Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1916

Question Number 18527    Answers: 0   Comments: 0

from 1 to 100 isn′t(10,20,30,40,50,60,70,80,90,100), totalizing 10 times the number 0 apears from 1 to 100?

$${from}\:\mathrm{1}\:{to}\:\mathrm{100}\:{isn}'{t}\left(\mathrm{10},\mathrm{20},\mathrm{30},\mathrm{40},\mathrm{50},\mathrm{60},\mathrm{70},\mathrm{80},\mathrm{90},\mathrm{100}\right),\:{totalizing}\:\mathrm{10}\:{times}\:{the}\:{number}\:\mathrm{0}\:{apears}\:{from}\:\mathrm{1}\:{to}\:\mathrm{100}? \\ $$

Question Number 18524    Answers: 2   Comments: 0

The number of solutions of the equation sin^3 x − 3sinxcos^2 x + 2cos^3 x = 0 in [−(π/4), (π/4)] is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{sin}^{\mathrm{3}} {x}\:−\:\mathrm{3sin}{x}\mathrm{cos}^{\mathrm{2}} {x}\:+\:\mathrm{2cos}^{\mathrm{3}} {x}\:=\:\mathrm{0}\:\mathrm{in} \\ $$$$\left[−\frac{\pi}{\mathrm{4}},\:\frac{\pi}{\mathrm{4}}\right]\:\mathrm{is} \\ $$

Question Number 18523    Answers: 0   Comments: 0

Match the following Column-I (Trigonometric equation) (A) sin 9θ = cos ((π/2) − θ) (B) sin 5θ = sin ((π/2) + 2θ) (C) cos 11θ = cos 3θ (D) 3 tan (θ − 15°) = tan (θ + 15°) Column-II (Family of solutions) (p) (2n + 1)(π/(10)), n ∈ Z (q) ((nπ)/2) + (−1)^n (π/4), n ∈ Z (r) ((nπ)/7), n ∈ Z (s) (4n + 1)(π/(14)), n ∈ Z

$$\mathrm{Match}\:\mathrm{the}\:\mathrm{following} \\ $$$$\boldsymbol{\mathrm{Column}}-\boldsymbol{\mathrm{I}}\:\left(\boldsymbol{\mathrm{Trigonometric}}\:\boldsymbol{\mathrm{equation}}\right) \\ $$$$\left(\mathrm{A}\right)\:\mathrm{sin}\:\mathrm{9}\theta\:=\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{2}}\:−\:\theta\right) \\ $$$$\left(\mathrm{B}\right)\:\mathrm{sin}\:\mathrm{5}\theta\:=\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}\:+\:\mathrm{2}\theta\right) \\ $$$$\left(\mathrm{C}\right)\:\mathrm{cos}\:\mathrm{11}\theta\:=\:\mathrm{cos}\:\mathrm{3}\theta \\ $$$$\left(\mathrm{D}\right)\:\mathrm{3}\:\mathrm{tan}\:\left(\theta\:−\:\mathrm{15}°\right)\:=\:\mathrm{tan}\:\left(\theta\:+\:\mathrm{15}°\right) \\ $$$$\boldsymbol{\mathrm{Column}}-\boldsymbol{\mathrm{II}}\:\left(\boldsymbol{\mathrm{Family}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{solutions}}\right) \\ $$$$\left(\mathrm{p}\right)\:\left(\mathrm{2}{n}\:+\:\mathrm{1}\right)\frac{\pi}{\mathrm{10}},\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{q}\right)\:\frac{{n}\pi}{\mathrm{2}}\:+\:\left(−\mathrm{1}\right)^{{n}} \frac{\pi}{\mathrm{4}},\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{r}\right)\:\frac{{n}\pi}{\mathrm{7}},\:{n}\:\in\:{Z} \\ $$$$\left(\mathrm{s}\right)\:\left(\mathrm{4}{n}\:+\:\mathrm{1}\right)\frac{\pi}{\mathrm{14}},\:{n}\:\in\:{Z} \\ $$

Question Number 18502    Answers: 1   Comments: 0

The second overtone of a fixed viberating string fixed at both end is 200cm. Find the length of the string.

$$\mathrm{The}\:\mathrm{second}\:\mathrm{overtone}\:\mathrm{of}\:\mathrm{a}\:\mathrm{fixed}\:\mathrm{viberating}\:\mathrm{string}\:\mathrm{fixed}\:\mathrm{at}\:\mathrm{both}\:\mathrm{end}\:\mathrm{is}\:\mathrm{200cm}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{string}. \\ $$

Question Number 18498    Answers: 5   Comments: 1

How many times is digit 0 written when listing all numbers from 1 to 3333?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{times}\:\mathrm{is}\:\mathrm{digit}\:\mathrm{0}\:\mathrm{written}\:\mathrm{when} \\ $$$$\mathrm{listing}\:\mathrm{all}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{3333}? \\ $$

Question Number 18499    Answers: 0   Comments: 1

what is the in pounds of a vertical cylindrical tank that is 6ft in dia meter and 15ft in height.if it weig hs 20lbs per ft of height.

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{in}\:\mathrm{pounds}\:\mathrm{of}\:\mathrm{a}\:\mathrm{vertical} \\ $$$$\mathrm{cylindrical}\:\mathrm{tank}\:\mathrm{that}\:\mathrm{is}\:\mathrm{6ft}\:\mathrm{in}\:\mathrm{dia} \\ $$$$\mathrm{meter}\:\mathrm{and}\:\mathrm{15ft}\:\mathrm{in}\:\mathrm{height}.\mathrm{if}\:\mathrm{it}\:\mathrm{weig} \\ $$$$\mathrm{hs}\:\mathrm{20lbs}\:\mathrm{per}\:\mathrm{ft}\:\mathrm{of}\:\mathrm{height}. \\ $$

Question Number 18493    Answers: 1   Comments: 1

Draw the free body diagram of following system:

$$\mathrm{Draw}\:\mathrm{the}\:\mathrm{free}\:\mathrm{body}\:\mathrm{diagram}\:\mathrm{of}\:\mathrm{following} \\ $$$$\mathrm{system}: \\ $$

Question Number 18492    Answers: 1   Comments: 1

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.

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

Question Number 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

  Pg 1911      Pg 1912      Pg 1913      Pg 1914      Pg 1915      Pg 1916      Pg 1917      Pg 1918      Pg 1919      Pg 1920   

Terms of Service

Privacy Policy

Contact: [email protected]