Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 1921

Question Number 15919 Answers: 0 Comments: 1

multiply 3x+4y+5x−8y

$${multiply}\:\mathrm{3}{x}+\mathrm{4}{y}+\mathrm{5}{x}−\mathrm{8}{y} \\ $$

Question Number 15917 Answers: 1 Comments: 1

Question Number 15916 Answers: 2 Comments: 2

Question Number 15908 Answers: 1 Comments: 7

Question Number 15906 Answers: 1 Comments: 0

If λ_1 and λ_2 are respectively the wavelengths of the series limit of Lyman and Balmer series of Hydrogen atom, then the wavelength of the first line of the Lyman series of the H-atom is (1) λ_1 − λ_2 (2) (√(λ_1 λ_2 )) (3) ((λ_2 − λ_1 )/(λ_1 λ_2 )) (4) ((λ_1 λ_2 )/(λ_2 − λ_1 ))

$$\mathrm{If}\:\lambda_{\mathrm{1}} \:\mathrm{and}\:\lambda_{\mathrm{2}} \:\mathrm{are}\:\mathrm{respectively}\:\mathrm{the} \\ $$$$\mathrm{wavelengths}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}\:\mathrm{limit}\:\mathrm{of}\:\mathrm{Lyman} \\ $$$$\mathrm{and}\:\mathrm{Balmer}\:\mathrm{series}\:\mathrm{of}\:\mathrm{Hydrogen}\:\mathrm{atom}, \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{wavelength}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{line}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{Lyman}\:\mathrm{series}\:\mathrm{of}\:\mathrm{the}\:\mathrm{H}-\mathrm{atom}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\lambda_{\mathrm{1}} \:−\:\lambda_{\mathrm{2}} \\ $$$$\left(\mathrm{2}\right)\:\sqrt{\lambda_{\mathrm{1}} \lambda_{\mathrm{2}} } \\ $$$$\left(\mathrm{3}\right)\:\frac{\lambda_{\mathrm{2}} \:−\:\lambda_{\mathrm{1}} }{\lambda_{\mathrm{1}} \lambda_{\mathrm{2}} } \\ $$$$\left(\mathrm{4}\right)\:\frac{\lambda_{\mathrm{1}} \lambda_{\mathrm{2}} }{\lambda_{\mathrm{2}} \:−\:\lambda_{\mathrm{1}} } \\ $$

Question Number 15904 Answers: 2 Comments: 1

Question Number 15894 Answers: 0 Comments: 2

If the angles of a triangle ABC be in A.P., then (1) c^2 = a^2 + b^2 − ab (2) b^2 = a^2 + c^2 − ac (3) a^2 = b^2 + c^2 − ac (4) b^2 = a^2 + c^2

$$\mathrm{If}\:\mathrm{the}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:{ABC}\:\mathrm{be}\:\mathrm{in} \\ $$$$\mathrm{A}.\mathrm{P}.,\:\mathrm{then} \\ $$$$\left(\mathrm{1}\right)\:{c}^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:−\:{ab} \\ $$$$\left(\mathrm{2}\right)\:{b}^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:−\:{ac} \\ $$$$\left(\mathrm{3}\right)\:{a}^{\mathrm{2}} \:=\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:−\:{ac} \\ $$$$\left(\mathrm{4}\right)\:{b}^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \\ $$

Question Number 15891 Answers: 0 Comments: 0

Find out last odd digit in the expansion of 1000!

$$\mathrm{Find}\:\mathrm{out}\:\boldsymbol{\mathrm{last}}\:\boldsymbol{\mathrm{odd}}\:\boldsymbol{\mathrm{digit}}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\mathrm{1000}! \\ $$

Question Number 15889 Answers: 0 Comments: 0

Find out first non-five digit from right in the expansion of (1×3×5×...×625).

$$\mathrm{Find}\:\mathrm{out}\:\boldsymbol{\mathrm{first}}\:\boldsymbol{\mathrm{non}}-\boldsymbol{\mathrm{five}}\:\boldsymbol{\mathrm{digit}}\:\mathrm{from}\:\mathrm{right} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}×\mathrm{3}×\mathrm{5}×...×\mathrm{625}\right). \\ $$

Question Number 15888 Answers: 1 Comments: 0

Prove that in ΔABC, a^3 cos (B − C) + b^3 cos (C − A) + c^3 cos (A − B) = 3abc

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\Delta{ABC},\:{a}^{\mathrm{3}} \:\mathrm{cos}\:\left({B}\:−\:{C}\right)\:+ \\ $$$${b}^{\mathrm{3}} \:\mathrm{cos}\:\left({C}\:−\:{A}\right)\:+\:{c}^{\mathrm{3}} \:\mathrm{cos}\:\left({A}\:−\:{B}\right)\:=\:\mathrm{3}{abc} \\ $$

Question Number 15893 Answers: 1 Comments: 0

In ΔABC, sides a, b, c are roots of the equation x^3 − px^2 + qx − r = 0. Prove that area of ΔABC is (1/4)(√(p(4pq − p^3 − 8r)))

$$\mathrm{In}\:\Delta{ABC},\:\mathrm{sides}\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:{x}^{\mathrm{3}} \:−\:{px}^{\mathrm{2}} \:+\:{qx}\:−\:{r}\:=\:\mathrm{0}.\:\mathrm{Prove} \\ $$$$\mathrm{that}\:\mathrm{area}\:\mathrm{of}\:\Delta{ABC}\:\mathrm{is} \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}\sqrt{{p}\left(\mathrm{4}{pq}\:−\:{p}^{\mathrm{3}} \:−\:\mathrm{8}{r}\right)} \\ $$

Question Number 15881 Answers: 1 Comments: 1

Question Number 15880 Answers: 2 Comments: 0

Question Number 15869 Answers: 1 Comments: 1

If ax^2 +(b/x)≥c for all x,a,b>0 then prove minimum value of 27ab^2 is 4c^2 .

$$\mathrm{If}\:{ax}^{\mathrm{2}} +\frac{{b}}{{x}}\geqslant{c}\:\mathrm{for}\:\mathrm{all}\:{x},{a},{b}>\mathrm{0}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{27}{ab}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{4}{c}^{\mathrm{2}} . \\ $$

Question Number 15868 Answers: 1 Comments: 0

Find the equation and radius of the circumcircle of the triangle formed by the three line: 2y − 9x + 26 = 0 9y + 2x + 32 = 0 11y − 7x − 27 = 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{and}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circumcircle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{formed}\:\mathrm{by}\: \\ $$$$\mathrm{the}\:\mathrm{three}\:\mathrm{line}: \\ $$$$\mathrm{2y}\:−\:\mathrm{9x}\:+\:\mathrm{26}\:=\:\mathrm{0} \\ $$$$\mathrm{9y}\:+\:\mathrm{2x}\:+\:\mathrm{32}\:=\:\mathrm{0} \\ $$$$\mathrm{11y}\:−\:\mathrm{7x}\:−\:\mathrm{27}\:=\:\mathrm{0} \\ $$

Question Number 15865 Answers: 2 Comments: 0

a,b,c∈R^(+ ) andIf a+b+c=18 then maximum value of a^2 b^3 c^4 is

$${a},{b},{c}\in\mathbb{R}^{+\:} \mathrm{andIf}\:{a}+{b}+{c}=\mathrm{18}\:\mathrm{then}\:\mathrm{maximum}\:\mathrm{value} \\ $$$$\mathrm{of}\:{a}^{\mathrm{2}} {b}^{\mathrm{3}} {c}^{\mathrm{4}} \:\mathrm{is} \\ $$

Question Number 15856 Answers: 1 Comments: 0

A particle is moving along a straight line with uniform acceleration has velocities 7 m/s at P and 17 m/s at Q. If R is the midpoint of PQ, then the average velocity between P and R is?

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{along}\:\mathrm{a}\:\mathrm{straight} \\ $$$$\mathrm{line}\:\mathrm{with}\:\mathrm{uniform}\:\mathrm{acceleration}\:\mathrm{has} \\ $$$$\mathrm{velocities}\:\mathrm{7}\:\mathrm{m}/\mathrm{s}\:\mathrm{at}\:{P}\:\mathrm{and}\:\mathrm{17}\:\mathrm{m}/\mathrm{s}\:\mathrm{at}\:{Q}. \\ $$$$\mathrm{If}\:{R}\:\mathrm{is}\:\mathrm{the}\:\mathrm{midpoint}\:\mathrm{of}\:{PQ},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{average}\:\mathrm{velocity}\:\mathrm{between}\:{P}\:\mathrm{and}\:{R}\:\mathrm{is}? \\ $$

Question Number 15850 Answers: 0 Comments: 0

Let (X, T) be any topological space . Verify that the intersection of any finite number of members of T is a member of T. Use mathematical induction to prove your result.

$$\mathrm{Let}\:\left(\mathrm{X},\:\mathrm{T}\right)\:\mathrm{be}\:\mathrm{any}\:\mathrm{topological}\:\mathrm{space}\:.\:\mathrm{Verify}\:\mathrm{that}\:\mathrm{the}\:\mathrm{intersection}\:\mathrm{of}\:\mathrm{any}\: \\ $$$$\mathrm{finite}\:\mathrm{number}\:\mathrm{of}\:\mathrm{members}\:\mathrm{of}\:\mathrm{T}\:\mathrm{is}\:\mathrm{a}\:\mathrm{member}\:\mathrm{of}\:\mathrm{T}.\:\mathrm{Use}\:\mathrm{mathematical} \\ $$$$\mathrm{induction}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{your}\:\mathrm{result}. \\ $$

Question Number 15840 Answers: 1 Comments: 2

Solve the ODE (dy/dx) + x^2 y = x^4

$$\mathrm{Solve}\:\mathrm{the}\:\:\mathrm{ODE} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\mathrm{x}^{\mathrm{2}} \mathrm{y}\:=\:\mathrm{x}^{\mathrm{4}} \\ $$$$ \\ $$

Question Number 15839 Answers: 0 Comments: 1

Question Number 15835 Answers: 0 Comments: 1

Number of decimal digits in 50! is

$$\:\mathrm{Number}\:\mathrm{of}\: \\ $$$$\mathrm{decimal}\:\:\mathrm{digits}\: \\ $$$$\mathrm{in}\:\:\mathrm{50}!\:\mathrm{is} \\ $$

Question Number 15832 Answers: 1 Comments: 0

A passenger in a train moving at an acceleration a, drops a stone from the window. A person, standing on the ground, by the sides of the rails, observes the ball falling (1) Vertically with an acceleration (√(g^2 + a^2 )) (2) Horizontally with an acceleration (√(g^2 + a^2 )) (3) Along a parabola with an acceleration (√(g^2 + a^2 )) (4) Along a parabola with an acceleration g

$$\mathrm{A}\:\mathrm{passenger}\:\mathrm{in}\:\mathrm{a}\:\mathrm{train}\:\mathrm{moving}\:\mathrm{at}\:\mathrm{an} \\ $$$$\mathrm{acceleration}\:{a},\:\mathrm{drops}\:\mathrm{a}\:\mathrm{stone}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{window}.\:\mathrm{A}\:\mathrm{person},\:\mathrm{standing}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{ground},\:\mathrm{by}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rails}, \\ $$$$\mathrm{observes}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{falling} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Vertically}\:\mathrm{with}\:\mathrm{an}\:\mathrm{acceleration} \\ $$$$\sqrt{{g}^{\mathrm{2}} \:+\:{a}^{\mathrm{2}} } \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Horizontally}\:\mathrm{with}\:\mathrm{an}\:\mathrm{acceleration} \\ $$$$\sqrt{{g}^{\mathrm{2}} \:+\:{a}^{\mathrm{2}} } \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Along}\:\mathrm{a}\:\mathrm{parabola}\:\mathrm{with}\:\mathrm{an}\:\mathrm{acceleration} \\ $$$$\sqrt{{g}^{\mathrm{2}} \:+\:{a}^{\mathrm{2}} } \\ $$$$\left(\mathrm{4}\right)\:\mathrm{Along}\:\mathrm{a}\:\mathrm{parabola}\:\mathrm{with}\:\mathrm{an}\:\mathrm{acceleration} \\ $$$${g} \\ $$

Question Number 15828 Answers: 1 Comments: 0

In a ΔABC, let M_a , M_b and M_c denote the length of medians, s = ((M_a + M_b + M_c )/2) and Δ = ar(ΔABC). Prove that Δ = (4/3)(√(s(s − M_a )(s − M_b )(s − M_c )))

$$\mathrm{In}\:\mathrm{a}\:\Delta{ABC},\:\mathrm{let}\:{M}_{{a}} ,\:{M}_{{b}} \:\mathrm{and}\:{M}_{{c}} \:\mathrm{denote} \\ $$$$\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{medians}, \\ $$$${s}\:=\:\frac{{M}_{{a}} \:+\:{M}_{{b}} \:+\:{M}_{{c}} }{\mathrm{2}}\:\:\mathrm{and}\:\Delta\:=\:\mathrm{ar}\left(\Delta{ABC}\right). \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\Delta\:=\:\frac{\mathrm{4}}{\mathrm{3}}\sqrt{{s}\left({s}\:−\:{M}_{{a}} \right)\left({s}\:−\:{M}_{{b}} \right)\left({s}\:−\:{M}_{{c}} \right)} \\ $$

Question Number 15824 Answers: 2 Comments: 0

If in a ΔABC, cos A + cos B + cos C = (3/2) . Prove that ΔABC is an equilateral triangle.

$$\mathrm{If}\:\mathrm{in}\:\mathrm{a}\:\Delta{ABC},\:\mathrm{cos}\:{A}\:+\:\mathrm{cos}\:{B}\:+\:\mathrm{cos}\:{C}\:=\:\frac{\mathrm{3}}{\mathrm{2}}\:. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\Delta{ABC}\:\mathrm{is}\:\mathrm{an}\:\mathrm{equilateral} \\ $$$$\mathrm{triangle}. \\ $$

Question Number 15821 Answers: 2 Comments: 2

Five engineers A,B,C,D and E can complete a process in 8 hours, assuming that every engineer works with the same efficiency. They started working at 10:00am. If after 4:00pm..,one engineer is removed from the group every hour,what is the time when they will finish the work? (a)6:00pm (b)7:00pm (c)4:00pm (d)8:00pm

$$\mathrm{Five}\:\mathrm{engineers}\:\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D}\:\mathrm{and}\:\mathrm{E}\:\mathrm{can} \\ $$$$\mathrm{complete}\:\mathrm{a}\:\mathrm{process}\:\mathrm{in}\:\mathrm{8}\:\mathrm{hours}, \\ $$$$\mathrm{assuming}\:\mathrm{that}\:\mathrm{every}\:\mathrm{engineer}\: \\ $$$$\mathrm{works}\:\mathrm{with}\:\mathrm{the}\:\mathrm{same}\:\mathrm{efficiency}. \\ $$$$\mathrm{They}\:\mathrm{started}\:\mathrm{working}\:\mathrm{at}\:\mathrm{10}:\mathrm{00am}. \\ $$$$\mathrm{If}\:\mathrm{after}\:\mathrm{4}:\mathrm{00pm}..,\mathrm{one}\:\mathrm{engineer}\:\mathrm{is} \\ $$$$\mathrm{removed}\:\mathrm{from}\:\mathrm{the}\:\mathrm{group}\:\mathrm{every}\: \\ $$$$\mathrm{hour},\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{time}\:\mathrm{when}\:\mathrm{they} \\ $$$$\mathrm{will}\:\mathrm{finish}\:\mathrm{the}\:\mathrm{work}? \\ $$$$\left(\mathrm{a}\right)\mathrm{6}:\mathrm{00pm} \\ $$$$\left(\mathrm{b}\right)\mathrm{7}:\mathrm{00pm} \\ $$$$\left(\mathrm{c}\right)\mathrm{4}:\mathrm{00pm} \\ $$$$\left(\mathrm{d}\right)\mathrm{8}:\mathrm{00pm} \\ $$

Question Number 15803 Answers: 0 Comments: 0

∫(dx/((1+x)(√((1+x−x^2 ))) ))

$$\int\frac{\mathrm{dx}}{\left(\mathrm{1}+\mathrm{x}\right)\sqrt{\left(\mathrm{1}+\mathrm{x}−\mathrm{x}^{\mathrm{2}} \right)}\:} \\ $$

Pg 1916 Pg 1917 Pg 1918 Pg 1919 Pg 1920 Pg 1921 Pg 1922 Pg 1923 Pg 1924 Pg 1925

Contact: info@tinkutara.com