#### All Chapter 3 Marks

9th Standard

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Maths

Time : 01:30:00 Hrs
Total Marks : 90
30 x 3 = 90
1. Draw: Venn diagram for each of the following:
(i) $A\cup (B\cap C)$
(ii) $A\cap (B\cup C)$
(iii) $(A\cup B)\cap C$
(iv) $(A\cap B)\cup C$

2. If A={-2,0,1,3,5}, B={-1,0,2,5,6} and C={-1,2,5,6,7} then show that A-(BUC)=(A-B)∩(A-C).

3. If A={2,5,6,7} and B={3,5,7,8}, then verify the commulative property of : union sets

4. If A={2,5,6,7} and B={3,5,7,8}, then verify the commulative property of : intersection of sets

5. Express the following decimal expression into rational numbers. 0.86

6. Can you reduce the following numbers to surds of same order :
(i) $\sqrt{3}$
(ii) $\sqrt [ 4 ]{ 3 }$
(iii) $\sqrt [ 6 ]{ 3 }$

7. Compute and give the answer in the simplest form;$3\sqrt { 162 } \times 7\sqrt { 50 } \times 6\sqrt { 98 }$

8. Write in scientific notation :(0.00000004)3

9. Add the following polynomials and find the degree of the resultant polynomial.
p(x)=6x2-7x+2 q(x)=6x3-7x+15

10. Show that x+4 is a factor of x+ 6x- 7x - 60

11. Find the GCD of ax,ax+y,ax+y+z

12. Check whether (5, −1) is a solution of the simultaneous equations x – 2y = 7 and 2x + 3y = 7.

13. Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say ‘how’; if they are not congruent say ‘why’ and also say if a small modification would make them congruent:

14. ABCD is a parallelogram and AP and CQ are perpendic from vertex A and C on diagonal BD. Show that (i) ΔAPB ≅ ΔCQD (ii) AP=CQ

15. ABCD is a rectangle and P, Q, Rand S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

16. Draw the $\triangle$ABC , where AB = 6 cm, B = 110° and AC = 9 cm and construct the centroid.

17. Show that the following points taken in order form the vertices of a parallelogram A (–7, –3), B(5,10), C(15,8) and D(3, –5)

18. Read the coordinates of the vertices of the triangle ABC with the following figure.

19. Three vertices of a rectangle are (3, 2), (-4, 2) and (-4, 5). Plot the points and find the coordinates of the fourth vertex.

20. Plot the following points on a graph sheet by taking the scale as 1cm = 1 unit.
Find how far the points are from each other?
A (1,0) and D (4, 0). Find AD and also DA.
You plot another set of points and verify your Result.

21. In a research laboratory scientists treated 6 mice with lung cancer using natural medicine. Ten days later, they measured the volume of the tumor in each mouse and given the results in the table

 Mouse marking Tumor Volume(mm3) 1 2 3 4 5 6 145 148 142 141 139 140

Find the mean.

22. Calculate the mean of the following distribution using Assumed Mean Method:

 Class Interval Frequency 0-10 10-20 20-30 30-40 40-50 5 7 15 28 8
23. If the mean of the following data is 20.2, then find the value of p

 Marks 10 15 20 25 30 No.of students 6 8 p 10 6

24. For the data 11,15,17,x+1,19,x-2,3 if the mean is 14,find the value of x,Also find the mode of the data.

25. For the measures in the figure, compute sine, cosine and tangent ratios of the angle $\theta$

26. i) If cosecA = sec340, find A (ii) If tanB = cot 470, find B.

27. Find the Total Surface Area and Lateral Surface Area of the cube, whose side is 5 cm.

28. The total surface area of a cube is 864 cm2. Find its volume

29. When a dice is rolled, find the probability to get the number greater than 4?

30. In a recent year, of the 1184 centum scorers in various subjects in tenth standard public exams, 233 were in mathematics. 125 in social science and 106 in science. If one of the student is selected at random, find the probability of that selected student,
(i) is a centum scorer in Mathematics
(ii) is not a centum scorer in Science