Important Questions for CBSE Class 11 Maths Chapter 10

CBSE Class 11 Maths Chapter-10 Important Questions - Free PDF Download

1 Marks Questions

1. Find the slope of the lines passing through the point (3,-2) and (-1,4)

Ans. Slope of line through (3,-2) and (-1, 4)

2. Three points and lie on a line. Show that

Ans. Since P, Q, R are collinear

Slope of PQ= slope of QR

3. Write the equation of the line through the points and

Ans. Req. eq.

4. Find the measure of the angle between the lines and

Ans.

Slopes of the two lines are 1 and -1 as product of these two slopes is -1, the lines are at right angles.

5. Find the equation of the line that has y-intercept 4 and is to the line

Ans.

Slope =slope of any line it is

Req. eq. is

6. Find the equation of the line, which makes intercepts -3 and 2 on the and -axis respectively.

Ans. Req. eq.

2x - 3y + 6 = 0

7. Equation of a line is find its slope.

Ans.

8. Find the distance between the parallel lines and

Ans. and

9. Find the equation of a straight line parallel to -axis and passing through the point (4,-2)

Ans. Equation of line parallel to -axis is

Eq. passing through (-4,2)

10. If and represent the same straight line, find the values of a and b.

Ans. ATQ

11. Find the distance between and when PQ is parallel to the -axis.

Ans. When PQ is parallel to the -axis,

Then

12. Find the slope of the line, which makes an angle of with the positive direction of -axis measured anticlockwise.

Ans. Let be the inclination of the line

13. Determine so that the inclination of the line containing the points and is 135.

Ans.

14. Find the distance of the point from the line

Ans. Let d be the req. distance

15. Find the value of for which the points and are collinear.

Ans. Let

Slope of AB= Slope of BC

16. Find the angle between the -axis and the line joining the points and

Ans. [Slope of -axis]

slope of line joining points and

17. Using slopes, find the value of for which the points and are collinear.

Ans. Since the given points are collinear slope of the line joining points and =slope of the line joining points and

18. Find the value of so that the line may be parallel to

Ans. ATQ

Slope of 1st line = slope of 2nd line

19. Find the value of , given that the distance of the point from the line is 4 units.

Ans. We are given that distance of (4,0) from the line is 4

20. Find the equation of the line through the intersection of which cuts off equal intercepts on the axes.

Ans. Slope of a line which makes equal intercept on the axes is -1any line through the intersection of given lines is

21. Find the distance of the point from the line

Ans.

22. Find the equation of a line whose perpendicular distance from the origin is 5 units and angle between the positive direction of the -axis and the perpendicular is

Ans.

Req. eq.

23. Write the equation of the lines for which where Q is the inclination of the line andintercept is 4.

Ans. and

24. Find the Angle between the -axis and the line joining the points and

Ans. Let

Slope of

25. Find the equation of the line intersecting the -axis at a distance of 3 unit to the left of origin with slope -2.

Ans. The line passing through (-3,0) and has slope = -2

Req. eq. is

4 Marks Questions

1. If p is the length of the from the origin on the line whose intercepts on the axes are a and b. show that

Ans. Equation of the line is

The distance of this line from the origin is P

Sq. both side

2.Find the value of p so that the three lines and may intersect at one point.

Ans.

On solving eq. and

And

Put in eq.

3.Find the equation to the straight line which passes through the point (3,4) and has intercept on the axes equal in magnitude but opposite in sign.

Ans. Let intercept be a and –a the equation of the line is

Since it passes through the point (3, 4)

Put the value of a in eq. (i)

4.By using area of . Show that the points and are collinear.

Ans. Area of

5. Find the slope of a line, which passes through the origin, and the midpoint of the line segment joining the point and

Ans. Let be the midpoint of segment PQ then

Slope of

6.Find equation of the line passing through the point and cutting off intercepts on the axes whose sum is 9

Ans. Req. eq. be

This line passes through

7.Reduce the equation into normal form. Find the values p and.

Ans.

Dividing by 2

Comparing with

8. Without using the Pythagoras theorem show that the points and are the vertices of a right angled .

Ans. The given points are and

Slope of

Slope of slope of

Hence ABC is right angled at A.

9.The owner of a milk store finds that, he can sell 980 liters of milk each week at 14 liter and 1220 liter of milk each week at Rs 16 liter. Assuming a linear relationship between selling price and demand how many liters could he sell weekly at Rs 17 liter?

Ans. Assuming sell along -axis and cost per litre along -axis, we have two points and in plane

When

litres.

10.The line through the points (h,3) and (4,1) intersects the line at right angle. Find the value of h.

Ans. Slope of line joining (h,3) and (4,1)

Given line is

Slope of this line =

ATQ

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

Ans. ATQ

Put b in eq.

When

Eq. of the line is

When

Eq. of the line is

12. The slope of a line is double of the slope of another line. If tangent of the angle between them is , find the slopes of the lines.

Ans. Let the slope of one line is and other line is

13.Point divides a line segment between the axes in the ratio 1:2. Find equation of the line.

Ans. Let eq. be

It is given that divides AB in the ratio 1:2

Put a and b in eq.………

14.The Fahrenheit temperature F and absolute temperature K satisfy a linear equation. Given that K=273 when F=32 and that K= 373 when F=212 Express K in terms of F and find the value of F when K=0

Ans. Let F along -axis and K along -axis

15. If three points and lie on a line, show that

Ans. Let

Slope of AB = slope of BC

16.is the mid point of a line segment between axes. Show that equation of the line is

Ans. Req. eq. be

P is the mid point

Coordinate of

Put the value of C and D in eq. (i)

17.The line to the line segment joining the points and divides it in the ratio find the equation of the line.

Ans. Coordinate of

Eq. of PQ is

6 Marks Questions

1. Find the values of for the line

(a). Parallel to the -axis

(b). Parallel to -axis

(c). Passing through the origin

Ans.

(a) The line parallel to -axis if coeff. Of =0

(b) The line parallel to -axis if coeff. Of =0

(c)Given line passes through the origin if (0, 0) lies on given eq.

2. If p and q are the lengths of from the origin to the lines.

and respectively, prove that

Ans.

Squaring andand adding

3.Prove that the product of the drawn from the points and to the line is .

Ans. Let

Similarly be the distance from to given line

4. Find equation of the line mid way between the parallel lines and

Ans. The equations are

Let the eq. of the line mid way between the parallel lines (i) and (ii) be

ATQ

Distance between (i) and (iii) = distance between (ii) and (iii)

Req. eq. is

5. Assuming that straight lines work as the plane mirror for a point, find the image of the point (1,2) in the line

Ans.Let is the image of the point in the line.

Coordinate of midpoint of

This point will satisfy the eq. ……(i)

(Slope of line PQ) slope of line

On solving (i) and (ii)

and

6.A person standing at the junction (crossing) of two straight paths represented by the equations and wants to reach the path whose equation is in the least time. Find equation of the path that he should follow.