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Question Number 18530 Answers: 1 Comments: 0

In an atom the last electron is present in f-orbital and for its outermost shell the graph of Ψ^2 has 6 maximas. What is the sum of group and period of that element?

$$\mathrm{In}\:\mathrm{an}\:\mathrm{atom}\:\mathrm{the}\:\mathrm{last}\:\mathrm{electron}\:\mathrm{is}\:\mathrm{present} \\ $$$$\mathrm{in}\:{f}-\mathrm{orbital}\:\mathrm{and}\:\mathrm{for}\:\mathrm{its}\:\mathrm{outermost}\:\mathrm{shell} \\ $$$$\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:\Psi^{\mathrm{2}} \:\mathrm{has}\:\mathrm{6}\:\mathrm{maximas}.\:\mathrm{What} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{group}\:\mathrm{and}\:\mathrm{period}\:\mathrm{of}\:\mathrm{that} \\ $$$$\mathrm{element}? \\ $$

Question Number 19238 Answers: 0 Comments: 4

Let ABCD be a parallelogram. Two points E and F are chosen on the sides BC and CD, respectively, such that ((EB)/(EC)) = m, and ((FC)/(FD)) = n. Lines AE and BF intersect at G. Prove that the ratio ((AG)/(GE)) = (((m + 1)(n + 1))/(mn)).

$$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{parallelogram}.\:\mathrm{Two} \\ $$$$\mathrm{points}\:{E}\:\mathrm{and}\:{F}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{on}\:\mathrm{the}\:\mathrm{sides} \\ $$$${BC}\:\mathrm{and}\:{CD},\:\mathrm{respectively},\:\mathrm{such}\:\mathrm{that} \\ $$$$\frac{{EB}}{{EC}}\:=\:{m},\:\mathrm{and}\:\frac{{FC}}{{FD}}\:=\:{n}.\:\mathrm{Lines}\:{AE}\:\mathrm{and}\:{BF} \\ $$$$\mathrm{intersect}\:\mathrm{at}\:{G}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\frac{{AG}}{{GE}}\:=\:\frac{\left({m}\:+\:\mathrm{1}\right)\left({n}\:+\:\mathrm{1}\right)}{{mn}}. \\ $$

Question Number 19236 Answers: 1 Comments: 0

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

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.

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

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

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