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Question Number 23000 Answers: 0 Comments: 0

Let n be a positive integer and p_1 , p_2 , ..., p_n be n prime numbers all larger than 5 such that 6 divides p_1 ^2 + p_2 ^2 + ... + p_n ^2 . Prove that 6 divides n.

$$\mathrm{Let}\:{n}\:\mathrm{be}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{and}\:{p}_{\mathrm{1}} ,\:{p}_{\mathrm{2}} , \\ $$$$...,\:{p}_{{n}} \:\mathrm{be}\:{n}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{all}\:\mathrm{larger} \\ $$$$\mathrm{than}\:\mathrm{5}\:\mathrm{such}\:\mathrm{that}\:\mathrm{6}\:\mathrm{divides}\:{p}_{\mathrm{1}} ^{\mathrm{2}} \:+\:{p}_{\mathrm{2}} ^{\mathrm{2}} \:+\:...\:+ \\ $$$${p}_{{n}} ^{\mathrm{2}} .\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{6}\:\mathrm{divides}\:{n}. \\ $$

Question Number 22999 Answers: 0 Comments: 0

ΔH_f ^o of N_2 O is 82 kJ/mol and bond energy for N_2 , N = N, O = O and N = O bonds are 946, 418, 498 and 607 kJ/mol respectively, then resonance energy of N_2 O is

$$\Delta\mathrm{H}_{\mathrm{f}} ^{\mathrm{o}} \:\mathrm{of}\:\mathrm{N}_{\mathrm{2}} \mathrm{O}\:\mathrm{is}\:\mathrm{82}\:\mathrm{kJ}/\mathrm{mol}\:\mathrm{and}\:\mathrm{bond} \\ $$$$\mathrm{energy}\:\mathrm{for}\:\mathrm{N}_{\mathrm{2}} ,\:\mathrm{N}\:=\:\mathrm{N},\:\mathrm{O}\:=\:\mathrm{O}\:\mathrm{and}\:\mathrm{N}\:=\:\mathrm{O} \\ $$$$\mathrm{bonds}\:\mathrm{are}\:\mathrm{946},\:\mathrm{418},\:\mathrm{498}\:\mathrm{and}\:\mathrm{607}\:\mathrm{kJ}/\mathrm{mol} \\ $$$$\mathrm{respectively},\:\mathrm{then}\:\mathrm{resonance}\:\mathrm{energy}\:\mathrm{of} \\ $$$$\mathrm{N}_{\mathrm{2}} \mathrm{O}\:\mathrm{is} \\ $$

Question Number 22990 Answers: 1 Comments: 0

A train weighing 100 metric ton is running on a level track with a uniform speed of 72 km h^(−1) . If the frictional resistance amounts to 0.5 kg per metric ton, find the power of the engine.

$$\mathrm{A}\:\mathrm{train}\:\mathrm{weighing}\:\mathrm{100}\:\mathrm{metric}\:\mathrm{ton}\:\mathrm{is} \\ $$$$\mathrm{running}\:\mathrm{on}\:\mathrm{a}\:\mathrm{level}\:\mathrm{track}\:\mathrm{with}\:\mathrm{a}\:\mathrm{uniform} \\ $$$$\mathrm{speed}\:\mathrm{of}\:\mathrm{72}\:\mathrm{km}\:\mathrm{h}^{−\mathrm{1}} .\:\mathrm{If}\:\mathrm{the}\:\mathrm{frictional} \\ $$$$\mathrm{resistance}\:\mathrm{amounts}\:\mathrm{to}\:\mathrm{0}.\mathrm{5}\:\mathrm{kg}\:\mathrm{per}\:\mathrm{metric} \\ $$$$\mathrm{ton},\:\mathrm{find}\:\mathrm{the}\:\mathrm{power}\:\mathrm{of}\:\mathrm{the}\:\mathrm{engine}. \\ $$

Question Number 22975 Answers: 0 Comments: 5

Question Number 22972 Answers: 0 Comments: 0

Can anyone please solve question number 22956

$${Can}\:{anyone}\:{please}\:{solve}\:{question} \\ $$$${number}\:\mathrm{22956} \\ $$

Question Number 22993 Answers: 2 Comments: 0

For which of the following, the hydration energy of Mg^(2+) is larger? (1) Na^+ (2) Al^(3+) (3) Be^(2+) (4) Cr^(3+) .

$$\mathrm{For}\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following},\:\mathrm{the} \\ $$$$\mathrm{hydration}\:\mathrm{energy}\:\mathrm{of}\:\mathrm{Mg}^{\mathrm{2}+} \:\mathrm{is}\:\mathrm{larger}? \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Na}^{+} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Al}^{\mathrm{3}+} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Be}^{\mathrm{2}+} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{Cr}^{\mathrm{3}+} . \\ $$

Question Number 22968 Answers: 0 Comments: 2

Question Number 22959 Answers: 0 Comments: 0

Question Number 22947 Answers: 0 Comments: 0

lim_(x→π/2) (1^(sec^2 x) +2^(sec^2 x) +3^(sec^2 x) +.... ...+n^(sec^2 x) )^(cos^2 x) = ?

$$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\left(\mathrm{1}^{\mathrm{sec}\:^{\mathrm{2}} {x}} +\mathrm{2}^{\mathrm{sec}\:^{\mathrm{2}} {x}} +\mathrm{3}^{\mathrm{sec}\:^{\mathrm{2}} {x}} +....\right. \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...+{n}^{\mathrm{sec}\:^{\mathrm{2}} {x}} \right)^{\mathrm{cos}\:^{\mathrm{2}} {x}} \:=\:? \\ $$$$ \\ $$

Question Number 22946 Answers: 2 Comments: 0

∫_1 ^3 ((4x+1)/(2x^2 +x−2))dx ?solve

$$\underset{\mathrm{1}} {\overset{\mathrm{3}} {\int}}\frac{\mathrm{4}\boldsymbol{\mathrm{x}}+\mathrm{1}}{\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}−\mathrm{2}}\boldsymbol{\mathrm{dx}}\:\:\:?\boldsymbol{\mathrm{solve}} \\ $$

Question Number 22945 Answers: 0 Comments: 0

Question Number 22940 Answers: 0 Comments: 1

Question Number 22939 Answers: 1 Comments: 0

Question Number 22937 Answers: 0 Comments: 0

Question Number 22930 Answers: 1 Comments: 0

Question Number 22929 Answers: 1 Comments: 0

Question Number 22928 Answers: 1 Comments: 0

Question Number 22956 Answers: 1 Comments: 4

Question Number 22923 Answers: 1 Comments: 0

Question Number 22922 Answers: 0 Comments: 0

Question Number 22896 Answers: 0 Comments: 1

how can demonstred 17^(4n+1) +3×9^(2n+1) ≡0[11]

$${how}\:{can}\:{demonstred} \\ $$$$\mathrm{17}^{\mathrm{4}{n}+\mathrm{1}} +\mathrm{3}×\mathrm{9}^{\mathrm{2}{n}+\mathrm{1}} \equiv\mathrm{0}\left[\mathrm{11}\right] \\ $$

Question Number 22941 Answers: 1 Comments: 3

Question Number 22893 Answers: 1 Comments: 0

A wedge has two equally rough faces each inclined at 30° to the horizontal.Masses of 5kg and 2kg ,one on each face,are connected by a light string passing over a smooth pulley at the top of the wedge.The coefficient of friction μ, between each masses and the surface of the wedge is 0.2.Find the acceleration of the masses when they are released.

$${A}\:{wedge}\:{has}\:{two}\:{equally}\:{rough} \\ $$$${faces}\:{each}\:{inclined}\:{at}\:\mathrm{30}°\:{to}\:{the} \\ $$$${horizontal}.{Masses}\:{of}\:\mathrm{5}{kg}\:{and}\:\mathrm{2}{kg} \\ $$$$,{one}\:{on}\:{each}\:{face},{are}\:{connected} \\ $$$${by}\:{a}\:{light}\:{string}\:{passing}\:{over}\:{a} \\ $$$${smooth}\:{pulley}\:{at}\:{the}\:{top}\:{of}\:{the} \\ $$$${wedge}.{The}\:{coefficient}\:{of}\:{friction}\: \\ $$$$\mu,\:{between}\:{each}\:{masses}\:{and}\:{the} \\ $$$${surface}\:{of}\:{the}\:{wedge}\:{is}\:\mathrm{0}.\mathrm{2}.{Find} \\ $$$${the}\:{acceleration}\:{of}\:{the}\:{masses} \\ $$$${when}\:{they}\:{are}\:{released}. \\ $$

Question Number 22892 Answers: 0 Comments: 3

A horizontal force of 10N just prevents a mass of 2kg from sliding down a rough plane inclined at 45° to the horizontal. Find the coefficient of friction.

$${A}\:{horizontal}\:{force}\:{of}\:\mathrm{10}{N}\:{just} \\ $$$${prevents}\:{a}\:{mass}\:{of}\:\mathrm{2}{kg}\:{from} \\ $$$${sliding}\:{down}\:{a}\:{rough}\:{plane} \\ $$$${inclined}\:{at}\:\mathrm{45}°\:{to}\:{the}\:{horizontal}. \\ $$$${Find}\:{the}\:{coefficient}\:{of}\:{friction}. \\ $$

Question Number 22883 Answers: 1 Comments: 1

The correct order of second ionisation energy in the following : (a) F > O > N > C (b) O > F > N > C (c) O > N > F > C (d) C > N > O > F

$$\mathrm{The}\:\mathrm{correct}\:\mathrm{order}\:\mathrm{of}\:\mathrm{second}\:\mathrm{ionisation} \\ $$$$\mathrm{energy}\:\mathrm{in}\:\mathrm{the}\:\mathrm{following}\:: \\ $$$$\left({a}\right)\:\mathrm{F}\:>\:\mathrm{O}\:>\:\mathrm{N}\:>\:\mathrm{C} \\ $$$$\left({b}\right)\:\mathrm{O}\:>\:\mathrm{F}\:>\:\mathrm{N}\:>\:\mathrm{C} \\ $$$$\left({c}\right)\:\mathrm{O}\:>\:\mathrm{N}\:>\:\mathrm{F}\:>\:\mathrm{C} \\ $$$$\left({d}\right)\:\mathrm{C}\:>\:\mathrm{N}\:>\:\mathrm{O}\:>\:\mathrm{F} \\ $$

Question Number 22881 Answers: 0 Comments: 3

which is your favourite subject?

$${which}\:{is}\:{your}\:{favourite}\:{subject}? \\ $$

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