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Question Number 35533 Answers: 1 Comments: 0

If the roots of the equation x^2 −px+q=0 differ by unity, then

$$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} −{px}+{q}=\mathrm{0} \\ $$$$\mathrm{differ}\:\mathrm{by}\:\mathrm{unity},\:\mathrm{then} \\ $$

Question Number 35527 Answers: 0 Comments: 1

Question Number 35513 Answers: 1 Comments: 0

g(x)= 6x^2 − 5ax + b^2 given that g(x) has only two roots and are (x−1) and (x−2) find the value of a and b.Using (x−1) as a root detemine the extend to which (x−2) is a root (occurance as a root).

$${g}\left({x}\right)=\:\mathrm{6}{x}^{\mathrm{2}} −\:\mathrm{5}{ax}\:+\:{b}^{\mathrm{2}} \\ $$$${given}\:{that}\:{g}\left({x}\right)\:{has}\:{only}\:{two}\:{roots} \\ $$$${and}\:{are}\:\left({x}−\mathrm{1}\right)\:{and}\:\left({x}−\mathrm{2}\right) \\ $$$${find}\:{the}\:{value}\:{of}\:{a}\:{and}\:{b}.{Using} \\ $$$$\left({x}−\mathrm{1}\right)\:{as}\:{a}\:{root}\:{detemine}\:{the}\: \\ $$$${extend}\:{to}\:{which}\:\left({x}−\mathrm{2}\right)\:{is}\:{a}\:{root} \\ $$$$\left({occurance}\:{as}\:{a}\:{root}\right). \\ $$

Question Number 35512 Answers: 1 Comments: 0

Given that (x+1,3,x) are lengths of the sides of a right angled triangle(pythagoras tripple) find the value of x.

$$\:{Given}\:{that}\:\left({x}+\mathrm{1},\mathrm{3},{x}\right)\:{are}\:{lengths} \\ $$$${of}\:{the}\:{sides}\:{of}\:{a}\:{right}\:{angled} \\ $$$${triangle}\left({pythagoras}\:{tripple}\right) \\ $$$${find}\:{the}\:{value}\:{of}\:{x}. \\ $$

Question Number 35507 Answers: 0 Comments: 3

Question Number 35502 Answers: 0 Comments: 3

Question Number 35496 Answers: 1 Comments: 1

Question Number 35493 Answers: 0 Comments: 2

Question Number 35491 Answers: 3 Comments: 1

prove that 3^x =9x

$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\mathrm{3}^{\boldsymbol{{x}}} =\mathrm{9}\boldsymbol{{x}} \\ $$

Question Number 35482 Answers: 0 Comments: 1

Let A and B are 3 ×3 matrices. The statements below which is True is ... (A) AB = BA (B) If AB = 0, then only A = 0 or B = 0 is true (C) If AB = I, then only A = I or A = −I is true (D) There exist A where A ≠ 0, and yet A^2 = 0 (E) ∣A + B∣ = ∣A∣ + ∣B∣

$$\mathrm{Let}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{3}\:×\mathrm{3}\:\mathrm{matrices}.\:\mathrm{The}\:\mathrm{statements}\:\mathrm{below} \\ $$$$\mathrm{which}\:\mathrm{is}\:{True}\:\mathrm{is}\:... \\ $$$$\left(\mathrm{A}\right)\:{AB}\:=\:{BA} \\ $$$$\left(\mathrm{B}\right)\:\mathrm{If}\:{AB}\:=\:\mathrm{0},\:\mathrm{then}\:\mathrm{only}\:{A}\:=\:\mathrm{0}\:\mathrm{or}\:{B}\:=\:\mathrm{0}\:\mathrm{is}\:\mathrm{true} \\ $$$$\left(\mathrm{C}\right)\:\mathrm{If}\:{AB}\:=\:{I},\:\mathrm{then}\:\mathrm{only}\:{A}\:=\:{I}\:\mathrm{or}\:{A}\:=\:−{I}\:\mathrm{is}\:\mathrm{true} \\ $$$$\left(\mathrm{D}\right)\:\mathrm{There}\:\mathrm{exist}\:{A}\:\mathrm{where}\:{A}\:\neq\:\mathrm{0},\:\mathrm{and}\:\mathrm{yet}\:{A}^{\mathrm{2}} \:=\:\mathrm{0} \\ $$$$\left(\mathrm{E}\right)\:\mid{A}\:+\:{B}\mid\:=\:\mid{A}\mid\:+\:\mid{B}\mid \\ $$

Question Number 35481 Answers: 1 Comments: 1

if x^p y^p =(x + y)^(p +q) prove that (dy/dx)=(y/x)

$${if}\:{x}^{{p}} {y}^{{p}} =\left({x}\:+\:{y}\right)\:^{{p}\:+{q}} \:\:\: \\ $$$${prove}\:{that}\:\frac{{dy}}{{dx}}=\frac{{y}}{{x}} \\ $$

Question Number 35478 Answers: 0 Comments: 1

((3(√2)(2−i)))^(1/5) =...??

$$\sqrt[{\mathrm{5}}]{\mathrm{3}\sqrt{\mathrm{2}}\left(\mathrm{2}−{i}\right)}=...?? \\ $$

Question Number 35476 Answers: 0 Comments: 2

In a match between A and B.The probability of A winning is (4/(11)), the probabilith of B winning is (2/(11)). What is the probability if they were to draw the match?

$${In}\:{a}\:{match}\:{between}\:{A}\:{and}\:{B}.{The} \\ $$$${probability}\:{of}\:{A}\:{winning}\:{is}\:\frac{\mathrm{4}}{\mathrm{11}}, \\ $$$${the}\:{probabilith}\:{of}\:{B}\:{winning}\:{is}\:\frac{\mathrm{2}}{\mathrm{11}}. \\ $$$${What}\:{is}\:{the}\:{probability}\:{if}\:{they} \\ $$$${were}\:{to}\:{draw}\:{the}\:{match}? \\ $$

Question Number 35475 Answers: 1 Comments: 0

Is Rational Number Countable? If yes how do we count it with one to one correspondence with set of natural number N?

$${Is}\:{Rational}\:{Number}\:{Countable}? \\ $$$${If}\:{yes}\:{how}\:{do}\:{we}\:{count}\:{it}\:{with}\:{one}\:{to}\:{one}\:{correspondence}\:{with}\:{set}\:{of}\:{natural}\:{number}\:\mathbb{N}? \\ $$

Question Number 35474 Answers: 0 Comments: 0

while proving F=ma newtons 2nd law we put F=1 when m=1 and a=1 and thus k=1 why not F=other value except 1...

$${while}\:{proving}\:{F}={ma}\:{newtons}\:\mathrm{2}{nd}\:{law}\:{we}\:{put} \\ $$$${F}=\mathrm{1}\:{when}\:{m}=\mathrm{1}\:{and}\:{a}=\mathrm{1}\:{and}\:{thus}\:{k}=\mathrm{1} \\ $$$${why}\:{not}\:{F}={other}\:{value}\:{except}\:\mathrm{1}... \\ $$

Question Number 35473 Answers: 0 Comments: 0

vector has both magnetude and direction...then why time and current not vector...

$${vector}\:{has}\:{both}\:{magnetude}\:{and}\:{direction}...{then} \\ $$$${why}\:{time}\:{and}\:{current}\:{not}\:{vector}... \\ $$

Question Number 35472 Answers: 1 Comments: 0

Mr. Crone started from his house at 8.00 a.m. and walked t to his office at an average speed of 4 km/h. Mettle started from Mr. Crones at 8.30 a.m. and travelled by cycle in the same direction as Mr. Crone at average speed of of 6 km/h. If the two arrive arrived at the office at the same time .(i) Find the time of arrival (ii) Find the distance between Mr. Crones house and the office

$${Mr}.\:{Crone}\:{started}\:{from}\:{his}\: \\ $$$${house}\:{at}\:\mathrm{8}.\mathrm{00}\:{a}.{m}.\:{and}\:{walked}\:{t} \\ $$$${to}\:{his}\:{office}\:{at}\:{an}\:{average}\:{speed} \\ $$$${of}\:\mathrm{4}\:{km}/{h}.\:{Mettle}\:{started}\:{from} \\ $$$${Mr}.\:{Crones}\:{at}\:\mathrm{8}.\mathrm{30}\:{a}.{m}.\:{and}\:{travelled} \\ $$$${by}\:{cycle}\:{in}\:{the}\:{same}\:{direction} \\ $$$${as}\:{Mr}.\:{Crone}\:{at}\:{average}\:{speed} \\ $$$${of}\:\:{of}\:\:\mathrm{6}\:{km}/{h}.\:{If}\:{the}\:{two}\:{arrive} \\ $$$${arrived}\:{at}\:{the}\:{office}\:{at}\:{the}\:{same}\:{time} \\ $$$$.\left({i}\right)\:{Find}\:{the}\:{time}\:{of}\:{arrival} \\ $$$$\left({ii}\right)\:{Find}\:{the}\:{distance}\:{between}\:{Mr}. \\ $$$${Crones}\:{house}\:{and}\:{the}\:{office} \\ $$

Question Number 35471 Answers: 0 Comments: 0

∫_a ^b f(x)dx=area under the curve but say why what is the meaning of ∫ ←this sign

$$\int_{{a}} ^{{b}} {f}\left({x}\right){dx}={area}\:{under}\:{the}\:{curve}\:{but}\:{say}\:{why} \\ $$$${what}\:{is}\:{the}\:{meaning}\:{of}\:\int\:\leftarrow{this}\:{sign} \\ $$

Question Number 35470 Answers: 2 Comments: 0

prove sin0^o =0 and cos0^o =1

$${prove}\:{sin}\mathrm{0}^{{o}} =\mathrm{0}\:\:{and}\:{cos}\mathrm{0}^{{o}} =\mathrm{1} \\ $$

Question Number 35469 Answers: 0 Comments: 0

find distance between (x_(1,) y_1 ) and (x_2 ,y_2 ) when x axis and y axis inclined ai angle θ

$${find}\:{distance}\:{between}\:\left({x}_{\mathrm{1},} {y}_{\mathrm{1}} \right)\:{and}\:\left({x}_{\mathrm{2}} ,{y}_{\mathrm{2}} \right)\:{when} \\ $$$${x}\:{axis}\:{and}\:{y}\:{axis}\:{inclined}\:{ai}\:{angle}\:\theta \\ $$

Question Number 35467 Answers: 1 Comments: 0

If x = 32 − 16 ÷ 2 × 4, then x=

$$\mathrm{If}\:\:{x}\:=\:\mathrm{32}\:−\:\mathrm{16}\:\boldsymbol{\div}\:\mathrm{2}\:×\:\mathrm{4},\:\mathrm{then}\:{x}= \\ $$

Question Number 35461 Answers: 1 Comments: 0

Question Number 35460 Answers: 1 Comments: 1

Find the values of k for which the equation (((k −3)),((10 −k+1)) ) ((x),(y) ) = (((k−1)),(8) ) have a) a unique solution b) no solution c)an infinite solution hence Find the image of the point (3,1) after reflection in the line with equation a) x=1 b) y= −1 c) y+x= 1

$${Find}\:{the}\:{values}\:{of}\:{k}\:{for}\:{which} \\ $$$${the}\:{equation}\: \\ $$$$\begin{pmatrix}{{k}\:\:\:\:\:\:\:\:\:−\mathrm{3}}\\{\mathrm{10}\:\:\:\:\:\:\:−{k}+\mathrm{1}}\end{pmatrix}\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:\begin{pmatrix}{{k}−\mathrm{1}}\\{\mathrm{8}}\end{pmatrix} \\ $$$${have} \\ $$$$\left.{a}\right)\:{a}\:\:{unique}\:{solution} \\ $$$$\left.{b}\right)\:{no}\:{solution} \\ $$$$\left.{c}\right){an}\:{infinite}\:{solution} \\ $$$${hence} \\ $$$${Find}\:{the}\:{image}\:{of}\:{the}\:{point}\: \\ $$$$\left(\mathrm{3},\mathrm{1}\right)\:{after}\:{reflection}\:{in}\:{the}\:{line} \\ $$$${with}\:{equation} \\ $$$$\left.{a}\left.\right)\left.\:{x}=\mathrm{1}\:\:\:\:{b}\right)\:{y}=\:−\mathrm{1}\:\:\boldsymbol{{c}}\right)\:\boldsymbol{{y}}+\boldsymbol{{x}}=\:\mathrm{1} \\ $$

Question Number 35456 Answers: 2 Comments: 0

∫(dx/(x(x^(2018) +1)))

$$\int\frac{{dx}}{{x}\left({x}^{\mathrm{2018}} +\mathrm{1}\right)} \\ $$

Question Number 35446 Answers: 1 Comments: 1

Question Number 35440 Answers: 1 Comments: 2

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

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{2}{x}^{\mathrm{2}} \:\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

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