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AllQuestion and Answers: Page 1832

Question Number 23539    Answers: 1   Comments: 0

∫tan^6 x dx

$$\int\mathrm{tan}\:^{\mathrm{6}} \mathrm{x}\:\mathrm{dx} \\ $$

Question Number 23537    Answers: 1   Comments: 8

Question Number 23531    Answers: 1   Comments: 3

Question Number 23524    Answers: 0   Comments: 0

Question Number 23523    Answers: 0   Comments: 0

The order and degree of the differential equation are y^(11) =(y−y^1^3 )^(2/3)

$${The}\:{order}\:{and}\:{degree}\:{of}\:{the}\:{differential}\:{equation}\:{are}\:{y}^{\mathrm{11}} =\left({y}−{y}^{\mathrm{1}^{\mathrm{3}} } \right)^{\mathrm{2}/\mathrm{3}} \\ $$

Question Number 23522    Answers: 0   Comments: 1

the particular integral of the differential equation f(D)y=e^(ax) where f(D)=(D−a)g(D),g(a)≠0 is

$${the}\:{particular}\:{integral}\:{of}\:{the}\:{differential}\:{equation}\:{f}\left({D}\right){y}={e}^{{ax}} {where}\:{f}\left({D}\right)=\left({D}−{a}\right){g}\left({D}\right),{g}\left({a}\right)\neq\mathrm{0}\:{is} \\ $$

Question Number 23520    Answers: 0   Comments: 3

A wooden block of mass 10 gm is dropped from the top of a tower 100 m high. Simultaneously, a bullet of mass 10 gm is fired from the foot of the tower vertically upwards with a velocity of 100 m/sec. If the bullet is embedded in it, how high will it rise above the tower before it starts falling? (Consider g = 10 m/sec^2 )

$$\mathrm{A}\:\mathrm{wooden}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{10}\:\mathrm{gm}\:\mathrm{is} \\ $$$$\mathrm{dropped}\:\mathrm{from}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tower}\:\mathrm{100}\:\mathrm{m} \\ $$$$\mathrm{high}.\:\mathrm{Simultaneously},\:\mathrm{a}\:\mathrm{bullet}\:\mathrm{of}\:\mathrm{mass} \\ $$$$\mathrm{10}\:\mathrm{gm}\:\mathrm{is}\:\mathrm{fired}\:\mathrm{from}\:\mathrm{the}\:\mathrm{foot}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tower} \\ $$$$\mathrm{vertically}\:\mathrm{upwards}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of} \\ $$$$\mathrm{100}\:\mathrm{m}/\mathrm{sec}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{bullet}\:\mathrm{is}\:\mathrm{embedded}\:\mathrm{in} \\ $$$$\mathrm{it},\:\mathrm{how}\:\mathrm{high}\:\mathrm{will}\:\mathrm{it}\:\mathrm{rise}\:\mathrm{above}\:\mathrm{the}\:\mathrm{tower} \\ $$$$\mathrm{before}\:\mathrm{it}\:\mathrm{starts}\:\mathrm{falling}?\:\left(\mathrm{Consider}\:{g}\:=\right. \\ $$$$\left.\mathrm{10}\:\mathrm{m}/\mathrm{sec}^{\mathrm{2}} \right) \\ $$

Question Number 23535    Answers: 0   Comments: 0

if a compound statement is made up of three simple statements then the number of rows in the truth table is

$${if}\:{a}\:{compound}\:{statement}\:{is}\:{made}\:{up}\:{of}\:{three}\:{simple}\:{statements}\:{then}\:{the}\:{number}\:{of}\:{rows}\:{in}\:{the}\:{truth}\:{table}\:{is} \\ $$

Question Number 23508    Answers: 1   Comments: 1

Question Number 23518    Answers: 0   Comments: 5

A ball of mass 1 kg moving with velocity 3 m/s collides with spring of natural length 2 m and force constant 144 N/m. What will be length of compressed spring?

$$\mathrm{A}\:\mathrm{ball}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1}\:\mathrm{kg}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{velocity} \\ $$$$\mathrm{3}\:\mathrm{m}/\mathrm{s}\:\mathrm{collides}\:\mathrm{with}\:\mathrm{spring}\:\mathrm{of}\:\mathrm{natural} \\ $$$$\mathrm{length}\:\mathrm{2}\:\mathrm{m}\:\mathrm{and}\:\mathrm{force}\:\mathrm{constant}\:\mathrm{144}\:\mathrm{N}/\mathrm{m}. \\ $$$$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{length}\:\mathrm{of}\:\mathrm{compressed} \\ $$$$\mathrm{spring}? \\ $$

Question Number 23492    Answers: 0   Comments: 5

Question Number 23489    Answers: 1   Comments: 2

A rectangular wire frame ABCD is in vertical plane is moving with a constant acceleration a into the plane. Direction of gravity is shown in figure. A collar can move on wire AC of length l. Coefficient of friction between wire and collar is μ. Find (i) The minimum acceleration a so that collar does not slip on wire. (ii) The time taken by collar to reach C if acceleration is half the value calculated in part (i)

$$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{wire}\:\mathrm{frame}\:{ABCD}\:\mathrm{is}\:\mathrm{in} \\ $$$$\mathrm{vertical}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{a}\:\mathrm{constant} \\ $$$$\mathrm{acceleration}\:{a}\:\mathrm{into}\:\mathrm{the}\:\mathrm{plane}.\:\mathrm{Direction} \\ $$$$\mathrm{of}\:\mathrm{gravity}\:\mathrm{is}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{figure}.\:\mathrm{A}\:\mathrm{collar} \\ $$$$\mathrm{can}\:\mathrm{move}\:\mathrm{on}\:\mathrm{wire}\:{AC}\:\mathrm{of}\:\mathrm{length}\:{l}. \\ $$$$\mathrm{Coefficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{between}\:\mathrm{wire} \\ $$$$\mathrm{and}\:\mathrm{collar}\:\mathrm{is}\:\mu.\:\mathrm{Find} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{The}\:\mathrm{minimum}\:\mathrm{acceleration}\:{a}\:\mathrm{so}\:\mathrm{that} \\ $$$$\mathrm{collar}\:\mathrm{does}\:\mathrm{not}\:\mathrm{slip}\:\mathrm{on}\:\mathrm{wire}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{The}\:\mathrm{time}\:\mathrm{taken}\:\mathrm{by}\:\mathrm{collar}\:\mathrm{to}\:\mathrm{reach}\:{C} \\ $$$$\mathrm{if}\:\mathrm{acceleration}\:\mathrm{is}\:\mathrm{half}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{calculated}\:\mathrm{in}\:\mathrm{part}\:\left(\mathrm{i}\right) \\ $$

Question Number 23488    Answers: 0   Comments: 0

area of a(1−cos θ)

$${area}\:{of}\:{a}\left(\mathrm{1}−\mathrm{cos}\:\theta\right) \\ $$

Question Number 23485    Answers: 0   Comments: 0

(1/(cos (x−a)cos (x−b)))

$$\frac{\mathrm{1}}{\mathrm{cos}\:\left({x}−{a}\right)\mathrm{cos}\:\left({x}−{b}\right)} \\ $$

Question Number 23481    Answers: 0   Comments: 5

Which of the diagrams represents variation of total mechanical energy of a pendulum oscillating in air as function of time?

$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{diagrams}\:\mathrm{represents} \\ $$$$\mathrm{variation}\:\mathrm{of}\:\mathrm{total}\:\mathrm{mechanical}\:\mathrm{energy}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{pendulum}\:\mathrm{oscillating}\:\mathrm{in}\:\mathrm{air}\:\mathrm{as}\:\mathrm{function} \\ $$$$\mathrm{of}\:\mathrm{time}? \\ $$

Question Number 23479    Answers: 0   Comments: 0

Common solution. (d/dy)(u_x +u)+2x^2 y(u_x +u)=0.

$$\boldsymbol{\mathrm{Common}}\:\:\boldsymbol{\mathrm{solution}}. \\ $$$$\frac{\boldsymbol{\mathfrak{d}}}{\boldsymbol{\mathfrak{d}\mathrm{y}}}\left(\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{x}}} +\boldsymbol{\mathrm{u}}\right)+\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}\left(\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{x}}} +\boldsymbol{\mathrm{u}}\right)=\mathrm{0}. \\ $$

Question Number 23477    Answers: 0   Comments: 0

Find the value of x, ∫_(−∞) ^x dx = ∫∣± sinh cot ln (15−(√(33+x)))∣ dx

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}, \\ $$$$\:\:\:\:\:\:\:\int_{−\infty} ^{{x}} {d}\mathrm{x}\:=\:\int\mid\pm\:\mathrm{sinh}\:\mathrm{cot}\:\mathrm{ln}\:\left(\mathrm{15}−\sqrt{\mathrm{33}+{x}}\right)\mid\:\mathrm{dx} \\ $$

Question Number 23476    Answers: 0   Comments: 0

Question Number 23472    Answers: 1   Comments: 1

Question Number 23471    Answers: 1   Comments: 0

Prove that ΣΣ_(0≤i<j≤n) ((1/(^n C_i )) + (1/(^n C_j ))) = Σ_(r=0) ^(n−1) ((n − r)/(^n C_r )) + Σ_(r=1) ^n (r/(^n C_r ))

$${Prove}\:{that} \\ $$$$\underset{\mathrm{0}\leqslant{i}<{j}\leqslant{n}} {\Sigma\Sigma}\left(\frac{\mathrm{1}}{\:^{{n}} {C}_{{i}} }\:+\:\frac{\mathrm{1}}{\:^{{n}} {C}_{{j}} }\right)\:=\:\underset{{r}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\frac{{n}\:−\:{r}}{\:^{{n}} {C}_{{r}} }\:+\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{r}}{\:^{{n}} {C}_{{r}} } \\ $$

Question Number 23458    Answers: 0   Comments: 1

Question Number 23445    Answers: 1   Comments: 0

Solve the equation: (∂^2 u/(∂x∂y)) = sin(x)cos(y), subjected to the boundary conditions at y = (π/2), (∂u/∂x) = 2x and x = π, u = 2sin(y)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}:\:\:\:\frac{\partial^{\mathrm{2}} \mathrm{u}}{\partial\mathrm{x}\partial\mathrm{y}}\:=\:\mathrm{sin}\left(\mathrm{x}\right)\mathrm{cos}\left(\mathrm{y}\right),\:\:\:\mathrm{subjected}\:\mathrm{to}\:\mathrm{the}\:\mathrm{boundary} \\ $$$$\mathrm{conditions}\:\mathrm{at}\:\:\:\mathrm{y}\:=\:\frac{\pi}{\mathrm{2}},\:\:\:\:\frac{\partial\mathrm{u}}{\partial\mathrm{x}}\:=\:\mathrm{2x}\:\:\:\:\mathrm{and}\:\:\:\:\:\mathrm{x}\:=\:\pi,\:\:\:\:\mathrm{u}\:=\:\mathrm{2sin}\left(\mathrm{y}\right) \\ $$

Question Number 23444    Answers: 0   Comments: 0

Question Number 23442    Answers: 1   Comments: 2

Find a unit vector which is perpendicula to a vector A(3coma5coma1) Sorry for writing coma cuz i dnt see a key for it

$$\mathrm{Find}\:\mathrm{a}\:\mathrm{unit}\:\mathrm{vector}\:\mathrm{which}\:\mathrm{is}\:\mathrm{perpendicula} \\ $$$$\mathrm{to}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{A}\left(\mathrm{3coma5coma1}\right) \\ $$$$ \\ $$$$\mathrm{Sorry}\:\mathrm{for}\:\mathrm{writing}\:\mathrm{coma}\:\mathrm{cuz}\:\mathrm{i}\:\mathrm{dnt}\:\mathrm{see}\:\mathrm{a}\:\mathrm{key}\:\mathrm{for}\:\mathrm{it} \\ $$

Question Number 23433    Answers: 0   Comments: 0

∫_0 ^∞ X^6 e^(−x/2) dx=

$$\int_{\mathrm{0}} ^{\infty} {X}^{\mathrm{6}} {e}^{−{x}/\mathrm{2}} {dx}= \\ $$

Question Number 23432    Answers: 1   Comments: 0

∫_0 ^a f(x)dx=

$$\int_{\mathrm{0}} ^{{a}} {f}\left({x}\right){dx}= \\ $$

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