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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.

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

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

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

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