11th Standard Syllabus & Materials
11th Standard
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Published on: 13/05/2022
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Questions + Answers key
Take MCQ Maths Test1.
Transform the equation 3x + 4y + 12 = 0 in to normal form.
2.
Find the angle between the pair of straight lines given by
(a2 - 3b2)x2 + 8ab xy+(b2 -3a2)y2 =0.
3.
A line passing through the points (a, 2a) and (-2, 3) is perpendicular to the line 4x+3y+ 5 = 0, find the value of a.
4.
Find the combined equation of the straight lines whose separate equations are x - 2y - 3 = 0 and x + y + 5 = 0.
5.
If the equation 12x2 - 10xy + 2y2 + 14x - 5y + k = 0 represents a pair of straight lines, find k, find separate equation and also angle between them.
1.
4x - 3y + 1= 0; l ∈ R
2.
Angle between the lines is given by tanθ=\(\frac { \pm 2\sqrt { { h }^{ 2 }-ab } }{ a+b } \)
In this problem, tanθ =\(\frac { \pm 2\sqrt { 16{ a }^{ 2 }{ b }^{ 2 }-({ a }^{ 2 }3{ b }^{ 2 })({ b }^{ 2 }-3{ a }^{ 2 }) } }{ { a }^{ 2 }-3{ b }^{ 2 }+{ b }^{ 2 }-3{ a }^{ 2 } } \)
=\(\frac { \pm 2\sqrt { 16{ a }^{ 2 }{ b }^{ 2 }-{ a }^{ 2 }{ b }^{ 2 }+3{ b }^{ 4 }+3{ a }^{ 4 }-9{ a }^{ 2 }{ b }^{ 2 } } }{ -2{ a }^{ 2 }-2{ b }^{ 2 } } \)
=\(\frac { \pm 2\sqrt { 3{ a }^{ 4 }+3{ b }^{ 4 }+6{ a }^{ 2 }{ b }^{ 2 } } }{ -2({ a }^{ 2 }+{ b }^{ 2 }) } =\pm \sqrt { 3 } \)
tanθ = 60° [If we take the acute angle]
3.
Let m be the slope of the line joining A (a, 2a) and B (-2,3).Then m1 = \(\frac { 2a-3 }{ a+2 } \)
Let m2 be the slope of the line 4 x + 3y + 5=0. Then m2=-\(\frac { 4 }{ 3 } \)
Since given lines are perpendicular. Therefore,
m1m2=-1 ⇒ \(\frac { 2a-3 }{ a+2 } \times -\frac { 4 }{ 3 } \)=-1 ⇒ 3a+6 ⇒ a=18/5.
4.
The combined equation of straight lines
(x - 2y - 3) (x + y + 5) = 0
x2 + xy + 5x - 2xy - 2y2- 10y - 3x - 3y - 15 = 0
x2- 2y2- xy + 2x -13y - 15 = 0
5.
k = 2, 2x - y + 2 = 0, 6x - 2y + 1 = 0, \(\theta={\tan}^{-1}\left({1\over 7} \right)\)
11th Standard Syllabus & Materials
11th Standard
TN 11th Tamil பீடு பெற நில் - செய்யுள் - காவடிச்சிந்து Important Questions And Answers Study Material - QB365 Set A
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TN 11th Tamil மாமழை போற்றுதும் - செய்யுள் - ஐங்குறுநூறு Important Questions And Answers Study Material - QB365 Set A
Tamilnadu Stateboard 11th Standard Subjects
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Maths
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