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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.

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

Question Number 24351    Answers: 0   Comments: 0

Question Number 24347    Answers: 0   Comments: 2

Question Number 24352    Answers: 0   Comments: 1

for what value of y will ((x^2 + 4)/(6x − 8)) lies between a positive integer.

$$\mathrm{for}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:\mathrm{will}\:\:\frac{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4}}{\mathrm{6x}\:−\:\mathrm{8}}\:\:\mathrm{lies}\:\mathrm{between}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer}. \\ $$

Question Number 24233    Answers: 2   Comments: 0

if (d^2 y/dx^2 )=ksiny then y=?

$${if}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }={ksiny}\:{then}\:{y}=? \\ $$

Question Number 24227    Answers: 3   Comments: 1

Question Number 24186    Answers: 0   Comments: 4

(n − 1) equal point masses each of mass m are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector a with respect to the centre of the polygon. Find the position vector of centre of mass.

$$\left({n}\:−\:\mathrm{1}\right)\:\mathrm{equal}\:\mathrm{point}\:\mathrm{masses}\:\mathrm{each}\:\mathrm{of}\:\mathrm{mass} \\ $$$${m}\:\mathrm{are}\:\mathrm{placed}\:\mathrm{at}\:\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{a}\:\mathrm{regular} \\ $$$${n}-\mathrm{polygon}.\:\mathrm{The}\:\mathrm{vacant}\:\mathrm{vertex}\:\mathrm{has}\:\mathrm{a} \\ $$$$\mathrm{position}\:\mathrm{vector}\:{a}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{centre}\:\mathrm{of}\:\mathrm{the}\:\mathrm{polygon}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{position} \\ $$$$\mathrm{vector}\:\mathrm{of}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{mass}. \\ $$

Question Number 24184    Answers: 0   Comments: 9

Question Number 24181    Answers: 1   Comments: 0

if the points C(−1,2) divides internally the line segment joining the points A(2,5) and B(x,y) in the ratio 3:4 find the value of x^2 +y^2

$${if}\:{the}\:{points}\:{C}\left(−\mathrm{1},\mathrm{2}\right)\:{divides}\:{internally}\:{the}\:{line}\:{segment}\:{joining}\:{the}\:{points}\:{A}\left(\mathrm{2},\mathrm{5}\right)\:{and}\:{B}\left({x},{y}\right)\:{in}\:{the}\:{ratio}\:\mathrm{3}:\mathrm{4}\:{find}\:{the}\:{value}\:{of}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$

Question Number 24178    Answers: 0   Comments: 6

A block is released from rest at the top of a frictionless incline plane 16.00m long.It reaches the bottom 4.0s later.A second block is projected up the plane from the bottom at the instant the first one is released in such a way that it returns to the bottom simultaneously with the first block.Find: a)the acceleration of each block on the incline plane b)the initial velocity of the first block. c)how far up the incline plane did the second block travel. d)What angle does the plane makes with the horizontal. (g=10m/s^2 )

$${A}\:{block}\:{is}\:{released}\:{from}\:{rest}\:{at}\:{the} \\ $$$${top}\:{of}\:{a}\:{frictionless}\:{incline} \\ $$$${plane}\:\mathrm{16}.\mathrm{00}{m}\:{long}.{It}\:{reaches}\:{the} \\ $$$${bottom}\:\mathrm{4}.\mathrm{0}{s}\:{later}.{A}\:{second}\:{block} \\ $$$${is}\:{projected}\:{up}\:{the}\:{plane}\:{from}\:{the} \\ $$$${bottom}\:{at}\:{the}\:{instant}\:{the}\:{first}\:{one} \\ $$$${is}\:{released}\:{in}\:{such}\:{a}\:{way}\:{that}\:{it} \\ $$$${returns}\:{to}\:{the}\:{bottom}\:{simultaneously} \\ $$$${with}\:{the}\:{first}\:{block}.{Find}: \\ $$$$\left.{a}\right){the}\:{acceleration}\:{of}\:{each}\:{block} \\ $$$${on}\:{the}\:{incline}\:{plane} \\ $$$$\left.{b}\right){the}\:{initial}\:{velocity}\:{of}\:{the}\:{first} \\ $$$${block}. \\ $$$$\left.{c}\right){how}\:{far}\:{up}\:{the}\:{incline}\:{plane} \\ $$$${did}\:{the}\:{second}\:{block}\:{travel}. \\ $$$$\left.{d}\right){What}\:{angle}\:{does}\:{the}\:{plane}\:{makes} \\ $$$${with}\:{the}\:{horizontal}. \\ $$$$\left({g}=\mathrm{10}{m}/{s}^{\mathrm{2}} \right) \\ $$

Question Number 24177    Answers: 2   Comments: 1

A lorry goes round an unbanked curve.If the radius of the curve is 30m and the coefficient of friction between the ground and the tyre is 0.6. Calculate the maximum speed of the lorry. (g=10m/s^2 ) please buddies help

$${A}\:{lorry}\:{goes}\:{round}\:{an}\:{unbanked} \\ $$$${curve}.{If}\:{the}\:{radius}\:{of}\:{the}\:{curve} \\ $$$${is}\:\mathrm{30}{m}\:{and}\:{the}\:{coefficient}\:{of} \\ $$$${friction}\:{between}\:{the}\:{ground}\:{and} \\ $$$${the}\:{tyre}\:{is}\:\mathrm{0}.\mathrm{6}.\:{Calculate}\:{the} \\ $$$${maximum}\:{speed}\:{of}\:{the}\:{lorry}. \\ $$$$\left({g}=\mathrm{10}{m}/{s}^{\mathrm{2}} \right) \\ $$$$ \\ $$$$ \\ $$$${please}\:{buddies}\:{help} \\ $$

Question Number 24172    Answers: 1   Comments: 1

Question Number 24168    Answers: 0   Comments: 4

A plank of mass M kg is sliding on the smooth horizontal surface with constant velocity of 10 ms^(−1) . A another block of mass M kg is gently placed on it. The coefficient of friction between the block and the upper surface of the plank is 0.2. Assuming that plank is long enough such that the block does not fall from it. The velocity-time graph of the block is [Take g = 10 m/s^2 ]

$$\mathrm{A}\:\mathrm{plank}\:\mathrm{of}\:\mathrm{mass}\:{M}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{sliding}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{smooth}\:\mathrm{horizontal}\:\mathrm{surface}\:\mathrm{with}\:\mathrm{constant} \\ $$$$\mathrm{velocity}\:\mathrm{of}\:\mathrm{10}\:\mathrm{ms}^{−\mathrm{1}} .\:\mathrm{A}\:\mathrm{another}\:\mathrm{block}\:\mathrm{of} \\ $$$$\mathrm{mass}\:{M}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{gently}\:\mathrm{placed}\:\mathrm{on}\:\mathrm{it}.\:\mathrm{The} \\ $$$$\mathrm{coefficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{between}\:\mathrm{the} \\ $$$$\mathrm{block}\:\mathrm{and}\:\mathrm{the}\:\mathrm{upper}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plank} \\ $$$$\mathrm{is}\:\mathrm{0}.\mathrm{2}.\:\mathrm{Assuming}\:\mathrm{that}\:\mathrm{plank}\:\mathrm{is}\:\mathrm{long} \\ $$$$\mathrm{enough}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{block}\:\mathrm{does}\:\mathrm{not}\:\mathrm{fall} \\ $$$$\mathrm{from}\:\mathrm{it}.\:\mathrm{The}\:\mathrm{velocity}-\mathrm{time}\:\mathrm{graph}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{block}\:\mathrm{is}\:\left[\mathrm{Take}\:{g}\:=\:\mathrm{10}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} \right] \\ $$

Question Number 24164    Answers: 0   Comments: 1

Five moles of an ideal gas expand isothermally and reversibly from a pressure of 10 atm to 2 atm at 300 K. What is the largest mass (approx) which can be lifted through a height of 1 m in this expansion?

$$\mathrm{Five}\:\mathrm{moles}\:\mathrm{of}\:\mathrm{an}\:\mathrm{ideal}\:\mathrm{gas}\:\mathrm{expand} \\ $$$$\mathrm{isothermally}\:\mathrm{and}\:\mathrm{reversibly}\:\mathrm{from}\:\mathrm{a} \\ $$$$\mathrm{pressure}\:\mathrm{of}\:\mathrm{10}\:\mathrm{atm}\:\mathrm{to}\:\mathrm{2}\:\mathrm{atm}\:\mathrm{at}\:\mathrm{300}\:\mathrm{K}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{mass}\:\left(\mathrm{approx}\right) \\ $$$$\mathrm{which}\:\mathrm{can}\:\mathrm{be}\:\mathrm{lifted}\:\mathrm{through}\:\mathrm{a}\:\mathrm{height}\:\mathrm{of} \\ $$$$\mathrm{1}\:\mathrm{m}\:\mathrm{in}\:\mathrm{this}\:\mathrm{expansion}? \\ $$

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