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Question Number 194564    Answers: 2   Comments: 0

soit A(2,1) B(3,2) C(4,3) points du plan( ox,oy) 1)Determiner l ′ equation du cercle qui passe par A; B; C ? 2) points d intersection du cercle avec l axe(ox,oy)?

$$\mathrm{soit}\:\:\:\boldsymbol{\mathrm{A}}\left(\mathrm{2},\mathrm{1}\right)\:\:\:\:\:\boldsymbol{\mathrm{B}}\left(\mathrm{3},\mathrm{2}\right)\:\:\:\:\:\boldsymbol{\mathrm{C}}\left(\mathrm{4},\mathrm{3}\right)\:\:\mathrm{points}\:\mathrm{du}\: \\ $$$$\:\:\mathrm{plan}\left(\:\mathrm{ox},\mathrm{oy}\right)\:\: \\ $$$$ \\ $$$$\left.\:\mathrm{1}\right)\mathrm{Determiner}\:\:\mathrm{l}\:'\:\mathrm{equation}\:\mathrm{du}\:\mathrm{cercle}\:\mathrm{qui}\: \\ $$$$\:\:\:\:\mathrm{passe}\:\mathrm{par}\:\boldsymbol{\mathrm{A}};\:\boldsymbol{\mathrm{B}};\:\boldsymbol{\mathrm{C}}\:\:\:? \\ $$$$\left.\:\:\mathrm{2}\right)\:\mathrm{points}\:\mathrm{d}\:\mathrm{intersection}\:\mathrm{du}\:\mathrm{cercle}\:\mathrm{avec} \\ $$$$\:\:\:\:\:\mathrm{l}\:\mathrm{axe}\left(\mathrm{ox},\mathrm{oy}\right)? \\ $$

Question Number 194563    Answers: 0   Comments: 0

A mass of 12kg rests on a smooth inclined plane which is 6m long and 1m high. The mass is connected by a light inextensible string which passes over a smooth pulley fixed at the top of the plane to a mass of 4kg which is hanging freely. With the string taut, the system is released from rest. Using Polya problem solving approach find the following: a. acceleration of the system b i. velocity with which the 4kg mass hits the ground. b ii. time the 4kg mass takes to hit the ground

$$\mathrm{A}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{12kg}\:\mathrm{rests}\:\mathrm{on}\:\mathrm{a}\:\mathrm{smooth}\:\mathrm{inclined} \\ $$$$\mathrm{plane}\:\mathrm{which}\:\mathrm{is}\:\mathrm{6m}\:\mathrm{long}\:\mathrm{and}\:\mathrm{1m}\:\mathrm{high}. \\ $$$$\mathrm{The}\:\mathrm{mass}\:\mathrm{is}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{a}\:\mathrm{light}\:\mathrm{inextensible} \\ $$$$\mathrm{string}\:\mathrm{which}\:\mathrm{passes}\:\mathrm{over}\:\mathrm{a}\:\mathrm{smooth}\:\mathrm{pulley} \\ $$$$\mathrm{fixed}\:\mathrm{at}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{to}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of} \\ $$$$\mathrm{4kg}\:\mathrm{which}\:\mathrm{is}\:\mathrm{hanging}\:\mathrm{freely}.\:\mathrm{With}\:\mathrm{the} \\ $$$$\mathrm{string}\:\mathrm{taut},\:\mathrm{the}\:\mathrm{system}\:\mathrm{is}\:\mathrm{released}\:\mathrm{from}\:\mathrm{rest}. \\ $$$$\mathrm{Using}\:\mathrm{Polya}\:\mathrm{problem}\:\mathrm{solving}\:\mathrm{approach} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{following}: \\ $$$$\mathrm{a}.\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{system} \\ $$$$\mathrm{b}\:\mathrm{i}.\:\mathrm{velocity}\:\mathrm{with}\:\mathrm{which}\:\mathrm{the}\:\mathrm{4kg}\:\mathrm{mass}\:\mathrm{hits} \\ $$$$\mathrm{the}\:\mathrm{ground}. \\ $$$$\mathrm{b}\:\mathrm{ii}.\:\mathrm{time}\:\mathrm{the}\:\mathrm{4kg}\:\mathrm{mass}\:\mathrm{takes}\:\mathrm{to}\:\mathrm{hit}\:\mathrm{the}\:\mathrm{ground} \\ $$

Question Number 194560    Answers: 1   Comments: 0

Question Number 194559    Answers: 2   Comments: 0

repeat question Shiw that : Σ_(i=1) ^n ((1/(2i−1))−(1/(2i)))=Σ_(i=1) ^n (1/(n+i)) ?

$${repeat}\:{question} \\ $$$${Shiw}\:{that}\:: \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\:\left(\frac{\mathrm{1}}{\mathrm{2}{i}−\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{2}{i}}\right)=\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{{n}+{i}}\:\:? \\ $$

Question Number 194552    Answers: 2   Comments: 3

If a, b are real numbers & 4cos^2 θ = ((4a^2 +9b^2 +5)/(a+3b)), then the value of (a+b) will be: (a) (7/6) (b) (5/4) (c) ((11)/6) (d) ((17)/(12))

$$\mathrm{If}\:{a},\:{b}\:\mathrm{are}\:\mathrm{real}\:\mathrm{numbers}\:\&\:\mathrm{4cos}^{\mathrm{2}} \theta\:=\:\frac{\mathrm{4}{a}^{\mathrm{2}} +\mathrm{9}{b}^{\mathrm{2}} +\mathrm{5}}{{a}+\mathrm{3}{b}},\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left({a}+{b}\right)\:\mathrm{will}\:\mathrm{be}: \\ $$$$\left(\mathrm{a}\right)\:\frac{\mathrm{7}}{\mathrm{6}}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{5}}{\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\frac{\mathrm{11}}{\mathrm{6}}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\frac{\mathrm{17}}{\mathrm{12}} \\ $$

Question Number 194548    Answers: 2   Comments: 1

Question Number 194528    Answers: 2   Comments: 0

★ Let N be a natural number where N≤100. If HCF(N, 100) = 1 then find the sum of all the values of N ? (a) 400 (b) 1000 (c) 2000 (d) 4000

$$\bigstar\:\mathrm{Let}\:\mathrm{N}\:\mathrm{be}\:\mathrm{a}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{where}\:\mathrm{N}\leq\mathrm{100}. \\ $$$$\:\:\:\:\:\:\:\:\mathrm{If}\:\mathrm{HCF}\left(\mathrm{N},\:\mathrm{100}\right)\:=\:\mathrm{1}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{all}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\:\mathrm{N}\:? \\ $$$$\:\:\:\:\:\:\:\left(\mathrm{a}\right)\:\mathrm{400}\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{1000}\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{2000}\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{4000} \\ $$

Question Number 194526    Answers: 2   Comments: 0

((f(x+1))/(f(x)))=x^(2 ) f(x)=? ((f(6))/(f(3)))=?

$$\frac{{f}\left({x}+\mathrm{1}\right)}{{f}\left({x}\right)}={x}^{\mathrm{2}\:\:\:\:\:\:\:\:} \:\:\:\:{f}\left({x}\right)=? \\ $$$$\frac{{f}\left(\mathrm{6}\right)}{{f}\left(\mathrm{3}\right)}=? \\ $$

Question Number 194522    Answers: 7   Comments: 0

Question Number 194518    Answers: 1   Comments: 1

Question Number 194516    Answers: 0   Comments: 0

Question Number 194515    Answers: 1   Comments: 0

∣∫f(x)dx∣=∫∣f(x)∣dx

$$\mid\int{f}\left({x}\right){dx}\mid=\int\mid{f}\left({x}\right)\mid{dx} \\ $$

Question Number 194509    Answers: 2   Comments: 0

Question Number 194500    Answers: 1   Comments: 0

Σ_(0≤i^2 +j^2 ≤16) (i+j)=?

$$\underset{\mathrm{0}\leqslant{i}^{\mathrm{2}} +{j}^{\mathrm{2}} \leqslant\mathrm{16}} {\sum}\left({i}+{j}\right)=? \\ $$

Question Number 194499    Answers: 1   Comments: 3

3^x + 4^x = 5^x find x ?

$$\mathrm{3}^{\mathrm{x}} \:+\:\mathrm{4}^{\mathrm{x}} \:=\:\mathrm{5}^{\mathrm{x}} \\ $$$$\mathrm{find}\:\mathrm{x}\:? \\ $$

Question Number 194491    Answers: 1   Comments: 0

x=(√(4+(√(5(√3) +5(√(48−10(√(7+4(√3))))))))) determinant (((2x−1=?)))

$$\:\:\mathrm{x}=\sqrt{\mathrm{4}+\sqrt{\mathrm{5}\sqrt{\mathrm{3}}\:+\mathrm{5}\sqrt{\mathrm{48}−\mathrm{10}\sqrt{\mathrm{7}+\mathrm{4}\sqrt{\mathrm{3}}}}}}\: \\ $$$$\:\:\:\begin{array}{|c|}{\mathrm{2x}−\mathrm{1}=?}\\\hline\end{array} \\ $$

Question Number 194490    Answers: 1   Comments: 0

A research station supplies three varieties of seeds S1, S2 and S3 in the ratio 4: 2: 1. The probabilities of germination of S1, S2 and S3 are 50%, 60% and 80% respectively. Find the probability that a seed selected at random will germinate.

$$\mathrm{A}\:\mathrm{research}\:\mathrm{station}\:\mathrm{supplies}\:\mathrm{three}\:\mathrm{varieties}\: \\ $$$$\mathrm{of}\:\mathrm{seeds}\:\mathrm{S1},\:\mathrm{S2}\:\mathrm{and}\:\mathrm{S3}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{4}:\:\mathrm{2}:\:\mathrm{1}. \\ $$$$\mathrm{The}\:\mathrm{probabilities}\:\mathrm{of}\:\mathrm{germination}\:\mathrm{of}\: \\ $$$$\mathrm{S1},\:\mathrm{S2}\:\mathrm{and}\:\mathrm{S3}\:\mathrm{are}\:\mathrm{50\%},\:\mathrm{60\%}\:\mathrm{and}\:\mathrm{80\%} \\ $$$$\mathrm{respectively}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{a}\:\mathrm{seed}\:\mathrm{selected}\:\mathrm{at}\:\mathrm{random}\:\mathrm{will}\:\mathrm{germinate}. \\ $$

Question Number 194506    Answers: 0   Comments: 0

Gyanashram classes shivkund(Munger) by−Bittu sir 12 th physics test 1. 2. 3. 4. 5. ? 6. 7. 8. 5 ? 9. 30cm 5T 30^(o ) 10. ? 5 1. , 2. ,

$$\:\:\:\:\:\:\:\:\:\:\mathrm{Gyanashram}\:\mathrm{classes} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{shivkund}\left(\mathrm{Munger}\right)\:\:\:\:\mathrm{by}−\mathrm{Bittu}\:\mathrm{sir} \\ $$$$\:\:\:\mathrm{12}\:\:\mathrm{th}\:\mathrm{physics}\:\mathrm{test} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{1}. \: \: \: \: \: \: \: \: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{2}. \: \: \: \: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{3}. \: \: \: \: \: \: \: \: \: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{4}. \: \: \: \: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{5}. \: \: \: ? \\ $$$$\:\:\:\:\:\:\:\:\mathrm{6}.\: \: \: \: \: \: \: \: \: \: \: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{7}. \: \: \: \: \: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{8}.\: \: \: \: \:\mathrm{5}\: \: \: \: \: \: \: \: \\ $$$$\:\:\:\:\:\:\:\:\: \: \: \: ? \\ $$$$\:\:\:\:\:\:\:\mathrm{9}.\: \:\mathrm{30cm}\: \: \:\:\mathrm{5T}\: \: \: \: \:\mathrm{30}^{\mathrm{o}\:} \: \: \: \: \: \: \\ $$$$\:\:\:\:\:\:\:\: \: \: \: \: \: \\ $$$$\:\:\:\:\:\:\mathrm{10}. \: \: \: \: \: ? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}\: \: \: \\ $$$$\:\:\:\:\:\:\:\mathrm{1}. \: \: \: \: \:, \: \: \: \: \: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{2}. \: \: \:, \: \: \: \: \: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 194488    Answers: 0   Comments: 0

Question Number 194482    Answers: 1   Comments: 0

determinant (( ),((lim_(x→0) [(1/x^2 ) ((2/(cos x)) + cos x−3)] .)))

$$\:\:\:\:\:\begin{array}{|c|c|}{ }\\{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:\left(\frac{\mathrm{2}}{\mathrm{cos}\:\mathrm{x}}\:+\:\mathrm{cos}\:\mathrm{x}−\mathrm{3}\right)\right]\:.}\\\hline\end{array} \\ $$

Question Number 194475    Answers: 2   Comments: 2

How many sets of two factors of 720 are coprime to each other? (A) 63 (B) 64 (C) 65 (D) 67

$$\mathrm{How}\:\mathrm{many}\:\mathrm{sets}\:\mathrm{of}\:\mathrm{two}\:\mathrm{factors}\:\mathrm{of}\:\mathrm{720}\:\mathrm{are}\: \\ $$$$\mathrm{coprime}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}? \\ $$$$\left(\mathrm{A}\right)\:\mathrm{63}\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{64}\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{65}\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{67} \\ $$$$ \\ $$

Question Number 194467    Answers: 2   Comments: 0

f(x)= (√(8x−x^2 )) −(√(14x−x^2 −48))

$$\:\: \\ $$$$ \mathrm{f}\left(\mathrm{x}\right)=\:\sqrt{\mathrm{8x}−\mathrm{x}^{\mathrm{2}} }\:−\sqrt{\mathrm{14x}−\mathrm{x}^{\mathrm{2}} −\mathrm{48}} \\ $$

Question Number 194466    Answers: 2   Comments: 0

lim_(n→∞) Π_(k=1) ^n (1+(1/n)+(k/n^2 ))=?

$$\:\:\: \underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{n}}+\frac{\mathrm{k}}{\mathrm{n}^{\mathrm{2}} }\right)=? \\ $$

Question Number 194464    Answers: 1   Comments: 0

Question Number 194463    Answers: 1   Comments: 0

Question Number 194462    Answers: 1   Comments: 0

Prove that ∫^( +∞^ ) _( 0) ((1−e^(−x^2 ) )/x^2 )dx=(√𝛑)

$$\mathrm{Prove}\:\mathrm{that}\:\:\:\:\:\:\:\:\underset{\:\mathrm{0}} {\int}^{\:+\infty^{} } \frac{\mathrm{1}−\boldsymbol{{e}}^{−\boldsymbol{{x}}^{\mathrm{2}} } }{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}=\sqrt{\boldsymbol{\pi}} \\ $$

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