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Question Number 26480    Answers: 1   Comments: 0

Find the number of all possible different words into which the word INTERFERE can be converted by change of place of letters,if no two consonants must be together.

$${Find}\:{the}\:{number}\:{of}\:{all}\:{possible} \\ $$$${different}\:{words}\:{into}\:{which}\:{the} \\ $$$${word}\:{INTERFERE}\:{can}\:{be}\: \\ $$$${converted}\:{by}\:{change}\:{of}\:{place}\:{of}\: \\ $$$${letters},{if}\:{no}\:{two}\:{consonants} \\ $$$${must}\:{be}\:{together}. \\ $$

Question Number 26477    Answers: 1   Comments: 0

A number of four different digits is formed by using the digits 1,2,3,4,5,6,7,in all possible ways each digit occuring once only.find how many of them are greater than 3400

$${A}\:{number}\:{of}\:{four}\:{different} \\ $$$${digits}\:{is}\:{formed}\:{by}\:{using}\:{the}\: \\ $$$${digits}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7},{in}\:{all}\:{possible} \\ $$$${ways}\:{each}\:{digit}\:{occuring}\:{once} \\ $$$${only}.{find}\:{how}\:{many}\:{of}\:{them}\:{are} \\ $$$${greater}\:{than}\:\mathrm{3400} \\ $$

Question Number 26473    Answers: 1   Comments: 0

How many numbers less than 1000 and divisible by 5 can be formed with the digits 0, 1, 2 ,3 ,4 ,5 6 ,7 ,8 ,9,each digit not occuring more than once in each number?

$${How}\:{many}\:{numbers}\:{less}\:{than} \\ $$$$\mathrm{1000}\:{and}\:{divisible}\:{by}\:\mathrm{5}\:{can}\:{be} \\ $$$${formed}\:{with}\:{the}\:{digits}\:\mathrm{0},\:\mathrm{1},\:\mathrm{2}\:,\mathrm{3}\:,\mathrm{4}\:,\mathrm{5}\: \\ $$$$\mathrm{6}\:,\mathrm{7}\:,\mathrm{8}\:,\mathrm{9},{each}\:{digit}\:{not}\:{occuring} \\ $$$${more}\:{than}\:{once}\:{in}\:{each}\:{number}? \\ $$

Question Number 26463    Answers: 0   Comments: 1

∫_0 ^(2π) cos^2 θsin θdθ

$$\int_{\mathrm{0}} ^{\mathrm{2}\pi} \mathrm{cos}^{\mathrm{2}} \theta\mathrm{sin}\:\theta{d}\theta \\ $$

Question Number 26461    Answers: 0   Comments: 1

Question Number 26456    Answers: 0   Comments: 1

Question Number 26455    Answers: 0   Comments: 0

Question Number 26454    Answers: 0   Comments: 0

Question Number 26452    Answers: 1   Comments: 0

∫(√(tanx))

$$\int\sqrt{{tanx}} \\ $$

Question Number 26450    Answers: 2   Comments: 5

A man of mass M is standing on a platform of mass m_1 holding a string passing over a system of ideal pulleys. Another mass m_2 is hanging as shown (m_2 = 20 kg, m_1 = 10 kg, g = 10 m/s^2 ) Force exerted by man on string to accelerate upwards

$$\mathrm{A}\:\mathrm{man}\:\mathrm{of}\:\mathrm{mass}\:{M}\:\mathrm{is}\:\mathrm{standing}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{platform}\:\mathrm{of}\:\mathrm{mass}\:{m}_{\mathrm{1}} \:\mathrm{holding}\:\mathrm{a}\:\mathrm{string} \\ $$$$\mathrm{passing}\:\mathrm{over}\:\mathrm{a}\:\mathrm{system}\:\mathrm{of}\:\mathrm{ideal}\:\mathrm{pulleys}. \\ $$$$\mathrm{Another}\:\mathrm{mass}\:{m}_{\mathrm{2}} \:\mathrm{is}\:\mathrm{hanging}\:\mathrm{as}\:\mathrm{shown} \\ $$$$\left({m}_{\mathrm{2}} \:=\:\mathrm{20}\:\mathrm{kg},\:{m}_{\mathrm{1}} \:=\:\mathrm{10}\:\mathrm{kg},\:{g}\:=\:\mathrm{10}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} \right) \\ $$$$\mathrm{Force}\:\mathrm{exerted}\:\mathrm{by}\:\mathrm{man}\:\mathrm{on}\:\mathrm{string}\:\mathrm{to} \\ $$$$\mathrm{accelerate}\:\mathrm{upwards} \\ $$

Question Number 26449    Answers: 1   Comments: 0

Transform the equation 5x^2 + 4xy + 2y^2 − 2x + 4y + 4 = 0 into one without xy, x and y terms.

$${Transform}\:{the}\:{equation}\:\mathrm{5}{x}^{\mathrm{2}} \:+\:\mathrm{4}{xy} \\ $$$$+\:\mathrm{2}{y}^{\mathrm{2}} \:−\:\mathrm{2}{x}\:+\:\mathrm{4}{y}\:+\:\mathrm{4}\:=\:\mathrm{0}\:{into}\:{one} \\ $$$${without}\:{xy},\:{x}\:{and}\:{y}\:{terms}. \\ $$

Question Number 26447    Answers: 0   Comments: 1

Question Number 26446    Answers: 1   Comments: 0

Question Number 26442    Answers: 0   Comments: 1

find the lateral surface area of cuboid = L=13m 12m and 10m

$${find}\:{the}\:{lateral}\:{surface}\:{area}\:{of}\:{cuboid}\:= \\ $$$${L}=\mathrm{13}{m}\:\mathrm{12}{m}\:{and}\:\mathrm{10}{m} \\ $$

Question Number 26438    Answers: 1   Comments: 0

Question Number 26425    Answers: 0   Comments: 0

A body is projected vertically upward with an initial velocity of u. Another Another body is projected with the same initial velocity, t seconds after the first. If T is the time when the two bodies meet, and g the acceleration due to gravity, Show that T = ((2u + gt)/(2g))

$$\mathrm{A}\:\mathrm{body}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{vertically}\:\mathrm{upward}\:\mathrm{with}\:\mathrm{an}\:\mathrm{initial}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{u}.\:\mathrm{Another} \\ $$$$\mathrm{Another}\:\mathrm{body}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{with}\:\mathrm{the}\:\mathrm{same}\:\mathrm{initial}\:\mathrm{velocity},\:\mathrm{t}\:\mathrm{seconds}\:\mathrm{after} \\ $$$$\mathrm{the}\:\mathrm{first}.\:\mathrm{If}\:\:\mathrm{T}\:\mathrm{is}\:\mathrm{the}\:\mathrm{time}\:\mathrm{when}\:\mathrm{the}\:\mathrm{two}\:\mathrm{bodies}\:\mathrm{meet},\:\mathrm{and}\:\mathrm{g}\:\mathrm{the}\:\mathrm{acceleration} \\ $$$$\mathrm{due}\:\mathrm{to}\:\mathrm{gravity},\:\mathrm{Show}\:\mathrm{that}\:\:\:\boldsymbol{\mathrm{T}}\:=\:\frac{\mathrm{2u}\:+\:\mathrm{gt}}{\mathrm{2g}} \\ $$

Question Number 26424    Answers: 0   Comments: 0

The front of a train 80m long passes a signal at a speed of 72km/hr. If the rear of the train passes the signal 5s later, Find (a) The magnitude of the acceleration of the train. (b) The speed at which the rear of the train passes the signal.

$$\mathrm{The}\:\mathrm{front}\:\mathrm{of}\:\mathrm{a}\:\mathrm{train}\:\mathrm{80m}\:\mathrm{long}\:\mathrm{passes}\:\mathrm{a}\:\mathrm{signal}\:\mathrm{at}\:\mathrm{a}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{72km}/\mathrm{hr}.\:\mathrm{If}\:\mathrm{the} \\ $$$$\mathrm{rear}\:\mathrm{of}\:\mathrm{the}\:\mathrm{train}\:\mathrm{passes}\:\mathrm{the}\:\mathrm{signal}\:\mathrm{5s}\:\mathrm{later},\:\mathrm{Find} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{The}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{train}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{The}\:\mathrm{speed}\:\mathrm{at}\:\mathrm{which}\:\mathrm{the}\:\mathrm{rear}\:\mathrm{of}\:\mathrm{the}\:\mathrm{train}\:\mathrm{passes}\:\mathrm{the}\:\mathrm{signal}. \\ $$

Question Number 26405    Answers: 1   Comments: 0

Question Number 26403    Answers: 0   Comments: 5

developp the function f(x)=/x/ 2π periodic in fourier serie .(f even)

$${developp}\:{the}\:{function}\:{f}\left({x}\right)=/{x}/\:\mathrm{2}\pi \\ $$$${periodic}\:{in}\:{fourier}\:{serie}\:.\left({f}\:{even}\right) \\ $$

Question Number 26402    Answers: 1   Comments: 2

find the nature of the serie Σ_(n=0) ^∝ ((n!)/(1+2^n )) .

$${find}\:{the}\:{nature}\:{of}\:{the}\:{serie}\:\:\sum_{{n}=\mathrm{0}} ^{\propto} \frac{{n}!}{\mathrm{1}+\mathrm{2}^{{n}} }\:\:. \\ $$

Question Number 26401    Answers: 1   Comments: 1

find the sum of Σ_(n=1) ^∝ (1/(n 2^n )) .

$${find}\:{the}\:{sum}\:{of}\:\: \\ $$$$\sum_{{n}=\mathrm{1}} ^{\propto} \:\:\frac{\mathrm{1}}{{n}\:\:\mathrm{2}^{{n}} }\:\:. \\ $$

Question Number 26400    Answers: 1   Comments: 0

find the sequence (u_n ) wich verify u_n −2 u_(n−1) +1= 2^n

$${find}\:{the}\:{sequence}\:\left({u}_{{n}} \right)\:{wich}\:{verify}\:{u}_{{n}} \:−\mathrm{2}\:{u}_{{n}−\mathrm{1}} \:+\mathrm{1}=\:\mathrm{2}^{{n}} \\ $$

Question Number 26399    Answers: 2   Comments: 0

calculate ∫∫ _D cos(x^2 +y^2 )dxdy with D=C(o.(√(π/2))).

$${calculate}\:\:\int\int\:_{{D}} {cos}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dxdy}\:\:\:{with}\:\:{D}={C}\left({o}.\sqrt{\frac{\pi}{\mathrm{2}}}\right). \\ $$

Question Number 26398    Answers: 2   Comments: 2

find the value of ∫∫_D x^2 y dxdy on the domain D={(x.y)∈R^2 / x^2 +y^2 −2x≤0 and y≥0}

$${find}\:{the}\:{value}\:{of}\:\:\int\int_{{D}} \:{x}^{\mathrm{2}} {y}\:{dxdy}\:\:\:{on}\:{the}\:{domain} \\ $$$${D}=\left\{\left({x}.{y}\right)\in{R}^{\mathrm{2}} /\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:−\mathrm{2}{x}\leqslant\mathrm{0}\:{and}\:{y}\geqslant\mathrm{0}\right\} \\ $$

Question Number 26397    Answers: 2   Comments: 1

find ∫ (dx/(x(√(1+x^2 )))) and calculate ∫_1 ^3 (dx/(x(√(1+x^2 ))))

$${find}\:\int\:\:\frac{{dx}}{{x}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{and}\:{calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{3}} \:\frac{{dx}}{{x}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \\ $$

Question Number 26396    Answers: 1   Comments: 1

find the value of ∫_0 ^(1 ) (dx/(x^2 +2x +5)) .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}\:} \:\:\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{2}{x}\:+\mathrm{5}}\:. \\ $$

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