3rd Term Complete Study Material

9th Standard

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Maths

Time : 02:15:00 Hrs
Total Marks : 60

    I. Choose the best answer 

    10 x 1 = 10
  1. If (2,3) is a solution of linear equation 2x + 3y = k then, the value of k is

    (a)

    12

    (b)

    6

    (c)

    0

    (d)

    13

  2. If \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } \neq \frac { { b }_{ 1 } }{ { b }_{ 2 } } \) where a1x + b1y + c1 = 0 and a2x + b2 y + c2 = 0 then the given pair of linear equation has __________ solution(s)

    (a)

    no solution

    (b)

    two solutions

    (c)

    unique

    (d)

    infinite

  3. The coordinates of the point C dividing the line segment joining the points P(2,4) and Q(5,7) internally in the ratio 2:1 is

    (a)

    \((\frac{7}{2},\frac{11}{2})\)

    (b)

    (3,5)

    (c)

    (4,4)

    (d)

    (4,6)

  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 tan72°.tan18° is

    (a)

    0

    (b)

    1

    (c)

    180

    (d)

    720

  6. The value of \(\frac { sin{ 29 }^{ 0 }31' }{ cos{ 60 }^{ 0 }29' } \) is

    (a)

    0

    (b)

    2

    (c)

    1

    (d)

    -1

  7. The lateral surface area of a cube of side 12 cm is

    (a)

    144 cm2

    (b)

    196 cm2

    (c)

    576 cm2

    (d)

    664 cm2

  8. The volume of a cuboid is 660 cm3 and the area of the base is 33 cm2. Its height is

    (a)

    10 cm

    (b)

    12 cm

    (c)

    20 cm

    (d)

    22 cm

  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. Solve the following linear equations
    (i) \(\frac { 2(x+1) }{ 3 } =\frac { 3(x-2) }{ 5 } \)
    (ii) \(\frac { 2 }{ x+1 } =4-\frac { x }{ x+1 } ,(x\neq -)\)

  13. Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5. Find the numbers.

  14. The points A(−3,6) , B(0,7) and C(1,9) are the mid-points of the sides DE, EF and FD of a triangle DEF. Show that the quadrilateral ABCD is a parallellogram.

  15. Find the coordinates of the point which divides the line segment joining A(−5,11) and B(4,−7) in the ratio 7:2.

  16. A boy standing at a point O finds his kite flying at a point P with distance OP=25m. It is at a height of 5m from the ground. When the thread is extended by 10m from P, it reaches a point Q. What will be the height QN of the kite from the ground? (use trigonometric ratios) 

  17. Find the area of a right triangle whose hypotenuse is 10cm and one of the acute angle is 24024'

  18. A land is in the shape of rhombus. The perimeter of the land is 160 m and one of the diagonal is 48 m. Find the area of the land.

  19. The adjacent sides of a parallelogram measures 34 m, 20 m and the measure of the diagonal is 42 m. Find the area of parallelogram.

  20. Two dice are rolled, find the probability that the sum is
    (i) equal to 1
    (ii) equal to 4
    (iii) less than 13

  21. In a football match, a goalkeeper of a team can stop the goal, 32 times out of 40 attempts tried by a team. Find the probability that the opponent team can convert the attempt into a goal.

  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 2x + 3y = 14 and 3x − 4y = 4 by the method of elimination.

  25. If the centroid of a triangle is at (−2,1) and two of its vertices are (1,−6) and (−5,2), then find the third vertex of the triangle.

  26. Express (i) sin74° in terms of cosine (ii) tan12° in terms of cotangent (iii) cosec39° in terms of secant

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

  28. Find the value of sin 64034'.

  29. The lengths of sides of a triangular field are 28 m, 15 m and 41 m. Calculate the area of the field. Find the cost of levelling the field at the rate of ₹ 20 per m2

  30. The length, breadth and height of a hall are 25 m, 15 m and 5 m respectively. Find the cost of renovating its floor and four walls at the rate of \(\triangle\)80 per m2.

  31. Two identical cubes of side 7 cm are joined end to end. Find the total surface area and lateral surface area of the new resulting cuboid.

  32. Team I and Team II play 10 cricket matches each of 20 overs. Their total scores in each match are tabulated in the table as follows:

    Match numbers 1 2 3 4 5 6 7 8 9 10
    Team I 200 122 111 88 156 184 99 199 121 156
    Team II 143 123 156 92 164 72 100 201 98 157

    What is the relative frequency of Team I winning?

  33. 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

  34. IV. Answer in detail

    2 x 5 = 10
  35. Solve for x and y: 8x − 3y = 5xy, 6x − 5y = −2xy by the method of elimination.

  36. In what ratio does the point P(–2, 4) divide the line segment joining the points A(–3, 6) and B(1, –2) internally?

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