11th Standard Syllabus & Materials

11th Standard

TN 11th Tamil இயற்கை வேளாண்மை,சுற்றுச்சூழல் -செய்யுள் - மனோன்மணீயம் Important Questions And Answers Study Material - QB365 Set A

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TN 11th Tamil என்னுயிர் என்பேன் -துணைப்பாடம் - இசைத்தமிழர் இருவர் Important Questions And Answers Study Material - QB365 Set A

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TN 11th Tamil மொழி கலை -செய்யுள் - ஒவ்வொரு புல்லையும் Important Questions And Answers Study Material - QB365 Set A

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TN 11th Tamil பீடு பெற நில் - இலக்கணம் - பகுபத உறுப்புகள் Important Questions And Answers Study Material - QB365 Set A

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TN 11th Tamil பீடு பெற நில் - துணைப்பாடம் - வாடிவாசல் Important Questions And Answers Study Material - QB365 Set A

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TN 11th Tamil பீடு பெற நில் - செய்யுள் - குறுந்தொகை Important Questions And Answers Study Material - QB365 Set A

11th Standard Maths Two Dimensional Analytical Geometry English Medium Free Online Test One Mark Questions 2020 - 2021

Published on: 10/11/2020

Download Tamil Nadu 11th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.

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Std: 11th Standard - Maths

chapter: - Model Question paper

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Questions:

Multiple Choice Question

10 x 1 = 10

The equation of the straight line bisecting the line segment joining the points (2, 4) and (4, 2) and making an angle of 45^o with positive direction of x-axis is ______________

(a)

x + y = 6

(b)

x - y = 0

(c)

x - y = 6

(d)

x + y = 0

The equation of the bisectors of the angle between the co-ordinate axes are ______________

(a)

x+y=0

(b)

x-y=0

(c)

x\(\pm\)y=0

(d)

x=0

Find the nearest point on the line 3x + y = 10 from the origin is ______________

(a)

(2, 1)

(b)

(1, 2)

(c)

(3, 1)

(d)

(1,3)

If 7x² - 8xy +A = 0 represents a pair of perpendicular lines, the A is ______________

(a)

(b)

-7

(c)

-8

(d)

The equation of the line passing through (1, 5) and perpendicular to the line 3x -5y + 7 = 0 is ______________

(a)

5x + 3y - 20 = 0

(b)

3x - 5y + 7 = 0

(c)

3x - 5y + 6 = 0

(d)

5x + 3y + 7 = 0

If one of the lines given by 6x² - xy + 4cy² = 0 is 3x + 4y = 0, then c equals to

(a)

-3

(b)

-1

(c)

(d)

The length of \(\bot\) from the origin to the line \(\frac{x}{3}-\frac{y}{4}=1,\) is

(a)

\(\frac{11}{5}\)

(b)

\(\frac{5}{12}\)

(c)

\(\frac{12}{5}\)

(d)

\(\frac{-5}{12}\)

The point on the line 2x- 3y = 5 is equidistance from (1, 2) and (3, 4) is

(a)

(7, 3)

(b)

(4, 1)

(c)

(1, -1)

(d)

(-2, 3)

The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3, 4) with coordinate axes are

(a)

5, -5

(b)

5, 5

(c)

5, 3

(d)

5, -4

10.

The equation of the locus of the point whose distance from y-axis is half the distance from origin is

(a)

x²+ 3y²= 0

(b)

x²- 3y²= 0

(c)

3x²+ y²= 0

(d)

3x²- y²= 0

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Answers Key:

Multiple Choice Question

10 x 1 = 10

(b)
x - y = 0

(b)
-7

(a)
5x + 3y - 20 = 0

Let the other line be ax + by = 0
(3x + 4y) (ax + by) = 6x² - xy + 4cy²
\(3 a =6 \)
\(a =2 \)
\(4 a+3 b =-1 \)
\(3 b =-9 \)
\(b =-3 \)
\(4 b =4 c \)
\(c =-3 \)

Perpendicular distance from origin to the given line is
\(\frac{1}{\sqrt{\frac{1}{3^{2}}+\frac{1}{4^{2}}}}=\frac{1}{\sqrt{\frac{1}{9}+\frac{1}{16}}}=\frac{1}{\sqrt{\frac{16+9}{144}}}=\frac{12}{5}\)

Let (a, b) be on 2x - 3y= 5 = 2a - 3b = 5
It is equidistance from (1, 2) and (3, 4)
\(\sqrt{(a-1)^{2}+(6-2)^{2}}=\sqrt{(a-3)^{2}+(b-4)^{2}} \)
\((a-1)^{2}+(b-2)^{2}=(a-3)^{2}+(b-4)^{2} \)
\(a^{2}-2 a+1+b^{2}-4 b+4=a^{2}-6 a+9+b^{2} -8 b+16 \)
\(\begin{gathered} 4 a+4 b=20 \\ \Rightarrow {2 a+2 b=10}\\{2 a-3 b=5} \\ \hline 5 b=5 \end{gathered}\)
b = 1, a = 4
The point is (4, 1)

Equation of line joining (1, 2) and (3, 4) is
\(\frac{y-2}{4-2} =\frac{x-1}{3-1} \)
\(x-y+1 =0 \)
Any line perpendicular to this x + y + k = 0
This passes through midpoint of (1, 2) and (3, 4)
That is (2, 3)
k = -5, x+y-5 = 0
x intercept is 5, y intercept is 5.

10.

Let the point be (x, y)
Its distance from origin is \(\sqrt{x^{2}+y^{2}}\)
Given \(x =\frac{1}{2} \sqrt{x^{2}+y^{2}} \)
\(\Rightarrow 2 x =\sqrt{x^{2}+y^{2}} \)
\(4 x^{2} =x^{2}+y^{2} \)
\(3 x^{2}-y^{2}=0 \) is the required equation of the locus