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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

Question Number 23251 Answers: 0 Comments: 1

Question Number 23250 Answers: 0 Comments: 0

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

Question Number 23253 Answers: 1 Comments: 8

Question Number 23190 Answers: 1 Comments: 1

lim_(x→∞) (((x−2)/(3x+10)))^(5x)

$$\underset{\boldsymbol{\mathrm{x}}\rightarrow\infty} {\boldsymbol{\mathrm{lim}}}\left(\frac{\boldsymbol{\mathrm{x}}−\mathrm{2}}{\mathrm{3}\boldsymbol{\mathrm{x}}+\mathrm{10}}\right)^{\mathrm{5}\boldsymbol{\mathrm{x}}} \\ $$

Question Number 23208 Answers: 1 Comments: 0

Is it possible to find how many real roots exist in the equation x^4 + ∣x∣ = 3 without find all the value of x?

$$\mathrm{Is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{find}\:\mathrm{how}\:\mathrm{many}\:\mathrm{real}\:\mathrm{roots}\: \\ $$$$\mathrm{exist}\:\mathrm{in}\:\mathrm{the}\:\mathrm{equation} \\ $$$${x}^{\mathrm{4}} \:+\:\mid{x}\mid\:=\:\mathrm{3} \\ $$$$\mathrm{without}\:\mathrm{find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{x}? \\ $$

Question Number 23205 Answers: 0 Comments: 0

thank u.....

$${thank}\:{u}..... \\ $$

Question Number 23187 Answers: 0 Comments: 0

plz anyone answer the question 23181...plz plz plz...

$${plz}\:\:\:{anyone}\:{answer}\:{the}\:{question}\: \\ $$$$\mathrm{23181}...{plz}\:{plz}\:{plz}... \\ $$

Question Number 23181 Answers: 0 Comments: 2

show that the curve with parametric equcations x=t^2 −3t+5, y=t^3 +t^2 −10t+9 intersect at the point (3,1).

$${show}\:{that}\:{the}\:{curve}\:{with}\:{parametric}\: \\ $$$${equcations}\:\:{x}={t}^{\mathrm{2}} \:−\mathrm{3}{t}+\mathrm{5}, \\ $$$${y}={t}^{\mathrm{3}} \:+{t}^{\mathrm{2}} \:−\mathrm{10}{t}+\mathrm{9}\:{intersect}\:{at}\:{the}\: \\ $$$${point}\:\left(\mathrm{3},\mathrm{1}\right). \\ $$

Question Number 23179 Answers: 2 Comments: 1

Question Number 23212 Answers: 1 Comments: 1

Question Number 23170 Answers: 0 Comments: 2

Question Number 23215 Answers: 0 Comments: 0

Assertion: The element with electronic configuration [Xe]^(54) 4f^1 5d^1 6s^2 is a d- block element. Reason: The last electron enters the d- orbital.

$$\boldsymbol{\mathrm{Assertion}}:\:\mathrm{The}\:\mathrm{element}\:\mathrm{with}\:\mathrm{electronic} \\ $$$$\mathrm{configuration}\:\left[\mathrm{Xe}\right]^{\mathrm{54}} \:\mathrm{4}{f}^{\mathrm{1}} \:\mathrm{5}{d}^{\mathrm{1}} \:\mathrm{6}{s}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{a}\:{d}- \\ $$$$\mathrm{block}\:\mathrm{element}. \\ $$$$\boldsymbol{\mathrm{Reason}}:\:\mathrm{The}\:\mathrm{last}\:\mathrm{electron}\:\mathrm{enters}\:\mathrm{the}\:{d}- \\ $$$$\mathrm{orbital}. \\ $$

Question Number 23146 Answers: 0 Comments: 5

Square planar complex is formed by hybridisation of which atomic orbitals? (1) s, p_x , p_y , p_z (2) s, p_x , p_y , d_z^2 (3) s, p_x , p_y , d_(x^2 −y^2 ) (4) s, p_x , p_y , d_z^3

$$\mathrm{Square}\:\mathrm{planar}\:\mathrm{complex}\:\mathrm{is}\:\mathrm{formed}\:\mathrm{by} \\ $$$$\mathrm{hybridisation}\:\mathrm{of}\:\mathrm{which}\:\mathrm{atomic}\:\mathrm{orbitals}? \\ $$$$\left(\mathrm{1}\right)\:{s},\:{p}_{{x}} ,\:{p}_{{y}} ,\:{p}_{{z}} \\ $$$$\left(\mathrm{2}\right)\:{s},\:{p}_{{x}} ,\:{p}_{{y}} ,\:{d}_{{z}^{\mathrm{2}} } \\ $$$$\left(\mathrm{3}\right)\:{s},\:{p}_{{x}} ,\:{p}_{{y}} ,\:{d}_{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } \\ $$$$\left(\mathrm{4}\right)\:{s},\:{p}_{{x}} ,\:{p}_{{y}} ,\:{d}_{{z}^{\mathrm{3}} } \\ $$

Question Number 23135 Answers: 1 Comments: 0

The standard enthalpy of formation of gaseous H_2 O at 298 K is −241.82 kJ mol^(−1) . Estimate its value of 100°C given the following values of the molar heat capacities at constant pressure: H_2 O(g) : 35.58 JK^(−1) mol^(−1) , H_2 (g) : 28.84 J mol^(−1) K^(−1) and O_2 (g) : 29.37 J mol^(−1) K^(−1) . Assume heat capacity to be independent of temperature.

$$\mathrm{The}\:\mathrm{standard}\:\mathrm{enthalpy}\:\mathrm{of}\:\mathrm{formation}\:\mathrm{of} \\ $$$$\mathrm{gaseous}\:\mathrm{H}_{\mathrm{2}} \mathrm{O}\:\mathrm{at}\:\mathrm{298}\:\mathrm{K}\:\mathrm{is}\:−\mathrm{241}.\mathrm{82}\:\mathrm{kJ} \\ $$$$\mathrm{mol}^{−\mathrm{1}} .\:\mathrm{Estimate}\:\mathrm{its}\:\mathrm{value}\:\mathrm{of}\:\mathrm{100}°\mathrm{C}\:\mathrm{given} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{values}\:\mathrm{of}\:\mathrm{the}\:\mathrm{molar}\:\mathrm{heat} \\ $$$$\mathrm{capacities}\:\mathrm{at}\:\mathrm{constant}\:\mathrm{pressure}: \\ $$$$\mathrm{H}_{\mathrm{2}} \mathrm{O}\left(\mathrm{g}\right)\::\:\mathrm{35}.\mathrm{58}\:\mathrm{JK}^{−\mathrm{1}} \:\mathrm{mol}^{−\mathrm{1}} ,\:\mathrm{H}_{\mathrm{2}} \left(\mathrm{g}\right)\:: \\ $$$$\mathrm{28}.\mathrm{84}\:\mathrm{J}\:\mathrm{mol}^{−\mathrm{1}} \:\mathrm{K}^{−\mathrm{1}} \:\mathrm{and}\:\mathrm{O}_{\mathrm{2}} \left(\mathrm{g}\right)\::\:\mathrm{29}.\mathrm{37}\:\mathrm{J} \\ $$$$\mathrm{mol}^{−\mathrm{1}} \:\mathrm{K}^{−\mathrm{1}} .\:\mathrm{Assume}\:\mathrm{heat}\:\mathrm{capacity}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{independent}\:\mathrm{of}\:\mathrm{temperature}. \\ $$

Question Number 23138 Answers: 1 Comments: 1

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