Question and Answers Forum

AllQuestion and Answers: Page 1881

Question Number 18486 Answers: 0 Comments: 0

Why ionic radii of^(35) Cl <^(37) Cl^− ?

$$\mathrm{Why}\:\mathrm{ionic}\:\mathrm{radii}\:\mathrm{of}\:^{\mathrm{35}} \mathrm{Cl}\:<\:^{\mathrm{37}} \mathrm{Cl}^{−} ? \\ $$

Question Number 18477 Answers: 0 Comments: 0

F[topology]={G⊂X.G is finit.} please sol it

$$\mathscr{F}\left[{topology}\right]=\left\{{G}\subset{X}.{G}\:{is}\:{finit}.\right\} \\ $$$${please}\:{sol}\:{it} \\ $$

Question Number 18474 Answers: 1 Comments: 0

Assertion-Reason Type Question STATEMENT-1 : f(x) = log_(cosx) sinx is well defined in (0, (π/2)). and STATEMENT-2 : sinx and cosx are positive in (0, (π/2)).

$$\boldsymbol{\mathrm{Assertion}}-\boldsymbol{\mathrm{Reason}}\:\boldsymbol{\mathrm{Type}}\:\boldsymbol{\mathrm{Question}} \\ $$$$\mathrm{STATEMENT}-\mathrm{1}\::\:{f}\left({x}\right)\:=\:\mathrm{log}_{\mathrm{cos}{x}} \mathrm{sin}{x}\:\mathrm{is} \\ $$$$\mathrm{well}\:\mathrm{defined}\:\mathrm{in}\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right). \\ $$$$\boldsymbol{\mathrm{and}} \\ $$$$\mathrm{STATEMENT}-\mathrm{2}\::\:\mathrm{sin}{x}\:\mathrm{and}\:\mathrm{cos}{x}\:\mathrm{are} \\ $$$$\mathrm{positive}\:\mathrm{in}\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right). \\ $$

Question Number 18472 Answers: 1 Comments: 0

The general solution of 2^(sin x) + 2^(cos x) = 2^(1−(1/(√2))) is

$$\mathrm{The}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{2}^{\mathrm{sin}\:{x}} \:+\:\mathrm{2}^{\mathrm{cos}\:{x}} \\ $$$$=\:\mathrm{2}^{\mathrm{1}−\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}} \:\mathrm{is} \\ $$

Question Number 18466 Answers: 1 Comments: 0

The sum of the digits of a two digit number is 5 and their difference is 3. Find the number.

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{a}\:\mathrm{two}\:\mathrm{digit} \\ $$$$\mathrm{number}\:\mathrm{is}\:\mathrm{5}\:\mathrm{and}\:\mathrm{their}\:\mathrm{difference}\:\mathrm{is}\:\mathrm{3}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}. \\ $$

Question Number 18465 Answers: 1 Comments: 0

The sum of the digits of a two digit number is 5 and their difference is 3. Find the number.

Question Number 18464 Answers: 1 Comments: 0

3 numbers are chosen from 1 to 30. The probability that they are not consecutive is

$$\mathrm{3}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{30}.\:\mathrm{The} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{they}\:\mathrm{are}\:\mathrm{not}\:\mathrm{consecutive} \\ $$$$\mathrm{is} \\ $$

Question Number 18463 Answers: 1 Comments: 0

The solid angle subtended by a spherical surface of radius R at its centre is (π/2) steradian, then the surface area of corresponding spherical section is

$$\mathrm{The}\:\mathrm{solid}\:\mathrm{angle}\:\mathrm{subtended}\:\mathrm{by}\:\mathrm{a}\:\mathrm{spherical} \\ $$$$\mathrm{surface}\:\mathrm{of}\:\mathrm{radius}\:{R}\:\mathrm{at}\:\mathrm{its}\:\mathrm{centre}\:\mathrm{is}\:\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{steradian},\:\mathrm{then}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{area}\:\mathrm{of} \\ $$$$\mathrm{corresponding}\:\mathrm{spherical}\:\mathrm{section}\:\mathrm{is} \\ $$

Question Number 18461 Answers: 1 Comments: 0

Question Number 18460 Answers: 1 Comments: 0

Question Number 18457 Answers: 1 Comments: 0

The number of solutions of the equation sin θ + cos θ = 1 + sin θ cos θ in the interval [0, 4π] is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{sin}\:\theta\:+\:\mathrm{cos}\:\theta\:=\:\mathrm{1}\:+\:\mathrm{sin}\:\theta\:\mathrm{cos}\:\theta\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{interval}\:\left[\mathrm{0},\:\mathrm{4}\pi\right]\:\mathrm{is} \\ $$

Question Number 18456 Answers: 1 Comments: 0

The complete solution of the equation sin 2x − 12(sin x − cos x) + 12 = 0 is given by (1) x = 2nπ + (π/2), (2n − 1)(π/4), n ∈ Z (2) x = nπ + (π/2), (2n + 1)π, n ∈ Z (3) x = 2nπ + (π/2), (2n + 1)π, n ∈ Z (4) x = nπ + (π/2), (2n − 1)π, n ∈ Z

$$\mathrm{The}\:\mathrm{complete}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{sin}\:\mathrm{2}{x}\:−\:\mathrm{12}\left(\mathrm{sin}\:{x}\:−\:\mathrm{cos}\:{x}\right)\:+\:\mathrm{12}\:=\:\mathrm{0}\:\mathrm{is} \\ $$$$\mathrm{given}\:\mathrm{by} \\ $$$$\left(\mathrm{1}\right)\:{x}\:=\:\mathrm{2}{n}\pi\:+\:\frac{\pi}{\mathrm{2}},\:\left(\mathrm{2}{n}\:−\:\mathrm{1}\right)\frac{\pi}{\mathrm{4}},\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{2}\right)\:{x}\:=\:{n}\pi\:+\:\frac{\pi}{\mathrm{2}},\:\left(\mathrm{2}{n}\:+\:\mathrm{1}\right)\pi,\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{3}\right)\:{x}\:=\:\mathrm{2}{n}\pi\:+\:\frac{\pi}{\mathrm{2}},\:\left(\mathrm{2}{n}\:+\:\mathrm{1}\right)\pi,\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{4}\right)\:{x}\:=\:{n}\pi\:+\:\frac{\pi}{\mathrm{2}},\:\left(\mathrm{2}{n}\:−\:\mathrm{1}\right)\pi,\:{n}\:\in\:{Z} \\ $$

Question Number 18455 Answers: 1 Comments: 0

The equation cosec (x/2) + cosec (y/2) + cosec (z/2) = 6, where 0 < x, y, z < (π/2) and x + y + z = π, have (1) Three ordered triplet (x, y, z) solutions (2) Two ordered triplet (x, y, z) solutions (3) Just one ordered triplet (x, y, z) solution (4) No ordered triplet (x, y, z) solution

$$\mathrm{The}\:\mathrm{equation}\:\mathrm{cosec}\:\frac{{x}}{\mathrm{2}}\:+\:\mathrm{cosec}\:\frac{{y}}{\mathrm{2}}\:+ \\ $$$$\mathrm{cosec}\:\frac{{z}}{\mathrm{2}}\:=\:\mathrm{6},\:\mathrm{where}\:\mathrm{0}\:<\:{x},\:{y},\:{z}\:<\:\frac{\pi}{\mathrm{2}}\:\mathrm{and} \\ $$$${x}\:+\:{y}\:+\:{z}\:=\:\pi,\:\mathrm{have} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Three}\:\mathrm{ordered}\:\mathrm{triplet}\:\left({x},\:{y},\:{z}\right) \\ $$$$\mathrm{solutions} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Two}\:\mathrm{ordered}\:\mathrm{triplet}\:\left({x},\:{y},\:{z}\right) \\ $$$$\mathrm{solutions} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Just}\:\mathrm{one}\:\mathrm{ordered}\:\mathrm{triplet}\:\left({x},\:{y},\:{z}\right) \\ $$$$\mathrm{solution} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{No}\:\mathrm{ordered}\:\mathrm{triplet}\:\left({x},\:{y},\:{z}\right)\:\mathrm{solution} \\ $$

Question Number 18450 Answers: 0 Comments: 0

A $4000 note is signed, for 30 days at a discount rate of 12%. Find the proceeds. I′m not sure whether the $4000 is bank discount, principal or maturity value. Please help me

$${A}\:\$\mathrm{4000}\:{note}\:{is}\:{signed},\:{for}\:\mathrm{30}\:{days} \\ $$$${at}\:{a}\:{discount}\:{rate}\:{of}\:\mathrm{12\%}.\:{Find}\:{the} \\ $$$${proceeds}. \\ $$$$ \\ $$$${I}'{m}\:{not}\:{sure}\:{whether}\:{the}\:\$\mathrm{4000}\:{is} \\ $$$${bank}\:{discount},\:{principal}\:{or}\:{maturity}\:{value}. \\ $$$$ \\ $$$${Please}\:{help}\:{me} \\ $$

Question Number 18448 Answers: 1 Comments: 0

If a, b, c, d are in GP and a^x = b^y = c^z = d^u , then x, y, z, u are in

$$\mathrm{If}\:\:{a},\:{b},\:{c},\:{d}\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP}\:\mathrm{and}\:\:{a}^{{x}} =\:{b}^{{y}} =\:{c}^{{z}} =\:{d}^{{u}} , \\ $$$$\mathrm{then}\:{x},\:{y},\:{z},\:{u}\:\mathrm{are}\:\mathrm{in} \\ $$

Question Number 18446 Answers: 0 Comments: 0

Question Number 18440 Answers: 0 Comments: 0

Question Number 18439 Answers: 0 Comments: 3

Question Number 18432 Answers: 1 Comments: 0

Find interval p so (p − 2)x^2 + 2px + p − 1 = 0 have negative roots

$$\mathrm{Find}\:\mathrm{interval}\:{p}\:\mathrm{so} \\ $$$$\left({p}\:−\:\mathrm{2}\right){x}^{\mathrm{2}} \:+\:\mathrm{2}{px}\:+\:{p}\:−\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{have}\:\mathrm{negative}\:\mathrm{roots} \\ $$

Question Number 18431 Answers: 1 Comments: 0

x^2 =16^x find x

$$\mathrm{x}^{\mathrm{2}} =\mathrm{16}^{\mathrm{x}} \\ $$$$\mathrm{find}\:\mathrm{x} \\ $$

Question Number 18430 Answers: 1 Comments: 0

x^2 =3^x find x

$$\mathrm{x}^{\mathrm{2}} =\mathrm{3}^{\mathrm{x}} \\ $$$$\mathrm{find}\:\mathrm{x} \\ $$

Question Number 18426 Answers: 0 Comments: 0

The equation 2 cot 2x − 3 cot 3x = tan 2x has (1) Two solutions in (0, (π/3)) (2) One solution in (0, (π/3)) (3) No solution in (−∞, ∞) (4) Three solution in (0, π)

$$\mathrm{The}\:\mathrm{equation}\:\mathrm{2}\:\mathrm{cot}\:\mathrm{2}{x}\:−\:\mathrm{3}\:\mathrm{cot}\:\mathrm{3}{x}\:=\:\mathrm{tan}\:\mathrm{2}{x} \\ $$$$\mathrm{has} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Two}\:\mathrm{solutions}\:\mathrm{in}\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{3}}\right) \\ $$$$\left(\mathrm{2}\right)\:\mathrm{One}\:\mathrm{solution}\:\mathrm{in}\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{3}}\right) \\ $$$$\left(\mathrm{3}\right)\:\mathrm{No}\:\mathrm{solution}\:\mathrm{in}\:\left(−\infty,\:\infty\right) \\ $$$$\left(\mathrm{4}\right)\:\mathrm{Three}\:\mathrm{solution}\:\mathrm{in}\:\left(\mathrm{0},\:\pi\right) \\ $$

Question Number 18428 Answers: 0 Comments: 0

Question Number 18416 Answers: 0 Comments: 0

The number of integral values of x which satisfies (((x − 5)^(10) (x − 13)^(20) (x − 19)^(13) )/((x − 10)^(18) (x − 25)^(19) )) ≥ 0 and 2 ≤ x ≤ 30 are (1) 23 (2) 24 (3) 25 (4) 26

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{integral}\:\mathrm{values}\:\mathrm{of}\:{x} \\ $$$$\mathrm{which}\:\mathrm{satisfies} \\ $$$$\frac{\left({x}\:−\:\mathrm{5}\right)^{\mathrm{10}} \left({x}\:−\:\mathrm{13}\right)^{\mathrm{20}} \left({x}\:−\:\mathrm{19}\right)^{\mathrm{13}} }{\left({x}\:−\:\mathrm{10}\right)^{\mathrm{18}} \left({x}\:−\:\mathrm{25}\right)^{\mathrm{19}} }\:\geqslant\:\mathrm{0}\:\mathrm{and} \\ $$$$\mathrm{2}\:\leqslant\:{x}\:\leqslant\:\mathrm{30}\:\mathrm{are} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{23} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{24} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{25} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{26} \\ $$

Question Number 18415 Answers: 1 Comments: 1

Calculate the magnetic field produced at ground level by a 15A current flowing in a long horizontal wire suspended at a height of 7.5m

$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{magnetic}\:\mathrm{field}\:\mathrm{produced}\:\mathrm{at}\:\mathrm{ground}\:\mathrm{level}\:\mathrm{by}\:\mathrm{a}\:\mathrm{15A}\:\mathrm{current} \\ $$$$\mathrm{flowing}\:\mathrm{in}\:\mathrm{a}\:\mathrm{long}\:\mathrm{horizontal}\:\mathrm{wire}\:\mathrm{suspended}\:\mathrm{at}\:\mathrm{a}\:\mathrm{height}\:\mathrm{of}\:\mathrm{7}.\mathrm{5m} \\ $$

Question Number 18411 Answers: 1 Comments: 0

A glass bulb contains 2.24 L of H_2 and 1.12 L of D_2 at S.T.P. It is connected to a fully evacuated bulb by a stopcock with a small opening. The stopcock is opened for sometime and then closed. The first bulb now contains 0.1 g of D_2 . Calculate the percentage composition by weight of the gases in the second bulb.

$$\mathrm{A}\:\mathrm{glass}\:\mathrm{bulb}\:\mathrm{contains}\:\mathrm{2}.\mathrm{24}\:\mathrm{L}\:\mathrm{of}\:\mathrm{H}_{\mathrm{2}} \:\mathrm{and} \\ $$$$\mathrm{1}.\mathrm{12}\:\mathrm{L}\:\mathrm{of}\:\mathrm{D}_{\mathrm{2}} \:\mathrm{at}\:\mathrm{S}.\mathrm{T}.\mathrm{P}.\:\mathrm{It}\:\mathrm{is}\:\mathrm{connected}\:\mathrm{to} \\ $$$$\mathrm{a}\:\mathrm{fully}\:\mathrm{evacuated}\:\mathrm{bulb}\:\mathrm{by}\:\mathrm{a}\:\mathrm{stopcock} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{small}\:\mathrm{opening}.\:\mathrm{The}\:\mathrm{stopcock}\:\mathrm{is} \\ $$$$\mathrm{opened}\:\mathrm{for}\:\mathrm{sometime}\:\mathrm{and}\:\mathrm{then}\:\mathrm{closed}. \\ $$$$\mathrm{The}\:\mathrm{first}\:\mathrm{bulb}\:\mathrm{now}\:\mathrm{contains}\:\mathrm{0}.\mathrm{1}\:\mathrm{g}\:\mathrm{of}\:\mathrm{D}_{\mathrm{2}} . \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{percentage}\:\mathrm{composition} \\ $$$$\mathrm{by}\:\mathrm{weight}\:\mathrm{of}\:\mathrm{the}\:\mathrm{gases}\:\mathrm{in}\:\mathrm{the}\:\mathrm{second} \\ $$$$\mathrm{bulb}. \\ $$

Pg 1876 Pg 1877 Pg 1878 Pg 1879 Pg 1880 Pg 1881 Pg 1882 Pg 1883 Pg 1884 Pg 1885

Contact: info@tinkutara.com