time taken to cover l metres at _____ km/h.

$$\mathrm{The}\:\mathrm{time}\:\mathrm{taken}\:\mathrm{by}\:\mathrm{a}\:\mathrm{train}\:{l}\:\mathrm{metres}\:\mathrm{long} \\ $$$$\mathrm{running}\:\mathrm{at}\:{x}\:\mathrm{km}/\mathrm{h}\:\mathrm{to}\:\mathrm{pass}\:\mathrm{a}\:\mathrm{man}\:\mathrm{who} \\ $$$$\mathrm{is}\:\mathrm{running}\:\mathrm{at}\:{y}\:\mathrm{km}/\mathrm{h}\:\mathrm{in}\:\mathrm{the}\:\mathrm{direction} \\ $$$$\mathrm{opposite}\:\mathrm{to}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{train}\:=\:\mathrm{The}\:\mathrm{time} \\ $$$$\mathrm{taken}\:\mathrm{to}\:\mathrm{cover}\:{l}\:\mathrm{metres}\:\mathrm{at}\:\_\_\_\_\_\:\mathrm{km}/\mathrm{h}. \\ $$

Question Number 24438 Answers: 0 Comments: 2

Find the sum to infinite terms of the series (x/(1−x^2 ))+(x^2 /(1−x^4 ))+(x^4 /(1−x^8 ))+......

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{infinite}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{series}\:\frac{{x}}{\mathrm{1}−{x}^{\mathrm{2}} }+\frac{{x}^{\mathrm{2}} }{\mathrm{1}−{x}^{\mathrm{4}} }+\frac{{x}^{\mathrm{4}} }{\mathrm{1}−{x}^{\mathrm{8}} }+...... \\ $$

Question Number 24411 Answers: 1 Comments: 0

Question Number 24405 Answers: 0 Comments: 0

Find the horizontal assymptot lim_(x→∞ ) (((3x^2 +4))^(1/6) /((1−2x^3 ))^(1/9) )

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{horizontal}\:\mathrm{assymptot} \\ $$$$\underset{{x}\rightarrow\infty\:} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{6}}]{\mathrm{3x}^{\mathrm{2}} +\mathrm{4}}}{\sqrt[{\mathrm{9}}]{\mathrm{1}−\mathrm{2x}^{\mathrm{3}} }} \\ $$$$ \\ $$

Question Number 24404 Answers: 0 Comments: 0

put a_n = (1/(2n))∙(3/(2n))∙(5/(2n))∙ ... ∙((2n−1)/(2n))∙e^n lim_(n→∞) a_n = ?

$${put}\:{a}_{{n}} =\:\frac{\mathrm{1}}{\mathrm{2}{n}}\centerdot\frac{\mathrm{3}}{\mathrm{2}{n}}\centerdot\frac{\mathrm{5}}{\mathrm{2}{n}}\centerdot\:...\:\centerdot\frac{\mathrm{2}{n}−\mathrm{1}}{\mathrm{2}{n}}\centerdot{e}^{{n}} \\ $$$$\underset{{n}\rightarrow\infty} {{lim}a}_{{n}} =\:? \\ $$$$ \\ $$

Question Number 24387 Answers: 1 Comments: 0

Two particle move along an x−axis. The position of particle 1 is given; by x=6.00t^2 +3.00t+2.00((m/s)) the acceleration of particle 2 is given by a=−8.00t((m/s^2 )) and,at t=0,its velocity is 20 ((m/s)).when the velocities of the particles match, what is their velocity? plzz help

Question Number 24379 Answers: 2 Comments: 0

Question Number 24371 Answers: 0 Comments: 5

Two blocks are moving together under the action of a constant horizontal external force F. If the smaller block is at rest with respect to the bigger block due to the friction between them, then the normal reaction between the bigger block and floor is

$$\mathrm{Two}\:\mathrm{blocks}\:\mathrm{are}\:\mathrm{moving}\:\mathrm{together}\:\mathrm{under} \\ $$$$\mathrm{the}\:\mathrm{action}\:\mathrm{of}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{horizontal} \\ $$$$\mathrm{external}\:\mathrm{force}\:{F}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{smaller}\:\mathrm{block}\:\mathrm{is} \\ $$$$\mathrm{at}\:\mathrm{rest}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\mathrm{the}\:\mathrm{bigger}\:\mathrm{block} \\ $$$$\mathrm{due}\:\mathrm{to}\:\mathrm{the}\:\mathrm{friction}\:\mathrm{between}\:\mathrm{them},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{normal}\:\mathrm{reaction}\:\mathrm{between}\:\mathrm{the}\:\mathrm{bigger} \\ $$$$\mathrm{block}\:\mathrm{and}\:\mathrm{floor}\:\mathrm{is} \\ $$

Question Number 24369 Answers: 0 Comments: 2

Question Number 24366 Answers: 1 Comments: 1

Given the 7-element set A = {a, b, c, d, e, f, g}, find a collection T of 3- element subsets of A such that each pair of elements from A occurs exactly in one of the subsets of T.

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{7}-\mathrm{element}\:\mathrm{set}\:{A}\:=\:\left\{{a},\:{b},\:{c},\right. \\ $$$$\left.{d},\:{e},\:{f},\:{g}\right\},\:\mathrm{find}\:\mathrm{a}\:\mathrm{collection}\:{T}\:\mathrm{of}\:\mathrm{3}- \\ $$$$\mathrm{element}\:\mathrm{subsets}\:\mathrm{of}\:{A}\:\mathrm{such}\:\mathrm{that}\:\mathrm{each} \\ $$$$\mathrm{pair}\:\mathrm{of}\:\mathrm{elements}\:\mathrm{from}\:{A}\:\mathrm{occurs}\:\mathrm{exactly} \\ $$$$\mathrm{in}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{subsets}\:\mathrm{of}\:{T}. \\ $$

Question Number 24363 Answers: 3 Comments: 0

∫(ae)^x dx

$$\int\left({ae}\right)^{{x}} {dx} \\ $$

Question Number 24360 Answers: 0 Comments: 1

Question Number 24359 Answers: 1 Comments: 1

Question Number 24362 Answers: 0 Comments: 1

if the points P,Q(x,7),R,S(6,y) in this order divide the line segment joining A(2,p) and B(7,10) in 5 equal parts find x,y, and p.

$${if}\:{the}\:{points}\:{P},{Q}\left({x},\mathrm{7}\right),{R},{S}\left(\mathrm{6},{y}\right)\:{in}\:{this}\:{order}\:{divide}\:{the}\:{line}\:{segment}\:{joining}\:{A}\left(\mathrm{2},{p}\right)\:{and}\:{B}\left(\mathrm{7},\mathrm{10}\right)\:{in}\:\mathrm{5}\:{equal}\:{parts}\:{find}\:{x},{y},\:{and}\:{p}. \\ $$

Question Number 24355 Answers: 1 Comments: 0

(√(1+(√(4+(√(16+(√(256.....))))))))=?

$$\sqrt{\mathrm{1}+\sqrt{\mathrm{4}+\sqrt{\mathrm{16}+\sqrt{\mathrm{256}.....}}}}=? \\ $$

Question Number 24332 Answers: 0 Comments: 0

z^(−4_(=1/3(1−(√(3i)))) ) ?

$$\mathrm{z}^{−\mathrm{4}_{=\mathrm{1}/\mathrm{3}\left(\mathrm{1}−\sqrt{\left.\mathrm{3i}\right)}\right.} } ? \\ $$

Question Number 24303 Answers: 1 Comments: 0

Assertion: Enthalpy of combustion is negative. Reason: Combustion reaction can be exothermic or endothermic.

$$\boldsymbol{\mathrm{Assertion}}:\:\mathrm{Enthalpy}\:\mathrm{of}\:\mathrm{combustion}\:\mathrm{is} \\ $$$$\mathrm{negative}. \\ $$$$\boldsymbol{\mathrm{Reason}}:\:\mathrm{Combustion}\:\mathrm{reaction}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{exothermic}\:\mathrm{or}\:\mathrm{endothermic}. \\ $$

Question Number 24301 Answers: 0 Comments: 4

In the figure shown below, all surfaces are smooth, strings and pulley are ideal. If the wedge is moving with acceleration a towards the right, then the acceleration of the block with respect to the wedge at that instant is

$$\mathrm{In}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{shown}\:\mathrm{below},\:\mathrm{all}\:\mathrm{surfaces} \\ $$$$\mathrm{are}\:\mathrm{smooth},\:\mathrm{strings}\:\mathrm{and}\:\mathrm{pulley}\:\mathrm{are}\:\mathrm{ideal}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{wedge}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{acceleration} \\ $$$${a}\:\mathrm{towards}\:\mathrm{the}\:\mathrm{right},\:\mathrm{then}\:\mathrm{the}\:\mathrm{acceleration} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{block}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\mathrm{the}\:\mathrm{wedge} \\ $$$$\mathrm{at}\:\mathrm{that}\:\mathrm{instant}\:\mathrm{is} \\ $$

Question Number 24294 Answers: 1 Comments: 0

Find value(s) of x if sin [2cos^(−1) {cot (2tan^(−1) x)}]=0 .

$${Find}\:{value}\left({s}\right)\:{of}\:\boldsymbol{{x}}\:{if} \\ $$$$\:\:\mathrm{sin}\:\left[\mathrm{2cos}^{−\mathrm{1}} \left\{\mathrm{cot}\:\left(\mathrm{2tan}^{−\mathrm{1}} {x}\right)\right\}\right]=\mathrm{0}\:. \\ $$

Question Number 24293 Answers: 1 Comments: 2

Find the centre of mass of a uniform (a) half-disc, (b) quarter-disc.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{a}\:\mathrm{uniform} \\ $$$$\left({a}\right)\:\mathrm{half}-\mathrm{disc},\:\left({b}\right)\:\mathrm{quarter}-\mathrm{disc}. \\ $$

Question Number 24287 Answers: 0 Comments: 0

In a fuel cell, methanol is used as a fuel and O_2 is used as oxidizer. The standard enthalpy of combustion of methanol is −726 kJ mol^(−1) . The standard free energies of formation of CH_3 OH(l), CO_2 (g) and H_2 O(l) are −166.3, −394.4 and −237.1 kJ mol^(−1) respectively. The standard internal energy change of the cell reaction will be

$$\mathrm{In}\:\mathrm{a}\:\mathrm{fuel}\:\mathrm{cell},\:\mathrm{methanol}\:\mathrm{is}\:\mathrm{used}\:\mathrm{as}\:\mathrm{a}\:\mathrm{fuel} \\ $$$$\mathrm{and}\:\mathrm{O}_{\mathrm{2}} \:\mathrm{is}\:\mathrm{used}\:\mathrm{as}\:\mathrm{oxidizer}.\:\mathrm{The}\:\mathrm{standard} \\ $$$$\mathrm{enthalpy}\:\mathrm{of}\:\mathrm{combustion}\:\mathrm{of}\:\mathrm{methanol}\:\mathrm{is} \\ $$$$−\mathrm{726}\:\mathrm{kJ}\:\mathrm{mol}^{−\mathrm{1}} .\:\mathrm{The}\:\mathrm{standard}\:\mathrm{free} \\ $$$$\mathrm{energies}\:\mathrm{of}\:\mathrm{formation}\:\mathrm{of}\:\mathrm{CH}_{\mathrm{3}} \mathrm{OH}\left(\mathrm{l}\right), \\ $$$$\mathrm{CO}_{\mathrm{2}} \left(\mathrm{g}\right)\:\mathrm{and}\:\mathrm{H}_{\mathrm{2}} \mathrm{O}\left(\mathrm{l}\right)\:\mathrm{are}\:−\mathrm{166}.\mathrm{3},\:−\mathrm{394}.\mathrm{4} \\ $$$$\mathrm{and}\:−\mathrm{237}.\mathrm{1}\:\mathrm{kJ}\:\mathrm{mol}^{−\mathrm{1}} \:\mathrm{respectively}.\:\mathrm{The} \\ $$$$\mathrm{standard}\:\mathrm{internal}\:\mathrm{energy}\:\mathrm{change}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{cell}\:\mathrm{reaction}\:\mathrm{will}\:\mathrm{be} \\ $$

Question Number 24286 Answers: 1 Comments: 0

If ∣x∣ < 1 then (x + 1)(x^2 + 1)(x^4 + 1)(x^8 + 1)(x^(16) + 1)..... is equal to

$$\mathrm{If}\:\mid{x}\mid\:<\:\mathrm{1}\:\mathrm{then} \\ $$$$\left({x}\:+\:\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\left({x}^{\mathrm{4}} \:+\:\mathrm{1}\right)\left({x}^{\mathrm{8}} \:+\:\mathrm{1}\right)\left({x}^{\mathrm{16}} \:+\:\mathrm{1}\right)..... \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 24263 Answers: 0 Comments: 5

The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct? (1) T_1 = T_2 (2) T_3 > T_1 (3) w_(isothermal) > w_(adiabatic) (3) ΔU_(isothermal) > ΔU_(adiabatic)

$$\mathrm{The}\:\mathrm{reversible}\:\mathrm{expansion}\:\mathrm{of}\:\mathrm{an}\:\mathrm{ideal} \\ $$$$\mathrm{gas}\:\mathrm{under}\:\mathrm{adiabatic}\:\mathrm{and}\:\mathrm{isothermal} \\ $$$$\mathrm{conditions}\:\mathrm{is}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{the}\:\mathrm{figure}.\:\mathrm{Which} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{statement}\left(\mathrm{s}\right)\:\mathrm{is}\:\left(\mathrm{are}\right) \\ $$$$\mathrm{correct}? \\ $$$$\left(\mathrm{1}\right)\:\mathrm{T}_{\mathrm{1}} \:=\:\mathrm{T}_{\mathrm{2}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{T}_{\mathrm{3}} \:>\:\mathrm{T}_{\mathrm{1}} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{w}_{\mathrm{isothermal}} \:>\:\mathrm{w}_{\mathrm{adiabatic}} \\ $$$$\left(\mathrm{3}\right)\:\Delta\mathrm{U}_{\mathrm{isothermal}} \:>\:\Delta\mathrm{U}_{\mathrm{adiabatic}} \\ $$

Question Number 24260 Answers: 0 Comments: 3

When a system of forces acts on a body moving in a circular path what happens to the resultant force when: 1)there′s no friction 2)there′s friction

$${When}\:{a}\:{system}\:{of}\:{forces}\:{acts}\:{on} \\ $$$${a}\:{body}\:{moving}\:{in}\:{a}\:{circular}\:{path} \\ $$$${what}\:{happens}\:{to}\:{the}\:{resultant} \\ $$$${force}\:{when}: \\ $$$$\left.\mathrm{1}\right){there}'{s}\:{no}\:{friction} \\ $$$$\left.\mathrm{2}\right){there}'{s}\:{friction} \\ $$$$ \\ $$$$ \\ $$

Question Number 24259 Answers: 0 Comments: 0

Which of the following reaction is/are exothermic reaction/s? (1) CaCO_3 → CaO + CO_2 (2) Fe + S → FeS (3) NaOH + HCl → NaCl + H_2 O (4) CH_4 + O_2 → CO_2 + 2H_2 O.

$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{reaction}\:\mathrm{is}/\mathrm{are} \\ $$$$\mathrm{exothermic}\:\mathrm{reaction}/\mathrm{s}? \\ $$$$\left(\mathrm{1}\right)\:\mathrm{CaCO}_{\mathrm{3}} \:\rightarrow\:\mathrm{CaO}\:+\:\mathrm{CO}_{\mathrm{2}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Fe}\:+\:\mathrm{S}\:\rightarrow\:\mathrm{FeS} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{NaOH}\:+\:\mathrm{HCl}\:\rightarrow\:\mathrm{NaCl}\:+\:\mathrm{H}_{\mathrm{2}} \mathrm{O} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{CH}_{\mathrm{4}} \:+\:\mathrm{O}_{\mathrm{2}} \:\rightarrow\:\mathrm{CO}_{\mathrm{2}} \:+\:\mathrm{2H}_{\mathrm{2}} \mathrm{O}. \\ $$

Question Number 24324 Answers: 0 Comments: 2

Find the minimum possible least common multiple (lcm) of twenty (not necessarily distinct) natural numbers whose sum is 801.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{possible}\:\mathrm{least} \\ $$$$\mathrm{common}\:\mathrm{multiple}\:\left(\mathrm{lcm}\right)\:\mathrm{of}\:\mathrm{twenty}\:\left(\mathrm{not}\right. \\ $$$$\left.\mathrm{necessarily}\:\mathrm{distinct}\right)\:\mathrm{natural}\:\mathrm{numbers} \\ $$$$\mathrm{whose}\:\mathrm{sum}\:\mathrm{is}\:\mathrm{801}. \\ $$

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