9th Class Mathematics Second half Book Paper

Q1. Multiple choice questions (Attempt all · 48 × 0.75 = 36)

1. Which of the following is measure of central tendency?
   1. variance
   2. standard deviation
   3. range
   4. arithmetic mean
2. If LM = 4 cm, MN = 4.7 cm and ∠M = 120°, the given angle lies between:
   1. LM and MN
   2. LM and LN
   3. MN and LN
   4. None
3. If slopes of two lines are m₁ and m₂, then tan θ is:
   1. (m₂−m₁)/(1+m₁m₂)
   2. (m₁+m₂)/(1−m₁m₂)
   3. m₁m₂
   4. m₂/m₁
4. In the figure, AB = 21 cm and P divides AB in the ratio 3 : 4. What is length of $\overline{AP}$ ?
   1. 8 cm
   2. 10 cm
   3. 12 cm
   4. 9 cm
5. Mid-point of ( c , d ) and ( - d , c ) is.
   1. $\left(\frac{c-d}{2},\frac{c+d}{2}\right)$
   2. $\left(\frac{-c-d}{2},\frac{d-c}{2}\right)$
   3. $\left(\frac{-d+c}{2},\frac{c-d}{2}\right)$
   4. ( c - d , - d + c )
6. For class interval 31–40, the class mark is:
   1. 35
   2. 35.5
   3. 36
   4. 40.5
7. Which instrument is used to draw an arc of a specified radius?
   1. Protractor
   2. Compass
   3. Set square
   4. Scale only
8. Slope of the line joining (−2, 4) and (1, −3) is:
   1. $-\frac{7}{3}$
   2. $\frac{7}{2}$
   3. $-\frac{3}{7}$
   4. $\frac{1}{7}$
9. A regular polygon has exterior angle 15°. Number of sides is:
   1. 20
   2. 21
   3. 24
   4. 25
10. ( 5 , 2 ) , ( 7 , 0 ) , ( 1 , - 2 ) and ( -1 , 0 ) are the vertices of a
    1. parallelogram
    2. square
    3. trapezium
    4. kite
11. An event which can never happen is called.
    1. sure event
    2. certain event
    3. possible event
    4. impossible event
12. The sum of interior angles of a triangle is:
    1. 90°
    2. 180°
    3. 270°
    4. 360°
13. A constant rate of change in a situation is represented graphically by a:
    1. Circle
    2. Straight line
    3. Parabola
    4. Triangle
14. For similar figures, ratio of their areas is equal to:
    1. Ratio of corresponding sides
    2. Square of ratio of corresponding sides
    3. Cube of ratio of sides
    4. Sum of sides
15. The mid point of the hypotenuse of a right triangle with vertices ( 4 , 0 ) , ( 2 , 1 ) and ( - 1 , - 5 ) is.
    1. $\left(2,\frac{1}{2}\right)$
    2. $\left(\frac{1}{2},-2\right)$
    3. $\left(\frac{3}{2},-\frac{5}{2}\right)$
    4. $\left(\frac{3}{2},\frac{5}{2}\right)$
16. A wheel has 8 equal sectors. Probability of stopping at one specified sector is:
    1. '1/4
    2. '1/6
    3. '1/8
    4. '1/10
17. If two given sides are 5.7 cm and 7.5 cm and the angle 105° is opposite the 7.5 cm side, the construction involves:
    1. An oblique triangle case
    2. Only an equilateral triangle
    3. A square
    4. A circle only
18. The equation 5x − 6 = 0 represents a line parallel to the:
    1. x-axis
    2. y-axis
    3. Line y = x
    4. Origin
19. A square has perimeter 48 ft. Its side is:
    1. 8 ft
    2. 10 ft
    3. 12 ft
    4. 16 ft
20. If AB + BC = AC, then points A, B and C are:
    1. Non-collinear
    2. Collinear with B between A and C
    3. Vertices of a square
    4. Vertices of a circle
21. If a coin is tossed 10 times and head occurs 6 times, relative frequency of head is:
    1. 0.4
    2. 0.5
    3. 0.6
    4. 0.8
22. The three altitudes of a triangle meet at the:
    1. Incentre
    2. Centroid
    3. Orthocentre
    4. Midpoint
23. Slope-intercept form of a straight line is:
    1. y = mx + c
    2. ax + by = 1
    3. x/a + y/b = 0
    4. y − y₁ = x − x₁
24. In the figure, $\overline{DH}\parallel\overline{EF}$ . Then a : b = ?
    1. DG : DE
    2. DG : DH
    3. DG : GE
    4. DE : EF
25. If all four sides of a quadrilateral are equal and its diagonals bisect each other at right angles, it can be a:
    1. Rectangle only
    2. Rhombus
    3. Trapezium
    4. Scalene triangle
26. Probability of picking an ace from a well shuffled pack of 52 playing cards is.
    1. $\frac{1}{52}$
    2. $\frac{1}{13}$
    3. $\frac{4}{13}$
    4. None of these
27. In ΔPQR, if PQ = 7.2 cm, ∠P = 45° and ∠Q = 75°, then ∠R is:
    1. 50°
    2. 60°
    3. 70°
    4. 80°
28. Point of intersection of lines 9x - 7y = 0 and 8x - 11y = 0, is.
    1. ( 0 , 0 )
    2. ( 0 , 7 )
    3. ( 9 , 0 )
    4. ( 7 , 9 )
29. The locus of points equidistant from two fixed points is the:
    1. Angle bisector
    2. Perpendicular bisector
    3. Median
    4. Diameter
30. If P ( 2 , 3 ) is the mid point of A ( x , 4 ) and B ( - 3 , y ), then the coordinates of ( x , y ) are.
    1. $\left(\frac{-1}{2},\frac{3+b}{2}\right)$
    2. ( 5 , - 1 )
    3. $\left(\frac{x-3}{2},\frac{y+4}{2}\right)$
    4. ( 7 , 2 )
31. A decagonal die is labelled 4, 4, 4, 4, 5, 5, 6, 7, 8, 8. Probability of getting 4 is:
    1. '1/5
    2. '2/5
    3. '3/5
    4. '4/5
32. The centroid divides each median in the ratio:
    1. $1:1$
    2. $1:2$
    3. $2:1$
    4. $3:1$
33. The line y = 5x - 3 is written in the form.
    1. point - slope
    2. two - intercept
    3. slope - intercept
    4. two - point
34. Sum of interior angles of a 10-sided polygon is:
    1. 1080°
    2. 1260°
    3. 1440°
    4. 1620°
35. If two points have the same y-coordinate, the distance between them is the absolute difference of their:
    1. y-coordinates
    2. x-coordinates
    3. products
    4. slopes
36. A wheel has 8 equal sectors. Probability of stopping at one specified sector is:
    1. '1/4
    2. '1/6
    3. '1/8
    4. '1/10
37. Medians of a triangle are:
    1. Parallel
    2. Concurrent
    3. Perpendicular
    4. Collinear
38. The equation y = 0 represents the:
    1. x-axis
    2. y-axis
    3. Origin
    4. Vertical line x = 0
39. How many sides a regular polygon has if its exterior angle is 15?
    1. 20
    2. 21
    3. 24
    4. 25
40. The below figure is a kite, what will be the coordinates of the point of intersection of both diagonals?
    1. ( 0 , 2 )
    2. $({2}\frac{1}{2},0)$
    3. ( 0 , 0 )
    4. ( 2 , 0 )
41. Which measure of central tendency can have more than one value?
    1. weighted mean
    2. median
    3. mode
    4. arithmetic mean
42. In an obtuse triangle, the circumcentre generally lies:
    1. Inside
    2. Outside
    3. At a vertex
    4. At the centroid
43. The slope of a line having inclination θ is:
    1. sin θ
    2. cos θ
    3. tan θ
    4. cot θ
44. Rectangles 12 × 16 and 6 × 8 are:
    1. Similar
    2. Not similar
    3. Congruent
    4. Equilateral
45. A point P ( x , y ) is at equal distance from both the axes and lies in the third quadrant. If it is at a distance of 4 units from y-axis, then its coordinates are.
    1. ( - 4 , 4 )
    2. ( 4 , - 4 )
    3. ( 4 , 4 )
    4. ( - 4 , - 4 )
46. Which of the following is a class mark of the interval ( 10 - 15 )?
    1. 10
    2. 12.5
    3. 15
    4. 16
47. If three lines meet at a point, they are called.
    1. intersection
    2. perpendicular
    3. collinear
    4. concurrent
48. A linear model is appropriate when the rate of change is:
    1. Constant
    2. Random
    3. Always zero
    4. Exponential