Cantonment Public School & College, Saidpur

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Special Test-2020 Class: IX (E.V) Sub: General Mathematics

Time: 2.30 hours Marks:70

(Answer 7 questions in total taking 4 from A group, 3 from B group.

Each question carries 10 marks)

Group: A (Algebra) 1. A = {2, 3, 4}, B = {4, 5}, C = {1, 6} and

R = {

 

x,y :xA,yA and x – y = 2}

a. If



x y,3

 

 5,3x



then find the value of

 

x,y 2 b. Show that,



^A^B



^C



^A^C

 

 ^B^C



4 c. Express R in tabular method and determine dom R and range R. 4

2. , where x N.and

a. Find the value of and 2

b. Prove that, 4

c. Prove that, is an irrational number. where 4 3. A,B,C are three sets, where

A={x:x N and 5 and }

B={x:x N and 5 }

C={x:x N and x , x is even number }

a. If . 2

b. Find the value of (A C) . 4

c. Show that, P(B C)= P(B) P(C) . 4

4. and S={(x, y) : , and y=1-x},

Where, A = {-2, -1, 0,1, 2}.

a. If then find the value of . 2

b. Determine the value of . 4

c. Express the relation S in tabular method and determine domain and Range. 4

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5.

A= { x : x N and - 5x+6=0 }

B= { x : x N and 2 x 6 }and C= {2,4,6}

a. Express the set A in tabular method 2 b.According to stem prove that, 4 c. Show that, if the number of element of B is n then the number of

element of P(B) will be . 4

6. are four recurring decimal fraction.

a. Write two rational number and two irrational numbers between

2.312 and 3.152 . 2

b. Add first three numbers mentioned in the stem . 4 c.Multiply last two numbers . 4 Group: B (Trigonometry)

7. x = tan+sin, y = tan- sin

a. If tanA=

12

5 then find the value of sinA. 2 b. Show that, x² – y² = 4 xy . 4 c. Show that, 1 1 2cot 2cot³





 y

x . 4 8. p= sin, qcos, tan r

a. Show that, ¹₂ ¹₂ p² q² q

P    2

b. p+q= 2q, prove that,q-p= 2p 4

c If ,

3

 1

r find the value of

A Sec A Co

A Sec A ec

2 2

sec cos



 +2 . 4

9.

and

a. In the figure, Find the value of tan +sin . 2 b. According to the stem prove that,

4

c. According to the stem prove that,



 

 1 sin

sin ) 1

sec

(tan ²



 

 . 4

10. i. . ii. _cotA=

y x iii.

a. Using (i) then find the value of . 2

b. Using (ii), find the value of . cos sin

cos sin

A x A y



 4

c.Using (iii) Show that, 4

11. , R= secA

a. If find the value of . 2

b. Prove that, . 4

c. Prove that, 1 0

1  

  P R R

P . 4

A

B C

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Cantonment Public School & College, Saidpur

Special test-2020 Class: IX (E.V)

Sub: General Mathematics (Multiple Choice Question)

Time: 30 minutes Marks: 30

[N.B. Give the tick mark at the letter among the letters against the numeric number of questions to supplied multiple choice answer script. Each question denotes 1 full mark]

1. What is the value of 0.160.3? a) 3

2 b) 3

1 c)

9

1 d)

18 1 2. If



x y,0

 

 1,xy

  

, x,y what?

a)

 

0,0 b)

 

1,1

c) (2,2) d) 



 



 2 ,1 2 1 3. If A=



xN:ox4





i. A set has 2 prime numbers ii. P(A) has 8 elements

iii. There is 1 numbers in set A which is divisible by 2 Which one is correct?

a) i and ii b) i and iii c) ii and iii d) i, ii and iii

Answer to the questions nos. 4-5 from the following information:

.

3

. a ,

.

7

.

b ,

.

4

. c 4. abcwhat?

a)

. .

4 .

1 b) 14 c) 1.4 d)

.

4 . 1 5. abwhat?

a) .148148 b) .148 c)

. .

8 4 1

. d)

. .

8 4 1 . 6. If ( ) ,then what is the value of ( ) ?

a. 2 b. - 2

c. 4 d. - 6

7.

a. b.

c. d.

8. If sin ,

2

 3

 then what the value of tanθ?

a. 3 b. 3 3 c.

7

3 d. 3

9. = ?

a. b.

c. d. 0.17

10. Which one is irrational number?

a. b. .3

c. ⁴16 d. ³

4 32

11. If = then what is the value of

2 A cos = ?

a. b. - c.

2

1 d. 0

12. Which one of the following is the value of 0.20.04?

a. 0.05 b. 0.5

c. 5 d. 0.005

13. If A = {0, 2, 3}, then how many proper subsets of A?

a. 8 b. 7 c. 6 d. 3

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14.If

6 cot 5

cos   then cosec² cot²  What?

a) 6

1 b)

6

5 c) 1 d)

5 6

15. If

 

3 90 4

cot ⁰   then which one is the value of cos? a) 5

3 b)

4

3 c) 3

4 d)

3 5 16.

Which one is the value of ( cotθ .tanθ - 4

1) on the above figure?

a. b.

c. d.

17. If (x+y, x-y) = (7, 5) then which one of the following is the value of

2

3 y

x  ?

a.216 b. 215

c.6 d. 35

18. 9.45 2.863

.

 = ?

a. 3.0 b. 3.3 c. d. 0.17 18. Which one is irrational number?

a. 5 b.

5

80 c.

.

5 3

. d. 0.10 20. For trigonometric ratios-

i. 1

1 5 cos 2

1 5

sin² 2 ² 



 





x x x

x

ii. sec  .cos  1 x

y x x

y x

iii. sin .cos 1 x ec y y x

Which one of the following is correct?

a) i & ii b) i & iii c) ii & iii d) i, ii & iii A={ xN:x<8 and x is odd number}

B={xN :x<7 and x is even number}

C={ xN : x<11 and x is prime number}

Answer to the questions nos. 21&22 the above information:

21. A-C=what?

a. {1,2,9} b. {1}

c. {2} d. {2,11}

22.How many is the number of element of A ?

a. 4 b. 12

c. 8 d. 16

23. Which one of the following is the recurring decimal fraction of ? a.

•

4 2 .

0 b.

•

4 2 0 . 0 c.

•

0 4 2 .

0 d.

•

4 2 . 0

24.If then what?

a. b.

c. d.

25. What is the tabular form of {x : x is natural number and x < 4}

a. {1, 2, 3, 4} b. {0, 2, 3, 4}

c. {1, 2, 3} d. {1, 0, 3, 4}

26. = what ?

a. b.

c. d. 0.2

27. If f(y) (3y² 1) then, what is the value of f(-1)?

a. -1 b. 2 c.-2 d. 2 28. (p + 5, -5) = (5, q- 5) then (p, q) = what?

a.(-10, 10) b.(10, -10)

c.(0, 0) d.(1, 1)

29. What is the expression of set A



x:xN and 2x6



by tabular method?

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a) A



3,4,5,6



b) A



3,4,5,6



c) A



2,3,4,5



d) ^A^



^³^,^⁴^,^⁵^,^⁶



30. If x+y=1,xy=2 then- i. x³ y³ 5 ii. x²  y² xy6 iii.



xy



² 1

Which one is correct?

a) i, ii and ii b) ii and iii c) i and iii d) i and i