STRAIGHT LINES - Gujarat Board (GSEB) STD 11 Science MATHS Questions

Q 1MCQ1 Mark

Two lines are said to be perpendicular if the product of their slope is equal to:

✓
-1
B
0
C
1
D
$\frac{1}{2}$

Answer: A.

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Q 2MCQ1 Mark

If slope of a line is 4 and y-intercept made by the line is 2 then the equation of line will be:

A
y = 4x - 2
✓
y = 4x + 2
C
y = 2x + 4
D
y = 2x - 4

Answer: B.

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Q 3MCQ1 Mark

Given the three straight lines with equations 5x + 4y = 0, x + 2y - 10 = 0 and 2x + y + 5 = 0, then these lines are:

A
None of these
B
The sides of a right angled triangle
✓
Concurrent
D
The sides of an equilateral triangle

Answer: C.

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Q 4MCQ1 Mark

Choose the correct answer. A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 is:

A
(1, -1)
✓
(1, 1)
C
(0, 0)
D
(0, 1)

Answer: B.

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Q 5MCQ1 Mark

Find the equation of line parallel to 4x + y = 2 and pass through (2, 5):

✓
4x + y - 13 = 0
B
4x + y + 13 = 0
C
4x - y - 13 = 0
D
4x - y + 13 = 0

Answer: A.

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Q 6(Each question 1 marks)1 Mark

Find the values of $k$ for which the line $(k-3) x-\left(4-k^2\right) y+k^2-7 k+6=0$ is passing through the origin.

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Q 7(Each question 1 marks)1 Mark

Find the values of k for which the line $(k–3) x – (4 – k^2 ) y + k^2 –7k + 6 = 0$ is parallel to the y-axis.

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Q 8(Each question 1 marks)1 Mark

Find the values of k for which the line $(k–3) x – (4 – k^2 ) y + k^2 –7k + 6 = 0$ is parallel to the x-axis.

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Q 9(Each question 1 marks)1 Mark

Find the equation of the line parallel to the line 3x - 4y + 2 = 0 and passing through the point (–2, 3).

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Q 10(Each question 1 marks)1 Mark

Reduce the equation into slope-intercept form and find the slope and the y-intercept.
y = 0

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Q 11(Each question 2 marks)2 Marks

Find the value of p so that three lines 3x + y - 2 = 0, px + 2y - 3 = 0 and 2x - y - 3 = 0 may intersect at one point.

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Q 12(Each question 2 marks)2 Marks

Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines x - 7y + 5 = 0 and 3x + y = 0

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Q 13(Each question 2 marks)2 Marks

What are the points on the y-axis whose distance from the line $\frac{x}{3} + \frac{y}{4} = 1$ is 4 units.

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Q 14(Each question 2 marks)2 Marks

Find the values of $\theta $ and p, if the equation $x\cos \theta + y\sin \theta = p$ is the normal form of the line $\sqrt 3 x + y + 2 = 0$

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Q 15(Each question 2 marks)2 Marks

Find the angles between the lines $\sqrt 3 x + y = 1$ and $x + \sqrt 3 y = 1$

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Q 16(Each question 3 marks)3 Marks

Find the equation of a line drawn perpendicular to the line $\frac{x}{4}+\frac{y}{6}=1$ through the point where it meets the Y-axis.

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Q 17(Each question 3 marks)3 Marks

Find the perpendicular distance from the origin of the line joining the points $(\cos \theta ,\sin \theta )$ and $(\cos \phi ,\sin \phi )$.

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Q 18(Each question 3 marks)3 Marks

Find the equations of the lines which cut-off intercepts on the axes whose sum and product are 1 and -6 respectively.

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Q 19(Each question 3 marks)3 Marks

A person standing at the junction (crossing) of two straight paths represented by the equations 2x - 3y + 4 = 0 and 3x + 4y - 5 = 0 wants to reach the path whose equation is 6x - 7y + 8 = 0 in the least time. Find equation of the path that he should follow.

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Q 20(Each question 3 marks)3 Marks

Prove that the product of the lengths of the perpendiculars drawn from the points $\left( {\sqrt {{a^2} - {b^2}} ,0} \right)$ and $\left( { - \sqrt {{a^2} - {b^2}} ,0} \right)$ to the line $\frac{x}{a}\cos \theta + \frac{y}{b}\sin \theta = 1$ is $b^2$.

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Q 21(Each question 4 marks)4 Marks

Find the area of the triangle formed by the lines $y - x = 0, x + y = 0$ and $x - k = 0$.

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Q 22(Each question 4 marks)4 Marks

Find the direction in which a straight line must be drawn through the point $(-1, 2)$ so that its point of intersection with the line $x + y = 4$ may be at a distance of $3$ units from this point.

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Q 23(Each question 4 marks)4 Marks

Show that the equation of the line passing through the origin and making an angle $\theta$ with the line $y = mx + c$ is $\frac{y}{x} = \frac{{m \pm \tan \theta }}{{1 \mp m\tan \theta }}$.

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Q 24(Each question 4 marks)4 Marks

Find the equation of the line passing through the point of intersection of the lines 4x + 7y - 3 = 0 and 2x - 3y + 1 = 0 that has equal intercepts on the axis.

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Q 25(Each question 4 marks)4 Marks

In the triangle ABC with vertices A(2, 3), B (4, -1) and C (1, 2) find the equation and length of altitude from the vertex A.

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STRAIGHT LINES question types

STRAIGHT LINES questions

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STRAIGHT LINES MATHS - STRAIGHT LINES

STRAIGHT LINES question types

STRAIGHT LINES questions

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