.

## Wednesday, December 11, 2019

### Periodic Test 2 Question Papers class 9 and 10 Math Sample Papers For Periodic Test – 1 (Class VI-X)

Peridic Test - II Question Papers 2017-18 class 9 and 10

9th Maths Periodic Test 2 Question Paper 2017-18-1

9th Maths Periodic Test 2 Question Paper 2017-18-2

9th Hindi Periodic Test 2 Question Paper 2017-18-1

9th Science Periodic Test 2 Question Paper 2017-18-1

9th Science Periodic Test 2 Question Paper 2017-18-2

9th English Periodic Test 2 Question Paper 2017-18-1

9th S St.Periodic Test 2 Question Paper 2017-18-1

10th Maths Periodic Test 2 Question Paper 2017-18-1

10th Science Periodic Test 2 Question Paper 2017-18-1

10th S St. Science Periodic Test 2 Question Paper 2017-18-1

9th English Periodic Test 2 Question Paper 2017-18-1

Source: Jsuniltutorial

### CBSE TEST PAPER 10TH MATHEMATICS Distance and Section Formulae

1. Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1).

[Hint: let the point be P(x, y, z). given points be A(1, 2, 3) and B(3, 2, - 1). Then PA = PB] ans: x – 2z = 0

2.Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (– 4, 0, 0) is equal to 10.

[Hint: let the point be P(x, y, z). given points be A(4, 0, 0) and B(-4, 0, 0). Then PA + PB = 10]

3.Find the coordinates of the point which divides the line segment joining the points (– 2, 3, 5) and (1, – 4, 6) in the ratio (i) 2 : 3 internally, (ii) 2 : 3 externally.

Ans: i) (-4/5, 1/5, 27/5) ii) (-8, 17, 3)

4.Given that P (3, 2, – 4), Q (5, 4, – 6) and R (9, 8, –10) are collinear. Find the ratio in which Q divides PR.

Ans : 1:2

5. Find the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8).

[hint: any point on YZ plane is of the form (0, y, z)] ans: 2:3

6. Find the equation of the set of the points P such that its distances from the points A (3, 4, –5) and B (– 2, 1, 4) are equal.

[hint: using distance formula PA and PB and equate it.] ans: 10 x + 6y – 18z – 29 = 0

7. Find the coordinates of the points which trisect the line segment joining the points P (4, 2, – 6) and Q (10, –16, 6).

[hint: points of trisection divides the line segment into three equal parts. So use the ratio 1 : 2 and 2 : 1]
Ans : (6, -4, -2) and (8, -10, 2)

8. The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of A and B are (3, –5, 7) and (–1, 7, – 6), respectively, find the coordinates of the point C.

[hint: use centroid formula. Let the third vertex be C(p, q, r)]
ans: (1, 1, 2)

9. Three vertices of a parallelogram ABCD are A(3, – 1, 2), B (1, 2, – 4) and C (– 1, 1, 2). Find the coordinates of the fourth vertex.
Ans: (1, - 2, 8)

10. If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (– 4, 3b, –10) and R(8, 14, 2c), then  find the values of a, b and c.

[hint: use centroid formula] ans: a = - 2 , b = - 16/3, c = 2

Practice:

1.A point R with x-coordinate 4 lies on the line segment joining the points P(2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R.
[hint: let coordinate of R = (4, y, z). let R divide PQ in the ratio k:1. Using section formula, find the coordinate of R and equate its x – coordinate to 4. Solve to find value of k. then using value of k , find y and z]
ans: (4, -2, 6)

2. A is a point on the y-axis whose ordinate is 5 and B is the point (-3, 1). Calculate the length of AB.

3. The distance between A(1, 3) and B(x, 7) is 5. Find the possible values of x.

4. P and Q have co-ordinates (-1, 2) and (6, 3) respectively. Reflect P in the x-axis to P'. Find the length of the segment P'Q.

5. Point A(2, -4) is reflected in the origin as A'. Point B(-3, 2) is reflected in x-axis at B'. Write the co-ordinates of A' and B'. Calculate the distance A'B' correct to one decimal place.

6. The center of a circle of radius 13 units is the point (3, 6). P(7, 9) is a point inside the circle. APB is a chord of the circle such that AP = PB. Calculate the length of AB.

7. A and B have co-ordinates (4, 3) and (0, 1) respectively. Find (i) the image A' of A under reflection in the y-axis.(ii) the image B' of B under reflection in the line AA'.
(iii) the length of A'B'.

8. What point (or points) on the x-axis are at a distance of 5 units from the point (5, -4)?

9. Find point (or points) which are at a distance of 10 from the point (4, 3), given that the ordinate of the point (or points) is twice the abscissa.

10. Show that the points (3, 3), (9, 0) and (12, 21) are the vertices of a right angled triangle.

11. Show that the points (0, -1), (-2, 3), (6, 7) and (8, 3) are the vertices of a rectangle.

12. The points A(0, 3), B(-2, a) and C(-1, 4) are the vertices of a right angled triangle at A, find the value of a.

13. Show by distance formula that the points (-1, -1), (2, 3) and (8, 11) are collinear.

14. Calculate the co-ordinates of the point P that divides the line joining the points A (-1, 3) and B(5, -6)
internally in the ratio 1:2.

15. Find the co-ordinates of the points of trisection of the line segment joining the points (3, -3) and (6, 9).

16. The line segment joining A(-3, 1) and B(5, -4) is a diameter of a circle whose center is C. Find the co-
ordinates of the point C.

17. The mid-point of the line joining (a, 2) and (3, 6) is (2, b). Find the values of a and b.

18. The mid-point of the line segment joining (2a, 4) and (-2, 3b) is (1, 2a +1). Find the values of a and b.

19. The center of a circle is (1, -2) and one end of a diameter is (-3, 2), find the co-ordinates of the other end.

20. Find the reflection of the point (5, -3) in the point (-1, 3).

 Answers 1. 3.61 units 2. 5units 3. 4 or -2 4. 74 units 5. A'(-2, 4), B'(-3, -2); 6. 1 units  6.24 units 7. (i) (-4, 3) (ii) (0, 5) (iii) 2 5 units 8. (2, 0) and (8, 0 ) 9. (1, 2), (3, 6) 10. 67.5 sq. units 12. 1 14. (1, 0) 15. (4, 1), (5, 5) 16. (1,-3/2) 17. a = 1, b = 4 18. a = 2, b = 2 19. (5,-6) 20. (-7, 9)
10th Maths SA-2 Chapter Quick links
Circles
Co-ordinate Geometry
Arithmetic Progressions
Area Related to Circles
Probability
Height and Distance
Surface Areas and Volumes
Sample papers

### X CBSE NCERT Maths Chap 11 - Constructions Solved Questions

CONSTRUCTIONS Questions for self practice

1. Draw a line segment AB of length 4.4cm. Taking A as centre, draw a circle of radius 2cm and taking B as centre, draw another circle of radius 2.2cm. Construct tangents to each circle from the centre of the other circle.

2. Draw a pair of tangents to a circle of radius 2cm that are inclined to each other at an angle of 90.

3. Construct a tangent to a circle of radius 2cm from a point on the concentric circle of radius 2.6cm and measure its length. Also, verify the measurements by actual calculations. (length of tangent =2.1cm)

4. Construct an isosceles triangle whose base is 7cm and altitude 4cm and then construct another similar triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.

5. Draw a line segment AB of length 8cm. taking A as center, draw a circle of radius 4cm and taking B as centre, draw another circle of radius 3cm. Construct tangents to each circle from the center of the other circle.
Section-B
PRACTICE EXERCISE

1. Divide a line segment of length 10 cm internally in the ratio 3 : 5. Also, justify your construction.

2. Divide a line segment of length 7.8 cm internally in the ratio 4 : 3. Also, justify your construction.

3. Draw a right angled triangle ABC with AB = 4.5 cm, AC = 7.5 cm and < B = 90°. Construct another DA’BC’ whose corresponding sides are 5/3 times of given triangle.

4. Construct a D ABC with BC = 6 cm, <A = 60° and median AD through A is 5 cm long. Construct a DA’BC’ similar to DABC with BC = 8 cm.

5. Construct a DABC similar to a given equilateral triangle PQR with side 5 cm such that each of its sides is 6/7 th of the corresponding sides of DPQR.

6. Construct a DABC, BC = 6.5 cm, <B = 45° and <A = 100°. Construct another triangle similar to the triangle ABC whose sides are 6/5 times of the triangle ABC

7. Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation. (Ans. 4.5 cm approx)

8. Draw a circle of radius 3.5 cm. Take two points A and B on one of its extended diameter each at a distance of 8 cm from its centre. Draw tangents to the circle from these two points A and B.

9. Draw a line segment AB of length 11 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

10. Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and <B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

10th Maths SA-2 Chapter Quick links