Question and Answers Forum

AllQuestion and Answers: Page 1925

Question Number 15961 Answers: 0 Comments: 5

Path of a projectile as seen from another projectile is a (1) Straight line (2) Parabola (3) Ellipse (4) Hyperbola

$$\mathrm{Path}\:\mathrm{of}\:\mathrm{a}\:\mathrm{projectile}\:\mathrm{as}\:\mathrm{seen}\:\mathrm{from}\:\mathrm{another} \\ $$$$\mathrm{projectile}\:\mathrm{is}\:\mathrm{a} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Straight}\:\mathrm{line} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Parabola} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Ellipse} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{Hyperbola} \\ $$

Question Number 15955 Answers: 0 Comments: 2

The motion of a particle moving along x-axis is represented by the equation (dv/dt) = 6 − 3v, where v is in m/s and t is in second. If the particle is at rest at t = 0, then (1) The speed of the particle is 2 m/s when the acceleration of particle is zero (2) After a long time the particle moves with a constant velocity of 2 m/s (3) The speed is 0.1 m/s, when the acceleration is half of its initial value (4) The magnitude of final acceleration is 6 m/s^2

$$\mathrm{The}\:\mathrm{motion}\:\mathrm{of}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{moving}\:\mathrm{along} \\ $$$${x}-\mathrm{axis}\:\mathrm{is}\:\mathrm{represented}\:\mathrm{by}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\frac{{dv}}{{dt}}\:=\:\mathrm{6}\:−\:\mathrm{3}{v},\:\mathrm{where}\:{v}\:\mathrm{is}\:\mathrm{in}\:\mathrm{m}/\mathrm{s}\:\mathrm{and}\:{t}\:\mathrm{is} \\ $$$$\mathrm{in}\:\mathrm{second}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{at}\:\mathrm{rest}\:\mathrm{at}\:{t}\:= \\ $$$$\mathrm{0},\:\mathrm{then} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{The}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{2}\:\mathrm{m}/\mathrm{s} \\ $$$$\mathrm{when}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{particle}\:\mathrm{is} \\ $$$$\mathrm{zero} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{After}\:\mathrm{a}\:\mathrm{long}\:\mathrm{time}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{moves} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{2}\:\mathrm{m}/\mathrm{s} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{The}\:\mathrm{speed}\:\mathrm{is}\:\mathrm{0}.\mathrm{1}\:\mathrm{m}/\mathrm{s},\:\mathrm{when}\:\mathrm{the} \\ $$$$\mathrm{acceleration}\:\mathrm{is}\:\mathrm{half}\:\mathrm{of}\:\mathrm{its}\:\mathrm{initial}\:\mathrm{value} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{The}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{final}\:\mathrm{acceleration} \\ $$$$\mathrm{is}\:\mathrm{6}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} \\ $$

Question Number 15948 Answers: 1 Comments: 1

Question Number 15943 Answers: 0 Comments: 0

Solve: x(dy/dx) + 3y = 3x^x y^(2/3)

$$\mathrm{Solve}: \\ $$$$\mathrm{x}\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\mathrm{3y}\:=\:\mathrm{3x}^{\mathrm{x}} \:\mathrm{y}^{\mathrm{2}/\mathrm{3}} \\ $$

Question Number 15942 Answers: 1 Comments: 0

Help. solve(x+2)dy/dx=3−2y/x

$$\mathrm{Help}. \\ $$$$\mathrm{solve}\left(\mathrm{x}+\mathrm{2}\right)\mathrm{dy}/\mathrm{dx}=\mathrm{3}−\mathrm{2y}/\mathrm{x} \\ $$

Question Number 15932 Answers: 1 Comments: 1

A particle is projected from the foot of an inclined plane having inclination 45°, with the velocity u at an angle θ (> 45°) with the horizontal in a vertical plane containing the line of greatest slope through the point of projection. Find the value of tan θ if the particle strikes the plane (i) Horizontally (ii) Normally

Question Number 15939 Answers: 0 Comments: 1

Question Number 15927 Answers: 0 Comments: 5

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.

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

Pg 1920 Pg 1921 Pg 1922 Pg 1923 Pg 1924 Pg 1925 Pg 1926 Pg 1927 Pg 1928 Pg 1929

Contact: info@tinkutara.com