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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

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

Question Number 18918 Answers: 0 Comments: 17

A bird sits on a stretched telegraph wire. The additional tension produced in the wire is (1) Zero (2) Greater than weight of the bird (3) Less than the weight of the bird (4) Equal to the weight of the bird

$$\mathrm{A}\:\mathrm{bird}\:\mathrm{sits}\:\mathrm{on}\:\mathrm{a}\:\mathrm{stretched}\:\mathrm{telegraph} \\ $$$$\mathrm{wire}.\:\mathrm{The}\:\mathrm{additional}\:\mathrm{tension}\:\mathrm{produced} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Zero} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Greater}\:\mathrm{than}\:\mathrm{weight}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bird} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Less}\:\mathrm{than}\:\mathrm{the}\:\mathrm{weight}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bird} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{Equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{weight}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bird} \\ $$

Question Number 18940 Answers: 0 Comments: 3

A light rope is passed over a pulley such that at its one end a block is attached, and on the other end a boy is climbing up with acceleration (g/2) relative to rope. Mass of the block is 30 kg and that of the boy is 40 kg. Find the tension and acceleration of the rope.

$$\mathrm{A}\:\mathrm{light}\:\mathrm{rope}\:\mathrm{is}\:\mathrm{passed}\:\mathrm{over}\:\mathrm{a}\:\mathrm{pulley}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{at}\:\mathrm{its}\:\mathrm{one}\:\mathrm{end}\:\mathrm{a}\:\mathrm{block}\:\mathrm{is}\:\mathrm{attached}, \\ $$$$\mathrm{and}\:\mathrm{on}\:\mathrm{the}\:\mathrm{other}\:\mathrm{end}\:\mathrm{a}\:\mathrm{boy}\:\mathrm{is}\:\mathrm{climbing} \\ $$$$\mathrm{up}\:\mathrm{with}\:\mathrm{acceleration}\:\frac{{g}}{\mathrm{2}}\:\mathrm{relative}\:\mathrm{to}\:\mathrm{rope}. \\ $$$$\mathrm{Mass}\:\mathrm{of}\:\mathrm{the}\:\mathrm{block}\:\mathrm{is}\:\mathrm{30}\:\mathrm{kg}\:\mathrm{and}\:\mathrm{that}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{boy}\:\mathrm{is}\:\mathrm{40}\:\mathrm{kg}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{tension}\:\mathrm{and} \\ $$$$\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rope}. \\ $$

Question Number 18916 Answers: 0 Comments: 0

x^2 −7x+12<mod(x−4)

$${x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{12}<{mod}\left({x}−\mathrm{4}\right) \\ $$

Question Number 18909 Answers: 0 Comments: 1

What does a_ .b_ and a_ ×b_ means ? someone please explain it.

$${What}\:{does}\:\underset{} {{a}}.\underset{} {{b}}\:\:{and}\:\underset{} {{a}}×\underset{} {{b}}\:{means}\:? \\ $$$${someone}\:{please}\:{explain}\:{it}. \\ $$

Question Number 18908 Answers: 0 Comments: 5

Why Does ∣A^→ ×B^→ ∣=ABSinθ ?

$${Why}\:{Does} \\ $$$$\mid\overset{\rightarrow} {{A}}×\overset{\rightarrow} {{B}}\mid={ABSin}\theta\:? \\ $$

Question Number 18907 Answers: 0 Comments: 3

Why Does A^→ .B^→ =ABCosθ?