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Question Number 20337 Answers: 0 Comments: 0

Why oxidising character of F_2 > Cl_2 ?

$$\mathrm{Why}\:\mathrm{oxidising}\:\mathrm{character}\:\mathrm{of}\:\mathrm{F}_{\mathrm{2}} \:>\:\mathrm{Cl}_{\mathrm{2}} ? \\ $$

Question Number 20335 Answers: 0 Comments: 0

Covalent radius of an element having 82 electrons in extranuclear part and 82 protons in the nucleus is 146 A^o . Calculate the electronegativity on Allred Rochow scale of that element.

$$\mathrm{Covalent}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{an}\:\mathrm{element}\:\mathrm{having} \\ $$$$\mathrm{82}\:\mathrm{electrons}\:\mathrm{in}\:\mathrm{extranuclear}\:\mathrm{part}\:\mathrm{and}\:\mathrm{82} \\ $$$$\mathrm{protons}\:\mathrm{in}\:\mathrm{the}\:\mathrm{nucleus}\:\mathrm{is}\:\mathrm{146}\:\overset{\mathrm{o}} {\mathrm{A}}.\:\mathrm{Calculate} \\ $$$$\mathrm{the}\:\mathrm{electronegativity}\:\mathrm{on}\:\mathrm{Allred}\:\mathrm{Rochow} \\ $$$$\mathrm{scale}\:\mathrm{of}\:\mathrm{that}\:\mathrm{element}. \\ $$

Question Number 20334 Answers: 0 Comments: 0

Choose the correct regarding E.N. (1) B > Al > Ga > In (2) B > Al = Ga = In (3) B > In > Ga = Al (4) B > In > Ga > Al

$$\mathrm{Choose}\:\mathrm{the}\:\mathrm{correct}\:\mathrm{regarding}\:\mathrm{E}.\mathrm{N}. \\ $$$$\left(\mathrm{1}\right)\:\mathrm{B}\:>\:\mathrm{Al}\:>\:\mathrm{Ga}\:>\:\mathrm{In} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{B}\:>\:\mathrm{Al}\:=\:\mathrm{Ga}\:=\:\mathrm{In} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{B}\:>\:\mathrm{In}\:>\:\mathrm{Ga}\:=\:\mathrm{Al} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{B}\:>\:\mathrm{In}\:>\:\mathrm{Ga}\:>\:\mathrm{Al} \\ $$

Question Number 20326 Answers: 0 Comments: 1

The number of positive inegral solutions of abc = 30 is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{inegral} \\ $$$$\mathrm{solutions}\:\mathrm{of}\:\:\:{abc}\:=\:\mathrm{30}\:\mathrm{is} \\ $$

Question Number 20316 Answers: 0 Comments: 8

If at a height of 40 m, the direction of motion of a projectile makes an angle π/4 with the horizontal, then its initial velocity and angle of projection are, respectively (a) 30, (1/2)cos^(−1) (−(4/5)) (b) 30, (1/2)cos^(−1) (−(1/2)) (c) 50, (1/2)cos^(−1) (−(8/(25))) (d) 60, (1/2)cos^(−1) (−(1/4))

$$\mathrm{If}\:\mathrm{at}\:\mathrm{a}\:\mathrm{height}\:\mathrm{of}\:\mathrm{40}\:\mathrm{m},\:\mathrm{the}\:\mathrm{direction}\:\mathrm{of} \\ $$$$\mathrm{motion}\:\mathrm{of}\:\mathrm{a}\:\mathrm{projectile}\:\mathrm{makes}\:\mathrm{an}\:\mathrm{angle} \\ $$$$\pi/\mathrm{4}\:\mathrm{with}\:\mathrm{the}\:\mathrm{horizontal},\:\mathrm{then}\:\mathrm{its}\:\mathrm{initial} \\ $$$$\mathrm{velocity}\:\mathrm{and}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{projection}\:\mathrm{are}, \\ $$$$\mathrm{respectively} \\ $$$$\left({a}\right)\:\mathrm{30},\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}^{−\mathrm{1}} \left(−\frac{\mathrm{4}}{\mathrm{5}}\right) \\ $$$$\left({b}\right)\:\mathrm{30},\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}^{−\mathrm{1}} \left(−\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$$\left({c}\right)\:\mathrm{50},\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}^{−\mathrm{1}} \left(−\frac{\mathrm{8}}{\mathrm{25}}\right) \\ $$$$\left({d}\right)\:\mathrm{60},\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}^{−\mathrm{1}} \left(−\frac{\mathrm{1}}{\mathrm{4}}\right) \\ $$

Question Number 20309 Answers: 0 Comments: 0

∫x^x dx

$$\int{x}^{{x}} {dx} \\ $$

Question Number 20308 Answers: 1 Comments: 0

For what value of k, (x + y + z)^2 + k(x^2 + y^2 + z^2 ) can be resolved into linear rational factors?

$$\mathrm{For}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:{k},\:\left({x}\:+\:{y}\:+\:{z}\right)^{\mathrm{2}} \:+ \\ $$$${k}\left({x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{z}^{\mathrm{2}} \right)\:\mathrm{can}\:\mathrm{be}\:\mathrm{resolved}\:\mathrm{into} \\ $$$$\mathrm{linear}\:\mathrm{rational}\:\mathrm{factors}? \\ $$

Question Number 20307 Answers: 2 Comments: 0

Show that a(b − c)x^2 + b(c − a)xy + c(a − b)y^2 will be a perfect square if a, b, c are in H.P.

$$\mathrm{Show}\:\mathrm{that}\:{a}\left({b}\:−\:{c}\right){x}^{\mathrm{2}} \:+\:{b}\left({c}\:−\:{a}\right){xy}\:+ \\ $$$${c}\left({a}\:−\:{b}\right){y}^{\mathrm{2}} \:\mathrm{will}\:\mathrm{be}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}\:\mathrm{if}\:{a}, \\ $$$${b},\:{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{H}.\mathrm{P}. \\ $$

Question Number 20366 Answers: 1 Comments: 0

tan^2 x+2tan x (sin y+cos y)+2=0 Find x,y .

$$\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{2tan}\:{x}\:\left(\mathrm{sin}\:{y}+\mathrm{cos}\:{y}\right)+\mathrm{2}=\mathrm{0} \\ $$$${Find}\:{x},{y}\:. \\ $$

Question Number 20298 Answers: 1 Comments: 0

Question Number 20297 Answers: 1 Comments: 0

Prove that the expression ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 can be resolved into two linear rational factors if Δ = abc + 2fgh − af^2 − bg^2 − ch^2 = 0

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{expression}\:{ax}^{\mathrm{2}} \:+\:\mathrm{2}{hxy} \\ $$$$+\:{by}^{\mathrm{2}} \:+\:\mathrm{2}{gx}\:+\:\mathrm{2}{fy}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{resolved}\:\mathrm{into}\:\mathrm{two}\:\mathrm{linear}\:\mathrm{rational}\:\mathrm{factors} \\ $$$$\mathrm{if}\:\Delta\:=\:{abc}\:+\:\mathrm{2}{fgh}\:−\:{af}^{\mathrm{2}} \:−\:{bg}^{\mathrm{2}} \:−\:{ch}^{\mathrm{2}} \:=\:\mathrm{0} \\ $$

Question Number 20293 Answers: 1 Comments: 0

∫(√(((a+x)/x)dx))

$$\int\sqrt{\frac{{a}+{x}}{{x}}{dx}} \\ $$

Question Number 20292 Answers: 1 Comments: 0

∫(dx/((x+1)^(1/2) +(√(x−1))))

$$\int\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} +\sqrt{{x}−\mathrm{1}}} \\ $$

Question Number 20291 Answers: 1 Comments: 0

(√(((1−x)/(1+x)) dx))

$$\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\:{dx}} \\ $$

Question Number 20296 Answers: 2 Comments: 0

If (m_r , (1/m_r )) ; r = 1, 2, 3, 4 be four pairs of values of x and y satisfy the equation x^2 + y^2 + 2gx + 2fy + c = 0, then prove that m_1 .m_2 .m_3 .m_4 = 1.

$$\mathrm{If}\:\left({m}_{{r}} \:,\:\frac{\mathrm{1}}{{m}_{{r}} }\right)\:;\:{r}\:=\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4}\:\mathrm{be}\:\mathrm{four}\:\mathrm{pairs} \\ $$$$\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{x}\:\mathrm{and}\:{y}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation} \\ $$$${x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:\mathrm{2}{gx}\:+\:\mathrm{2}{fy}\:+\:{c}\:=\:\mathrm{0},\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:{m}_{\mathrm{1}} .{m}_{\mathrm{2}} .{m}_{\mathrm{3}} .{m}_{\mathrm{4}} \:=\:\mathrm{1}. \\ $$

Question Number 20449 Answers: 0 Comments: 0

∫(dx/(sin^(1/2) xcos^(7/2) x))

$$\int\frac{{dx}}{\mathrm{sin}\:^{\frac{\mathrm{1}}{\mathrm{2}}} {x}\mathrm{cos}\:^{\frac{\mathrm{7}}{\mathrm{2}}} {x}} \\ $$

Question Number 20259 Answers: 1 Comments: 0

Find the number of real roots of the equation f(x) = x^3 + 2x^2 + 2x + 1 = 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:{f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:+\:\mathrm{2}{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 20257 Answers: 1 Comments: 0

∫(dx/((1−x)(√(1+x))))

$$\int\frac{{dx}}{\left(\mathrm{1}−{x}\right)\sqrt{\mathrm{1}+{x}}} \\ $$

Question Number 20256 Answers: 1 Comments: 0

∫(dx/((x−4)(√(x+3))))