Post mathematic related questions here

[rst]

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[rst]

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C(n+1,5) -C(n,4) = 56

solving we get
n (n-1)(n-2)(n-3)(n-4)= 6720

1) At most 7

not possible

2)Atleast 10
not possible

3) n=8 will give the correct ans

Ans is (3)

 

[nisargshah95]

Here is a really good question of functions I found in one of Arihant's books -

If f(x) = 4[SUP]x[/SUP]/(4[SUP]x[/SUP] +2), then [ f(1/2008) + f(2/2008) + ... + f(2007/2008) ] - 1000 is equal to _ (where [.] Denotes the greatest integer function)


Answer -

Spoiler

3

 

[rst]

Here is a really good question of functions I found in one of Arihant's books -

If f(x) = 4[SUP]x[/SUP]/(4[SUP]x[/SUP] +2), then [ f(1/2008) + f(2/2008) + ... + f(2007/2008) ] - 1000 is equal to _ (where [.] Denotes the greatest integer function)


Answer -

Spoiler

3

f(x) = 4[SUP]x[/SUP]/(4[SUP]x[/SUP] +2)

f(1-x)=2/(4[SUP]x[/SUP] +2)

so f(x) + f(1-x)=1

f(1/2008) + f(2007/2008)=1
f(2/2008) + f(2006/2008)=1
f(3/2008) + f(2005/2008)=1
.
.
.
f(1003/2008) + f(1005/2008)=1
f(1004/2008)=1/2

Adding above ,we get
f(1/2008) + f(2/2008)+f(3/2008)+............ +f(2007/2008)=2007/2
=1003.5

Hence [ f(1/2008) + f(2/2008) + ... + f(2007/2008) ] - 1000 =[1003.5]-1000
=1003-1000
=3

 

[nisargshah95]

Dude did you solve this on your own or just copied the solution? Its amazing if you did it on your own. Really needs a lot of brains to find that f(x) + f(1-x) = 1. Never occurred to me.

 

[rst]

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NEW OBJECTIVE QUESTION

*img163.imageshack.us/img163/9162/combau.png

Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋

 

[rst]

----------------------------------------------------------------------------------------------------------------------
NEW OBJECTIVE QUESTION

*img163.imageshack.us/img163/9162/combau.png

Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋

total people =15
7 people can be selected in ¹⁵C₇ ways
7 people can be seated around round table in 6! ways

remaining 8 people can be seated around round table in 7! ways

total ways =¹⁵C₇ x 6! x 7!

 

[rst]

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NEW OBJECTIVE QUESTION

*img90.imageshack.us/img90/51/workpaint.png

Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋

 

[hari1]

Evaluate sin(cot^(-1)x)

 

[rst]

Evaluate sin(cot^(-1)x)

sin(cot^(-1)x)

sin [sin⁻¹(1/√(1+x² )]
=1/√(1+x² )
----------------------------------------------
long method:-

sin(cot^(-1)x)---(1)

let cot^(-1)x =y----------(2)
then cot y = x

sin y = 1/√(1+x² )

y= sin⁻¹(1/√(1+x² )

using in (2) we get,
cot^(-1)x =sin⁻¹(1/√(1+x² )

hence (1) becomes
sin [sin⁻¹(1/√(1+x² )]
=1/√(1+x² )

 

[rst]

----------------------------------------------------------------------------------------------------------------------
NEW OBJECTIVE QUESTION

*img90.imageshack.us/img90/51/workpaint.png

Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋

let number of days be x

If one person works 4 hours daily
Then each person will work (8+8+8+8+4)/5
=36/5 hours each day

Now number of persons and no. of days are in indirect proportion
Also number of hours and no. of days are in indirect proportion

So 5 * 3 * 8= 5 * x *(36/5)
x=10/3

(i think there is misprinting in option D )
(It should be 10/3)

 

[rst]

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NEW OBJECTIVE QUESTION

*img407.imageshack.us/img407/9670/limitd.png

Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋

 

[Thetrueblueviking]

Here solve the limit in two parts -

part 1 - sinx^1/x - you can easily see it is approaching zero because sinx tends to 0 and you are raising a number tending to 0 to a number tending to infinity - so the obvious result = 0.

part 2 - [1/x]^sinx = 1^sinx/x^sinx = 1/x^sinx since 1^y = 1 where y ∈ R.
So part 2 = 1/x^sinx.
lets solve for x^sinx -
x^sinx = y
take logarithm - sinx log x = log y
∴ logx / cosec x = log y
now the lhs is turned into an infinity/infinty limit - so apply l'hospital's rule -
lhs = -[1/x]/cosecx.cotx = -sinx.sinx/x.cosx = -sinx/cosx = 0
∴log y = 0
∴ y = x^sinx = 1
∴1/x^sinx = 1

now final answer - sinx^1/x + [1/x]^sinx = 0 + 1 = 1 = D. NONE OF THESE

Why is it that every time you your-self answer your question - are you trying to take a test of the TD members asking questions to which you already know the answers or do you seriously dont have the answers to them when you ask the qts //

 

[rst]

Here solve the limit in two parts -

part 1 - sinx^1/x - you can easily see it is approaching zero because sinx tends to 0 and you are raising a number tending to 0 to a number tending to infinity - so the obvious result = 0.

part 2 - [1/x]^sinx = 1^sinx/x^sinx = 1/x^sinx since 1^y = 1 where y ∈ R.
So part 2 = 1/x^sinx.
lets solve for x^sinx -
x^sinx = y
take logarithm - sinx log x = log y
∴ logx / cosec x = log y
now the lhs is turned into an infinity/infinty limit - so apply l'hospital's rule -
lhs = -[1/x]/cosecx.cotx = -sinx.sinx/x.cosx = -sinx/cosx = 0
∴log y = 0
∴ y = x^sinx = 1
∴1/x^sinx = 1

now final answer - sinx^1/x + [1/x]^sinx = 0 + 1 = 1 = D. NONE OF THESE

Great explanation

Thanks a lot

Why is it that every time you your-self answer your question - are you trying to take a test of the TD members asking questions to which you already know the answers or do you seriously dont have the answers to them when you ask the qts //

I dont have the answers to them when I ask the qts
But If don't get answer then I try myself to give ans.

 

[Thetrueblueviking]

You're welcome - btw I love maths.

 

[rst]

----------------------------------------------------------------------------------------------------------------------
NEW OBJECTIVE QUESTION

*img713.imageshack.us/img713/5994/limitint.png

Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋

 

[Thetrueblueviking]

Is the answer - b ? If so, then I would post my explanation.

 

[rst]

Well, I don't know ans

 

[Thetrueblueviking]

I got 1 but through a very long method - It'd be painful to type.

 

[rst]

Give ans in short

Write only main steps or just give hint