Term 3 Important Questions

9th Standard

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Maths

Time : 02:30:00 Hrs
Total Marks : 100
    I. Choose the best answer 
    10 x 1 = 10
  1. Find the value of m from the equation 2x + 3y = m. If its one solution is x = 2 and y = −2 .

    (a)

    2

    (b)

    -2

    (c)

    10

    (d)

    0

  2. Which of the following is a solution of the equation 2x − y = 6

    (a)

    (2,4)

    (b)

    (4,2)

    (c)

    (3, −1)

    (d)

    (0,6)

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

    (a)

    (b)

    (c)

    (d)

  4. 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)

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

  5. The ratio in which the x-axis divides the line segment joining the points A(a1,b1) and B(a2 ,b2 ) is

    (a)

    b1 : b2

    (b)

    −b1 : b2

    (c)

    a1 : a2

    (d)

    −a1 : a2

  6. The value of \(\frac { tan15° }{ cot75° } \) is

    (a)

    cos900

    (b)

    sin300

    (c)

    tan450

    (d)

    cos300

  7. The value of \(\frac { 1-{ tan }^{ 2 }{ 45 }^{ 0 } }{ 1+{ tan }^{ 2 }{ 45 }^{ 0 } } \)

    (a)

    2

    (b)

    1

    (c)

    0

    (d)

    \(\frac { 1 }{ 2 } \)

  8. The perimeter of an equilateral triangle is 30 cm. The area is

    (a)

    \(10\sqrt { 3 } \) cm2

    (b)

    \(12\sqrt { 3 } \) cm2

    (c)

    \(15\sqrt { 3 } \) cm2

    (d)

    \(25\sqrt { 3 } \) cm 2

  9. The probability based on the concept of relative frequency theory is called

    (a)

    Empirical probability

    (b)

    Classical probability

    (c)

    Both (1) and (2)

    (d)

    Neither (1) nor (2)

  10. The six faces of the dice are called equally likely if the dice is

    (a)

    Small

    (b)

    Fair

    (c)

    Six-faced

    (d)

    Round

  11. II. Answer the questions shortly 
    15 x 2 = 30
  12. Check whether \(\frac { 1 }{ 4 } \) is a solution of the equation 3(x + 1) = 3( 5–x) – 2( 5 + x).

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

  14. 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.

  15. The age of Arjun is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father

  16. If the mid-point (x,y) of the line joining (3,4) and (p,7) lies on 2x + 2y +1 = 0 , then what will be the value of p?

  17. If the centroid of a triangle is at (4,−2) and two of its vertices are (3,−2) and (5,2) then find the third vertex of the triangle.

  18. If  \(\left( \frac { 3 }{ 2 } ,5 \right) ,\left( 7,\frac { -9 }{ 2 } \right) \)and\((\frac{13}{2},\frac{-13}{2})\) are mid-points of the sides of a triangle, then find the centroid of the triangle.

  19. From the given figure find all the trigonometric ratios of angle B.

  20. If cos A = \(\frac { 3 }{ 5 } \), then find the value of \(\frac { sinA-cosA }{ 2tanA } \)

  21. 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) 

  22. Find the area of an equilateral triangle whose perimeter is 180 cm.

  23. A park is in the shape of a quadrilateral. The sides of the park are 15 m, 20 m, 26 m and 17 m and the angle between the first two sides is a right angle. Find the area of the park.

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

  25. The dimensions of a brick are 24 cm × 12 cm × 8 cm. How many such bricks will be required to build a wall of 20 m length, 48 cm breadth and 6 m height?

  26. 1500 families were surveyed and following data was recorded about their maids at homes

    Type of maids Only part time Only full time Both
    Number of families 860 370 250

    A family is selected at random. Find the probability that the family selected has
    (i) Both types of maids
    (ii) Part time maids
    (iii) No maids

  27. III. Answer all the questions:
    5 x 3 = 15
  28. Draw the graph for the following
    (i) y = 2x
    (ii) y = 4x - 1
    (iii) \(y=\left( \frac { 3 }{ 2 } \right) x+3\)
    (iv) 3x + 2y = 14

  29. Solve by cross multiplication method : 3x + 5y = 21; −7x − 6y = −49

  30. If (x,3), (6,y), (8,2) and (9,4) are the vertices of a parallelogram taken in order, then find the value of x and y.

  31. Find the six trigonometric ratios of the angle \(\theta\) using the given diagram.

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

  33. IV. Answer all in detail
    9 x 5 = 45
  34. (Graphing made easier!) Draw the graph of the line given by the equation y = 4x – 3.

  35. Use graphical method to solve the following system of equations x + y = 5; 2x – y = 4.

  36. The sum of the digits of a given two digit number is 5. If the digits are reversed, the new number is reduced by 27. Find the given number.

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

  38. Solve 2x = −7y + 5; −3x = −8y −11 by cross multiplication method.

  39. Find the points of trisection of the line segment joining (−2,−1) and (4, 8)

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

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

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

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