The Straight Lines - Maharashtra Board STD 11 Science Maths Questions

Q 1MCQ1 Mark

Three vertices of a parallelogram taken in order are $(-1, -6), (2, -5)$ and $(7, 2$). The fourth vertex is :

A
$(1, 4)$
✓
$(4, 1)$
C
$(1, 1)$
D
$(4, 4)$

Answer: B.

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Q 2MCQ1 Mark

The point which divides the join of $(1, 2)$ and $(3, 4)$ externally in the ratio $1 : 1$ :

A
Lies in the $III$ quadrant.
B
Lies in the $II$ quadrant.
C
Lies in the $I$ quadrant.
✓
Cannot be found.

Answer: D.

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Q 3MCQ1 Mark

$L$ is a variable line such that the algebraic sum of the distances of the points $(1, 1), (2, 0)$ and $(0, 2)$ from the line is equal to zero. The line $L$ will always pass through:

✓
$(1, 1)$
B
$(2, 1)$
C
$(1, 2)$
D
none of these.

Answer: A.

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Q 4MCQ1 Mark

The acute angle between the medians drawn from the acute angles of $a$ right angled isosceles triangle is:

A
$\cos^{-1}\big(\frac{2}{3}\big)$
✓
$\cos^{-1}\big(\frac{3}{4}\big)$
C
$\cos^{-1}\big(\frac{4}{5}\big)$
D
$\cos^{-1}\big(\frac{5}{6}\big)$

Answer: B.

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Q 5MCQ1 Mark

The medians $AD$ and $BE$ of a triangle with vertices $A(0, b), B(0, 0)$ and $C(a, 0)$ are perpendicular to each other, if

A
$\text{a}=\frac{\text{b}}{2}$
B
$\text{b}=\frac{\text{a}}{2}$
C
$\text{ab}=1$
✓
$\text{a}=\pm\sqrt{2}\text{b}$

Answer: D.

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Q 6Solve the following Question.(1 Marks)1 Mark

Write the coordinates of the orthocentre of the triangle formed by the lines $x^2-y^2=0$ and $x+6 y=18$.

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Q 7Solve the following Question.(1 Marks)1 Mark

Write the locus of a point the sum of whose distances from the coordinates axes is unity.

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Q 8Solve the following Question.(1 Marks)1 Mark

Determine the distance between the following pair of parallel lines:
$4x - 3y - 9 = 0$ and $4x - 3y - 24 = 0$

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Q 9Solve the following Question.(1 Marks)1 Mark

Find the equation of the straight line which passes through (1, -2) and cuts off equal intercepts on the axes.

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Q 10Solve the following Question.(1 Marks)1 Mark

Write the integral values of m for which the x-coordinate of the point of intersection of the lines y = mx + 1 and 3x + 4y = 9 is an integer.

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Q 11Solve the Following Question.(2 Marks)2 Marks

Classify the following pairs of lines as coincident, parallel or intersecting:
2x + y - 1 = 0 and 3x + 2y + 5 = 0

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Q 12Solve the Following Question.(2 Marks)2 Marks

Find the equation of a straight line:
with slope $\frac{-1}{3}$ and y-intercept -4.

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Q 13Solve the Following Question.(2 Marks)2 Marks

Find the equation of a line passing through $(3, -2)$ and perpendicular to the line $x - 3y + 5 = 0.$

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Q 14Solve the Following Question.(2 Marks)2 Marks

Find the equation of a line making an angle of 150° with the x-axis and cutting off an intercept 2 from y-axis.

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Q 15Solve the Following Question.(2 Marks)2 Marks

Find the equation of the straight line intersecting y-axis at a distance of $2$ units above the origin and making an angle of $30^\circ $ with the positive direction of the x-axis.

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Q 16Solve the Following Question.(3 Marks)3 Marks

Find the equation of the straight line which makes a triangle of area $96\sqrt{3}$ with the axes and perpendicular from the origin to it makes an angle of 30° with Y-axis.

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Q 17Solve the Following Question.(3 Marks)3 Marks

Find the equations of the sides of the triangles the coordinates of whose angular points are respectively:
(1, 4), (2, -3) and (-1, -2)

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Q 18Solve the Following Question.(3 Marks)3 Marks

Find the area of the triangle formed by the lines:
$y = m_1x + c_1, y = m_2x + c_2$ and $x = 0$

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Q 19Solve the Following Question.(3 Marks)3 Marks

Find the orthocentre of the triangle the equations of whose sides are x + y = 1, 2x + 3y = 6 and 4x - y + 4 = 0.

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Q 20Solve the Following Question.(3 Marks)3 Marks

Prove that the lines $\sqrt{3}\text{x}+\text{y}=0,\sqrt{3}\text{y}+\text{x}=0,\sqrt{3}\text{x}+\text{y}=1$ and $\sqrt{3}\text{y}+\text{x}=1$ form a rhombus.

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Q 21Solve the Following Question.(4 Marks)4 Marks

Find the equations of the two straight lines through (1, 2) forming two sides of a square of which 4x + 7y = 12 is one diagonal.

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Q 22Solve the Following Question.(4 Marks)4 Marks

Find the equation of the straight line passing through the point of intersection of the lines 5x - 6y - 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x - 5y + 11 = 0

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Q 23Solve the Following Question.(4 Marks)4 Marks

Find the equations of the straight lines which pass through the origin and trisect the portion of the straight line 2x + 3y = 6 which is intercepted between the axes.

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Q 24Solve the Following Question.(4 Marks)4 Marks

Find the equation of a straight line passing through the point of intersection of 2x - 7y + 11 = 0 and x + 3y - 8 = 0 and is parallel to (i) x-axis (ii) y-axis.

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Q 25Solve the Following Question.(4 Marks)4 Marks

Find the area of the triangle formed by the lines:
$x + y - 6 = 0, x - 3y - 2 = 0$ and $5x - 3y + 2 = 0$

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Q 26Solve the Following Question.(5 Marks)5 Marks

Show that the straight lines $L_1 = (b + c)x + ay + 1 = 0, L_2 = (c + a)x + by + 1 = 0$ and $L_3 = (a + b)x + cy + 1 = 0$ are concurrent.

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Q 27Solve the Following Question.(5 Marks)5 Marks

A line is such that its segment between the straight lines 5x - y - 4 = 0 and 3x + 4y - 4 = 0 is bisected at the point (1, 5). Obtain its equation.

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Q 28Solve the Following Question.(5 Marks)5 Marks

Find the values of the parameter a so that the point (a, 2) is an interior point of the triangle formed by the lines x + y - 4 = 0, 3x - 7y - 8 = 0 and 4x - y - 31 = 0.

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Q 29Solve the Following Question.(5 Marks)5 Marks

Find the equations to the straight lines which go through the origin and trisect the portion of the straight line 3x + y = 12 which is intercepted between the axes of coordinates.

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Q 30Solve the Following Question.(5 Marks)5 Marks

Find the image of the point (2, 1) with respect to the line mirror x + y - 5 = 0.

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The Straight Lines question types

The Straight Lines questions

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The Straight Lines Maths - The Straight Lines

The Straight Lines question types

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