#### All Chapter 5 Marks

9th Standard

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Maths

Time : 02:00:00 Hrs
Total Marks : 140
28 x 5 = 140
1. If A, B and C are overlapping sets, then draw Venn diagram for the following sets:
(i) (A-B)$\cap$C
(ii) (A$\cup$C)-B
(iii) A-(A$\cap$C)
(iv) (B$\cup$C)-A
(v) A$\cap$B$\cap$C

2. Draw Venn diagram for $A\cap B\cap C$

3. Verify $n\left( A\cup B\cup C \right)$ = n(A) + n(B) +n(C) - $n\left( A\cap B \right) -n\left( B\cap C \right) -n\left( A\cap C \right) -n\left( A\cap C \right) +\left( A\cap B\cap C \right)$ for the following A={1,3,5,6,8} C={1,2,3,6}

4. In an examination 50% of the students passed in Mathematics and 70% of students passed in Science while 10% students failed in both subjects. 300 students passed in atleast one subject. Find the total number of students who appeared in the examination, if they took examination in only two subjects.

5. Represent the following irrational numbers on the number line $\sqrt { 6.5 }$

6. Consider the ten real numbers
$\sqrt { 2 } ,\frac { 7 }{ 9 }$,-1.32,$\frac { 6 }{ 9 } ,-\sqrt { 3 }$ , 2.151155 .....,$\frac { 23 }{ 6 } ,\frac { 48 }{ 5 }$, -3.010010001... and 12.353553555.
(i) Arrange the ten real numbers in the given boxes in ascending order.

(ii) Arrange the same numbers in the boxes given below in descending order

7. Find any three rational numbers between $\frac { 1 }{ 2 }$ and $\frac { 1 }{ 5 }$

8. Represent $-\frac { 2 }{ 11 } ,-\frac { 5 }{ 11 } and-\frac { 9 }{ 11 }$on the number line.

9. If both (x -2) and $\left( x-\frac { 1 }{ 2 } \right)$ are the factors of ax2+5x+b, then show that a=b.

10. Find the quotient and remainder when  5x3 - 9x2 + 10x + 2 is divided by x + 2 using synthetic division

11. Factorise  2x3- x2 - 12x - 9 into linear factors

12. Draw the graph for the following
(i) y = 3x - 1
(ii) $y=\left( \frac { 2 }{ 3 } \right) x+3$

13. Construct the right triangle PQR whose perpendicular sides are 4.5 cm and 6 cm. Also locate its circumcentre and draw the circumcircle.

14. Draw ΔABC, where AB = 6 cm, ㄥB = 1100 and BC = 5 cm and construct its Orthocentre.

15. Construct  $\triangle$ABC in which AB = BC = 8cm and $\angle$B =70o. Locate its in centre and draw the incircle

16. Construct the centroid of $\triangle$PQR such that PQ = 9 cm, PQ = 7cm, RP = 8 cm.

17. Find the value of ‘a’ such that PQ = QR where P, Q, and R are the points whose coordinates are (6, –1), (1, 3) and (a, 8) respectively

18. Show that the given points (1, 1), (5, 4), (-2, 5) are the vertices of an isosceles right angled triangle.

19. Show that the point A (3,7) B (6, 5) and C (15, -1) are collinear.

20. The mid-points of the sides of a triangle are (5,1), (3,−5) and (−5,−1). Find the coordinates of the vertices of the triangle.

21. Calculate the median for the following data:

 Height (cm) No. of Students 160 150 152 161 156 154 155 12 8 4 4 3 3 7
22. Find the mode for the following data

 Marks No. of students 1-5 6-10 11-15 16-20 21-25 7 10 16 32 24
23. In the class, weight of students is measured for the class records. Caculate mean weight of the students using direct method.

 Weight in kg 15-25 25-35 35-45 45-55 55-65 56-75 No.of students 4 11 19 14 0 2
24. The monthly salary of 10 employees in a factory are givan below:
Rs.5000,Rs7000Rs,5000,Rs7000,Rs8000,Rs7000,Rs7000,Rs8000,Rs7000,Rs5000
Find the mean,median and mode.

25. Find the values of the following:
(i) (cos00 + sin450 + sin300)(sin900 - cos450 + cos600)
(ii) tan2600 - 2tan2450 - cot2300 +2sin2300$\frac { 3 }{ 4 }$ cosec2 450

26. Find the value of $\theta$ if
(i) sin $\theta$ = 0.9858
(ii)tan $\theta$ = 0.5902
(iii)cos$\theta$ = 07656

27. Find the area of a quadrilateral ABCD whose sides are AB = 8cm, BC = 15 cm, CD = 12 cm, AD = 25 cm and = 90°.

28. A farmer has a field in the shape of a rhombus. The perimeter of the field is 400 m and one of its diagonal is 120 m. He wants to divide the field into two equal parts to grow two different types of vegetables. Find the area of the field.