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Question Number 18761 Answers: 0 Comments: 1

If x ∈ R, then the expression 9^x −3^x +1 assumes

$$\mathrm{If}\:\:{x}\:\in\:{R},\:\:\:\mathrm{then}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{9}^{{x}} −\mathrm{3}^{{x}} +\mathrm{1} \\ $$$$\mathrm{assumes}\: \\ $$

Question Number 18760 Answers: 0 Comments: 1

If the coefficient of x^7 and x^8 in (2+(x/3))^n are equal then r is equal to

$$\mathrm{If}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{\mathrm{7}} \mathrm{and}\:{x}^{\mathrm{8}} \:\mathrm{in}\:\left(\mathrm{2}+\frac{{x}}{\mathrm{3}}\right)^{{n}} \\ $$$$\mathrm{are}\:\mathrm{equal}\:\mathrm{then}\:{r}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 18759 Answers: 2 Comments: 0

The coefficient of the middle term in the expansion of (1+x)^(2n) is

$$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{the}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+{x}\right)^{\mathrm{2}{n}} \:\mathrm{is} \\ $$

Question Number 18758 Answers: 1 Comments: 0

If the coefficient of r^(th) and (r+1)^(th) terms in the expansion of (3+7x)^(29) are equal, then r equals

$$\mathrm{If}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\:{r}^{\mathrm{th}} \:\mathrm{and}\:\left({r}+\mathrm{1}\right)^{\mathrm{th}} \:\mathrm{terms} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{3}+\mathrm{7}{x}\right)^{\mathrm{29}} \:\mathrm{are}\:\mathrm{equal}, \\ $$$$\mathrm{then}\:\:{r}\:\mathrm{equals} \\ $$

Question Number 18757 Answers: 0 Comments: 0

If a_1 , a_2 , a_3 , a_4 are the coefficient of any four four consecutive terms in the expansion of (1+x)^n , then (a_1 /(a_1 +a_2 )) + (a_3 /(a_3 +a_4 )) is equal to

$$\mathrm{If}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:{a}_{\mathrm{3}} ,\:{a}_{\mathrm{4}} \:\mathrm{are}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{any} \\ $$$$\mathrm{four}\:\mathrm{four}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\left(\mathrm{1}+{x}\right)^{{n}} ,\:\mathrm{then}\:\frac{{a}_{\mathrm{1}} }{{a}_{\mathrm{1}} +{a}_{\mathrm{2}} }\:+\:\frac{{a}_{\mathrm{3}} }{{a}_{\mathrm{3}} +{a}_{\mathrm{4}} }\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 18755 Answers: 1 Comments: 0

In a △ABC, if c = 2, A = 120°, a = (√6) , then C =

$$\mathrm{In}\:\mathrm{a}\:\bigtriangleup{ABC},\:\mathrm{if}\:{c}\:=\:\mathrm{2},\:{A}\:=\:\mathrm{120}°,\:{a}\:=\:\sqrt{\mathrm{6}}\:, \\ $$$$\mathrm{then}\:\:{C}\:= \\ $$

Question Number 18803 Answers: 1 Comments: 1

Question Number 18752 Answers: 0 Comments: 0

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Question Number 18749 Answers: 1 Comments: 1

Motion in two dimensions, in a plane can be studied by expressing position, velocity and acceleration as vectors in Cartesian co-ordinates A^→ = A_x i^∧ + A_y j^∧ where i^∧ and j^∧ are unit vector along x and y directions, respectively and A_x and A_y are corresponding components of A^→ (Figure). Motion can also be studied by expressing vectors in circular polar co-ordinates as A^→ = A_r r^∧ + A_θ θ^∧ where r^∧ = (r^→ /r) = cos θ i^∧ + sin θ j^∧ and θ^∧ = −sin θ i^∧ + cos θ j^∧ are unit vectors along direction in which ′r′ and ′θ′ are increasing. (a) Express i^∧ and j^∧ in terms of r^∧ and θ^∧ (b) Show that both r^∧ and θ^∧ are unit vectors and are perpendicular to each other. (c) Show that (d/dt)(r^∧ ) = ωθ^∧ where ω = (dθ/dt) and (d/dt)(θ^∧ ) = −ωr^∧ (d) For a particle moving along a spiral given by r^→ = αθr^∧ , where α = 1 (unit), find dimensions of ′α′. (e) Find velocity and acceleration in polar vector representation for particle moving along spiral described in (d) above.

Question Number 18748 Answers: 1 Comments: 0