The Straight Lines - Gujarat Board (GSEB) 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 6(Each question 1 marks)1 Mark

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

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Q 7(Each 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 8(Each 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 9(Each 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 10(Each 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 11(Each 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 12(Each 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 13(Each 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 14(Each 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 15(Each 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° with the positive direction of the x-axis.

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Q 16(Each 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 17(Each 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 18(Each 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 19(Each 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 20(Each 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 21(Each question 4 marks)4 Marks

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

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Q 22(Each question 4 marks)4 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 23(Each question 4 marks)4 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 24(Each question 4 marks)4 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 25(Each question 4 marks)4 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 MATHS - The Straight Lines

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