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Question Number 17939 Answers: 1 Comments: 1

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Question Number 17938 Answers: 2 Comments: 2

If only downward motion along lines is allowed, what is the total number of paths from point P to point Q in the figure below?

$$\mathrm{If}\:\mathrm{only}\:\mathrm{downward}\:\mathrm{motion}\:\mathrm{along}\:\mathrm{lines}\:\mathrm{is} \\ $$$$\mathrm{allowed},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{paths}\:\mathrm{from}\:\mathrm{point}\:\mathrm{P}\:\mathrm{to}\:\mathrm{point}\:\mathrm{Q}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{figure}\:\mathrm{below}? \\ $$

Question Number 17936 Answers: 2 Comments: 1

Two particles start moving towards each other with constant acceleration of 1 m/s^2 . If their initial separation is 100 m, find after what time they will meet each other (A) 40s (B) 45s (C) 50 s (D)55s

$$\mathrm{Two}\:\mathrm{particles}\:\mathrm{start}\:\mathrm{moving}\:\mathrm{towards} \\ $$$$\mathrm{each}\:\mathrm{other}\:\mathrm{with}\:\mathrm{constant}\:\mathrm{acceleration} \\ $$$$\mathrm{of}\:\:\mathrm{1}\:{m}/{s}^{\mathrm{2}} .\:\mathrm{If}\:\mathrm{their}\:\mathrm{initial}\:\mathrm{separation}\:\mathrm{is} \\ $$$$\mathrm{100}\:\mathrm{m},\:\mathrm{find}\:\mathrm{after}\:\mathrm{what}\:\mathrm{time}\:\mathrm{they}\:\mathrm{will} \\ $$$$\mathrm{meet}\:\mathrm{each}\:\mathrm{other} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{40}{s}\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{45}{s}\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{50}\:{s}\:\left(\mathrm{D}\right)\mathrm{55}{s} \\ $$

Question Number 17919 Answers: 0 Comments: 0

How do the electronic configurations of the elements with Z = 107 − 109 differ from one another?

$$\mathrm{How}\:\mathrm{do}\:\mathrm{the}\:\mathrm{electronic}\:\mathrm{configurations}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{elements}\:\mathrm{with}\:\mathrm{Z}\:=\:\mathrm{107}\:−\:\mathrm{109}\:\mathrm{differ} \\ $$$$\mathrm{from}\:\mathrm{one}\:\mathrm{another}? \\ $$

Question Number 17918 Answers: 0 Comments: 0

Write the electronic configuration and the block to which an element with Z = 90 belongs.

$$\mathrm{Write}\:\mathrm{the}\:\mathrm{electronic}\:\mathrm{configuration}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{block}\:\mathrm{to}\:\mathrm{which}\:\mathrm{an}\:\mathrm{element}\:\mathrm{with} \\ $$$$\mathrm{Z}\:=\:\mathrm{90}\:\mathrm{belongs}. \\ $$

Question Number 17901 Answers: 1 Comments: 2

Question Number 17895 Answers: 0 Comments: 2

Question Number 17909 Answers: 0 Comments: 1

Please answer Q. 17525

$${Please}\:{answer}\:{Q}.\:\mathrm{17525} \\ $$

Question Number 17890 Answers: 0 Comments: 0

Question Number 17948 Answers: 1 Comments: 3

Question Number 17886 Answers: 0 Comments: 7

Question Number 17884 Answers: 1 Comments: 1

Question Number 17879 Answers: 0 Comments: 0

Question Number 17878 Answers: 0 Comments: 0

Question Number 17872 Answers: 2 Comments: 0

Solve : ∣x − 1∣ + ∣x∣ + ∣x + 1∣ = x + 2

$$\mathrm{Solve}\:: \\ $$$$\mid{x}\:−\:\mathrm{1}\mid\:+\:\mid{x}\mid\:+\:\mid{x}\:+\:\mathrm{1}\mid\:=\:{x}\:+\:\mathrm{2} \\ $$

Question Number 17867 Answers: 1 Comments: 0

prove that (2+(√3))^(2n) +(2−(√3))^(2n) is an even integer and that (2+(√3))^(2n) −(2−(√3))^(2n) =w(√3) for some integers w,for all integer n≥1.

$${prove}\:{that}\:\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}} +\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}} {is}\:{an} \\ $$$${even}\:{integer}\:{and}\:{that}\:\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}} −\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{2}{n}} ={w}\sqrt{\mathrm{3}} \\ $$$${for}\:{some}\:{integers}\:{w},{for}\:{all}\:{integer}\:{n}\geqslant\mathrm{1}. \\ $$$$ \\ $$

Question Number 17866 Answers: 1 Comments: 0

Prove that sin 5A = 5 cos^4 A sin A − 10 cos^2 A sin^3 A + sin^5 A

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{sin}\:\mathrm{5}{A}\:=\:\mathrm{5}\:\mathrm{cos}^{\mathrm{4}} \:{A}\:\mathrm{sin}\:{A}\:− \\ $$$$\mathrm{10}\:\mathrm{cos}^{\mathrm{2}} \:{A}\:\mathrm{sin}^{\mathrm{3}} \:{A}\:+\:\mathrm{sin}^{\mathrm{5}} \:{A} \\ $$

Question Number 17852 Answers: 0 Comments: 1

A particle moves in a straight line (x-axis) with the velocity shown in the figure. Knowing that x = −16 m at t = 0, draw the a-t and x-t curves for the interval 0 < t < 40 s and determine (i) Maximum value of the position coordinate of the particle. (ii) The values of t for which the particle is at a distance of 50 m from the origin.

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line} \\ $$$$\left({x}-\mathrm{axis}\right)\:\mathrm{with}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{figure}.\:\mathrm{Knowing}\:\mathrm{that}\:{x}\:=\:−\mathrm{16}\:\mathrm{m}\:\mathrm{at} \\ $$$${t}\:=\:\mathrm{0},\:\mathrm{draw}\:\mathrm{the}\:{a}-{t}\:\mathrm{and}\:{x}-{t}\:\mathrm{curves}\:\mathrm{for} \\ $$$$\mathrm{the}\:\mathrm{interval}\:\mathrm{0}\:<\:{t}\:<\:\mathrm{40}\:\mathrm{s}\:\mathrm{and}\:\mathrm{determine} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{position} \\ $$$$\mathrm{coordinate}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{The}\:\mathrm{values}\:\mathrm{of}\:{t}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the} \\ $$$$\mathrm{particle}\:\mathrm{is}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{50}\:\mathrm{m}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{origin}. \\ $$

Question Number 17935 Answers: 0 Comments: 0

Ball A is dropped from the top of a building. At the same instant ball B is thrown vertically upwards from the ground. When the ball collide, they are moving in opposite directions and the speed of A(u) is twice the speed of B. The relative velocity of the ball just before collision and relative acceleration between them is (only their magnitudes) (A) 0 and 0 (B) ((3u)/2) and 0 (C) ((3u)/2) and 2g (D) ((3u)/2) and g

$$\mathrm{Ball}\:{A}\:\mathrm{is}\:\mathrm{dropped}\:\mathrm{from}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{building}. \\ $$$$\mathrm{At}\:\mathrm{the}\:\mathrm{same}\:\mathrm{instant}\:\mathrm{ball}\:{B}\:\mathrm{is}\:\mathrm{thrown} \\ $$$$\mathrm{vertically}\:\mathrm{upwards}\:\mathrm{from}\:\mathrm{the}\:\mathrm{ground}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{collide},\:\mathrm{they}\:\mathrm{are}\:\mathrm{moving}\:\:\mathrm{in} \\ $$$$\mathrm{opposite}\:\mathrm{directions}\:\mathrm{and}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:{A}\left({u}\right) \\ $$$$\mathrm{is}\:\mathrm{twice}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:{B}.\:\mathrm{The}\:\mathrm{relative}\: \\ $$$$\mathrm{velocity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{just}\:\mathrm{before}\:\mathrm{collision} \\ $$$$\mathrm{and}\:\mathrm{relative}\:\mathrm{acceleration}\:\mathrm{between}\:\mathrm{them} \\ $$$$\mathrm{is}\:\left(\mathrm{only}\:\mathrm{their}\:\mathrm{magnitudes}\right) \\ $$$$\left(\mathrm{A}\right)\:\mathrm{0}\:\mathrm{and}\:\mathrm{0}\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\frac{\mathrm{3}{u}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{0} \\ $$$$\left(\mathrm{C}\right)\:\frac{\mathrm{3}{u}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{2}{g}\:\:\:\left(\mathrm{D}\right)\:\frac{\mathrm{3}{u}}{\mathrm{2}}\:\mathrm{and}\:{g} \\ $$

Question Number 17835 Answers: 2 Comments: 1

A rocket is moving in a gravity free space with a constant acceleration of 2 m/s^2 along + x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in +x direction with a speed of 0.3 m/s relative to the rocket. At the same time, another ball is thrown in −x direction with a speed of 0.2 m/s from its right end relative to the rocket. The time in seconds when the two balls hit each other is

$$\mathrm{A}\:\mathrm{rocket}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{in}\:\mathrm{a}\:\mathrm{gravity}\:\mathrm{free} \\ $$$$\mathrm{space}\:\mathrm{with}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{acceleration}\:\mathrm{of} \\ $$$$\mathrm{2}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} \:\mathrm{along}\:+\:\mathrm{x}\:\mathrm{direction}\:\left(\mathrm{see}\:\mathrm{figure}\right). \\ $$$$\mathrm{The}\:\mathrm{length}\:\mathrm{of}\:\mathrm{a}\:\mathrm{chamber}\:\mathrm{inside}\:\mathrm{the} \\ $$$$\mathrm{rocket}\:\mathrm{is}\:\mathrm{4}\:\mathrm{m}.\:\mathrm{A}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{thrown}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{left}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{chamber}\:\mathrm{in}\:+{x}\:\mathrm{direction} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{0}.\mathrm{3}\:\mathrm{m}/\mathrm{s}\:\mathrm{relative}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{rocket}.\:\mathrm{At}\:\mathrm{the}\:\mathrm{same}\:\mathrm{time},\:\mathrm{another}\:\mathrm{ball} \\ $$$$\mathrm{is}\:\mathrm{thrown}\:\mathrm{in}\:−{x}\:\mathrm{direction}\:\mathrm{with}\:\mathrm{a}\:\mathrm{speed} \\ $$$$\mathrm{of}\:\mathrm{0}.\mathrm{2}\:\mathrm{m}/\mathrm{s}\:\mathrm{from}\:\mathrm{its}\:\mathrm{right}\:\mathrm{end}\:\mathrm{relative}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{rocket}.\:\mathrm{The}\:\mathrm{time}\:\mathrm{in}\:\mathrm{seconds}\:\mathrm{when} \\ $$$$\mathrm{the}\:\mathrm{two}\:\mathrm{balls}\:\mathrm{hit}\:\mathrm{each}\:\mathrm{other}\:\mathrm{is} \\ $$

Question Number 17830 Answers: 2 Comments: 0

Two candles of the same height are lighted together. First one gets burnt up completely in 3 hours while the second in 4 hours. At what point of time, the length of second candle will be double the length of the first candle?

$$\mathrm{Two}\:\mathrm{candles}\:\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{height}\:\mathrm{are} \\ $$$$\mathrm{lighted}\:\mathrm{together}.\:\mathrm{First}\:\mathrm{one}\:\mathrm{gets}\:\mathrm{burnt}\:\mathrm{up} \\ $$$$\mathrm{completely}\:\mathrm{in}\:\mathrm{3}\:\mathrm{hours}\:\mathrm{while}\:\mathrm{the}\:\mathrm{second} \\ $$$$\mathrm{in}\:\mathrm{4}\:\mathrm{hours}.\:\mathrm{At}\:\mathrm{what}\:\mathrm{point}\:\mathrm{of}\:\mathrm{time},\:\mathrm{the} \\ $$$$\mathrm{length}\:\mathrm{of}\:\mathrm{second}\:\mathrm{candle}\:\mathrm{will}\:\mathrm{be}\:\mathrm{double} \\ $$$$\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{candle}? \\ $$

Question Number 17828 Answers: 1 Comments: 0

Question Number 17815 Answers: 1 Comments: 4

For x ∈ (0, π), the equation sin x + 2 sin 2x − sin 3x = 3 has (1) Infinitely many solutions (2) Three solutions (3) One solution (4) No solution

$$\mathrm{For}\:{x}\:\in\:\left(\mathrm{0},\:\pi\right),\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{sin}\:{x}\:+\:\mathrm{2}\:\mathrm{sin}\:\mathrm{2}{x}\:−\:\mathrm{sin}\:\mathrm{3}{x}\:=\:\mathrm{3}\:\mathrm{has} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Infinitely}\:\mathrm{many}\:\mathrm{solutions} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Three}\:\mathrm{solutions} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{One}\:\mathrm{solution} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{No}\:\mathrm{solution} \\ $$

Question Number 17805 Answers: 0 Comments: 0

If θ=t^n e^(−r^(2/(ut)) ) ,find the value of n which will make (1/r^2 ) (∂/∂r)(r^2 (∂θ/(∂r))) equal to (∂θ/∂t)

$${If}\:\theta={t}^{{n}} {e}^{−{r}^{\frac{\mathrm{2}}{{ut}}} } ,{find}\:{the}\:{value}\:{of} \\ $$$${n}\:{which}\:{will}\:{make}\:\frac{\mathrm{1}}{{r}^{\mathrm{2}} }\:\frac{\partial}{\partial{r}}\left({r}^{\mathrm{2}} \frac{\partial\theta}{\left.\partial{r}\right)}\right. \\ $$$${equal}\:{to}\:\frac{\partial\theta}{\partial{t}} \\ $$

Question Number 17782 Answers: 0 Comments: 1

let a,b,c,x,y and z be complex numbers such that : a=((b+c)/(x−2)), b=((c+a)/(y−2)), c=((a+b)/(z−2)) if xy+yz+zx=1000 and x+y+z=2016, find the value of xyz

$${let}\:{a},{b},{c},{x},{y}\:{and}\:{z}\:{be}\:{complex}\:{numbers} \\ $$$${such}\:{that}\:: \\ $$$${a}=\frac{{b}+{c}}{{x}−\mathrm{2}},\:{b}=\frac{{c}+{a}}{{y}−\mathrm{2}},\:{c}=\frac{{a}+{b}}{{z}−\mathrm{2}} \\ $$$${if}\:{xy}+{yz}+{zx}=\mathrm{1000}\:{and}\:{x}+{y}+{z}=\mathrm{2016}, \\ $$$${find}\:{the}\:{value}\:{of}\:{xyz} \\ $$

Question Number 17779 Answers: 1 Comments: 0

show that {log_a ab}{log_b ab}=logab_a +logab_b

$${show}\:{that}\:\left\{{lo}\underset{{a}} {{g}ab}\right\}\left\{{lo}\underset{{b}} {{g}ab}\right\}={loga}\underset{{a}} {{b}}+{loga}\underset{{b}} {{b}} \\ $$

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