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Question Number 19080 Answers: 0 Comments: 1

Question Number 19064 Answers: 1 Comments: 2

Question Number 19063 Answers: 2 Comments: 0

find the possible values of x if ((8^x +27^x )/(12^x +18^x ))=(7/6)

$$\mathrm{find}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{if} \\ $$$$\frac{\mathrm{8}^{\mathrm{x}} +\mathrm{27}^{\mathrm{x}} }{\mathrm{12}^{\mathrm{x}} +\mathrm{18}^{\mathrm{x}} }=\frac{\mathrm{7}}{\mathrm{6}} \\ $$

Question Number 19058 Answers: 0 Comments: 0

Question Number 19055 Answers: 1 Comments: 0

Find the cubic equation whose roots are the radius of three escribed circles in term of inradius, circumradius and semiperimeter.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{cubic}\:\mathrm{equation}\:\mathrm{whose}\:\mathrm{roots} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{three}\:\mathrm{escribed}\:\mathrm{circles} \\ $$$$\mathrm{in}\:\mathrm{term}\:\mathrm{of}\:\mathrm{inradius},\:\mathrm{circumradius}\:\mathrm{and} \\ $$$$\mathrm{semiperimeter}. \\ $$

Question Number 19033 Answers: 2 Comments: 1

Question Number 19073 Answers: 0 Comments: 0

Question Number 19025 Answers: 0 Comments: 0

Question Number 19077 Answers: 1 Comments: 0

∫ sec^3 x dx

$$\int\:\mathrm{sec}^{\mathrm{3}} \:{x}\:{dx} \\ $$

Question Number 19021 Answers: 0 Comments: 4

Question Number 19060 Answers: 1 Comments: 2

Question Number 19009 Answers: 1 Comments: 0

The sum of four consecutive 2−digit numbers when divided by 10 becomes a perfect square.Which of the following can possibly be one of these four numbers? (a)21(b)25(c)41(d)67(e)73 please show workings

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{four}\:\mathrm{consecutive} \\ $$$$\mathrm{2}−\mathrm{digit}\:\mathrm{numbers}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by} \\ $$$$\mathrm{10}\:\mathrm{becomes}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}.\mathrm{Which} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{can}\:\mathrm{possibly}\:\mathrm{be} \\ $$$$\mathrm{one}\:\mathrm{of}\:\mathrm{these}\:\mathrm{four}\:\mathrm{numbers}? \\ $$$$\left(\mathrm{a}\right)\mathrm{21}\left(\mathrm{b}\right)\mathrm{25}\left(\mathrm{c}\right)\mathrm{41}\left(\mathrm{d}\right)\mathrm{67}\left(\mathrm{e}\right)\mathrm{73} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{show}\:\mathrm{workings} \\ $$

Question Number 19002 Answers: 1 Comments: 0

what is the maximum number of time three divides 333^(505)

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{number}\:\mathrm{of}\:\:\mathrm{time}\:\mathrm{three}\:\mathrm{divides}\:\mathrm{333}^{\mathrm{505}} \\ $$

Question Number 19117 Answers: 0 Comments: 0

Σ_(n=1) ^7 (n/((n^2 +1))) = ? please help

$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\mathrm{7}} {\sum}}\:\frac{\mathrm{n}}{\left(\mathrm{n}^{\mathrm{2}} +\mathrm{1}\right)}\:=\:? \\ $$$$\mathrm{please}\:\mathrm{help} \\ $$

Question Number 19053 Answers: 1 Comments: 0

Find the sum: (1/2) − (1/3) + (1/4) − (1/5) + (1/6) − (1/7) + (1/8) − (1/9) + ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}:\:\frac{\mathrm{1}}{\mathrm{2}}\:−\:\frac{\mathrm{1}}{\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\:−\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$−\:\frac{\mathrm{1}}{\mathrm{7}}\:+\:\frac{\mathrm{1}}{\mathrm{8}}\:−\:\frac{\mathrm{1}}{\mathrm{9}}\:+\:... \\ $$

Question Number 18979 Answers: 0 Comments: 0

Question Number 18969 Answers: 1 Comments: 0

If ((a/b))+((b/a))=2, then find ((a/b))^(10) − ((b/a))^(10) .

$$\mathrm{If}\:\left(\frac{{a}}{{b}}\right)+\left(\frac{{b}}{{a}}\right)=\mathrm{2},\:\mathrm{then}\:\mathrm{find}\:\left(\frac{{a}}{{b}}\right)^{\mathrm{10}} −\:\left(\frac{{b}}{{a}}\right)^{\mathrm{10}} . \\ $$

Question Number 18965 Answers: 1 Comments: 3

Two blocks of masses M and 2M are connected to each other through a light spring as shown in figure. If we push the mass M with a force F which cause acceleration a in mass M, what will the acceleration in 2M?

$$\mathrm{Two}\:\mathrm{blocks}\:\mathrm{of}\:\mathrm{masses}\:{M}\:\mathrm{and}\:\mathrm{2}{M}\:\mathrm{are} \\ $$$$\mathrm{connected}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}\:\mathrm{through}\:\mathrm{a}\:\mathrm{light} \\ $$$$\mathrm{spring}\:\mathrm{as}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{figure}.\:\mathrm{If}\:\mathrm{we}\:\mathrm{push}\:\mathrm{the} \\ $$$$\mathrm{mass}\:{M}\:\mathrm{with}\:\mathrm{a}\:\mathrm{force}\:{F}\:\mathrm{which}\:\mathrm{cause} \\ $$$$\mathrm{acceleration}\:\mathrm{a}\:\mathrm{in}\:\mathrm{mass}\:{M},\:\mathrm{what}\:\mathrm{will}\:\mathrm{the} \\ $$$$\mathrm{acceleration}\:\mathrm{in}\:\mathrm{2}{M}? \\ $$

Question Number 18963 Answers: 0 Comments: 4

Two blocks A and B each of mass 1 kg are placed on a smooth horizontal surface. Two horizontal forces 5 N and 10 N are applied on the blocks A and B respectively as shown in figure. The block A does not slide on block B. Then the normal reaction between the two block is

$$\mathrm{Two}\:\mathrm{blocks}\:{A}\:\mathrm{and}\:{B}\:\mathrm{each}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1}\:\mathrm{kg} \\ $$$$\mathrm{are}\:\mathrm{placed}\:\mathrm{on}\:\mathrm{a}\:\mathrm{smooth}\:\mathrm{horizontal} \\ $$$$\mathrm{surface}.\:\mathrm{Two}\:\mathrm{horizontal}\:\mathrm{forces}\:\mathrm{5}\:\mathrm{N}\:\mathrm{and} \\ $$$$\mathrm{10}\:\mathrm{N}\:\mathrm{are}\:\mathrm{applied}\:\mathrm{on}\:\mathrm{the}\:\mathrm{blocks}\:{A}\:\mathrm{and}\:{B} \\ $$$$\mathrm{respectively}\:\mathrm{as}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{figure}.\:\mathrm{The} \\ $$$$\mathrm{block}\:{A}\:\mathrm{does}\:\mathrm{not}\:\mathrm{slide}\:\mathrm{on}\:\mathrm{block}\:{B}.\:\mathrm{Then} \\ $$$$\mathrm{the}\:\mathrm{normal}\:\mathrm{reaction}\:\mathrm{between}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{block}\:\mathrm{is} \\ $$

Question Number 18962 Answers: 1 Comments: 0

The number of solutions of the equation sin^5 θ + (1/(sin θ)) = (1/(cos θ)) + cos^5 θ where θ ∈ (0, (π/2)) , is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{sin}^{\mathrm{5}} \:\theta\:+\:\frac{\mathrm{1}}{\mathrm{sin}\:\theta}\:=\:\frac{\mathrm{1}}{\mathrm{cos}\:\theta}\:+\:\mathrm{cos}^{\mathrm{5}} \:\theta\:\mathrm{where} \\ $$$$\theta\:\in\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right)\:,\:\mathrm{is} \\ $$

Question Number 18961 Answers: 1 Comments: 0

Find arg(z), z = i^i^i .

$$\mathrm{Find}\:\mathrm{arg}\left({z}\right),\:{z}\:=\:{i}^{{i}^{{i}} } . \\ $$

Question Number 18951 Answers: 0 Comments: 0

Question Number 18949 Answers: 1 Comments: 1

Find the number of numbers ≤ 10^8 which are neither perfect squares, nor perfect cubes, nor perfect fifth powers.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{numbers}\:\leqslant\:\mathrm{10}^{\mathrm{8}} \\ $$$$\mathrm{which}\:\mathrm{are}\:\mathrm{neither}\:\mathrm{perfect}\:\mathrm{squares},\:\mathrm{nor} \\ $$$$\mathrm{perfect}\:\mathrm{cubes},\:\mathrm{nor}\:\mathrm{perfect}\:\mathrm{fifth}\:\mathrm{powers}. \\ $$

Question Number 18945 Answers: 0 Comments: 1

A point ′A′ is randomly chosen in a square of side length 1 unit. Find the probability the distance from A to the centre of the square does not exceed x.

$$\mathrm{A}\:\mathrm{point}\:'\mathrm{A}'\:\mathrm{is}\:\mathrm{randomly}\:\mathrm{chosen}\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{square}\:\mathrm{of}\:\mathrm{side}\:\mathrm{length}\:\mathrm{1}\:\mathrm{unit}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{A}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{centre}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\mathrm{does}\:\mathrm{not}\:\mathrm{exceed}\:\mathrm{x}. \\ $$

Question Number 18924 Answers: 1 Comments: 0

A spring of force constant k is cut into two pieces such that one piece is twice as long as the other. Then the longer piece will have a force constant of

$$\mathrm{A}\:\mathrm{spring}\:\mathrm{of}\:\mathrm{force}\:\mathrm{constant}\:{k}\:\mathrm{is}\:\mathrm{cut}\:\mathrm{into} \\ $$$$\mathrm{two}\:\mathrm{pieces}\:\mathrm{such}\:\mathrm{that}\:\mathrm{one}\:\mathrm{piece}\:\mathrm{is}\:\mathrm{twice} \\ $$$$\mathrm{as}\:\mathrm{long}\:\mathrm{as}\:\mathrm{the}\:\mathrm{other}.\:\mathrm{Then}\:\mathrm{the}\:\mathrm{longer} \\ $$$$\mathrm{piece}\:\mathrm{will}\:\mathrm{have}\:\mathrm{a}\:\mathrm{force}\:\mathrm{constant}\:\mathrm{of} \\ $$

Question Number 18922 Answers: 0 Comments: 3

Consider a block sliding over a smooth inclined surface of inclination θ. Relating to Newton′s second law applied on the block, select the incorrect alternative. (1) ΣF_(y′) ≠ 0 (2) ΣF_y = 0 (3) ΣF_x = −mg sin θ (4) ΣF_(x′) < 0

$$\mathrm{Consider}\:\mathrm{a}\:\mathrm{block}\:\mathrm{sliding}\:\mathrm{over}\:\mathrm{a}\:\mathrm{smooth} \\ $$$$\mathrm{inclined}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{inclination}\:\theta.\:\mathrm{Relating} \\ $$$$\mathrm{to}\:\mathrm{Newton}'\mathrm{s}\:\mathrm{second}\:\mathrm{law}\:\mathrm{applied}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{block},\:\mathrm{select}\:\mathrm{the}\:\mathrm{incorrect}\:\mathrm{alternative}. \\ $$$$\left(\mathrm{1}\right)\:\Sigma{F}_{{y}'} \:\neq\:\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:\Sigma{F}_{{y}} \:=\:\mathrm{0} \\ $$$$\left(\mathrm{3}\right)\:\Sigma{F}_{{x}} \:=\:−{mg}\:\mathrm{sin}\:\theta \\ $$$$\left(\mathrm{4}\right)\:\Sigma{F}_{{x}'} \:<\:\mathrm{0} \\ $$

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