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Question Number 23849 Answers: 2 Comments: 0

∫((x^6 +1)/(x^4 +1))dx

$$\int\frac{{x}^{\mathrm{6}} +\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}{dx} \\ $$

Question Number 23833 Answers: 1 Comments: 3

f(x^2 + x) + 2f(x^2 − 3x + 2) = 9x^2 − 15x then what is the value of f(10) ?

$${f}\left({x}^{\mathrm{2}} \:+\:{x}\right)\:+\:\mathrm{2}{f}\left({x}^{\mathrm{2}} \:−\:\mathrm{3}{x}\:+\:\mathrm{2}\right)\:=\:\mathrm{9}{x}^{\mathrm{2}} \:−\:\mathrm{15}{x} \\ $$$$\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{f}\left(\mathrm{10}\right)\:? \\ $$

Question Number 23827 Answers: 0 Comments: 0

∫ (√(cosecx)) dx

$$\int\:\sqrt{\mathrm{cosecx}}\:\:\:\mathrm{dx} \\ $$

Question Number 23823 Answers: 1 Comments: 0

The period of a simple pendulum A is 6 secs. Find the period of a simple pendulum B, if A makes 30 oscillation in the time it takes B to make 70 oscillation.

$$\mathrm{The}\:\mathrm{period}\:\mathrm{of}\:\mathrm{a}\:\mathrm{simple}\:\mathrm{pendulum}\:\mathrm{A}\:\mathrm{is}\:\mathrm{6}\:\mathrm{secs}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{period}\:\mathrm{of}\:\mathrm{a}\:\mathrm{simple} \\ $$$$\mathrm{pendulum}\:\mathrm{B},\:\mathrm{if}\:\mathrm{A}\:\mathrm{makes}\:\mathrm{30}\:\mathrm{oscillation}\:\mathrm{in}\:\mathrm{the}\:\mathrm{time}\:\mathrm{it}\:\mathrm{takes}\:\mathrm{B}\:\mathrm{to}\:\mathrm{make}\:\mathrm{70} \\ $$$$\mathrm{oscillation}. \\ $$

Question Number 23814 Answers: 1 Comments: 1

Question Number 23781 Answers: 0 Comments: 0

P(X=299), μ=318, standard deviation=42 P(z=((299−318)/(42))) P(z=−0.45) Is it P(z=−0.45)=P(−0.45<z<−0.44)? If not, how to find P(z=−0.45)?

$${P}\left({X}=\mathrm{299}\right),\:\mu=\mathrm{318},\:{standard}\:{deviation}=\mathrm{42} \\ $$$${P}\left({z}=\frac{\mathrm{299}−\mathrm{318}}{\mathrm{42}}\right) \\ $$$${P}\left({z}=−\mathrm{0}.\mathrm{45}\right) \\ $$$$ \\ $$$${Is}\:{it}\:{P}\left({z}=−\mathrm{0}.\mathrm{45}\right)={P}\left(−\mathrm{0}.\mathrm{45}<{z}<−\mathrm{0}.\mathrm{44}\right)? \\ $$$$ \\ $$$${If}\:{not},\:{how}\:{to}\:{find}\:{P}\left({z}=−\mathrm{0}.\mathrm{45}\right)? \\ $$

Question Number 23777 Answers: 0 Comments: 0

please solve question no 23764 and 23765

$${please}\:{solve}\:{question}\:{no}\:\mathrm{23764}\:{and}\:\mathrm{23765} \\ $$

Question Number 23773 Answers: 0 Comments: 2

I have a leaderboard with the data of ′runners′. Each runner has a ′place′ (1st, 2nd, etc.), and a ′time′ (in seconds). Every day I have been comparing the data. What information is important to note when looking at data such as this? Is it possible to make predictions of future data? I′d love advice for things I can do with monitoring these kinds of statistics!

$$\mathrm{I}\:\mathrm{have}\:\mathrm{a}\:\mathrm{leaderboard}\:\mathrm{with}\:\mathrm{the}\:\mathrm{data}\:\mathrm{of}\:'\mathrm{runners}'. \\ $$$$\mathrm{Each}\:\mathrm{runner}\:\mathrm{has}\:\mathrm{a}\:'\mathrm{place}'\:\left(\mathrm{1st},\:\mathrm{2nd},\:\mathrm{etc}.\right), \\ $$$$\mathrm{and}\:\mathrm{a}\:'\mathrm{time}'\:\left(\mathrm{in}\:\mathrm{seconds}\right). \\ $$$$\: \\ $$$$\mathrm{Every}\:\mathrm{day}\:\mathrm{I}\:\mathrm{have}\:\mathrm{been}\:\mathrm{comparing}\:\mathrm{the}\:\mathrm{data}. \\ $$$$\mathrm{What}\:\mathrm{information}\:\mathrm{is}\:\mathrm{important}\:\mathrm{to}\:\mathrm{note}\:\mathrm{when} \\ $$$$\mathrm{looking}\:\mathrm{at}\:\mathrm{data}\:\mathrm{such}\:\mathrm{as}\:\mathrm{this}? \\ $$$$\: \\ $$$$\mathrm{Is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{make}\:\mathrm{predictions}\:\mathrm{of}\:\mathrm{future}\:\mathrm{data}? \\ $$$$\: \\ $$$$\mathrm{I}'\mathrm{d}\:\mathrm{love}\:\mathrm{advice}\:\mathrm{for}\:\mathrm{things}\:\mathrm{I}\:\mathrm{can}\:\mathrm{do}\:\mathrm{with}\:\mathrm{monitoring} \\ $$$$\mathrm{these}\:\mathrm{kinds}\:\mathrm{of}\:\mathrm{statistics}! \\ $$

Question Number 23769 Answers: 1 Comments: 9

guys , how was kvpy ( SA)?? : tinkutara , physicslover,etc....... i screwd in bio completely. how much you guys are expecting and do you have any idea of cutoff ?

$$\mathrm{guys}\:,\:\mathrm{how}\:\mathrm{was}\:\mathrm{kvpy}\:\left(\:\mathrm{SA}\right)?? \\ $$$$:\:\mathrm{tinkutara}\:,\:\mathrm{physicslover},\mathrm{etc}....... \\ $$$$\mathrm{i}\:\mathrm{screwd}\:\mathrm{in}\:\mathrm{bio}\:\mathrm{completely}. \\ $$$$\mathrm{how}\:\mathrm{much}\:\mathrm{you}\:\mathrm{guys}\:\mathrm{are}\:\mathrm{expecting} \\ $$$$\mathrm{and}\:\mathrm{do}\:\mathrm{you}\:\mathrm{have}\:\mathrm{any}\:\mathrm{idea}\:\mathrm{of}\: \\ $$$$\mathrm{cutoff}\:? \\ $$

Question Number 23768 Answers: 0 Comments: 2

Find the last two digit of 20^(17) + 17^(20)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{of}\:\:\:\:\:\mathrm{20}^{\mathrm{17}} \:+\:\mathrm{17}^{\mathrm{20}} \\ $$

Question Number 23765 Answers: 0 Comments: 0

lim_(x→∝) ((cot^(−1) (x^(−a) ln _a x))/(sec^(−1) (a^x ln _x a))) (a>1)

$$\underset{{x}\rightarrow\propto} {\mathrm{lim}}\:\frac{\mathrm{cot}^{−\mathrm{1}} \left({x}^{−{a}} \mathrm{ln}\:_{{a}} \:{x}\right)}{\mathrm{sec}^{−\mathrm{1}} \left({a}^{{x}} \:\mathrm{ln}\:_{{x}} {a}\right)}\:\: \\ $$$$\left({a}>\mathrm{1}\right) \\ $$$$ \\ $$

Question Number 23764 Answers: 0 Comments: 0

lim_(x→∝) (((2^x^n )^(1/e^x ) −(3^x^n )^(1/e^x ) )/x^n ) where nεN

$$\underset{{x}\rightarrow\propto} {\mathrm{lim}}\:\frac{\left(\mathrm{2}^{{x}^{{n}} } \overset{\mathrm{1}/{e}^{{x}} } {\right)}−\left(\mathrm{3}^{{x}^{{n}} } \right)^{\mathrm{1}/{e}^{{x}} } }{{x}^{{n}} } \\ $$$${where}\:{n}\varepsilon{N} \\ $$$$ \\ $$

Question Number 23767 Answers: 0 Comments: 0

suppose that n is the number of balls in a basket.If pronability of pulling A and B together is 0.05 what is the value of n?

$$\mathrm{suppose}\:\mathrm{that}\:\mathrm{n}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{balls}\:\mathrm{in}\:\mathrm{a}\:\mathrm{basket}.\mathrm{If}\:\mathrm{pronability}\:\mathrm{of} \\ $$$$\mathrm{pulling}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{together}\:\mathrm{is}\:\mathrm{0}.\mathrm{05} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}? \\ $$

Question Number 23758 Answers: 1 Comments: 0

solve ∫tan^(−1) x ln (1+x^2 )dx

$${solve} \\ $$$$\int\mathrm{tan}^{−\mathrm{1}} {x}\:\mathrm{ln}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 23759 Answers: 0 Comments: 3

Question Number 23831 Answers: 0 Comments: 0

What is the answer for P(z=0.23)?

$${What}\:{is}\:{the}\:{answer}\:{for}\:{P}\left({z}=\mathrm{0}.\mathrm{23}\right)? \\ $$$$ \\ $$$$ \\ $$

Question Number 23830 Answers: 0 Comments: 2

∫sin(101x)sin^(99) xdx

$$\int\mathrm{sin}\left(\mathrm{101x}\right)\mathrm{sin}^{\mathrm{99}} \mathrm{xdx} \\ $$

Question Number 23752 Answers: 1 Comments: 0

∫_1 ^2 x^3 +1=?

$$\int_{\mathrm{1}} ^{\mathrm{2}} {x}^{\mathrm{3}} +\mathrm{1}=? \\ $$

Question Number 23785 Answers: 2 Comments: 0

A function f is define by f : → 3 − 2sinx, for 0 ≤ x ≤ 360 find the range of f

$$\mathrm{A}\:\mathrm{function}\:\mathrm{f}\:\mathrm{is}\:\mathrm{define}\:\mathrm{by}\:\:\mathrm{f}\::\:\rightarrow\:\mathrm{3}\:−\:\mathrm{2sinx},\:\:\mathrm{for}\:\:\mathrm{0}\:\leqslant\:\mathrm{x}\:\leqslant\:\mathrm{360} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\:\mathrm{f} \\ $$

Question Number 23748 Answers: 1 Comments: 1

Question Number 23741 Answers: 1 Comments: 0

(1+i)(2+i)

$$\left(\mathrm{1}+{i}\right)\left(\mathrm{2}+{i}\right) \\ $$

Question Number 23715 Answers: 0 Comments: 0

Why ΔS > 0 for the reaction 2HgO(s) → 2Hg(l) + O_2 (g)?

$$\mathrm{Why}\:\Delta\mathrm{S}\:>\:\mathrm{0}\:\mathrm{for}\:\mathrm{the}\:\mathrm{reaction} \\ $$$$\mathrm{2HgO}\left(\mathrm{s}\right)\:\rightarrow\:\mathrm{2Hg}\left({l}\right)\:+\:\mathrm{O}_{\mathrm{2}} \left(\mathrm{g}\right)? \\ $$

Question Number 23711 Answers: 1 Comments: 0

A certain ideal gas has C_(v, m) = a + bT, where a = 25 J/(mol. K) and b = 0.03 J(mol.K^2 ). Let 2 mole of this gas go from 300 K and 2 litre volume to 600 K and 4 litre. ΔS_(gas) is

$$\mathrm{A}\:\mathrm{certain}\:\mathrm{ideal}\:\mathrm{gas}\:\mathrm{has}\:\mathrm{C}_{\mathrm{v},\:\mathrm{m}} \:=\:\mathrm{a}\:+\:\mathrm{bT}, \\ $$$$\mathrm{where}\:\mathrm{a}\:=\:\mathrm{25}\:\mathrm{J}/\left(\mathrm{mol}.\:\mathrm{K}\right)\:\mathrm{and}\:\mathrm{b}\:=\:\mathrm{0}.\mathrm{03} \\ $$$$\mathrm{J}\left(\mathrm{mol}.\mathrm{K}^{\mathrm{2}} \right).\:\mathrm{Let}\:\mathrm{2}\:\mathrm{mole}\:\mathrm{of}\:\mathrm{this}\:\mathrm{gas}\:\mathrm{go} \\ $$$$\mathrm{from}\:\mathrm{300}\:\mathrm{K}\:\mathrm{and}\:\mathrm{2}\:\mathrm{litre}\:\mathrm{volume}\:\mathrm{to}\:\mathrm{600}\:\mathrm{K} \\ $$$$\mathrm{and}\:\mathrm{4}\:\mathrm{litre}.\:\Delta\mathrm{S}_{\mathrm{gas}} \:\mathrm{is} \\ $$

Question Number 23707 Answers: 1 Comments: 4

Two blocks A and B of mass 1 kg and 2 kg respectively are connected by a string, passing over a light frictionless pulley. Both the blocks are resting on a horizontal floor and the pulley is held such that string remains just taut. At time t = 0, a force F = 20t N, starts acting on the pulley along vertically upward direction. Calculate vertical displacement of the pulley upto the instant when B loses contact with the floor.

$$\mathrm{Two}\:\mathrm{blocks}\:{A}\:\mathrm{and}\:{B}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1}\:\mathrm{kg}\:\mathrm{and} \\ $$$$\mathrm{2}\:\mathrm{kg}\:\mathrm{respectively}\:\mathrm{are}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{a} \\ $$$$\mathrm{string},\:\mathrm{passing}\:\mathrm{over}\:\mathrm{a}\:\mathrm{light}\:\mathrm{frictionless} \\ $$$$\mathrm{pulley}.\:\mathrm{Both}\:\mathrm{the}\:\mathrm{blocks}\:\mathrm{are}\:\mathrm{resting}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{horizontal}\:\mathrm{floor}\:\mathrm{and}\:\mathrm{the}\:\mathrm{pulley}\:\mathrm{is}\:\mathrm{held} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{string}\:\mathrm{remains}\:\mathrm{just}\:\mathrm{taut}.\:\mathrm{At} \\ $$$$\mathrm{time}\:{t}\:=\:\mathrm{0},\:\mathrm{a}\:\mathrm{force}\:{F}\:=\:\mathrm{20}{t}\:\mathrm{N},\:\mathrm{starts} \\ $$$$\mathrm{acting}\:\mathrm{on}\:\mathrm{the}\:\mathrm{pulley}\:\mathrm{along}\:\mathrm{vertically} \\ $$$$\mathrm{upward}\:\mathrm{direction}.\:\mathrm{Calculate}\:\mathrm{vertical} \\ $$$$\mathrm{displacement}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pulley}\:\mathrm{upto}\:\mathrm{the} \\ $$$$\mathrm{instant}\:\mathrm{when}\:{B}\:\mathrm{loses}\:\mathrm{contact}\:\mathrm{with}\:\mathrm{the} \\ $$$$\mathrm{floor}. \\ $$

Question Number 24506 Answers: 0 Comments: 8

A spot light S rotates in a horizontal plane with a constant angular velocity of 0.1 rad/s. The spot of light P moves along the wall at a distance 3 m. What is the velocity of the spot P when θ = 45°?

$$\mathrm{A}\:\mathrm{spot}\:\mathrm{light}\:{S}\:\mathrm{rotates}\:\mathrm{in}\:\mathrm{a}\:\mathrm{horizontal} \\ $$$$\mathrm{plane}\:\mathrm{with}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{angular}\:\mathrm{velocity} \\ $$$$\mathrm{of}\:\mathrm{0}.\mathrm{1}\:\mathrm{rad}/\mathrm{s}.\:\mathrm{The}\:\mathrm{spot}\:\mathrm{of}\:\mathrm{light}\:{P}\:\mathrm{moves} \\ $$$$\mathrm{along}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{3}\:\mathrm{m}.\:\mathrm{What} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{spot}\:{P}\:\mathrm{when}\:\theta\:=\:\mathrm{45}°? \\ $$

Question Number 23700 Answers: 0 Comments: 3

If (1 − x^3 )^n = Σ_(r=0) ^n a_r x^r (1 − x)^(3n−2r) , then the value of a_r , where n ∈ N is (1)^n C_r ∙3^r (2)^n C_(3r) (3)^n C_(r−1) 2^(r−1) (4)^n C_r 2^r

$$\mathrm{If}\:\left(\mathrm{1}\:−\:{x}^{\mathrm{3}} \right)^{{n}} \:=\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}{a}_{{r}} {x}^{{r}} \left(\mathrm{1}\:−\:{x}\right)^{\mathrm{3}{n}−\mathrm{2}{r}} ,\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{a}_{{r}} ,\:\mathrm{where}\:{n}\:\in\:{N}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:^{{n}} {C}_{{r}} \centerdot\mathrm{3}^{{r}} \\ $$$$\left(\mathrm{2}\right)\:^{{n}} {C}_{\mathrm{3}{r}} \\ $$$$\left(\mathrm{3}\right)\:^{{n}} {C}_{{r}−\mathrm{1}} \mathrm{2}^{{r}−\mathrm{1}} \\ $$$$\left(\mathrm{4}\right)\:^{{n}} {C}_{{r}} \mathrm{2}^{{r}} \\ $$

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