IX STD Model Question

9th Standard

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Maths

Time : 02:30:00 Hrs
Total Marks : 60

I. Choose the best answer

10 x 1 = 10
1. Which of the following is not a linear equation in two variable

(a)

ax + by + c = 0

(b)

0x + 0y + c = 0

(c)

0x + by + c = 0

(d)

ax + 0y + c = 0

2. A pair of linear equations has no solution then the graphical representation is

(a)

(b)

(c)

(d)

3. If $P(\frac{a}{3},\frac{b}{2})$is the mid-point of the line segment joining A(−4,3) and B(−2,4) then (a,b) is

(a)

(-9, 7)

(b)

$(-3, \frac{7}{2})$

(c)

(9, -7)

(d)

$(3, -\frac{7}{2})$

4. If the coordinates of the mid-points of the sides AB, BC and CA of a triangle are (3,4), (1,1) and (2,−3) respectively, then the vertices A and B of the triangle are

(a)

(3,2), (2,4)

(b)

(4,0), (2,8)

(c)

(3,4), (2,0)

(d)

(4,3), (2,4)

5. The value of $\frac { 2tan30° }{ 1-{ tan }^{ 2 }30° }$ is equal to

(a)

cos600

(b)

sin600

(c)

tan600

(d)

sin300

6. The value of tan1°.tan2°.tan3°...tan89° is

(a)

0

(b)

1

(c)

2

(d)

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

7. The semi-perimeter of a triangle having sides 15 cm, 20 cm and 25 cm is

(a)

60 cm

(b)

45 cm

(c)

30 cm

(d)

15 cm

8. If the ratio of the sides of two cubes are 2:3, then ratio of their surface areas will be

(a)

4 : 6

(b)

4 : 9

(c)

6 : 9

(d)

16 : 36

9. A number between 0 and 1 that is used to measure uncertainty is called

(a)

Random variable

(b)

Trial

(c)

Simple event

(d)

Probability

10. Probability lies between

(a)

−1 and +1

(b)

0 and 1

(c)

0 and n

(d)

0 and $\infty$

11. II. Answer any 8 questions

8 x 2 = 16
12. Akshaya has 2 rupee coins and 5 rupee coins in her purse. If in all she has 80 coins totalling Rs 220, how many coins of each kind does she have.

13. It takes 24 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 8 hours and the pipe of the smaller diameter is used for 18 hours. Only half of the pool is filled. How long would each pipe take to fill the swimming pool.

14. The centre of a circle is (−4,2). If one end of the diameter of the circle is (−3,7) then find the other end.

15. Find the coordinates of the point which divides the line segment joining the points A(4,−3) and B(9,7) in the ratio 3:2.

16. From the given figure, find the values of  (i) sinB (ii) secB (iii) cot B  (iv) cosC (v) tanC (vi) cosecC

17. If 2cos $\theta$ = $\sqrt { 3 }$, then find all the trigonometric ratios of angle $\theta$

18. Find the TSA and LSA of the cube whose side is (i) 8 m (ii) 21 cm (iii) 7.5 cm

19. The volume of a cuboid is 1800 cm3. If its length is 15 cm and height 12 cm, then find the breadth of the cuboid.

20. A company manufactures 10000 Laptops in 6 months. In that 25 of them are found to be defective. When you choose one Laptop from the manufactured, what is the probability that selected Laptop is a good one.

21. If a probability of a player winning a particular tennis match is 0.72. What is the probability of the player loosing the match?

22. III. Answer any 8 questions in the following

8 x 3 = 24
23. Check whether (5, −1) is a solution of the simultaneous equations x – 2y = 7 and 2x + 3y = 7.

24. Solve by cross-multiplication method
(i) 8x − 3y = 12 ; 5x = 2y + 7
(ii) 6x + 7y −11 = 0 ; 5x + 2y = 13
(iii) $\frac { 2 }{ x } +\frac { 3 }{ y } =5;\frac { 3 }{ x } -\frac { 1 }{ y } +9=0$

25. Find the centroid of the triangle whose veritices are A(6,−1), B(8,3) and C(10,−5).

26. Evaluate: (i) $\frac { sin49° }{ cos41° }$ (ii) $\frac { sec63° }{ cosec27° }$

27. Find the value of tan70013'

28. Find the value of (i) sin38036' + tan12012' (ii) tan60025' - cos 49020'

29. The sides of a triangular park are in the ratio 9:10:11 and its perimeter is 300 m. Find the area of the triangular park.

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

31. The side of a metallic cube is 12 cm. It is melted and formed into a cuboid whose length and breadth are 18 cm and 16 cm respectively. Find the height of the cuboid.

32. In an office, where 42 staff members work, 7 staff members use cars, 20 staff members use two-wheelers and the remaining 15 staff members use cycles. Find the relative frequencies.

33. The probability that it will rain tomorrow is $\\ \frac { 91 }{ 100 }$. What is the probability that it will not rain tomorrow?

34. IV. Answer the following in deatil

2 x 5 = 10
35. Solve graphically
(i) x + y = 7; x − y = 3
(ii) 3x + 2y = 4; 9x + 6y −12 = 0
(iii) $\frac { x }{ 2 } +\frac { y }{ 4 } =1;\frac { x }{ 2 } +\frac { y }{ 4 } =2$
(iv) x − y = 0; y + 3 = 0
(v) x − 2y = 1; x − 2y + 5 = 0
(vi) 2x + y = 4; 4x + 2y = 8
(vii) y = 2x +1; y + 3x − 6 = 0
(viii) x = –3; y = 3

36. 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.