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Question Number 16616 Answers: 1 Comments: 1

A particle starts from the origin with velocity (√(44)) ms^(−1) on a straight horizontal road. Its acceleration varies with displacement as shown. The velocity of the particle as it passes through the position x = 0.2 km is [Answer: 18 ms^(−1) ]

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{the}\:\mathrm{origin}\:\mathrm{with} \\ $$$$\mathrm{velocity}\:\sqrt{\mathrm{44}}\:\mathrm{ms}^{−\mathrm{1}} \:\mathrm{on}\:\mathrm{a}\:\mathrm{straight} \\ $$$$\mathrm{horizontal}\:\mathrm{road}.\:\mathrm{Its}\:\mathrm{acceleration}\:\mathrm{varies} \\ $$$$\mathrm{with}\:\mathrm{displacement}\:\mathrm{as}\:\mathrm{shown}.\:\mathrm{The} \\ $$$$\mathrm{velocity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{as}\:\mathrm{it}\:\mathrm{passes} \\ $$$$\mathrm{through}\:\mathrm{the}\:\mathrm{position}\:{x}\:=\:\mathrm{0}.\mathrm{2}\:\mathrm{km}\:\mathrm{is} \\ $$$$\left[\mathrm{Answer}:\:\mathrm{18}\:\mathrm{ms}^{−\mathrm{1}} \right] \\ $$

Question Number 16156 Answers: 0 Comments: 2

A body in a uniform horizontal circular motion possesses a variable velocity. Does it mean that the K.E. of the body is also variable?

$$\mathrm{A}\:\mathrm{body}\:\mathrm{in}\:\mathrm{a}\:\mathrm{uniform}\:\mathrm{horizontal} \\ $$$$\mathrm{circular}\:\mathrm{motion}\:\mathrm{possesses}\:\mathrm{a}\:\mathrm{variable} \\ $$$$\mathrm{velocity}.\:\mathrm{Does}\:\mathrm{it}\:\mathrm{mean}\:\mathrm{that}\:\mathrm{the}\:\mathrm{K}.\mathrm{E}. \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{body}\:\mathrm{is}\:\mathrm{also}\:\mathrm{variable}? \\ $$

Question Number 16155 Answers: 1 Comments: 0

A body of mass m is projected with a speed v making an angle θ with the vertical. What is the change in momentum of the body along the Y- axis; between the starting point and the highest point of its path?

$$\mathrm{A}\:\mathrm{body}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{m}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{with}\:\mathrm{a} \\ $$$$\mathrm{speed}\:{v}\:\mathrm{making}\:\mathrm{an}\:\mathrm{angle}\:\theta\:\mathrm{with}\:\mathrm{the} \\ $$$$\mathrm{vertical}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{change}\:\mathrm{in} \\ $$$$\mathrm{momentum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{body}\:\mathrm{along}\:\mathrm{the}\:\mathrm{Y}- \\ $$$$\mathrm{axis};\:\mathrm{between}\:\mathrm{the}\:\mathrm{starting}\:\mathrm{point}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{highest}\:\mathrm{point}\:\mathrm{of}\:\mathrm{its}\:\mathrm{path}? \\ $$

Question Number 16153 Answers: 1 Comments: 0

Is angular displacement a vector quantity?

$$\mathrm{Is}\:\mathrm{angular}\:\mathrm{displacement}\:\mathrm{a}\:\mathrm{vector} \\ $$$$\mathrm{quantity}? \\ $$

Question Number 16152 Answers: 1 Comments: 0

In long jump, does it matter how high you jump? What factors determine the span of the jump?

$$\mathrm{In}\:\mathrm{long}\:\mathrm{jump},\:\mathrm{does}\:\mathrm{it}\:\mathrm{matter}\:\mathrm{how}\:\mathrm{high} \\ $$$$\mathrm{you}\:\mathrm{jump}?\:\mathrm{What}\:\mathrm{factors}\:\mathrm{determine}\:\mathrm{the} \\ $$$$\mathrm{span}\:\mathrm{of}\:\mathrm{the}\:\mathrm{jump}? \\ $$

Question Number 16150 Answers: 1 Comments: 1

A projectile is fired at an angle θ with the horizontal direction from O. Neglecting the air friction, it hits the ground at B after 3 seconds. What is the height of point A from ground? [Use g = 10 m/s^2 ]

$$\mathrm{A}\:\mathrm{projectile}\:\mathrm{is}\:\mathrm{fired}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\theta\:\mathrm{with} \\ $$$$\mathrm{the}\:\mathrm{horizontal}\:\mathrm{direction}\:\mathrm{from}\:{O}. \\ $$$$\mathrm{Neglecting}\:\mathrm{the}\:\mathrm{air}\:\mathrm{friction},\:\mathrm{it}\:\mathrm{hits}\:\mathrm{the} \\ $$$$\mathrm{ground}\:\mathrm{at}\:{B}\:\mathrm{after}\:\mathrm{3}\:\mathrm{seconds}.\:\mathrm{What}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{height}\:\mathrm{of}\:\mathrm{point}\:{A}\:\mathrm{from}\:\mathrm{ground}? \\ $$$$\left[\mathrm{Use}\:{g}\:=\:\mathrm{10}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} \right] \\ $$

Question Number 16140 Answers: 2 Comments: 0

Question Number 16139 Answers: 2 Comments: 0

Path of the bomb released from an aeroplane moving with uniform velocity at certain height as observed by the pilot is (a) a straight line (b) a parabola (c) a circle (d) none of the above

$$\mathrm{Path}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bomb}\:\mathrm{released}\:\mathrm{from}\:\mathrm{an} \\ $$$$\mathrm{aeroplane}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{uniform} \\ $$$$\mathrm{velocity}\:\mathrm{at}\:\mathrm{certain}\:\mathrm{height}\:\mathrm{as}\:\mathrm{observed} \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{pilot}\:\mathrm{is} \\ $$$$\left({a}\right)\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line} \\ $$$$\left({b}\right)\:\mathrm{a}\:\mathrm{parabola} \\ $$$$\left({c}\right)\:\mathrm{a}\:\mathrm{circle} \\ $$$$\left({d}\right)\:\mathrm{none}\:\mathrm{of}\:\mathrm{the}\:\mathrm{above} \\ $$

Question Number 16138 Answers: 0 Comments: 0

How many nodal planes are present in 4d_z^2 ?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{nodal}\:\mathrm{planes}\:\mathrm{are}\:\mathrm{present}\:\mathrm{in} \\ $$$$\mathrm{4d}_{\mathrm{z}^{\mathrm{2}} } \:? \\ $$

Question Number 16137 Answers: 0 Comments: 0

For 2s orbital Ψ_r = (1/(√8))((z/a_0 ))^(3/2) (2 − ((zr)/a_0 ))e^(−((zr)/(2a_0 ))) then, hydrogen radial node will be at the distance of (1) a_0 (2) 2a_0 (3) (a_0 /2) (4) (a_0 /3)

$$\mathrm{For}\:\mathrm{2}{s}\:\mathrm{orbital}\:\Psi_{\mathrm{r}} \:=\:\frac{\mathrm{1}}{\sqrt{\mathrm{8}}}\left(\frac{\mathrm{z}}{\mathrm{a}_{\mathrm{0}} }\right)^{\frac{\mathrm{3}}{\mathrm{2}}} \left(\mathrm{2}\:−\:\frac{\mathrm{zr}}{\mathrm{a}_{\mathrm{0}} }\right)\mathrm{e}^{−\frac{\mathrm{zr}}{\mathrm{2a}_{\mathrm{0}} }} \\ $$$$\mathrm{then},\:\mathrm{hydrogen}\:\mathrm{radial}\:\mathrm{node}\:\mathrm{will}\:\mathrm{be}\:\mathrm{at} \\ $$$$\mathrm{the}\:\mathrm{distance}\:\mathrm{of} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{a}_{\mathrm{0}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2a}_{\mathrm{0}} \\ $$$$\left(\mathrm{3}\right)\:\frac{\mathrm{a}_{\mathrm{0}} }{\mathrm{2}} \\ $$$$\left(\mathrm{4}\right)\:\frac{\mathrm{a}_{\mathrm{0}} }{\mathrm{3}} \\ $$

Question Number 16136 Answers: 1 Comments: 0

Photoelectric emission is observed from a surface when lights of frequency n_1 and n_2 incident. If the ratio of maximum kinetic energy in two cases is K : 1 then (Assume n_1 > n_2 ) threshold frequency is (1) (K − 1) × (Kn_2 − n_1 ) (2) ((Kn_1 − n_2 )/(1 − K)) (3) ((K − 1)/(Kn_1 − n_2 )) (4) ((Kn_2 − n_1 )/(K − 1))

$$\mathrm{Photoelectric}\:\mathrm{emission}\:\mathrm{is}\:\mathrm{observed}\:\mathrm{from} \\ $$$$\mathrm{a}\:\mathrm{surface}\:\mathrm{when}\:\mathrm{lights}\:\mathrm{of}\:\mathrm{frequency}\:{n}_{\mathrm{1}} \\ $$$$\mathrm{and}\:{n}_{\mathrm{2}} \:\mathrm{incident}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{maximum} \\ $$$$\mathrm{kinetic}\:\mathrm{energy}\:\mathrm{in}\:\mathrm{two}\:\mathrm{cases}\:\mathrm{is}\:\mathrm{K}\::\:\mathrm{1} \\ $$$$\mathrm{then}\:\left(\mathrm{Assume}\:{n}_{\mathrm{1}} \:>\:{n}_{\mathrm{2}} \right)\:\mathrm{threshold} \\ $$$$\mathrm{frequency}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\left(\mathrm{K}\:−\:\mathrm{1}\right)\:×\:\left(\mathrm{K}{n}_{\mathrm{2}} \:−\:{n}_{\mathrm{1}} \right) \\ $$$$\left(\mathrm{2}\right)\:\frac{\mathrm{K}{n}_{\mathrm{1}} \:−\:{n}_{\mathrm{2}} }{\mathrm{1}\:−\:\mathrm{K}} \\ $$$$\left(\mathrm{3}\right)\:\frac{\mathrm{K}\:−\:\mathrm{1}}{\mathrm{K}{n}_{\mathrm{1}} \:−\:{n}_{\mathrm{2}} } \\ $$$$\left(\mathrm{4}\right)\:\frac{\mathrm{K}{n}_{\mathrm{2}} \:−\:{n}_{\mathrm{1}} }{\mathrm{K}\:−\:\mathrm{1}} \\ $$

Question Number 16135 Answers: 0 Comments: 0

An electron is moving in 3^(rd) orbit of Hydrogen atom. The frequency of moving electron is (1) 2.19 × 10^(14) rps (2) 7.3 × 10^(14) rps (3) 2.44 × 10^(14) rps (4) 7.3 × 10^(10) rps

$$\mathrm{An}\:\mathrm{electron}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{in}\:\mathrm{3}^{\mathrm{rd}} \:\mathrm{orbit}\:\mathrm{of} \\ $$$$\mathrm{Hydrogen}\:\mathrm{atom}.\:\mathrm{The}\:\mathrm{frequency}\:\mathrm{of} \\ $$$$\mathrm{moving}\:\mathrm{electron}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{2}.\mathrm{19}\:×\:\mathrm{10}^{\mathrm{14}} \:\mathrm{rps} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{7}.\mathrm{3}\:×\:\mathrm{10}^{\mathrm{14}} \:\mathrm{rps} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{2}.\mathrm{44}\:×\:\mathrm{10}^{\mathrm{14}} \:\mathrm{rps} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{7}.\mathrm{3}\:×\:\mathrm{10}^{\mathrm{10}} \:\mathrm{rps} \\ $$

Question Number 16134 Answers: 0 Comments: 0

The mathematical expression which is true for the uncertainty principle is (1) (Δx) (Δv) ≥ (h/(4π)) (2) (ΔE) (Δx) ≥ (h/(4π)) (3) (Δθ) (Δφ) ≥ (h/(4π)) (4) (Δx) (Δm) ≥ (h/(4π))

Question Number 16133 Answers: 1 Comments: 0

H_α line of Balmer series is 6500 A^o . The wave length of Hγ is (1) 4815 A^o (2) 4298 A^o (3) 7800 A^o (4) 3800 A^o

$$\mathrm{H}_{\alpha} \:\mathrm{line}\:\mathrm{of}\:\mathrm{Balmer}\:\mathrm{series}\:\mathrm{is}\:\mathrm{6500}\:\overset{\mathrm{o}} {\mathrm{A}}.\:\mathrm{The} \\ $$$$\mathrm{wave}\:\mathrm{length}\:\mathrm{of}\:\mathrm{H}\gamma\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{4815}\:\overset{\mathrm{o}} {\mathrm{A}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{4298}\:\overset{\mathrm{o}} {\mathrm{A}} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{7800}\:\overset{\mathrm{o}} {\mathrm{A}} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{3800}\:\overset{\mathrm{o}} {\mathrm{A}} \\ $$

Question Number 16116 Answers: 0 Comments: 0

Question Number 16115 Answers: 0 Comments: 0

Question Number 16110 Answers: 0 Comments: 1

let a_1 >a_2 >0 and a_(n+1) =(√(a_n a_(n−1 ) )) where n is greater than equal to 2 Then The sequence {a_(2n) } is (1) monotonic increasing (2)monotonic decreasing (3)non monotonic (4)unbounded

$$\mathrm{let}\:\mathrm{a}_{\mathrm{1}} >\mathrm{a}_{\mathrm{2}} >\mathrm{0}\:\mathrm{and}\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} =\sqrt{\mathrm{a}_{\mathrm{n}} \mathrm{a}_{\mathrm{n}−\mathrm{1}\:\:\:} } \\ $$$$\mathrm{where}\:\mathrm{n}\:\mathrm{is}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{2}\: \\ $$$$\mathrm{Then} \\ $$$$\mathrm{The}\:\mathrm{sequence}\:\left\{\mathrm{a}_{\mathrm{2n}} \right\}\:\mathrm{is}\: \\ $$$$\left(\mathrm{1}\right)\:\mathrm{monotonic}\:\mathrm{increasing} \\ $$$$\left(\mathrm{2}\right)\mathrm{monotonic}\:\mathrm{decreasing} \\ $$$$\left(\mathrm{3}\right)\mathrm{non}\:\mathrm{monotonic} \\ $$$$\left(\mathrm{4}\right)\mathrm{unbounded} \\ $$$$ \\ $$

Question Number 16108 Answers: 1 Comments: 1

Question Number 16107 Answers: 0 Comments: 0

∫ ((x+2)/((x^2 +3x+3)(√(x+1)))) dx =

$$\int\:\frac{{x}+\mathrm{2}}{\left({x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{3}\right)\sqrt{{x}+\mathrm{1}}}\:{dx}\:= \\ $$

Question Number 16102 Answers: 0 Comments: 0

Question Number 16093 Answers: 0 Comments: 2

The number of solutions of ∣sin x∣ = tan x in [0, 4π] is/are?

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of} \\ $$$$\mid\mathrm{sin}\:{x}\mid\:=\:\mathrm{tan}\:{x}\:\mathrm{in}\:\left[\mathrm{0},\:\mathrm{4}\pi\right]\:\mathrm{is}/\mathrm{are}? \\ $$

Question Number 16092 Answers: 0 Comments: 5

Find the set of values of x ∈ [0, 2π] which satisfy sin x > cos x. (1) ((π/4), ((3π)/4)) ∪ (((5π)/4), 2π) (2) (0, (π/4)) ∪ (((5π)/4), 2π) (3) ((π/4), ((5π)/4)) (4) (0, ((3π)/4)) ∪ (((5π)/4), 2π)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{x}\:\in\:\left[\mathrm{0},\:\mathrm{2}\pi\right] \\ $$$$\mathrm{which}\:\mathrm{satisfy}\:\mathrm{sin}\:{x}\:>\:\mathrm{cos}\:{x}. \\ $$$$\left(\mathrm{1}\right)\:\left(\frac{\pi}{\mathrm{4}},\:\frac{\mathrm{3}\pi}{\mathrm{4}}\right)\:\cup\:\left(\frac{\mathrm{5}\pi}{\mathrm{4}},\:\mathrm{2}\pi\right) \\ $$$$\left(\mathrm{2}\right)\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{4}}\right)\:\cup\:\left(\frac{\mathrm{5}\pi}{\mathrm{4}},\:\mathrm{2}\pi\right) \\ $$$$\left(\mathrm{3}\right)\:\left(\frac{\pi}{\mathrm{4}},\:\frac{\mathrm{5}\pi}{\mathrm{4}}\right) \\ $$$$\left(\mathrm{4}\right)\:\left(\mathrm{0},\:\frac{\mathrm{3}\pi}{\mathrm{4}}\right)\:\cup\:\left(\frac{\mathrm{5}\pi}{\mathrm{4}},\:\mathrm{2}\pi\right) \\ $$

Question Number 16090 Answers: 1 Comments: 0

The maximum value of the expression ∣(√(sin^2 x + 2a^2 )) − (√(2a^2 − 3 − cos^2 x))∣; where ′a′ and ′x′ are real numbers, is (1) 4 (2) 2 (3) (√2) (4) 0

$$\mathrm{The}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression} \\ $$$$\mid\sqrt{\mathrm{sin}^{\mathrm{2}} \:{x}\:+\:\mathrm{2}{a}^{\mathrm{2}} }\:−\:\sqrt{\mathrm{2}{a}^{\mathrm{2}} \:−\:\mathrm{3}\:−\:\mathrm{cos}^{\mathrm{2}} \:{x}}\mid; \\ $$$$\mathrm{where}\:'{a}'\:\mathrm{and}\:'{x}'\:\mathrm{are}\:\mathrm{real}\:\mathrm{numbers},\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{4} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2} \\ $$$$\left(\mathrm{3}\right)\:\sqrt{\mathrm{2}} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{0} \\ $$

Question Number 16089 Answers: 0 Comments: 2

The range of function f(θ) = sin^2 θ + (1/(1 + sin^2 θ)) is (1) [1, ∞) (2) [2, ∞) (3) [1, (3/2)] (4) [(3/2), ∞)

$$\mathrm{The}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function} \\ $$$${f}\left(\theta\right)\:=\:\mathrm{sin}^{\mathrm{2}} \:\theta\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{sin}^{\mathrm{2}} \:\theta}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\left[\mathrm{1},\:\infty\right) \\ $$$$\left(\mathrm{2}\right)\:\left[\mathrm{2},\:\infty\right) \\ $$$$\left(\mathrm{3}\right)\:\left[\mathrm{1},\:\frac{\mathrm{3}}{\mathrm{2}}\right] \\ $$$$\left(\mathrm{4}\right)\:\left[\frac{\mathrm{3}}{\mathrm{2}},\:\infty\right) \\ $$

Question Number 16088 Answers: 0 Comments: 1

∫_( 0) ^(1000) e^(x−[x]) dx =

$$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1000}} {\int}}{e}^{{x}−\left[{x}\right]} {dx}\:= \\ $$

Question Number 16087 Answers: 0 Comments: 1

Number of solution of equation 2[−x] + 3x = 7{x} is? (where [∙] = Greatest Integer Function & {∙} fractional function.)

$$\mathrm{Number}\:\mathrm{of}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{equation} \\ $$$$\mathrm{2}\left[−{x}\right]\:+\:\mathrm{3}{x}\:=\:\mathrm{7}\left\{{x}\right\}\:\mathrm{is}?\:\left(\mathrm{where}\:\left[\centerdot\right]\:=\right. \\ $$$$\mathrm{Greatest}\:\mathrm{Integer}\:\mathrm{Function}\:\&\:\left\{\centerdot\right\} \\ $$$$\left.\mathrm{fractional}\:\mathrm{function}.\right) \\ $$

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