1. No category

JKD CLASSES Objective MATHS CLASS- 9TH
Que.1. Linear equation in the one variable is:
(A) 2x=y
(B) y2 = 3y + 5
(C) 4x-y = 5
(D) 3t +5 = 9t - 7
Que.2. The condition that the equation ax+by+c=0 represents a linear equation in
two variable are:
(A) a 0,b=0
(B) b 0,a=0
(C) a=0.b 0
(D) a 0,b 0
Que.3. Which of the following is not a linear equation?
(A) ax+by+c=0
(B) 0x+oy+c=0
(C) 0x+by+c=0
(D) ax+0y+c=0
Que.4.The linear equation 2x+5y=8 has:
(A) two solutions
(B) a unique solution
(C) no solution
(D) infinitely many solutions
Que.5.The linear equation 2y-3=0. represented as ax+by+c=0, has
(A) a unique solutions
(B) infinitely many solutions
(C) two solutions
(D) no solution
Que.6.Which of the following is not a solution of the equation 2x+y=7?
(A) (1,5)
(B) (3,1)
(C) (1,3)
(D) (0,7)
Que.7.x= 5,y=-2 is the solution of linear equation:
(A) 2x+y=9
(B) x+3y=1
(C) 2x-y=12
(D) x-3y=0
Que.8.Any solution of the linear equation 2x+0y=9 in two variables is of the form:
(A) a
9
2
(C) n,
,0
9
2
(B) a
n is a real number
9
2
(D) n,
,n ,n is a real number
9
2
Que.9. If a linear equation has solution (-2,2), (0,0) (2,-2) then it is of the form:
(A) y-x=0
(B) x+y=0
(C) -2x+y=0
(D) –x+2y=0
Que.10. If (2,0) is the solution of the linear equation 2x+3y = k, then the value of
kis:
(A) 4
(B) 6
(C) 5
(D) 2
Que.11. (0,-3) and 4,0) are solution`of linear equation:
(A) 3x+4y=12
(B) 4x-3y=12
(C) 4x+3y=12
(D) 3x-4y=12
Que.12. Check which of the following is (are) solution(s) of the equation 3y-2x=1
(A) (4,3)
(B) (2√ 2,3√ 2)
(C) -2x+y=0
(D) –x+2y=0
Que.13.In countries like the USA and Canada, temperature is measured in
Fahrenheit, whereas in countries like India, it is measured in Celsius. Here
is a linear equation that converts Fahrenheit to Celsius:
F=
𝟗
𝟓
C+32
(i) Draw the graph of the linear equation above using Celsius for x-axis and
Fahrenheit for y-axis.
(ii) If the temperature is 30oC, what is the temperature in Fahrenheit ?
(iii) If the temperature is 95 oF, what is the temperature in Celsius ?
(iv) If the temperature is 0 oC, what is the temperature in Fahrenheit and If
the temperature is 0oF what is the temperature in Celsius ?
(v) is there a temperature in which is numerically the same in both
Fahrenheit and Celsius ? If yes, find it.
Que.14. The positive solutions of equation ax+by+c=0 always lie in the:
(A) 1st quardant
(B) 2nd quardant
(C) 3rd quardant
(D) 4th quardant
Que.15. The graph of y = mx is a straight line:
(A) parallel to x-axis
(B) parallel to y-axis
(C) parallel through origin (D) coincides with x-axis
Que.16. Any point on the line x+y=0 is of the form:
(A) (-a,a)
(B) (a,a)
(C) (0,a)
(D) (a,0)
Que.17. The number of lines(s) passing through a point (3,4) is (are):
(A) Only one
(B) Two
(C) Infinite
(D) Three
Que.18. If the point (2,-1) lies on the graph of the equation 3x+ky=4,then the value
of k is:
(A) 1
(B) -1
(C) 2
(D) -2
Que.19. If the line represented by the equation 3x+ay=8 passes through the point
(2,2), then the value of a is:
(A) 4
(B) 1
(C) 3
(D) 0
Que.20. The graph of the equation ax+by+c=0 may be on the form:
(A)
(B)
(C)
(D)
Que.21. Age of ‘x’ exceeds age of ‘y’ by 7 years. This statement can be expressed
as linear equation as:
(A) x+y+7=0
(B) x-y+7=0
(C) x-y-7=0
(D) x+y-7=0
Que.22. The point of the form (a,a) always lies on:
(A) x-axis
(B) y-axis
(C) the line y=x
(D) the line x+y=0
Que.23. The graph of the equation of the form y=mx is line which always passes
through:
(A) (0,m)
(B) (x,0)
(C) (0,y)
(D) (0,0)
Que.24. The equation of x-axis is:
(A) x+y=0
(B) x-y=0
(C) y=0
(D) x=0
Que.26. Any point on the x-axis is of the form:
(A) (0,y)
(B) (x,0)
(C) (x,x)
(D) (x,y)
Que.27. The linear equation x=5 in two variables can be written as:
(A) 1x+5=0
(B) 0.x+1.y+(-5)=0
(C) 1.x+0.y+(-5)=0
(D) 1.x+1.y(-5)=0
Que.28. Equation of the line parallel to x-axis and 2-units above the origin is:
(A) x=2
(B) x=-2
(C) y=2
(D) y=-2
Que.26. Which of the following represents a line parallel to x-axis?
(A) x+y=7
(B) x+3=0
(C) y+2=3y-5
(D) 5x+3=4
Que.27. Graph of linear equation 4x=5 in a plane is:
(A)
to x-axis
(B) to x-axis
(C) lies along x-axis
(D) passes through origin
Que.28. Solve the equation 2x+1=x-3 and represent the solution on
(i) the number line
(ii) The Cartesian plane
Que.30. Give the geometric representation of 2x+5=0 as an equation:
(i) in one variable
(ii) in two variables
Que.31. Solve for x:
𝟑𝒙−𝟓
𝟑
+
𝟒(𝒙+𝟐)
𝟓
=
𝟐𝟓𝒙+𝟕
𝟏𝟓
Que.32. If in a quadrilateral ABCD, <A = 90 0 and AB=BC=CD=DA. Then ABCD is a:
(A) parallelogram
(B) rectangle
(C) square
(D) rhombus
Que.33. A quadrilateral whose diagonal are equal and bisect each other at right
angles is a:
(A) rhombus
(B) square
(C) trapezium
(D) rectangle
Que.34. Which of the following is not true for a parallelogram?
(A) opposite sides are equal (B) opposite angles are equa
(C)opposite angles are bisected by diagonals (D) diagonals biscet each other
Que.35. If APB and CQD are parallel lines and a transversal PQ cut them at P and
Q, then the bisectors of angles APQ, BPQ,CQP and PQD form a:
(A) rectangle
(B) rhombus
(C) square
(D) any other parallelogram
Que.36. Which of the following is not a parallelogram
(A) Rhombus
(B) Rectangle
(C) Trapezium
(D) Square
Que.37. A diagonal of parallelogram divides it into:
(A) two triangles
(B) two congruent triangles
(C) two triangles of equal area
(D) all of the bove
Que.38. If three angles of a quadrilateral are 70 o , 95o and 105o, then the fourth
angle is:
(A) 90o
(B) 100o
(C) 110o
(D) 95o
Que.39. The angles of quadrilateral are in the ratio 2:3:6:7 The largest angle of the
quadrilateral is:
(A) 40o
(B) 120o
(C) 140o
(D) 160o
Que.40. In a parallelogram ABCD , if <A=60 o,then <D is equal is:
(A) 110o
(B) 140o
(C) 120o
(D) 130o
Que.41. The diagonals AC and BD of a parallelogram ABCD intersect each other
at the point O. If<DAC=32 o,<AOB = 70o. then <DBC is equal to:
(A) 24o
(B) 88o
(C) 38o
(D) 32o
Que.42. If ABCD is a rhombus such that <ACB = 40o, then <ADB is:
(A) 40o
(B) 45o
(C) 50o
(D) 60o
Que.43. The diagonals of rhombus are of lengths 12cm and 16cm The length of
the side of the rhombus is :
(A) 10 cm
(B) 12 cm
(C) 16 cm
(D) 8 cm
Que.44. In parallelogram ABCD, if <A = 2x+15 o and <B = 3x-25o, then value of x is:
(A) 91o
(B) 89o
(C) 34o
(D) 38o
Que.45. If E,F,G and H are respectively the mid point of the sides of a
parallelogram ABCD and ar (EFGH) = 40cm2, then ar (ABCD) is:
(A) 40 cm2
(B) 20 cm2
(C) 80 cm2
(D) 60 cm2
Que.46. In quadrilateral ABCD , AP and BP are bisectors fo <A and <B
respectively. Then the value of x is:
(A) 60o
(B) 85o
(C) 95o
(D) 100o
A
D
130 o
60 o
B
C
Que.47. If PQRS is a parallelogram, then <Q -<B is equal to:
(A) 90o
(B) 120o
(C) 180o
(D) 0o
S
R
y
30o
P
Q
Que.48. If the diagonals of a quadrilateral bisect one another at night angles, then
quadrilateral is a:
(A) tapezium
(B) rhombus
(C) parallelogram
(D) rectangle
Que.49. In figure, ABCD is a parallelogram. If <DAB=60o and <DBC =80o,<CDB is:
(A) 40o
(B) 80o
(C) 60o
(D) 20o
D
C
60o
A
B
Que.50. The figure obtained by joining mid-points of adjacent sides of a rectangle
of sides 8 cm and 6cm is:
(A) a rectangle of area 24 cm2
(B) a square of area 25 cm2
(C) a trapezium of area 24 cm2
(D) a rhombus of area 24 cm2
Que.51. D,E and F are mid-points of sides BC,CA and AB of ΔABC If perimeter of
ΔABC is 12.8cm, then perimeter of ΔDEF :
(A) 17 cm
(B) 38.4 cm
(C) 25.6 cm
(D) 6.4 cm
Que.52. In an equilateral triangle ABC,D and E are the mid-points of sides AB and
AC respectively. Then length of DE is:
(A) Not possible to find
(C)
1
2
BC
(B) 3cm
(D)
3
2
BC
Que.53. In the given figure ABIIDC. Which of the following is true about the
figure?
(A) ar(AOD) =ar(BOC)
(B) ar(AOB) =ar(COD)
(C) ar(ADC) =ar(ABC)
(D) ar(AOB) = ar(ABCD)
1
4
C
D
O
A
B
Que.54. The ratio of the areas of two parallelograms on the same base and
between the same parallels is:
(A) 1:2
(B) 1:1
(C) 1:3
(D) 2:1
Que.55. In the given figure, if ABCD is a paral-lelogram then length of BE is:
(A) 24 cm
(B) 26 cm
(C) 6 cm
(D) 8 cm
3cm
B
C
6cm
A
4cm
R
E
Que.56. In figure, PQRS is a parallelogram, PM RS and RN
then the length of PS is equal to:
(A) 18 cm
(B) 9 cm
(C) 4 cm
(D)12 cm
PS, if PQ = 12 cm,
P
Q
N
S
M
R
Que.57. The diagonal of a square is 10 cm. Its area is:
(A) 20 cm2
(B) 25 cm2
(C) 50 cm2
(D) 100 cm2
Que.57. The length of the diagonal of the square is 10 cm The area of the square
is:
(A) 20 cm2
(B) 100 cm2
(C) 50 cm2
(D) 70 cm2
Que.58. P is a point in interior of a parallelogram ABCD.
If ar (II gm ABCD) = 18 cm2, then [ar(ΔAPD) + ar(ΔCPB)is:
(A) 9 cm2
(B) 12 cm2
(C) 8 cm2
(D) 15 cm2
Que.59. D,E and F are mid-points of sides AB,BC and CA of ΔABC, if ar (ΔABC) =
64 cm2 then area of ΔBDE is:
(A) 32 cm2
(B) 16 cm2
(C) 8 cm2
(D) 12 cm2
Que.60. In the given figure, if parallelogram ABCD and rectangle ABEF are of
equal area. Then:
(A) perimeter of ABCD=perimeter of ABEF
(B) perimeter of ABCD,perimeter of ABEF
(C) perimeter of ABCD>perimeter of ABEF
(D) perimeter of ABCD =
D
F
1
2
(perimeter of ABEF)
E
C
B
A
Que.61. If two triangles are on the same base and between the same parallels,
then the ratio of their areas is:
(A) 1:1
(B) 1:2
(C) 2:1
(D) 1:4
Que.62. In ΔABC, E is the mid-point of median AD.Ar(ΔBED) =
(A)
(C)
1
2
1
4
1
ar (ΔABC)
(B)
ar (ΔABC)
(D) none of the above
3
ar (ΔABC)
Que.63. If a triangle and a parallelogram are on same base and between same
parallels, then the ratio of the area of the triangle to the area of the
parallelogram is:
(A) 1:3
(B) 1:2
(C) 3:1
(D) 1:4
Que.64. AD is the median of a triangle ABC, Area of triangle ADC= 15 cm2, then
ar(ΔABC) is:
(A)15 cm2
(B) 22.5 cm2
(C) 30 cm2
(D) 37.5 cm2
Que.65. In ΔABC, AD is median of ΔABC and BE is median of ΔABD. If ar (ΔABE)
= 15 cm2, then ar(ΔABC) is:
(A) 60 cm2
(B) 50 cm2
(C) 40 cm2
(D) 30 cm2
A
E
B
C
D
Que.66. If area of II gm ABCD is 80 cm2 , then ar (ΔADP) is :
(A) 80 cm2
(B) 60 cm2
(C) 50 cm2
(D) 40 cm2
A
B
p
C
D
Que.67. Given ar (II gm ABCD) = 25cm2 and ar(ΔBCD)= xcm2, then value of x is:
(A) 25 cm2
(B) 12.5 cm
(C) 12.5 cm2
(D) 25 cm2
Que.68. If area of parallelogram ABCD is 25cm2 and on the same base CD, a
triangle BCD is given such that area BCD = xcm2, then value of x is
(A) 25 cm2
(B) 12.5 cm2
(C) 15 cm2
(D) 20 cm2
Que.69. In the given figure, ABIIDC, then the triangles that have equal area are:
(A) ΔADX, ΔACX,
(B) ΔADX, ΔXCB
(C) ΔACX, ΔXCB
(D) all of the above
D
A
C
X
B
Que.70. Fill in the blanks:
(i) A diameter of a circle is a chord that ----------------- the centre.
(ii) A radius of a circle is a line segment with one end point ----------- and the
other end -----------(iii) If we join any two points of a circle by a line segment, we obtain a -------- of
the circle.
(iv) Any part of a circle is called an ----------- of the circle.
(v) The figure bounded by an are and the two radii joining the end-points of the
are and the centre. Is called a ------------ of the circle.
Que.71. Write True or False. Give reasons for your answers.
(i) Each radius of a circle is also a chord of the circle.
(ii) Each diameter of a circle is also a chord of the circle.
(iii) The centre of a circle bisects each chord of the circle.
(iv) Segment is the region between the chord and its corresponding are.
(v) Chord of a circle is a line segment having its end point of the circle.
Que.72. In a circle with centre O, chord AB and CD are of length 5 cm and 6cm
respectively and subtend angles x o and yo at centre of circle respectively
Then:
(A) xo = yo
(B) xo < yo
(C) xo > yo
(D) None of the above
Que.73. The numbers of circles which can pass through three non-collinear point
is:
(A) One
(B) Two
(C) Many
(D) None
Que.74. Green three collinear point, then the number of circles which can be
drawn through three point is:
(A) Zero
(B) One
(C) Two
(D) Infinite
Que.75. Ad is a diameter of a circle and AB is a chord. IF AD=34 cm and AB=30cm
the distance of AB from the centre of the circle is:
(A) 17 cm
(B) 15 cm
(C) 4 cm
(D) 8 cm
Que.76. The length of chord which is at a distance of 12cm from centre of circle of
radius 13 cm is:
(A) 5 cm
(B) 12 cm
(C) 13 cm
(D) 10 cm
Que.77. The distance of a chord 8 cm long from the centre of a circle of radius 5
cm is:
(A) 4 cm
(B) 3 cm
(C) 2 cm
(D) 9 cm
Que.78. Give two concentric circles with centre O,A line cuts the circles at
A,B,C,D respectively. If AB=10 cm, then length of CD is:
(A) 5 cm
(B) 10 cm
(C) 7.5 cm
(D) none of these
Que.79. In the given figure, O is the centre of the circle, If <ACB=300, then <ABC is
equal to:
(A) 150
(B) 300
(C) 600
(D) 450
A
300
B
C
O
Que.80. In the given figure, O is the centre of the circle, If <ACB=36 0, The measure
of <AOC is:
(A) 360
(B) 720
(C) 1440
(D) 180
B
300
O
C
A
Que.81. In the given figure, O is the centre of the circle, with <AOB=85 0, and
<AOC = 1150, <BAC is :
(A) 1150
(B) 850
(C) 800
(D) 1000
A
300
1150
B
C
Que.82. Construct the following angles (using ruler and compasses only).
(A) 22.50
(B) 67.50
(C) 1500
(D) 37.50
Que.83. A cuboid has dimentions 5cmx4cmx2cm. Number of cubes of 2cm side
that can be cut from cuboid is:
(A) 18
(B) 5
(C) 10
(D) none of these
Que.84. The area of coloured paper required to completely cover a solid cubical
box of edge ‘x’ units is:
(A) 4𝑥 2
(B) 5𝑥 2
(C) 6𝑥 2
(D) 8𝑥 2
Que.85. If the lateral surface area of a cube is 1600 𝒄𝒎𝟐 , then its edge is:
(A) 15 cm
(B) 18 cm
(C) 20 cm
(D) 25 cm
Que.86. The length of the longest pole that can be put in a room of dimensions
10m x 10mx5m is:
(A) 15 m
(B) 16 m
(C) 10 m
(D) 12 m
Que.86. The curved surface area of a cylinder is 2200 sq. cm and circumference
of its base is 220cm. Then, the height of the cylinder is:
(A) 22 cm
(B) 10 cm
(C) 5 cm
(D) 2.2 cm
Que.87. In a cylinder, radius is doubled and height is halved. The curved surface
area will be:
(A) halved
(B) doubled
(C) same
(D) four times
Que.88. The height of a right circular cylinder with lateral surface area 792 sq cm
is 21 cm. The diameter of the base is:
(A) 3 cm
(B) 6 cm
(C) 12 cm
(D) 24 cm
Que.89. The curved surface area of a right circular cylinder of height 14 cm os 88
cm2. The diameter of the base of the cylinder is:
(A) 4 cm
(B) 1cm
(C) 2 cm
(D) 3 cm
Que.90. If slant height of a cone is 13 cm and the base radius is 5 cm, then the
height of cone is:
(A) 12 cm
(B) 8 cm
(C) 10 cm
(D) 18 cm
Que.91. The total surface area of a cone whose radius is 2r and slant height
𝑙
(A) 2πr (l+r)
(B) 2𝜋r
(C) 2𝜋r (𝑙+4r)
(D) 𝜋r (𝑙+4r)
2
𝒍
𝟐
is
+r
Que.92. The area of the base of a solid hemisphere is 𝟑𝟔𝒄𝒎𝟐 its curved surface
area is :
(A) 36𝑐𝑚2
(B) 7𝑐𝑚2
(C) 108 𝑐𝑚2
(D) 98 𝑐𝑚2
Que.93. The curved surface area of a hemisphere is 𝟕𝟕𝒄𝒎𝟐. Radius of the
hemisphere is:
(A) 3.5 cm
(B) 7 cm
(C) 10.5 cm
(D) 11 cm
Que.94. Diameter of the earth is four times (approximately) the diameter of the
moon, then the ratio of their surface area is :
(A) 4:1
(B) 8:1
(C) 16:1
(D) 64:1
Que.95. Curved surface area of hemisphere of diameter 2r is:
(A) 2𝜋r2
(B) 3𝜋r2
(C) 4𝜋r2
(D) 8𝜋r2
Que.96. If a right circular cylinder just encloses a sphere of radius a cm, then the
curved surface area of the cylinder is:
(A) 4𝜋r2 cm
(B) 2𝜋a2 cm2
(C) 3𝜋a2 cm
(D) 4𝜋a2 cm2
Que.97. The number of 4 cm cubes which can be cut from a solid cube whose
edge is 32 cm.
(A) 8
(B) 64
(C) 256
(D) 512
Que.98. The number of cubes of 3 cm side which can be cut out of a cuboid of
dimensions 𝑙 = 18 cm, b= 15 cm and h=2 cm is :
(A) 180
(B) 60
(C) 20
(D) Can’t be cut
Que.99. The lateral surface area of cube is 100 m 2 . The volume of the cube is:
(A) 1000 m2
(B) 100 m2
(C) 25 m3
(D) 125 m3
Que.100. If the volume of a cube is 3 √ 𝟑 a3 , then total surface area of the cube is:
(A) 6a2
(B) √ 3 a2
(C) 18a2
(D) 18√ 3 a2
Que.101. Ratio of volume of cone and a cylinder of same radius of base and same
height is:
(A) 1:1
(B) 1:2
(C) 1:3
(D) 1:4
Que.102. Area of base of a solid hemisphere is 36𝝅 sq. cm. Then its volume is:
(A) 288𝝅 cm3
(B) 108𝝅 cm3
(C) 144𝝅 cm3
(D) 72𝝅 cm3
Que.103. Given a cuboid of dimensions 𝑙 = 3 cm, b=2 cm and h=2 cm. How many
cubes of 1 cm side can be cut out of it ?
(A) 12
(B) 6
(C) 4
(D) 3
Que.104. If the volume and surface area of a sphere is numerically equal, then its
radius is :
(A) 2 units
(B) 3 Units
(C) 4 Units
(D) 5 Units
Que.105. Class mark of class interval 60-70 is:
(A) 60
(B) 70
(C) 65
(D) 75
Que.106. If the class marks in a frequency distribution are 19.5,26.5,33.5,40.5 then
the class corresponding to the class mark 33.5 is:
(A) 16-23
(B) 23-30
(C) 30-37
(D) 37-41
Que.107. The range of the data 25.7,16.3,2.8,21.7,24.3,22.7,24.9 is:
(A) 22
(B) 22.9
(C) 21.7
(D) 20.5
Que.108. Class mark of a particular class is 10.5 and class size is 7, then class
interval is:
(A) 10.5-17.5
(B) 3.5-10.5
(C) 7-17.5
(D) 7-14
Que.109. Class mark of a particular class is 6.5 and class size is 3, then class
interval is:
(A) 5-8
(B) 6.5-9.5
(C) 3.6-6.5
(D) 4.5-7.5
Que.110. The mean of prime numbers between 20 and 30 is:
(A) 21
(B) 26
(C) 25
(D) 27
Que.111. The mean of a and b is 8.5 and mean of a,b and c is 7. The value of c is:
(A) 2
(B) 4
(C) 5
(D) 9
Que.112. The mean of the factors of 24 is:
(A)
(C)
10
3
15
2
(B)
(D)
9
4
17
3
Que.113. The mean of 10 numbers is 55. If one number is excluded, their mean
becomes 50, the excluded number is:
(A) 60
(B) 70
(C) 80
(D) 100
Que.114. Median of the dara 5,9,8,6,3,5,7,12,15 is:
(A) 3
(B) 6
(C) 5
(D) 7
Que.115. Probability of getting an even number on a die is:
(A) 0
(C)
1
3
(B)
(D)
1
2
2
3
Que.116. A die is thrown once, a number is noted, Then, probability that it is a
prime number is:
(A)
(C)
1
6
3
6
(B)
(D)
2
6
4
6
Que.117. In an experiment, the sum of probabilities of all elementary event is:
(A) 0.5
(B) 1
(C) -2
(D) 3/8
Que.118. In a cricket match, a batsman hits a sixer 8 times out of 32 balls played.
The probability that a sixer is not hit in a ball is:
(A) 0.75
(B) 0.25
(C) -0.25
(D) 0.5
Que.119. A box has 390 bulbs. Out of these 26 are defective. A bulb is chosen at
random. Find the probability of the bulb chosen not being defective:
(A)
(C)
1
15
3
20
(B)
(D)
14
15
2
29
Que.120. If P(E) denotes the probability of an event E, then:
(A) P(E)<0
(B) P(E)>1
(C) -0<P(E) <1
(D) -1<P(E) <1
Que.121. The probability of happening of an event is 45% . The probability of the
event is:
(A) 45
(B) 4.5
(C) 0.45
(D) 0.045
JKD CLASSES Subjective Questions CLASS 9TH
Que.1. Express 3x=5y in the form ax+by+c=0 and hence indicate the values of a,b
and c.
Que.2.Give two solutions of the equation x+3y=8
Que.3. Find four solutions of 2x-y=4
Que.4. Find a value of p which x=-2,y=-1 is a solution of the linear equation
5x+2pv=2p.
Que.5. Find the value of a for which the equation 2x+ay=5 has (1,-1) as a solutions
Find two more solutions for the equation so obtained.
Que.6. Find two different solutions for the linear equation 3x+5y=15 and check
whether (2,3) is the solution.
Que.7. Express the equation y=2x+3 in the standard form and find its two
solutions is (2,3) its solution?
Que.8. Find four solutions of the following linear equation in two variable
2(x+3)-3(y-1) = 0
Que.9. Give the equation of one line passing through (2,14). How many more such
line are there and why?
Que.10. Express y in terms of x, given that 2x-5y=7. Check whether the point (-3,2) is on the given line.
Que.11. Find the coordinates of the points where the line 2x-y=3 meets both the
axis.
Que.12. The auto fares in a city are as follows. For the first kilometer, the fare is
Rs. 12 and the subsequent distance is Rs 7 per km. Taking the distance
covered as x km and the total fare as Rs y, write a linear equation.
Que.13. The taxi fare in a city is as follows : For the first kilometer, the fare is Rs.
8 and the subsequent distance it is Rs 5 per km. Taking the distance
covered as x km and total fare as Rs y, write a linear equation. For this
information.
Que.14. Draw graph of the following linear equations: 2x-y=3 and 3x+2y=3 and
3x+2y=1. Find point of intersection of these lines.
Que.15. Draw the graph of 2x-y=3 and 3x+2y=1 on the same graph paper Find the
point of intersection of these graphs.
Que.16. Draw the graph of the equation 3x+y=5 and write the co-ordinates of the
points where the line interests x-axis and y-axis.
Que.17. Draw the graph of two lines, whose equation are 3x-2y=4 and x+y-3= 0 on
the same graph paper and find the co-ordinates of the point where two
lines intersect.
Que.18. Draw the graph of equation 3x+y=6. Also, find the points when the line
interest x-axis and y-axis.
Que.19. The taxi fare for the first km is Rs 10 and fare for the subsequent distance
is Rs 6 per km If the distance covered is x km and total fare is Rs y, write
a linear equation for this statement and draw its graph.
Que.20. The taxi fare in a city is as follows : For the first kilometer, the fare is Rs.
8 and the subsequent distance it is Rs 5 per km. Taking the distance
covered as x km and total fare as Rs y, write a linear equation. For this
information.From the equation, calculate total fare of 15 km distance.
Que.21. The relation between temperature in Celsius Scale (oC) and in Fahrenheit
scale (oF) is c =
𝟓
𝟗
(F-32) Draw the graph of the above linear equation. Use
the graph to find corresponding temperature in Fahrenheit for 25oC.
Que.22. The food charges in a hostel are as follows: For the first day. The charges
are Rs 100 and for the subsequent days it is Rs. 50 per day. Taking the
number of days as x and total charges as Rs y, write a linear equation for
this information and draw its graph.
Que.23. Give the geometric representation of 2x+=0 as an equation:
(i) In one variable
(ii) in two variables
Que.24. Solve for x:
𝟑𝒙−𝟓
𝟑
+
𝟒(𝒙+𝟐)
𝟑
=
𝟐𝟓𝒙+𝟕
𝟏𝟓
Que.25. Solve for x:
𝟑𝒙+𝟐
𝟕
+
𝟒𝒙+𝟏
𝟓
=
𝟐
𝟑
(x+1)
Que.26. Solve for x:
𝒙+𝟑
𝟐
–
𝟑𝒙+𝟏
𝟒
=
𝟐(𝒙+𝟕)
𝟑
-2
Que.27. Solve for x:
𝟑𝒙−𝟕
𝟓
–
𝒙+𝟏
𝟔
=
𝟐𝒙+𝟐
𝟏𝟐
-1
Que.28. Find the measure of each angle of a parallelogram, if one of its angles is
30o less than twice the smallest angle.
Que.29. Prove that if the diagonals of a quadrilateral bisect each other, then it is a
parallelogram.
Que.30. ABCD is a quadrilateral in which P,Q,R and S are mid-points of AB,BC,CD
and DA respectively. Show that PQRS is a parallelogram:
R
D
C
S
Q
A
P
B
Que.31. The angle between the two altitudes of a parallelogram through the vertex
of an obtuse angle is 50 o Find the angles of the parallelogram.
Que.32. ABCD is a parallelogram and AP and CQ are perpendiculars from vertices
A and C on diagonal BD,Show that
(i) ΔAPB = ΔCQD
D
(ii) AP= CQ
C
P
A
Q
B
Que.33. ABCD is a parallelogram x and Y are points on DC and AB such that AY =
CX Prove that XY and BD bisect each other.
Que.34. ABCD is a parallelogram and line segments AX and CY bisect angles A
and C respectively Show that AXIIYC
X
D
C
B
A
Y
Que.35. In a quadrilateral ABCD,<B=130 o,<C= 60o and angle bisectors of <A and
<D meet at P. Find<APD.
A
B
130o
P
60o
C
D
Que.36. Show that the bisectors of angles of a parallelogram from a rectangle
Que.37. In the figure, it is given that BDEF and FDCE are parallelograms. Show
that BD=CD.
A
E
F
B
C
D
Que.38. D and E are the mid-points of sides AB and AC respectively of triangle
ABC If the perimeter of 𝚫ABC = 35o cm, find the perimeter of 𝚫ADE.
Que.39. ABCD is a quadrilateral in which P,Q,R and S are the mid-points of the
sides AB,BC,CD and DA respectively Show that PQRS is a parallelogram.
R
D
C
S
Q
A
B
P
Que.40. Show that the line segments joining the mid-points of opposite sides of
quadrilateral bisect each other.
Que.41. ABCD is a trapezium in which ABIIDC. E is the mid-point of AD. If F is a
point on side BC such that line segment EF is parallel to side DC, show
that EF =
𝟏
𝟐
(AB+CD).
Que.42. In the figure, ΔPQR is a triangle. PS and RT are median and SMIIRT.
Prove that QM =
𝟏
𝟒
PQ.
P
T
M
R
Q
S
Que.42. Show that the quadrilateral formed by joining mid-point of the sides of
rhombus, taken in order, from a rectangle.
Or
The diagonals of a quadrilateral ABCD are perpendicular Show that
quadrilateral. Show that quadrilateral formed by joining the mid-points of
its sides is rectangle.
Que.43. AD is the median of ΔABC. E is the mid-point of AD. BE produced meets
AC at F show that AF =
𝟏
𝟑
AC
A
F
E
C
B
D
Que.44. Prove that in a triangle, the line segment joining the mid-points of any
two sides is parallel to third side and is half of it.
Using the above if P,Q,R are the mid-points of sides BC,AC and AB of
ΔABC respectively and if PQ = 2.5 cm QR=3cm RP= 3.5cm, find the length
of AB,BC and CA.
Que.45. If ΔPQR and ΔLMN be two triangles given in such a way that PQIILM,
PQ=LM, QR= MN and QRIIMN, then show that PRIILN and PR=LN.
L
P
R
N
Q
M
Que.46. In figure, ABCD is a trapezium, BC = 17 cm, AB = 16 cm and DC = 8cm.
Find the area of ABCD.
D
8 cm
C
17 cm
B
A
F
8 cm
Que.47. In the figure, DE and BF are perpendiculars to the diagonal AC of a
parallelogram ABCD. Prove that DE=BF.
D
C
F
E
A
B
Que.48. In the given figure, M is a point in the interior of a parallelogram
PQRS.Show that.
(i) ar (ΔPMQ) + ar (ΔMRS)
=
1
2
ar (II gm PQRS)
(ii) ar (ΔPMS) + ar (ΔMQR)
= ar (ΔPMQ) + ar (ΔMRS)
P
Q
M
S
R
Que.49. Show that the median of a triangle divides it into two triangles of equal
areas.
Que.50. AD is a median of ΔABC. If is any point on AD. Show that ar (ΔABX)=
(ΔACX)
Que.51. D is the mid-point of side BC of ΔABC and E is the mid-point of AD, then
show that ar (BED) =
𝟏
𝟒
ar (ABC).
Que.52. Diagonal AC and BD of a quadrilateral ABCD intersect at O in such a way
that ar (AOD) = ar (BOC). Prove that ABCD is a trapezium.
Que.53. If medians of triangles ABC intersects at G show that:
Ar (ΔAGB) = ar (ΔAGC) = ar (ΔBGC)
=
A
F
G
𝟏
𝟑
ar (ΔABC).
E
C
B
D
Que.54. XY is a line parallel to side BC of a triangle ABC passing through A. If
BEII AC and CFIIAB meet XY at E and F respectively show that ar (ABE) =
ar (ACF)
Que.55. The side AB of a parallelogram ABCD is produced to any point P, A line
through A and parallel to CP meets CB produced at Q and then
parallelogram PBQR is completed Show that
ar (BCD) =
ar (PBQR)
Que.56. In the given figure ABCD is a parallelogram in which BC is produced to E
such that CE=BC. AE interests CD of F. Show that ar (ΔBDF) =
(ΔABCD).
A
D
B
C
F
E
𝟏
𝟒
ar
Que.57. Prove that equal chords of a circle subtend equal angles at the centre.
Que.58. Prove that if two area of a circle are congruent, then their corresponding
chords are equal.
Que.59. Prove that if two chords of a circle are equal, then their corresponding
ares are congruent.
Que.60. Suppose you are given a circle. Give a construction to find its centre.
Que.61. Two parallel chords of a circle whose diameter is 13 cm are respectively 5
cm and 12 cm. Find the distance between them if they lie on opposite
sides of centre.
Que.62. Two circles of radil 10cm and 8 cm interest and the length of the common
chord is 12cm. Find the distance between their centres.
Que.63. Two congruent circles intersect each other at points A and B. Through A
a line segment PAQ is drawn so that P and Q lie on the two circles. Prove
that BP=BQ
Que.64. If two interesting chords of a circle make equal angles with the diameter
passing through their point of intersection, prove that the chords are
equal.
Que.65. Two circles of radii 10 cm and 17 cm intersect at two centres is 21 cm.
Find length of the common chord.
Que.66. Two equal chords AB and CD of a circle when produced, intersect at
point P. Prove that PB=PD.
Que.67. ABC and ADC are two right triangles with common hypotenuse AC. Prove
that <CAD=<CBD.
Que.68. ABCD is a parallelogram. The circle through A,B and C intersects CD
(produced,If necessary) at E Prove that AE=AD.
Que.69. Prove that a cyclic parallelogram is a rectangle.
Que.70. Two circles intersect at two points A andB AD and AC are diameters to
the two circles. Prove that B lies on the line segment DC.
Que.71. If the non-parallel sides of a trapezium are equal, prove that it is cyclic
Que.72. Prove that quadrilateral formed (if possible) by the internal angle
bisectors of any quadrilateral is cyclic.
Que.73. Construct <EFG=60o, Bisect it. Bisect one of the parts to get an angle of
15o,
Que.74. Construct an equilateral triangle whose one side is 5.3 cm.
Que.75. Construct a triangle PQR, in which PQ=5cm, <P=60 o and PR+RQ=9cm.
Que.76. Construct a triangle ABC, in which BC=5cm, <B=45o and AB-AC=2.8cm.
Que.79. Construct a ΔABC, in which <B=60o, <C=45o and AB+BC+CA =11cm.
Que.80. Construct ΔABC, whose perimeter is 12 cm. <B=60 o, and <C=45o,.Justify
the construction.
Que.81. Construct a ΔPQR, with its perimeter = 10.4 cm and base angles of 75 o
and 30o
Que.82. Three cubes each of side 6 cm are joined end to end. Find the surface
area of the resulting cuboid.
Que.83. Find the cost of white washing the four walls of a room with dimensions
5cmx4m x3m at the rate of Rs 12/m2
Que.84. The length, breadth and height of a cube are 5 m, 4 m and 3 m
respectively. Find the cost of white washing the walls of the room and the
celling at the rate of Rs 7.50 per m2
Que.85. The paint in a certain container is sufficient to paint an area equal to
9.375 m2 How many bricks of dimensions 22.5 cmx10cmx7.5 cm csn be
painted out of the container?
Que.86. A man built a cubical water tank with lid for his house, with each other
edge 1.5 m long. He gets the outer surface of tank excluding the base
covered with square tiles of sides 25cm. Find how much be would spend
for the tiles. If cost of tiles is Rs. 480 per dozen.
Que.87. The total surface area of a solid right circular cylinder is 231 cm2 If curved
surface area is two-third of the total surface area, find the radius of the
base.
Que.88. The diameter of a cylindrical roller 120 cm long is 84cm. It takes 500
complete revolutions to level a playground. Find the cost of leveling it at
Rs 7.50 Sq m.
Que.89. An iron pipe 20 cm long has exterior diameter 25 cm. If the thickness of
the pipe is 1 cm, find the whole surface area of the pipe.
Que.90. The ratio between curved surface area and total surface area of a right
circular cylinder is 2:3 Find ratio between height and radius of cylinder.
Que.91. The radii of two right circular cylinders are in the ratio 2:3 and their
heights are in the ratio 5:4 Find the ratio of their curved surface areas.
Que.92. The diameter of a roller is 84 cm and its length is 120 cm. It takes 500
complete revolutions to move once over to level a playground. Find the
area of the playground in m2 use 𝝅=
𝟐𝟐
𝟕
Que.93. Circumference of the base of a cylinder, open at the top, is 132 cm. The
sum of radius and height is 41cm. Find cost of polishing the outer surface
area of cylinder at the rate Rs 10 per square
(decimeter) use 𝝅=
𝟐𝟐
𝟕
Que.94. Curved surface area of a cone of radius 4cm is 20𝝅cm2 Find total surface
area of the same cone in terms of 𝝅.
Que.95. How many square metres of canvas is required for a conical tent whose
height is 3.5 m and radius of whose base is 12m?
use 𝝅=
𝟐𝟐
𝟕
Que.96. If slant height of a cone is 21m and diameter of its base is 24 m. then find
its total surface area.
Que.97. A joker’s cap is in the form of a right circular cone of base radius 7 cm
and height 24 cm. Find the area of the sheet required to make 10 such
caps.
Que.98. Find the slant height and radius of the cone made from a quadrant of a
circle of radius 9.6cm.
Que.99. The radius and height of a cone are in the ratio 4:3 The area of its base is
154 cm2 Find its curved surface area.
Que.100. How many meters of 5 m wide cloth will be required to make a conical
tent, the radius of whose base is 3.5 m and height is12 m ?
Que.101. The height and base diameter of a conical tent is 16 m and 24 m
respectively Find the cost of canvas required to make it at the rate of Rs
210 per m2
Que.102. From a right circular cylinder with height 8 cm and radius 6cm, a right
circular cone of the same height and base is removed Find the total
surface area of the remaining solid.
Que.103. A tent is in the shape of a right circular cylinder upto a height of 3 m and
a cone above it. The maximum height of the tent above ground is 13.5
m. Calculate the cost of painting the inner side of the tent at the rate of
Rs 3 per sq. m if the radius of the base is 14 m.
Que.104. The radius of a spherical balloon is inflated from 1.5 cm to 2.5 cm by
pumping more air in it. Find the ratio of surface area of resulting balloon
to the original balloon.
Que.105. The radius of a spherical balloon increases from 7 cm to 14 cm as air is
being pumped into it. Find the ratio of surface areas of the balloon in
two cases.
Que.106. A hemispherical bowl is made of steel 0.25 cm chick. The inner radius of
the bowl is 5 cm. Find the outer curved surface area.
of the bowl
use 𝝅 =
𝟐𝟐
𝟕
Or
A hemispherical bowl is made of 0.25 cm thick metal sheet. The inner
radius of the bowl is 5 cm. Find the outer curved surface area.
Area of the bowl
use 𝝅 =
𝟐𝟐
𝟕
Que.107. A hemispherical dome of a building needs to be painted. If the
circumference of the base of the dome is 17.6 m. find the cost of
painting it, given the cost of painting in Rs 5 per 100cm2
Que.108. How many cubes of side 3 cm can be cut from a wooden solid cuboid
with dimensions 12 cm x12 cmx9 cm?
Que.109. The capacity of a cuboidal tank is 50000 litres of water, Find the breadth
of the tank, if its length and depth are respectively 2.5 m and 10m.
Que.110. Find the maximum nuber of cubes of sides 3 cm that can be cut out of a
cuboid of dimension 18 cmx12 cmx 9cm.
Que.111. A storage tank is in the form of a cube When it is full of water The
volume of water is 15.625 m3. If the present depth of water is 1.3 m, find
the volume of water used.
Que.112. A river 3 m deep and 40 m in wide is flowing at the rate of 2 km per hour.
How much water will fall into the sea in a minute?
Que.113. A class-room is 10 m long, 6.4 m wide and 5 m high. If each student be
given 1.6 m2 of the floor area, how many students can be accommoded
in the room ? How many cubic metres of air each student will get?
Que.114. A wall of length 10 m was to be built across an open ground. The height
of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be
built up with bricks whose dimensions are 24 cm x 10 cmx 8cm, how
many bricks would be required?
Que.115. A cube and cuboid have same volume. The dimensions of the cuboid
are in the ratio 1:2:4. If the difference between the cost of polishing the
cube and cuboid at the ratio of Rs. 5 per m 2 is Rs 80, find their volumes.
Que.116. If the volume of a right circular cone of height 9 cm is 48𝝅 cm3 , find the
radius of the base.
Que.117.The volume of a cylinder is 350 𝝅 cm3 and its height is 14 cm. Find its
curved sutface area.
Que.118.The curved surface area of a cylinder is 176 cm 2 and its area of the base
is 38.5 cm2 Find the volume of the cylinder (take 𝝅 = 22/7).
Que.119.The volume of a right circular cylinder is 3850 cubic cm. Find its height if
its diameter is 14 cm.
Que.120.A rectangular sheet of paper 66 cmx 20cm is rolled along its length to
form a cylinder. Find the radius and volume of the cylinder.
Que.121.The are of curved surface of cylinder is 1210 cm 2and its radius is 10 cm.
Find the volume of the cylinder.
Que.122.The radius and height of a cylinder are in the ratio 5:7 and its volume is
550 cm3 Find the diameter.
Use 𝝅 =
𝟐𝟐
𝟕
Que.123.The capacity of a closed vessel of height 1 m is 15.4 litres. How many
square metres of metal sheet would be needed to make
It ? Use 𝝅 =
𝟐𝟐
𝟕
Que.124.The curved surface area and volume of a cylinder pillar are 264 m 2 and
396 m3 and respectively. Find the diameter and height of the pillar.
Que.125.A School provides milk to the students daily in cylindrical glasses of
diameter 7 cm. If the glass is filled with milk upto a height of 12 cm. Find
how many litres of milk is needed to serve 1600 students.
Que.126.A solid cylinder has a total surface area of 462 cm 2 Its curved surface
area is one-third of its total surface area. Find the volume of the cylinder
take 𝝅 =
𝟐𝟐
𝟕
Que.127.A hollow cylindrical pipe 21 dm long is made of copper. Its outer and
inner diameters are 10 cm and 6 cm respectively.Find the volume of
copper used in making the pipe.
Que.128.The cost of painting the total outside surface of a closed cylindrical oil
tank at 60 paise per sq. cm is Rs 237.60 The height of the tank is 6 times
the radius of the base of the tank Find volume of cylindrical tank correct
to two decimal places.
Que.129.How many cylindrical glasses of 3 cm base radius and height 8 cm can
be refilled from a cylindrical vessel of base radius 15 cm which is filled
upto a height of 32 cm?
Que.130.The ratio of the total suface area to the curved surface area of a right
circular cylinder is 3:2 Find the volume of the cylinder, if its total surface
area is 8316 m2
Que.131.The inner diameter of a cylinder of cylindrical wooden pipe is 24 cm and
its outer diameter is 28 cm. The length of the pipe is 35 cm Find the mass
of the pipe, if 1 cm3 wood has a mass of 0.6g.
Que.132.A lead pencil consists of a cylinder of wood with a solid cylinder of
graphite filled in the interior The diameter of the pencil is 7 mm and the
diameter of graphite is 1 mm. If the length of the pencil is 14 cm. find the
volume of wood and that of graphite.
Que.133.The difference between the outer lateral surface area and inner lateral
surface area of a cylindrical metallic pipe 28 cm long is 176 cm 2 . Find
the outer and inner radii of the pipe, if the pipe is made of 352cm 3 .of
metal.
Que.134.If the volume of a right circular cone of height 9 cm is 48𝝅 cm3, find the
diameter of its base.
Que.135.The circumference of the base of a 9 m high wooden solid cone is 44 m
Find its volume Use 𝝅 =
𝟐𝟐
𝟕
Que.136.The height of the cone is 15 cm. If its volume is 1570 cm 3, find the radius
of the base (use 𝝅 = 3.14).
Que.137.A cone and cylinder are having equal base radius. Find the ratio of the
heights of cone and cylinder, if their volumes are equal.
Que.138.A semi-circular sheet of metal of diameter 28 cm is bent into an open
conical cup,Find the depth and capacity of the cup.
Que.139.From a height circular cylinder with height 10 cm and radius of base 6
cm, a right circular cone of the same height and base is removed. Find
the volume of the remaining solid
use 𝝅 =
𝟐𝟐
𝟕
Que.140.A solid right circular cylinder of radius 8 cm and height 3 cm is melted to
make a cone of height 3 times that of cylinder. Find the curved surface
area of the cone. ( use √ 𝟏𝟒𝟓 = 12).
Que.141.The radius and height of a right ciecular cone are in the ratio 5:12 If its
volume is 314 cm3, find slant height and curved surface area of the cone
(take 𝝅 = 3.14).
Que.142.A tailor has a piece of canvas whose area 552 m 2, He uses it to make a
coneical tent with base radius 7 m. Assuming that all stitching margins
and wastage incurred while cutting amounts to apperoximately 2 m2 find
volume of tent that can be made with it.
Que.143.A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about
the side 12 cm. Find the volume of the solid so obtained.
Que.144.A right triangle having sides 6 cm, 8 cm and 10 cm is revolved about the
side of length 8 cm Find the volume of the solid so formed.
Que.145.A corn cob, shaped like cone, has the radius of the base as 2.1 cm and
height as 20 cm. If each 1 sq cm of the surface of cob carries an average
of 4 grains, find how many grains you would find in the entire cub.
Que.146.A right circular cone is 5.4 cm high and radius of its base is 2 cm. It is
melted and recast into another right circular cone with radius of base as
1.5 cm. Find the height of the new cone formed.
Que.147.A conical vessel with radius 20 cm and height 30 cm is full of water. The
water of this vessel is transferred to cylindrical vessel of radius 8 cm.
Find upto what height will the cylindrical vessel fill.
Que.148.Find the volume and surface area of a sphere of radius 2.1 cm
use 𝝅 =
𝟐𝟐
𝟕
Que.149.The surface area of a sphere is 154 cm2, find its volume use 𝝅 =
𝟐𝟐
𝟕
Que.150. How many litres of milk can a hemispherical bowl of radius 10.5 cm
hold?
Que.151. If the ratio of the radii of two spheres is 2:3, then find the ratio of their
volumes.
Que.152.If numerical value of the volume of a sphere is divided by numerical
value of its surface area, then the result is 27. Find the radius of the
sphere.
Que.153.A solid spherical ball of diameter 4.2 cm is completely immersed in
water. How much water is displaced?
Que.154.Find the volume of metal used in making a hollow hemispherical bowl
with internal and external diameters 4 cm and 10 cm respectively.
use 𝝅 =
𝟐𝟐
𝟕
Que.155.A hemispherical bowl of internal and external diameters 6 m and 10 m is
melted and formed into a right circular cylinder of radius 14 m. Find the
height of the cylinder.
Que.156.A solid sphere of radius 3 cm is melted and then cast into small
spherical balls each of diameter 0.6 m. Find the number of balls thus
obtained.
Que.157.How many spherical lead shot each 4.2 cm diameter can be obtained
from a solid cuboid of lead with dimensions 60 cm, 42 cm and 21 cm?
Que.158.A cylindrical tub of radius 16 cm contains water to a depth of 30 cm. A
spherical iron ball is dropped into the tub and thus level of water is
raised by 9 cm. What is the radius of the ball?
Que.159.Twenty seven solid iron sphere, each of radius 2 cm are melted to form a
new solids sphere What will be the surface area of the new sphere?
Que.160.The diameter of a metallic ball is 21 cm What is the mass of the ball, if
the density of the metal is 5g per cm3?
Que.161.A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner
radius is 1 m, then find the volume of the iron used to make the tank
Que.162.Metal spheres, each of radius 2 cm, are packed into a rectangular box of
dimensions 16 cmx 8 cm x 8 cm When 16 spheres are packed in the box,
it is filled with preservative liquid. Find the volume of this liquid to the
nearest integer.
Que.163.What are (i) primary data (ii) secondary data?
Which of the two is more reliable and why?
Que.164.Explain the reasons behind grouping raw data. What advantage do we
get by grouping the data?
Que.165. Given below are the marks obtained by 40 students in an examination:
29 40
15
12
30
31
25
27
39 02
45
11
35
48
24
32
22 19
12
44
23
48
40
49
25 07
09
41
13
25
30
01
03 18
29
43
49
13
32
03
Taking class intervals 1-10,11 -20,----- 41-50, make a frequency table for
above data.
Que.166. Given below are the marks obtained by 30 students in an examination:
18 59
25
53
42
43
51
54
27 34
17
16
19
22
44
26
40 30
49
52
55
24
41
32
21 28
29
37
27
31
Taking class interval 10 – 20, 20-30 etc,, make a frequency table for the
above data.
Que.167. The weight (in grams) of 30 apples, picked at random from a basket of
apples, are given below.
45,55,30,110,75,100,40,60,65,40,100,75,70,60,70,70,60,95,85,80,35,45,40,50
,60,65,55,45,30,90.
Construct a frequency distribution table for the above data with equal
class intervals, one of them being 30-40(40 not included)
Que.168.The weights of new-born babies in kg in a hospital on a particular day
are as follows : 2.6,2.2,2.4,2.7,2.6,3.0,2.5,2.9,2.6,3.2,2.5,2.8,2.7,2.9 and 2.4.
Prepare a frequency distribution table for the above data.
Que.169.The maxium temperature (in oC) for a city for the month of June of a
certain year are given below, Construct a grouped frequency table for it.
37.5
32.5
32.5
32.5
31.2
28.6
31.9
31.3
32.4
30.4
32.6
32.6
35.3
36.4
36.9
32.5
34.4
37.3
36.9
36.5
34.9
35.2
34.5
36.6
34.3
33.4
35.6
36.8
37.0
36.9
Que.170.The water bills (in rupees) of 30 houses in a locality are given below,
Construct a grouped frequency distribution for it, with class size 10:
36,32,45,64,72,78,108,122,66,76,88,48,114,128,65,35,45,66,55,82,95,122,96,
118,88,44,54,112,44,34.
Que.171.The distribution of weight (in kg) of 100 people is given on next column:
Weight (in kg)
Frequency
40-45
13
45-50
25
50-55
28
55-60
15
60-65
12
65-70
5
70-75
2
Total
100
Construct a histogram and frequency polygon for the data.
Que.171.Draw a histogram for the following data:
Class Interval
10-14
15-19
20-24
25-29
30-34
35-39
40-44
Frequency
300
980
800
600
300
430
530
Que.172.Draw histogram to represent the following distribution:
Class Interval
5-10
10-15
15-25
25-45
45-75
Frequency
6
12
10
8
15
Que.173.Draw a histogram and frequency polygon for the following distribution:
Make obtained
0-10
10-20
20-30
30-40
40-50
50-60
60-70
70-80
No. of students
7
10
6
8
12
3
2
2
Que.173.In a city, the weekly observations made in a study on the cost of living
index are given in the following table:
Cost of living index
140-150
150-160
160-170
170-180
180-190
190-200
Total
No. of weeks
5
10
20
9
6
2
52
Draw histogram and frequency polygon of the above data.
Que.174.Find the mean of factor of 24.
Que.175.Find the mean of the first eight prime numbers.
Que.176.If the mean of 10,12,18,11,p and 19 is 15, find the value of p.
Que.177.The mean of ten observations is 20. If nine of observations are
16,20,18,17,22,16,15,20,17; find the tenth observation.
Que.178.The following observations have been arranged in ascending order. If
median of the data is 23.5 find the value of x.
12,16,17,19,x,x+3,27,37,38,40
Que.179.The mean of 25 observations in 36. Out of these observations, the mean
of first 13 observations is 32 and that of the last 13 observations is 40.
Find the 13th observation.
Que.180.Find the mean of the following data:
Marks
10
30
50
70
89
Frequency
7
8
10
15
10
Que.181.Find missing frequency p for the following distribution whose mean is
15:
X
5
10
15
20
25
ƒ
6
P
6
10
5
Que.182.Find the median of the following data:
19,25,59,48,35,37,30,32,51.
If 25 is replaced by 52 what will be the new median.
Que.182.Find the mean of 3,4,6,7,8 and 14. If 5 is added to each observation, what
will be the new mean?
X
2
4
6
10
p+5
ƒ
3
2
3
1
2
Que.183.The mean weight per student in a group of 7 students is 55 kg. The
individual weights of 6 of them in kg. are 52,54,55,56,54. Find the weight
of the seventh student.
Que.184.Find the missing frequencies ƒ 1 and ƒ2 in the following frequency
distribution, if it is known that the mean of the distribution is 1.46:
X1
0
1
2
3
4
5
Total
ƒ1
46
ƒ1
ƒ2
25
10
5
200
Que.185.The monthly salary (in thousand rupees) of 50 workers in a factory are
given below:
Salary (in thousand rupees)
Number of workers
5.2 6.9
8
9
8.2
10
10.5
12
12.2
6
14.0
5
Find the mean salary of a worker.
Que.186.Following table shows the marks obtained by 30 student in a class test:
Marks obtained
70
58
60
52
65
75
68
Number of student
3
5
4
7
6
2
3
Find the probability that a student secures:
(a) 60 marks
(b) less than 60 marks
Que.187.A dice is tossed 100 times and the outcomes are recorded as below:
Out come
1
Frequency
20
Even number less than 6
Odd number greater than 1
35
Find the probability of getting:
(a) The number 6
(b) Even number less than 6.
30
16
15
Que.188.A bag contains cards numbered from 1 to 25 A card is drawn at random
from the bag. Find the probability that selected card bears number which
is multiple of 2 or 3.
Que.189.1500 family with 2 children were selected randomly and the following
data was recorded:
Number of girls in family
Number of family
2
1
0
475
814
211
Compute the probability of a family chosen at random having:
(a) at most 1 girl
(b) at least 2 girls
Que.190.1500 families with 2 children were selected randomly and the following
data were recorded:
Number of girls in a family
Number of families
2
1
0
475
814
211
Compute the probability of a family, chosen at random having:
(a) 2 girls (b) 1 girl
(c) no girls.
Que.191.Three coins are tossed simultaneously 200 times with the following
frequencies of different outcomes:
Outcome
Frequency
3 heads
2 heads
1 head
No head
23
72
77
28
Find the probability of getting:
(i) 3 heads (ii) at least two heads (iii) two heads and one tail.
Que.192.Eleven bags of wheat flour, each marked 5 kg. actually contained the
following weights of flour (in kg) :
4.97,5.05,5.03,5.00,5.06,5.08,4.98,5.04,5.07,5.00
Find the probability that any one of these bags chosen at random
contains :
(i) mote than 5 kg
(ii) equal to 5 kg
(iii) less than 5 kg of flour.
Que.193.The ages (in years) of workers of a factory are as follows:
Age (in years)
Number of workers
10-19
20-29
30-39
40-49
50-59
60 and above
5
40
26
15
8
6
If a worker is selected at random, find the probability that the worker is:
(i) 30 years or more
(ii) below 50 years
(iii) having age from 10-19 years.
Que.194.The weekly pocket expenses of students are given in the following table:
Pocket expenses (in Rs)
145
140
159
171
158
147
165
Number of students
7
4
10
6
3
8
12
Find the probability that the weekly pocket money of a student is:
(a) Rs 159 (b) more than Rx 159 (C) less than Rs 159
Que.195.The percentage of marks obtained by a student in monthy unit test are
given below:
Unit test
% of marks
I
II
III
IV
V
70
72
65
68
85
Find the probability that the student gets:
(a) more than 70% marks
(b) more than 90% marks
Que.196.The following frequency distribution table gives the weights of 38
students of a class:
Weight in kg
30-35
35-40
40-45
45-50
50-55
55-60
Total
Number of students
10
5
15
5
1
2
38
Find the probability that the weight of a student is:
(i) more than or equal to 45 kg
(ii) less than 30 kg
(iii) more than or equal to 30 kg but less than 60 kg.