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Question Number 45500    Answers: 1   Comments: 0

Question Number 45498    Answers: 1   Comments: 3

Question Number 45495    Answers: 1   Comments: 0

Question Number 45494    Answers: 0   Comments: 0

Question Number 45477    Answers: 0   Comments: 4

Question Number 45482    Answers: 1   Comments: 0

Question Number 45464    Answers: 1   Comments: 3

Differentiate with respect to x arctan(((a^2 +x^2 )/(a^2 −x^2 )))

$$\boldsymbol{\mathrm{D}}\mathrm{ifferentiate}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\boldsymbol{\mathrm{x}} \\ $$$$\boldsymbol{\mathrm{arctan}}\left(\frac{\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right) \\ $$

Question Number 45456    Answers: 1   Comments: 5

Question Number 45451    Answers: 1   Comments: 0

Question Number 45450    Answers: 1   Comments: 1

Question Number 45448    Answers: 0   Comments: 5

Question Number 45443    Answers: 0   Comments: 0

Question Number 45440    Answers: 1   Comments: 0

show that ((1+2sin2θ−cos2θ)/(1+sin2θ+cos2θ)) ≡ tanθ

$${show}\:{that}\: \\ $$$$\frac{\mathrm{1}+\mathrm{2}{sin}\mathrm{2}\theta−{cos}\mathrm{2}\theta}{\mathrm{1}+{sin}\mathrm{2}\theta+{cos}\mathrm{2}\theta}\:\equiv\:{tan}\theta \\ $$

Question Number 45439    Answers: 2   Comments: 0

Show that the square of every odd integer is of the form 8m + 1

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of}\:\mathrm{every}\:\mathrm{odd}\:\mathrm{integer}\:\mathrm{is}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form}\:\:\:\mathrm{8m}\:+\:\mathrm{1} \\ $$

Question Number 45433    Answers: 1   Comments: 0

find the of differnt ways in which a cricket team consisting of 11people,can be choosen from the group of 16

$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{differnt}}\:\boldsymbol{\mathrm{ways}}\: \\ $$$$\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{which}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{cricket}}\:\boldsymbol{\mathrm{team}}\:\boldsymbol{\mathrm{consisting}}\:\boldsymbol{\mathrm{of}} \\ $$$$\mathrm{11}\boldsymbol{\mathrm{people}},\boldsymbol{\mathrm{can}}\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{choosen}} \\ $$$$\boldsymbol{\mathrm{from}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{group}}\:\boldsymbol{\mathrm{of}}\:\mathrm{16} \\ $$

Question Number 45429    Answers: 0   Comments: 0

a set containing (k+1) elements has 8 more subsets that of a set containing k elements. find the value of k

$$\mathrm{a}\:\mathrm{set}\:\mathrm{containing}\:\left(\boldsymbol{\mathrm{k}}+\mathrm{1}\right)\:\mathrm{elements} \\ $$$$\mathrm{has}\:\mathrm{8}\:\mathrm{more}\:\mathrm{subsets}\:\mathrm{that}\:\mathrm{of}\: \\ $$$$\mathrm{a}\:\mathrm{set}\:\mathrm{containing}\:\boldsymbol{\mathrm{k}}\:\mathrm{elements}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{\mathrm{k}} \\ $$

Question Number 45427    Answers: 0   Comments: 4

Question Number 45422    Answers: 1   Comments: 0

Three consecutive terms of a G.P are the 3rd, 5th and 8th term of an A.P. Find the common ratio.

$$\mathrm{Three}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{G}.\mathrm{P}\:\mathrm{are}\:\mathrm{the}\:\mathrm{3rd},\:\mathrm{5th}\:\mathrm{and}\:\mathrm{8th}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{common}\:\mathrm{ratio}. \\ $$

Question Number 45417    Answers: 1   Comments: 0

Find image of plane x−y+z−3=0 in plane 2x+y−z+4=0 ?

$${Find}\:{image}\:{of}\:{plane}\:{x}−{y}+{z}−\mathrm{3}=\mathrm{0}\:{in}\: \\ $$$${plane}\:\mathrm{2}{x}+{y}−{z}+\mathrm{4}=\mathrm{0}\:? \\ $$

Question Number 45413    Answers: 2   Comments: 1

if y=((sin^(−1) x)/(√(1+x^2 ))) show that (dy/dx)(1+x^2 )+xy=1

$$\boldsymbol{\mathrm{if}}\:\boldsymbol{{y}}=\frac{\boldsymbol{\mathrm{sin}}^{−\mathrm{1}} \boldsymbol{{x}}}{\sqrt{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} }}\:\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}}\left(\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} \right)+\boldsymbol{{xy}}=\mathrm{1} \\ $$

Question Number 45410    Answers: 1   Comments: 1

given the AP a,a +d ,a+2d,a+3d,... show that S_n = (n/2){(2a+(n−1)d}

$${given}\:{the}\:{AP} \\ $$$${a},{a}\:+{d}\:,{a}+\mathrm{2}{d},{a}+\mathrm{3}{d},... \\ $$$${show}\:{that}\: \\ $$$${S}_{{n}} =\:\frac{{n}}{\mathrm{2}}\left\{\left(\mathrm{2}{a}+\left({n}−\mathrm{1}\right){d}\right\}\right. \\ $$

Question Number 45399    Answers: 1   Comments: 0

using your knowlege on Arithmetic progressions, show that A= p(1+(r/(100)))^n

$${using}\:{your}\:{knowlege}\:{on}\:{Arithmetic}\:{progressions}, \\ $$$${show}\:{that}\:\:{A}=\:{p}\left(\mathrm{1}+\frac{{r}}{\mathrm{100}}\right)^{{n}} \\ $$

Question Number 45387    Answers: 0   Comments: 0

Question Number 45381    Answers: 0   Comments: 1

Question Number 45373    Answers: 1   Comments: 1

∫(t^3 /(1+t))dt=?

$$\int\frac{\mathrm{t}^{\mathrm{3}} }{\mathrm{1}+\mathrm{t}}\mathrm{dt}=? \\ $$

Question Number 45366    Answers: 2   Comments: 2

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