#### Term 2 FA(B) Model Question

9th Standard

Reg.No. :
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Maths

Time : 02:30:00 Hrs
Total Marks : 60
15 x 1 = 15
1. For any three sets P, Q and R, P-(Q$\\ \cap$R) is

(a)

P-(Q$\cup$R)

(b)

(P$\\ \cap$Q)-R

(c)

(P-Q)$\cup$(P-R)

(d)

(P-Q)$\\ \cap$(P-R)

2. Which of the following is true?

(a)

A-B=A$\cap$B

(b)

A−B = B −A

(c)

(A$\cup$B)'=A'$\cup$B'

(d)

(A$\cap$B)'=A'$\cup$B'

3. If n(A $\cup$ B $\cup$ C) = 40, n(A) = 30, n(B) = 25, n(C) = 20, n(A$\cap$B) = 12, n(B$\cap$C) = 18 and n(A$\cap$C) = 15 , then n(A$\cap$B$\cap$C) is

(a)

5

(b)

10

(c)

15

(d)

20

4. In simplest form, $\sqrt{640}$ is

(a)

8$\sqrt{10}$

(b)

10$\sqrt{8}$

(c)

2$\sqrt{20}$

(d)

4$\sqrt{5}$

5. When written with a rational denominator, the expression $\frac { 2\sqrt { 3 } }{ 3\sqrt { 2 } }$ can be simplified as

(a)

$\frac { \sqrt { 2 } }{ 3 }$

(b)

$\frac { \sqrt { 3 } }{ 2 }$

(c)

$\frac { \sqrt { 6 } }{ 3 }$

(d)

$\frac{2}{3}$

6. What is 5.92 x 10-3 written in decimal form?

(a)

0.000592

(b)

0.00592

(c)

0.0592

(d)

0.592

7. If x - 3 is a factor of p(x), then the remainder is

(a)

3

(b)

-3

(c)

p(3)

(d)

p(-3)

8. (x+y)(x2−xy+y2) is equal to

(a)

(x+y)3

(b)

(x-y)3

(c)

x3 + y3

(d)

x3 - y3

9. GCD of any two prime numbers is __________

(a)

-1

(b)

0

(c)

1

(d)

2

10. PQ and RS are two equal chords of a circle with centre O such that ㄥPOQ=70°, then ㄥOR

(a)

60°

(b)

70°

(c)

55°

(d)

80°

11. In the figure, PQRS and PTVS are two cyclic quadrilaterals, If ㄥQR = 80°, then ㄥTVS=

(a)

80°

(b)

100°

(c)

70°

(d)

90°

12. In the given figure, If OP=17cm PQ=30, cm and OS is perpendicular to PQ, then RS is

(a)

10cm

(b)

6cm

(c)

7cm

(d)

9cm.

13. Data available in an unorganized form is called ------------- data

(a)

Grouped data

(b)

class interval

(c)

mode

(d)

raw data

14. The mean of 5, 9, x, 17, and 21 is 13, then find the value of x

(a)

9

(b)

13

(c)

17

(d)

21

15. The mean of the square of first 11 natural numbers is

(a)

26

(b)

46

(c)

48

(d)

52

16. II. Answer any 8 questions
8 x 2 =16
17. If A=$\left\{ -\frac { 1 }{ 2 } ,0,\frac { 1 }{ 4 } ,\frac { 3 }{ 4 } ,2 \right\}$, B=$\left\{ 0,\frac { 1 }{ 4 } ,\frac { 3 }{ 4 } ,2,\frac { 5 }{ 2 } \right\}$ and C=$\left\{ -\frac { 1 }{ 2 } .\frac { 1 }{ 4 } ,1,2,\frac { 5 }{ 2 } \right\}$, then verify $A\cap (B\cap C)=(A\cap B)\cap C$ .

18. If A = {0, 2, 4, 6, 8},B ={x : x is a prime number and x < 11} and C={x:x$\in$N and 5 ≤ x < 9} then verify $A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$.

19. Rationalise the denominator
(i) $\frac { 1 }{ \sqrt { 50 } }$
(ii) $\frac { 5 }{ 3\sqrt { 5 } }$
(iii) $\frac { \sqrt { 75 } }{ \sqrt { 18 } }$
(iv) $\frac { 3\sqrt { 5 } }{ \sqrt { 6 } }$

(a)

(i) $\frac { \sqrt { 2 } }{ 10 }$
(ii) $\frac { \sqrt { 5 } }{ 3 }$
(iii) $\frac { 5\sqrt { 6 } }{ 6 }$
(iv) $\frac { \sqrt { 30 } }{ 2 }$

20. Simplify: (2.75 x 107)+(1.23 x 108)

21. Write the following in scientific notation: (4000000)3 ÷ (0.00002)4

22. Expand the following using identities: (5x+4y)(5x-4y)

23. Expand the following: (2a-3b+4c)2

24. Expand: (2a+3b)3

25. In the given figure, ㄥPOQ=1000 and ㄥPQR=300, then find ㄥRPO

26. A set of numbers consists of five 4’s, four 5’s, nine 6’s,and six 9’s. What is the mode.

27. III. Answer any 8 questions in the following
8 x 3 = 24
28. Verify $A-(B\cap C)=(A-B)\cup (A-C)$using Venn diagrams.

29. If U = {x: −4 ≤ x ≤ 4, x $\in$Z}, A = {x :−4 < x ≤ 2, x$\in$Z } and B = {x :−2 ≤ x ≤ 3,x $\in$ Z} , then verify De Morgan’s laws for complementation.

30. 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).

31. Find the value of a and b if $\frac { \sqrt { 7 } -2 }{ \sqrt { 7 } +2 }$=a$\sqrt{7}$+b

32. Represent the following information in scientific notation:
(i) The world population is nearly 7000,000,000.
(ii) One light year means the distance 9460528400000000 km.
(iii) Mass of an electron is
0.000 000 000 000 000 000 000 000 000 00091093822 kg.

33. Using algebraic identity, find the coefficients of x2, x and constant term without actual expansion.
(i) (x+5)(x+6)(x+7)
(ii) (2x+3)(2x−5)(2x-6)

34. If $\left( y-\frac { 1 }{ y } \right) ^{ 3 }$=27, then find the value of ${ y }^{ 3 }-\frac { 1 }{ { y }^{ 3 } }$ .

35. If the quotient obtained on dividing (8x4-2x2+6x-7) is (4x3+px2-qx+3), then find p, q and also the remainder

36. Draw and locate the centroid of the triangle ABC where right angle at A, AB = 4cm and AC = 3cm

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

38. Find the mean for the following frequency table:

 Class Interval Frequency 100-120 120-140 140-160 160-180 180-200 200-220 220-240 10 8 4 4 3 1 2
39. Find the sum of the deviations from the arithmetic mean for the following observations:
21, 30, 22, 16, 24, 28, 18, 17

40. If the arithmetic mean of 7 values is 30 and if each value is divided by 3, then find the arithmetic mean of new set of values