Question and Answers Forum

AllQuestion and Answers: Page 1933

Question Number 13491 Answers: 1 Comments: 0

Test 1. Solve equation (k^2 −1)x^2 +(k−1)x+(k+1)=0 k∈R (30) 2. Prove ((sin(x))/(1+cos(x)))=((1−cos(x))/(sin(x))) (35) 3.P(x)=−2x^3 −2x^2 −x+2409 Find P(−11) (35) Evaluate other answers and give marks I want to see how math teachers evaluate in other countries Sorry foy my english

$${Test} \\ $$$$\mathrm{1}.\:{Solve}\:{equation} \\ $$$$\left({k}^{\mathrm{2}} −\mathrm{1}\right){x}^{\mathrm{2}} +\left({k}−\mathrm{1}\right){x}+\left({k}+\mathrm{1}\right)=\mathrm{0}\:\:{k}\in\mathbb{R} \\ $$$$\left(\mathrm{30}\right) \\ $$$$\mathrm{2}.\:{Prove} \\ $$$$\frac{{sin}\left({x}\right)}{\mathrm{1}+{cos}\left({x}\right)}=\frac{\mathrm{1}−{cos}\left({x}\right)}{{sin}\left({x}\right)} \\ $$$$\left(\mathrm{35}\right) \\ $$$$\mathrm{3}.{P}\left({x}\right)=−\mathrm{2}{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} −{x}+\mathrm{2409} \\ $$$${Find}\:{P}\left(−\mathrm{11}\right) \\ $$$$\left(\mathrm{35}\right) \\ $$$$ \\ $$$${Evaluate}\:{other}\:{answers}\:{and}\:{give}\:{marks} \\ $$$${I}\:{want}\:{to}\:{see}\:{how}\:{math}\:{teachers}\:{evaluate}\:{in}\:{other}\:{countries} \\ $$$${Sorry}\:{foy}\:{my}\:{english} \\ $$

Question Number 13490 Answers: 1 Comments: 0

The area of a rectangle is 255 m^2 . If its length is decreased by 1 m, it becomes a square. The perimeter of the square is ____ m.

$$\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{rectangle}\:\mathrm{is}\:\mathrm{255}\:\mathrm{m}^{\mathrm{2}} .\:\mathrm{If} \\ $$$$\mathrm{its}\:\mathrm{length}\:\mathrm{is}\:\mathrm{decreased}\:\mathrm{by}\:\mathrm{1}\:\mathrm{m},\:\mathrm{it}\: \\ $$$$\mathrm{becomes}\:\mathrm{a}\:\mathrm{square}.\:\mathrm{The}\:\mathrm{perimeter}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{square}\:\mathrm{is}\:\_\_\_\_\:\mathrm{m}. \\ $$

Question Number 13478 Answers: 1 Comments: 0

The initial velocity of a particle is u (at t = 0) and acceleration f is given by f = at where t is time and ′a′ is a constant. Which of the following relations is valid? (1) v = u + at^2 (2) v = u + (1/2) at^2 (3) v = u + at (4) v = u

$$\mathrm{The}\:\mathrm{initial}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{is}\:{u} \\ $$$$\left(\mathrm{at}\:{t}\:=\:\mathrm{0}\right)\:\mathrm{and}\:\mathrm{acceleration}\:{f}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$${f}\:=\:{at}\:\mathrm{where}\:{t}\:\mathrm{is}\:\mathrm{time}\:\mathrm{and}\:'{a}'\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}. \\ $$$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{relations}\:\mathrm{is} \\ $$$$\mathrm{valid}? \\ $$$$\left(\mathrm{1}\right)\:{v}\:=\:{u}\:+\:{at}^{\mathrm{2}} \\ $$$$\left(\mathrm{2}\right)\:{v}\:=\:{u}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:{at}^{\mathrm{2}} \\ $$$$\left(\mathrm{3}\right)\:{v}\:=\:{u}\:+\:{at} \\ $$$$\left(\mathrm{4}\right)\:{v}\:=\:{u} \\ $$

Question Number 13475 Answers: 1 Comments: 0

An object starts from rest with constant acceleration 4 m/s^2 , then find the distance travelled by object in 5^(th) half second.

$$\mathrm{An}\:\mathrm{object}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{with}\:\mathrm{constant} \\ $$$$\mathrm{acceleration}\:\mathrm{4}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} ,\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{distance} \\ $$$$\mathrm{travelled}\:\mathrm{by}\:\mathrm{object}\:\mathrm{in}\:\mathrm{5}^{\mathrm{th}} \:\mathrm{half}\:\mathrm{second}. \\ $$

Question Number 13510 Answers: 1 Comments: 1

A body of mass 2 kg has an initial velocity of 3 ms^(−1) along OE and it is subjected to a force of 4 newton in OF direction perpendicular to OE. The distance of the body from O after 4 second will be (a) 12 m (b) 28 m (c) 20 m (d) 48 m

$$\mathrm{A}\:\mathrm{body}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{2}\:\mathrm{kg}\:\mathrm{has}\:\mathrm{an}\:\mathrm{initial}\:\mathrm{velocity} \\ $$$$\mathrm{of}\:\mathrm{3}\:\mathrm{ms}^{−\mathrm{1}} \:\mathrm{along}\:{OE}\:\mathrm{and}\:\mathrm{it}\:\mathrm{is}\:\mathrm{subjected} \\ $$$$\mathrm{to}\:\mathrm{a}\:\mathrm{force}\:\mathrm{of}\:\mathrm{4}\:\mathrm{newton}\:\mathrm{in}\:{OF}\:\mathrm{direction} \\ $$$$\mathrm{perpendicular}\:\mathrm{to}\:{OE}.\:\mathrm{The}\:\mathrm{distance}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{body}\:\mathrm{from}\:{O}\:\mathrm{after}\:\mathrm{4}\:\mathrm{second}\:\mathrm{will}\:\mathrm{be} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{12}\:\mathrm{m} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{28}\:\mathrm{m} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{20}\:\mathrm{m} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{48}\:\mathrm{m} \\ $$

Question Number 13449 Answers: 2 Comments: 0

Four particles A, B, C and D are situated at the corners of a square ABCD of side a at t = 0. Each of the particles moves with constant speed v. A always has its velocity along AB, B along BC, C along CD and D along DA. At what time will these particles meet each other?

$$\mathrm{Four}\:\mathrm{particles}\:{A},\:{B},\:{C}\:\mathrm{and}\:{D}\:\mathrm{are}\:\mathrm{situated} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{corners}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:{ABCD}\:\mathrm{of}\:\mathrm{side} \\ $$$${a}\:\mathrm{at}\:{t}\:=\:\mathrm{0}.\:\mathrm{Each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particles}\:\mathrm{moves} \\ $$$$\mathrm{with}\:\mathrm{constant}\:\mathrm{speed}\:{v}.\:{A}\:\mathrm{always}\:\mathrm{has}\:\mathrm{its} \\ $$$$\mathrm{velocity}\:\mathrm{along}\:{AB},\:{B}\:\mathrm{along}\:{BC},\:{C}\:\mathrm{along} \\ $$$${CD}\:\mathrm{and}\:{D}\:\mathrm{along}\:{DA}.\:\mathrm{At}\:\mathrm{what}\:\mathrm{time}\:\mathrm{will} \\ $$$$\mathrm{these}\:\mathrm{particles}\:\mathrm{meet}\:\mathrm{each}\:\mathrm{other}? \\ $$

Question Number 13438 Answers: 1 Comments: 0

7x^5 −4x^4 +9x^3 +12x^2 +5x−9=0 How many roots of this equation are Negative?

$$\mathrm{7}{x}^{\mathrm{5}} −\mathrm{4}{x}^{\mathrm{4}} +\mathrm{9}{x}^{\mathrm{3}} +\mathrm{12}{x}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{9}=\mathrm{0} \\ $$$${How}\:{many}\:{roots}\:{of}\:{this}\:{equation} \\ $$$${are}\:{Negative}? \\ $$$$ \\ $$

Question Number 13447 Answers: 0 Comments: 0

Question Number 13434 Answers: 1 Comments: 1

ΔABC∼ΔDEF ΔABC=25 ΔDEF=35 ((ΣMadian^2 of ΔABC)/(ΣMadian^2 of ΔDEF))=?

$$\Delta{ABC}\sim\Delta{DEF}\: \\ $$$$\Delta{ABC}=\mathrm{25} \\ $$$$\Delta{DEF}=\mathrm{35} \\ $$$$\frac{\Sigma{Madian}^{\mathrm{2}} {of}\:\Delta{ABC}}{\Sigma{Madian}^{\mathrm{2}} \:{of}\:\Delta{DEF}}=? \\ $$

Question Number 13429 Answers: 0 Comments: 2

Question Number 13427 Answers: 0 Comments: 0

Question Number 13412 Answers: 1 Comments: 0

e^(−kN) − kN − 1 = 0 Find the value of N

$$\mathrm{e}^{−\mathrm{kN}} \:−\:\mathrm{kN}\:\:−\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{N} \\ $$

Question Number 13403 Answers: 2 Comments: 2

If tan (A − B) = 1, sec (A + B) = (2/(√3)) , then prove that the smallest positive value of B is ((19π)/(24)) .

$$\mathrm{If}\:\mathrm{tan}\:\left({A}\:−\:{B}\right)\:=\:\mathrm{1},\:\mathrm{sec}\:\left({A}\:+\:{B}\right)\:=\:\frac{\mathrm{2}}{\sqrt{\mathrm{3}}}\:, \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive} \\ $$$$\mathrm{value}\:\mathrm{of}\:{B}\:\mathrm{is}\:\frac{\mathrm{19}\pi}{\mathrm{24}}\:. \\ $$

Question Number 13401 Answers: 1 Comments: 0

If sin (π cos θ) = cos (π sin θ), then prove that sin 2θ = ± (3/4)

$$\mathrm{If}\:\mathrm{sin}\:\left(\pi\:\mathrm{cos}\:\theta\right)\:=\:\mathrm{cos}\:\left(\pi\:\mathrm{sin}\:\theta\right),\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{sin}\:\mathrm{2}\theta\:=\:\pm\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$

Question Number 13395 Answers: 2 Comments: 0

Find all positive integers n for which n^2 + 96 is a perfect square.

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers}\:{n}\:\mathrm{for}\:\mathrm{which} \\ $$$${n}^{\mathrm{2}} \:+\:\mathrm{96}\:\mathrm{is}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$

Question Number 13394 Answers: 1 Comments: 0

Show that any circle with centre ((√2), (√3)) cannot pass through more than one lattice point. [Lattice points are points in cartesian plane, whose abscissa and ordinate both are integers.]

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{any}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{centre}\:\left(\sqrt{\mathrm{2}},\:\sqrt{\mathrm{3}}\right) \\ $$$$\mathrm{cannot}\:\mathrm{pass}\:\mathrm{through}\:\mathrm{more}\:\mathrm{than}\:\mathrm{one} \\ $$$$\mathrm{lattice}\:\mathrm{point}.\:\left[\mathrm{Lattice}\:\mathrm{points}\:\mathrm{are}\:\mathrm{points}\right. \\ $$$$\mathrm{in}\:\mathrm{cartesian}\:\mathrm{plane},\:\mathrm{whose}\:\mathrm{abscissa}\:\mathrm{and} \\ $$$$\left.\mathrm{ordinate}\:\mathrm{both}\:\mathrm{are}\:\mathrm{integers}.\right] \\ $$

Question Number 13391 Answers: 1 Comments: 0

A four digit number has the following properties: (a) It is a perfect square (b) The first two digits are equal (c) The last two digits are equal. Find all such numbers.

$$\mathrm{A}\:\mathrm{four}\:\mathrm{digit}\:\mathrm{number}\:\mathrm{has}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{properties}: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{It}\:\mathrm{is}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{The}\:\mathrm{first}\:\mathrm{two}\:\mathrm{digits}\:\mathrm{are}\:\mathrm{equal} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{The}\:\mathrm{last}\:\mathrm{two}\:\mathrm{digits}\:\mathrm{are}\:\mathrm{equal}. \\ $$$$\mathrm{Find}\:\mathrm{all}\:\mathrm{such}\:\mathrm{numbers}. \\ $$

Question Number 13389 Answers: 0 Comments: 5

Prove that [x] + [2x] + [4x] + [8x] + [16x] + [32x] = 12345 has no solution.

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\left[{x}\right]\:+\:\left[\mathrm{2}{x}\right]\:+\:\left[\mathrm{4}{x}\right]\:+\:\left[\mathrm{8}{x}\right]\:+\:\left[\mathrm{16}{x}\right]\:+\:\left[\mathrm{32}{x}\right]\:=\:\mathrm{12345} \\ $$$$\mathrm{has}\:\mathrm{no}\:\mathrm{solution}. \\ $$

Question Number 13388 Answers: 0 Comments: 5

Find the number of all rational numbers (m/n) such that (i) 0 < (m/n) < 1, (ii) m and n are relatively prime and (iii) mn = 25!.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{all}\:\mathrm{rational}\:\mathrm{numbers} \\ $$$$\frac{{m}}{{n}}\:\mathrm{such}\:\mathrm{that}\:\left(\mathrm{i}\right)\:\mathrm{0}\:<\:\frac{{m}}{{n}}\:<\:\mathrm{1},\:\left(\mathrm{ii}\right)\:{m}\:\mathrm{and} \\ $$$${n}\:\mathrm{are}\:\mathrm{relatively}\:\mathrm{prime}\:\mathrm{and}\:\left(\mathrm{iii}\right)\:{mn}\:=\:\mathrm{25}!. \\ $$

Question Number 13377 Answers: 1 Comments: 1