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AllQuestion and Answers: Page 1799

Question Number 23334 Answers: 1 Comments: 3

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Question Number 23330 Answers: 0 Comments: 0

The number of ordered pair(s) (x, y) satisfying the equations sinx.cosy = 1 and x^2 + y^2 ≤ 9π^2 is/are

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ordered}\:\mathrm{pair}\left(\mathrm{s}\right)\:\left({x},\:{y}\right) \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{sin}{x}.\mathrm{cos}{y}\:=\:\mathrm{1} \\ $$$$\mathrm{and}\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:\leqslant\:\mathrm{9}\pi^{\mathrm{2}} \:\mathrm{is}/\mathrm{are} \\ $$

Question Number 23317 Answers: 1 Comments: 0

∫sin^3 x cos x dx

$$\int\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}\:\mathrm{cos}\:\mathrm{x}\:\mathrm{dx} \\ $$

Question Number 23312 Answers: 1 Comments: 2

Question Number 23323 Answers: 0 Comments: 1

Question Number 23309 Answers: 0 Comments: 0

Question Number 23304 Answers: 1 Comments: 2

If sin^4 x + cos^4 y + 2 = 4 sinx.cosy & 0 ≤ x,y ≤ (π/2) , then the value of sinx + cosy is equal to

$$\mathrm{If}\:\mathrm{sin}^{\mathrm{4}} \mathrm{x}\:+\:\mathrm{cos}^{\mathrm{4}} \mathrm{y}\:+\:\mathrm{2}\:=\:\mathrm{4}\:\mathrm{sinx}.\mathrm{cosy}\:\& \\ $$$$\mathrm{0}\:\leqslant\:{x},{y}\:\leqslant\:\frac{\pi}{\mathrm{2}}\:,\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}{x}\:+ \\ $$$$\mathrm{cos}{y}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 23294 Answers: 1 Comments: 2

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Question Number 23288 Answers: 1 Comments: 3

A uniform chain of mass M and length L is hanging from the table. The chain is in limiting equilibrium when l length of chain over hangs. It is slightly disturbed from this position. Find the speed of the chain just after it completely comes off the table.

$$\mathrm{A}\:\mathrm{uniform}\:\mathrm{chain}\:\mathrm{of}\:\mathrm{mass}\:{M}\:\mathrm{and}\:\mathrm{length} \\ $$$${L}\:\mathrm{is}\:\mathrm{hanging}\:\mathrm{from}\:\mathrm{the}\:\mathrm{table}.\:\mathrm{The}\:\mathrm{chain} \\ $$$$\mathrm{is}\:\mathrm{in}\:\mathrm{limiting}\:\mathrm{equilibrium}\:\mathrm{when}\:{l}\:\mathrm{length} \\ $$$$\mathrm{of}\:\mathrm{chain}\:\mathrm{over}\:\mathrm{hangs}.\:\mathrm{It}\:\mathrm{is}\:\mathrm{slightly} \\ $$$$\mathrm{disturbed}\:\mathrm{from}\:\mathrm{this}\:\mathrm{position}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{chain}\:\mathrm{just}\:\mathrm{after}\:\mathrm{it}\:\mathrm{completely} \\ $$$$\mathrm{comes}\:\mathrm{off}\:\mathrm{the}\:\mathrm{table}. \\ $$

Question Number 23285 Answers: 0 Comments: 0

Mode=17 Mean=10.22 Median=10 What is the shape of the distribution?

$${Mode}=\mathrm{17} \\ $$$${Mean}=\mathrm{10}.\mathrm{22} \\ $$$${Median}=\mathrm{10} \\ $$$$ \\ $$$${What}\:{is}\:{the}\:{shape}\:{of}\:{the}\:{distribution}? \\ $$

Question Number 23283 Answers: 1 Comments: 0

Compute the area of a loop of the curve 𝛒=asin 2𝛉 ; and even sketch the curve, please.

$${Compute}\:{the}\:{area}\:{of}\:{a}\:{loop}\:{of} \\ $$$${the}\:{curve}\:\boldsymbol{\rho}=\boldsymbol{{a}}\mathrm{sin}\:\mathrm{2}\boldsymbol{\theta}\:;\:{and}\:{even} \\ $$$${sketch}\:{the}\:{curve},\:{please}. \\ $$

Question Number 23274 Answers: 0 Comments: 2

Assertion: Both N_2 and NO^+ are diamagnetic substances. Reason: NO^+ is isoelectronic with N_2 .

$$\boldsymbol{\mathrm{Assertion}}:\:\mathrm{Both}\:\mathrm{N}_{\mathrm{2}} \:\mathrm{and}\:\mathrm{NO}^{+} \:\mathrm{are} \\ $$$$\mathrm{diamagnetic}\:\mathrm{substances}. \\ $$$$\boldsymbol{\mathrm{Reason}}:\:\mathrm{NO}^{+} \:\mathrm{is}\:\mathrm{isoelectronic}\:\mathrm{with}\:\mathrm{N}_{\mathrm{2}} . \\ $$

Question Number 23272 Answers: 1 Comments: 1

Question Number 23270 Answers: 1 Comments: 0

The reaction CH_4 (g) + Cl_2 (g) → CH_3 Cl(g) + HCl(g) has ΔH = −25 kcal and bond dissociation energy of C − Cl, H − Cl, C − H and Cl − Cl is given as 84 kcal/mol, 103 kcal/mol, x kcal/mol and y kcal/mol respectively. Given x : y = 9 : 5, then bond energy of Cl − Cl bond in kcal/mol is

$$\mathrm{The}\:\mathrm{reaction}\:\mathrm{CH}_{\mathrm{4}} \left(\mathrm{g}\right)\:+\:\mathrm{Cl}_{\mathrm{2}} \left(\mathrm{g}\right)\:\rightarrow\:\mathrm{CH}_{\mathrm{3}} \mathrm{Cl}\left(\mathrm{g}\right) \\ $$$$+\:\mathrm{HCl}\left(\mathrm{g}\right)\:\mathrm{has}\:\Delta\mathrm{H}\:=\:−\mathrm{25}\:\mathrm{kcal}\:\mathrm{and}\:\mathrm{bond} \\ $$$$\mathrm{dissociation}\:\mathrm{energy}\:\mathrm{of}\:\mathrm{C}\:−\:\mathrm{Cl},\:\mathrm{H}\:−\:\mathrm{Cl}, \\ $$$$\mathrm{C}\:−\:\mathrm{H}\:\mathrm{and}\:\mathrm{Cl}\:−\:\mathrm{Cl}\:\mathrm{is}\:\mathrm{given}\:\mathrm{as}\:\mathrm{84}\:\mathrm{kcal}/\mathrm{mol}, \\ $$$$\mathrm{103}\:\mathrm{kcal}/\mathrm{mol},\:\mathrm{x}\:\mathrm{kcal}/\mathrm{mol}\:\mathrm{and}\:\mathrm{y}\:\mathrm{kcal}/\mathrm{mol} \\ $$$$\mathrm{respectively}.\:\mathrm{Given}\:\mathrm{x}\::\:\mathrm{y}\:=\:\mathrm{9}\::\:\mathrm{5},\:\mathrm{then} \\ $$$$\mathrm{bond}\:\mathrm{energy}\:\mathrm{of}\:\mathrm{Cl}\:−\:\mathrm{Cl}\:\mathrm{bond}\:\mathrm{in}\:\mathrm{kcal}/\mathrm{mol} \\ $$$$\mathrm{is} \\ $$

Question Number 23269 Answers: 1 Comments: 0

Prove that 3k+2 is not perfect square for all k∈{0,1,2,3,...}.

$$\mathbb{P}\mathrm{rove}\:\mathrm{that} \\ $$$$\:\mathrm{3k}+\mathrm{2}\:\mathrm{is}\:\mathrm{not}\:\mathrm{perfect}\:\mathrm{square}\:\mathrm{for} \\ $$$$\mathrm{all}\:\mathrm{k}\in\left\{\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},...\right\}. \\ $$

Question Number 23262 Answers: 0 Comments: 2

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If (1 + x)^n = C_0 + C_1 x + C_2 x^2 + C_3 x^3 + ... + C_n x^n , then prove that ΣΣ_(0≤i<j≤n) ((i/(^n C_i )) + (j/(^n C_j ))) = (n^2 /2)(Σ_(r=0) ^n (1/(^n C_r ))).

$${If}\:\left(\mathrm{1}\:+\:{x}\right)^{{n}} \:=\:{C}_{\mathrm{0}} \:+\:{C}_{\mathrm{1}} {x}\:+\:{C}_{\mathrm{2}} {x}^{\mathrm{2}} \:+\:{C}_{\mathrm{3}} {x}^{\mathrm{3}} \\ $$$$+\:...\:+\:{C}_{{n}} {x}^{{n}} ,\:{then}\:{prove}\:{that} \\ $$$$\underset{\mathrm{0}\leqslant{i}<{j}\leqslant{n}} {\Sigma\Sigma}\left(\frac{{i}}{\:^{{n}} {C}_{{i}} }\:+\:\frac{{j}}{\:^{{n}} {C}_{{j}} }\right)\:=\:\frac{{n}^{\mathrm{2}} }{\mathrm{2}}\left(\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\:^{{n}} {C}_{{r}} }\right). \\ $$

Question Number 23243 Answers: 0 Comments: 2

2^(n−1) sin a×sin 2a×sin 3a×......×sin (n−1)a=n why?

$$\mathrm{2}^{\mathrm{n}−\mathrm{1}} \mathrm{sin}\:\mathrm{a}×\mathrm{sin}\:\mathrm{2a}×\mathrm{sin}\:\mathrm{3a}×......×\mathrm{sin}\:\left(\mathrm{n}−\mathrm{1}\right)\mathrm{a}=\mathrm{n}\:\mathrm{why}? \\ $$

Question Number 23237 Answers: 0 Comments: 6

Question Number 23231 Answers: 1 Comments: 0

The number of solution(s) of the equation x^3 + x^2 + 4x + 2sinx = 0 in [0, 2π], is/are

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solution}\left(\mathrm{s}\right)\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$${x}^{\mathrm{3}} \:+\:{x}^{\mathrm{2}} \:+\:\mathrm{4}{x}\:+\:\mathrm{2sin}{x}\:=\:\mathrm{0}\:\mathrm{in}\:\left[\mathrm{0},\:\mathrm{2}\pi\right],\:\mathrm{is}/\mathrm{are} \\ $$

Question Number 23226 Answers: 1 Comments: 4

Question Number 23224 Answers: 0 Comments: 4

Consider the system shown in the figure. Initially the system was in rest. (i) Find the acceleration of block if man climbs the rod with acceleration a (w.r.t. rod) (ii) If the man climb to the top of the rod then find the distance moved by the block.

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{system}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{figure}.\:\mathrm{Initially}\:\mathrm{the}\:\mathrm{system}\:\mathrm{was}\:\mathrm{in}\:\mathrm{rest}. \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{block}\:\mathrm{if}\:\mathrm{man} \\ $$$$\mathrm{climbs}\:\mathrm{the}\:\mathrm{rod}\:\mathrm{with}\:\mathrm{acceleration}\:{a}\:\left(\mathrm{w}.\mathrm{r}.\mathrm{t}.\right. \\ $$$$\left.\mathrm{rod}\right) \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{If}\:\mathrm{the}\:\mathrm{man}\:\mathrm{climb}\:\mathrm{to}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{rod}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{moved}\:\mathrm{by}\:\mathrm{the} \\ $$$$\mathrm{block}. \\ $$

Question Number 23223 Answers: 1 Comments: 0

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