Question and Answers Forum

AllQuestion and Answers: Page 1931

Question Number 15452 Answers: 1 Comments: 0

Question Number 15448 Answers: 0 Comments: 2

A vector A^→ of magnitude A is turned through an angle θ. Calculate the change in the magnitude of vector.

$$\mathrm{A}\:\mathrm{vector}\:\overset{\rightarrow} {{A}}\:\mathrm{of}\:\mathrm{magnitude}\:{A}\:\mathrm{is}\:\mathrm{turned} \\ $$$$\mathrm{through}\:\mathrm{an}\:\mathrm{angle}\:\theta.\:\mathrm{Calculate}\:\mathrm{the} \\ $$$$\mathrm{change}\:\mathrm{in}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{vector}. \\ $$

Question Number 15440 Answers: 3 Comments: 9

Question Number 15434 Answers: 1 Comments: 8

Question Number 15407 Answers: 1 Comments: 0

A ball is thrown vertically upward with velocity 20 m/s from a rail road car moving with a velocity 5 m/s horizontally. A person standing on the ground observes its motion as projectile. Find maximum height attained by the ball if point of projection is at a height 3 m from the ground.

$$\mathrm{A}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{thrown}\:\mathrm{vertically}\:\mathrm{upward} \\ $$$$\mathrm{with}\:\mathrm{velocity}\:\mathrm{20}\:\mathrm{m}/\mathrm{s}\:\mathrm{from}\:\mathrm{a}\:\mathrm{rail}\:\mathrm{road} \\ $$$$\mathrm{car}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{5}\:\mathrm{m}/\mathrm{s} \\ $$$$\mathrm{horizontally}.\:\mathrm{A}\:\mathrm{person}\:\mathrm{standing}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{ground}\:\mathrm{observes}\:\mathrm{its}\:\mathrm{motion}\:\mathrm{as}\:\mathrm{projectile}. \\ $$$$\mathrm{Find}\:\mathrm{maximum}\:\mathrm{height}\:\mathrm{attained}\:\mathrm{by}\:\mathrm{the} \\ $$$$\mathrm{ball}\:\mathrm{if}\:\mathrm{point}\:\mathrm{of}\:\mathrm{projection}\:\mathrm{is}\:\mathrm{at}\:\mathrm{a}\:\mathrm{height} \\ $$$$\mathrm{3}\:\mathrm{m}\:\mathrm{from}\:\mathrm{the}\:\mathrm{ground}. \\ $$

Question Number 15405 Answers: 1 Comments: 0

A body is projected at time t = 0 from a certain point on a planet surface with a certain velocity at a certain angle with the planet′s surface (assumed horizontal). The horizontal and vertical displacement x and y in metre are related to time as x = 10(√3)t and y = 10t − 4t^2 . Find vertical component of velocity of the particle when it is at a height half of the maximum height attained.

$$\mathrm{A}\:\mathrm{body}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{at}\:\mathrm{time}\:{t}\:=\:\mathrm{0}\:\mathrm{from}\:\mathrm{a} \\ $$$$\mathrm{certain}\:\mathrm{point}\:\mathrm{on}\:\mathrm{a}\:\mathrm{planet}\:\mathrm{surface}\:\mathrm{with} \\ $$$$\mathrm{a}\:\mathrm{certain}\:\mathrm{velocity}\:\mathrm{at}\:\mathrm{a}\:\mathrm{certain}\:\mathrm{angle} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{planet}'\mathrm{s}\:\mathrm{surface}\:\left(\mathrm{assumed}\right. \\ $$$$\left.\mathrm{horizontal}\right).\:\mathrm{The}\:\mathrm{horizontal}\:\mathrm{and}\:\mathrm{vertical} \\ $$$$\mathrm{displacement}\:{x}\:\mathrm{and}\:{y}\:\mathrm{in}\:\mathrm{metre}\:\mathrm{are} \\ $$$$\mathrm{related}\:\mathrm{to}\:\mathrm{time}\:\mathrm{as}\:{x}\:=\:\mathrm{10}\sqrt{\mathrm{3}}{t}\:\mathrm{and} \\ $$$${y}\:=\:\mathrm{10}{t}\:−\:\mathrm{4}{t}^{\mathrm{2}} .\:\mathrm{Find}\:\mathrm{vertical}\:\mathrm{component} \\ $$$$\mathrm{of}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{when}\:\mathrm{it}\:\mathrm{is}\:\mathrm{at}\:\mathrm{a} \\ $$$$\mathrm{height}\:\mathrm{half}\:\mathrm{of}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{height} \\ $$$$\mathrm{attained}. \\ $$

Question Number 15393 Answers: 1 Comments: 0

A man observes that when he moves up a distance c metres on a slope, the angle of depression of a point on the horizontal plane from the base of the slope is 30°, and when he moves up further a distance c metres, the angle of depression of that point is 45°. The angle of inclination of the slope with the horizontal is?

$$\mathrm{A}\:\mathrm{man}\:\mathrm{observes}\:\mathrm{that}\:\mathrm{when}\:\mathrm{he}\:\mathrm{moves}\:\mathrm{up} \\ $$$$\mathrm{a}\:\mathrm{distance}\:{c}\:\mathrm{metres}\:\mathrm{on}\:\mathrm{a}\:\mathrm{slope},\:\mathrm{the} \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{depression}\:\mathrm{of}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{horizontal}\:\mathrm{plane}\:\mathrm{from}\:\mathrm{the}\:\mathrm{base}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{slope}\:\mathrm{is}\:\mathrm{30}°,\:\mathrm{and}\:\mathrm{when}\:\mathrm{he}\:\mathrm{moves}\:\mathrm{up} \\ $$$$\mathrm{further}\:\mathrm{a}\:\mathrm{distance}\:{c}\:\mathrm{metres},\:\mathrm{the}\:\mathrm{angle}\:\mathrm{of} \\ $$$$\mathrm{depression}\:\mathrm{of}\:\mathrm{that}\:\mathrm{point}\:\mathrm{is}\:\mathrm{45}°.\:\mathrm{The} \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{inclination}\:\mathrm{of}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{with}\:\mathrm{the} \\ $$$$\mathrm{horizontal}\:\mathrm{is}? \\ $$

Question Number 15392 Answers: 1 Comments: 0

Each side of an equilateral triangle subtends angle of 60° at the top of a tower of height h standing at the centre of the triangle. If 2a be the length of the side of the triangle, then (a^2 /h^2 ) = ?

$$\mathrm{Each}\:\mathrm{side}\:\mathrm{of}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle} \\ $$$$\mathrm{subtends}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{60}°\:\mathrm{at}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{tower}\:\mathrm{of}\:\mathrm{height}\:{h}\:\mathrm{standing}\:\mathrm{at}\:\mathrm{the}\:\mathrm{centre} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}.\:\mathrm{If}\:\mathrm{2}{a}\:\mathrm{be}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle},\:\mathrm{then}\:\frac{{a}^{\mathrm{2}} }{{h}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 15377 Answers: 1 Comments: 0

−39 mod 4 = ?

$$−\mathrm{39}\:\mathrm{mod}\:\mathrm{4}\:=\:? \\ $$

Question Number 15384 Answers: 1 Comments: 0

If a flagstaff subtends equal angles at 4 points A, B, C and D on the horizontal plane through the foot of the flagstaff, then A, B, C and D must be the vertices of (1) Square (2) Cyclic quadrilateral (3) Rectangle (4) Parallelogram

$$\mathrm{If}\:\mathrm{a}\:\mathrm{flagstaff}\:\mathrm{subtends}\:\mathrm{equal}\:\mathrm{angles}\:\mathrm{at}\:\mathrm{4} \\ $$$$\mathrm{points}\:{A},\:{B},\:{C}\:\mathrm{and}\:{D}\:\mathrm{on}\:\mathrm{the}\:\mathrm{horizontal} \\ $$$$\mathrm{plane}\:\mathrm{through}\:\mathrm{the}\:\mathrm{foot}\:\mathrm{of}\:\mathrm{the}\:\mathrm{flagstaff}, \\ $$$$\mathrm{then}\:{A},\:{B},\:{C}\:\mathrm{and}\:{D}\:\mathrm{must}\:\mathrm{be}\:\mathrm{the} \\ $$$$\mathrm{vertices}\:\mathrm{of} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Square} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Cyclic}\:\mathrm{quadrilateral} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Rectangle} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{Parallelogram} \\ $$

Question Number 15418 Answers: 2 Comments: 0

A grasshopper can jump a maximum horizontal distance of 40 cm. If it spends negligible time on the ground then in this case its speed along the horizontal road will be?

$$\mathrm{A}\:\mathrm{grasshopper}\:\mathrm{can}\:\mathrm{jump}\:\mathrm{a}\:\mathrm{maximum} \\ $$$$\mathrm{horizontal}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{40}\:\mathrm{cm}.\:\mathrm{If}\:\mathrm{it} \\ $$$$\mathrm{spends}\:\mathrm{negligible}\:\mathrm{time}\:\mathrm{on}\:\mathrm{the}\:\mathrm{ground} \\ $$$$\mathrm{then}\:\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{its}\:\mathrm{speed}\:\mathrm{along}\:\mathrm{the} \\ $$$$\mathrm{horizontal}\:\mathrm{road}\:\mathrm{will}\:\mathrm{be}? \\ $$

Question Number 15358 Answers: 1 Comments: 0

If a^→ , b^→ , c^→ are mutually perpendicular vectors of equal magnitudes, show that the vector a^→ + b^→ + c^→ is equally inclined to a^→ , b^→ and c^→ .

Question Number 15352 Answers: 0 Comments: 4

Let a^→ = i^∧ + 4j^∧ + 2k^∧ , b^→ = 3i^∧ − 2j^∧ + 7k^∧ and c^→ = 2i^∧ − j^∧ + 4k^∧ . Find a vector d^→ which is perpendicular to both a^→ and b^→ , and c^→ ∙ d^→ = 15.

Question Number 15348 Answers: 2 Comments: 0

Solve the equation z^2 + 2(1 + j)z + 2 = 0, Givin each result in form a + jb with a and b correct to 2dp.

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\:\mathrm{z}^{\mathrm{2}} \:+\:\mathrm{2}\left(\mathrm{1}\:+\:\mathrm{j}\right)\mathrm{z}\:+\:\mathrm{2}\:=\:\mathrm{0},\:\mathrm{Givin}\:\mathrm{each}\:\mathrm{result}\:\mathrm{in}\:\mathrm{form}\:\:\mathrm{a}\:+\:\mathrm{jb} \\ $$$$\mathrm{with}\:\:\mathrm{a}\:\:\mathrm{and}\:\:\mathrm{b}\:\:\mathrm{correct}\:\mathrm{to}\:\:\mathrm{2dp}. \\ $$

Question Number 15343 Answers: 0 Comments: 0

Question Number 15344 Answers: 0 Comments: 0

Question Number 15328 Answers: 1 Comments: 0

Prove that. sec^4 (x) − cosec^4 (x) = ((sin^2 (x) − cos^2 (x))/(sec^4 (x)))

$$\mathrm{Prove}\:\mathrm{that}. \\ $$$$\mathrm{sec}^{\mathrm{4}} \left(\mathrm{x}\right)\:−\:\mathrm{cosec}^{\mathrm{4}} \left(\mathrm{x}\right)\:=\:\frac{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)\:−\:\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{sec}^{\mathrm{4}} \left(\mathrm{x}\right)} \\ $$

Question Number 15322 Answers: 0 Comments: 6

Question Number 15318 Answers: 2 Comments: 6

Question Number 15311 Answers: 0 Comments: 0

In a toll-booth at a bridge , some cars can pass by paying a tax of Rs. 10 and some special vehicles are exempted from paying tax. The booth has to track number of vehicles and total tax collected. Define a class ′tollbooth′. It should contain two data items of type int to hold the number of cars and total tax connected. A constructor initalizes these two variable to zero. A memberfunction freecar() only increments the car total. Finally another memberfunction show() displays the two totals. Write a C++ program such that the user has to press the key ′T′ for printing number of taxable cars and total tax, ′F′ for printing number of free cars and ′Esc′ to exit.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{toll}-\mathrm{booth}\:\mathrm{at}\:\mathrm{a}\:\mathrm{bridge}\:,\:\mathrm{some}\:\mathrm{cars}\:\mathrm{can}\:\mathrm{pass}\:\mathrm{by}\:\mathrm{paying}\:\mathrm{a}\:\mathrm{tax}\:\mathrm{of}\:\mathrm{Rs}.\:\mathrm{10}\:\mathrm{and} \\ $$$$\mathrm{some}\:\mathrm{special}\:\mathrm{vehicles}\:\mathrm{are}\:\mathrm{exempted}\:\mathrm{from}\:\mathrm{paying}\:\mathrm{tax}.\:\mathrm{The}\:\mathrm{booth}\:\mathrm{has}\:\mathrm{to}\:\mathrm{track}\: \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{vehicles}\:\mathrm{and}\:\mathrm{total}\:\mathrm{tax}\:\mathrm{collected}.\:\mathrm{Define}\:\mathrm{a}\:\mathrm{class}\:'\mathrm{tollbooth}'.\:\mathrm{It}\:\mathrm{should}\:\mathrm{contain} \\ $$$$\mathrm{two}\:\mathrm{data}\:\mathrm{items}\:\mathrm{of}\:\mathrm{type}\:\mathrm{int}\:\mathrm{to}\:\mathrm{hold}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{cars}\:\mathrm{and}\:\mathrm{total}\:\mathrm{tax}\:\mathrm{connected}. \\ $$$$\mathrm{A}\:\mathrm{constructor}\:\mathrm{initalizes}\:\mathrm{these}\:\mathrm{two}\:\mathrm{variable}\:\mathrm{to}\:\mathrm{zero}.\:\mathrm{A}\:\mathrm{memberfunction}\:\mathrm{freecar}\left(\right)\:\mathrm{only} \\ $$$$\mathrm{increments}\:\mathrm{the}\:\mathrm{car}\:\mathrm{total}.\:\mathrm{Finally}\:\mathrm{another}\:\mathrm{memberfunction}\:\mathrm{show}\left(\right)\:\mathrm{displays}\:\mathrm{the} \\ $$$$\mathrm{two}\:\mathrm{totals}. \\ $$$$\:\:\:\mathrm{Write}\:\mathrm{a}\:\mathrm{C}++\:\mathrm{program}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{user}\:\mathrm{has}\:\mathrm{to}\:\mathrm{press}\:\mathrm{the}\:\mathrm{key}\:'\mathrm{T}'\:\mathrm{for} \\ $$$$\mathrm{printing}\:\mathrm{number}\:\mathrm{of}\:\mathrm{taxable}\:\mathrm{cars}\:\mathrm{and}\:\mathrm{total}\:\mathrm{tax},\:'\mathrm{F}'\:\mathrm{for}\:\mathrm{printing}\:\mathrm{number}\:\mathrm{of}\:\:\mathrm{free} \\ $$$$\mathrm{cars}\:\mathrm{and}\:'\mathrm{Esc}'\:\mathrm{to}\:\mathrm{exit}. \\ $$

Question Number 15302 Answers: 0 Comments: 0

Prove that number of commutative binary operations on a set having n elements is n^((n(n − 1))/2) .

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{number}\:\mathrm{of}\:\mathrm{commutative} \\ $$$$\mathrm{binary}\:\mathrm{operations}\:\mathrm{on}\:\mathrm{a}\:\mathrm{set}\:\mathrm{having}\:{n} \\ $$$$\mathrm{elements}\:\mathrm{is}\:{n}^{\frac{{n}\left({n}\:−\:\mathrm{1}\right)}{\mathrm{2}}} \:. \\ $$

Question Number 15301 Answers: 1 Comments: 0

With the help of graph, find the solution set of inequation tan x > −(√3) .

$$\mathrm{With}\:\mathrm{the}\:\mathrm{help}\:\mathrm{of}\:\mathrm{graph},\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\mathrm{inequation}\:\mathrm{tan}\:{x}\:>\:−\sqrt{\mathrm{3}}\:. \\ $$

Question Number 15300 Answers: 1 Comments: 3

Find the values of α and β, 0 < α, β < (π/2) satisfying the following equation cos α cos β cos (α + β) = −(1/8) .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\alpha\:\mathrm{and}\:\beta,\:\mathrm{0}\:<\:\alpha,\:\beta\:<\:\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{following}\:\mathrm{equation} \\ $$$$\mathrm{cos}\:\alpha\:\mathrm{cos}\:\beta\:\mathrm{cos}\:\left(\alpha\:+\:\beta\right)\:=\:−\frac{\mathrm{1}}{\mathrm{8}}\:. \\ $$

Question Number 15298 Answers: 1 Comments: 4

Solve for x and y x^2 + 2x sin(xy) + 1 = 0

$$\mathrm{Solve}\:\mathrm{for}\:{x}\:\mathrm{and}\:{y} \\ $$$${x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:\mathrm{sin}\left({xy}\right)\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 15294 Answers: 0 Comments: 1

A straigth conductor of length L is charged with q charge. What will be the electric field in the equatorial line at a distance d ? Ans: ((2q)/(4Πε_0 d(√(L^2 +4d^2 ))))

$$\mathrm{A}\:\mathrm{straigth}\:\mathrm{conductor}\:\mathrm{of}\:\mathrm{length} \\ $$$$\mathrm{L}\:\mathrm{is}\:\mathrm{charged}\:\mathrm{with}\:\mathrm{q}\:\mathrm{charge}.\:\mathrm{What} \\ $$$$\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{electric}\:\mathrm{field}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{equatorial}\:\mathrm{line}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{d}\:? \\ $$$$\mathrm{Ans}:\:\frac{\mathrm{2q}}{\mathrm{4}\Pi\epsilon_{\mathrm{0}} \mathrm{d}\sqrt{\mathrm{L}^{\mathrm{2}} +\mathrm{4d}^{\mathrm{2}} }} \\ $$

Question Number 15288 Answers: 0 Comments: 1

Pg 1926 Pg 1927 Pg 1928 Pg 1929 Pg 1930 Pg 1931 Pg 1932 Pg 1933 Pg 1934 Pg 1935

Contact: info@tinkutara.com