MATHS ASSIGNMENT
CLASS : IX
TERM : II
LINEAR EQUATIONS IN TWO VARIABLES:
Q1. If one is added to numerator & 4 is subtracted from denominator, the fraction becomes 1. Represent the
statement as a linear equation in two variables.
Q2. Write L.E. 3x + 2y = 18 in the form of ax + by + c = 0. Also, write the values of a, b & c. Are (4,3) & (1,2)
solutions of this equation?
Q3. Find the value of k so that x=1, y= -1 is a solution of 2x + ky = 19. Find two more solutions of the
resulting equation.
Q4. ABCD is a square. Coordinates of A & C are (-1, -1) & (1, 1) respectively. Write the coordinates of B &
D. Also write the equations of all the sides of the square.
Q5. Plot A(3, 0), B(0, 2), C(-3, 0) & D(0, -2) on a graph. Join A to B, B to C, C to D & D to A to form a
quadrilateral ABCD. Is ABCD a rhombus? Also, write the equations of AC & BD.
QUADRILATERALS
Q6. What is the mean of the perimeters of two sqares having sides x & y units.
Q7. Two sides DA & BC of quad. ABCD produced as shown in the given figure. show that m + n = x + y.
Q8. In a triangle ABC, median AD is produced to a point P such that AD = DP.
Q
Prove that ABPC is a parallelogram.
D m
Q9. In parallelogram ABCD, the bisector of angle C meets AD at E. CE & BA
C
n
A
are produced to meet at F. Prove that BC = BF.
B
x
Q10. ABCD is a parallelogram. If the bisectors DP & CP of angles D & C respectively meet at P on side AB,
then show that P is the of side AB.
Q11. Triangle PQR is right angled at Q. A & B are the mid-points of sides PQ & PR respectively. If PQ =
10cm & PR = 26cm, then find the length of AB.
Q12. In triangle ABC, A= 600,  B = 700 & C = 500. Points D, E & F are the mid-points of the sides BC,
AC & AB respectively. Find the measures of the angles of the triangle formed by joining by the mid-points of
the sides of triangle ABC.
P
T
Q
Q13. In the given fig., P &Q are two points which lie on the same side of
line XY. PS  XY & t is the mid-point of the line segment PQ.
Prove that TS = TR.
X
S
N
R
Y
SURFACE AREA & VOLUMES
Q14. Two cubes each of 5cm edge are joined end to end. Find the surface area of the resulting cuboid.
Q15. There is a solid cube which has been cut into cuboids of equal volumes. Find the ratio of the total surface
area of one cuboids to that of the given cube.
Q16.The dimensions of a rectangular box are in the ratio 2:3:4 & the difference between the cost of covering it
with paper at the rate of Rs.8 & Rs. 9.50 per m2 is Rs. 1248. Find the dimensions of the box.
Q17. Two cylinders have same lateral surface area. Their radii are in the ratio 3:2. Find the ratio of height of
first cylinder to that of second cylinder.
Q18. Find the ratio of curved surface areas of two cones, if their diameters of the bases are equal & slant
heights are in the ratio 4:3.
Q19.Find the percentage decrease in the C.S.A. of a sphere, if its diameters decreased by 25%.
Q20. The volume of a cube is numerically equal to its surface area. Find the length of its edge.
Q21.The diagonal of a cube is √12 cm. Find its volume.
Q22. A cuboidal water tank is 8m long, 4m wide & 7m deep. How many litres of water can it hold?
Q23. A cuboidal tank can hold 50,000 litres of water. If the length &depth of tank are 250cm &10m
respectively, find the breadth of the tank.
Q24. A cubical tank whose side is 2m is filled with water. The water from cubical tank is shifted to a cuboidal
tank whose length, breadth & height are 250cm, 200cm & 2m respectively. Find the depth of the tank which
will remain empty.
Q25. A metallic box is in the shape of a solid cuboid having dimensions 200 x 50 x 100 cm. It is recast into a
solid cube. Find the difference of surface areas of two solids.
Q26. A box with a lid is made of 2cm thick wood. Its external dimensions are 25x 18 x15 cm. How many
cubic cm of ice can be placed in it? Also, find the volume of wood used in the box.
Q27. Water flowing at the rate of 15km/hr through a cylindrical pipe of radius 7cm into a rectangular tank
which is 50 m long &44m wide. In how many hours will the water level in the tank raise by 21cm?
Q28. The ratio of T,S.A. to the C.S.A. of a cylinder is 3:2.Find the volume, if its T.S.A. is 14784cm2.
Q29. The height, C.S.A. & volume of a cone are h, c & V respectively. Prove that 3πVh3 - c2h2 + 9V2 = 0.
Q30. A cne, a hemisphere & a cylinder stand on equal bases &have the same height. Find the ratio of their
volumes.
STATISTICS
Q31. Find the mean of first seven even natural numbers.
Q32. For the given data: 11, 15, 17, y+1, 19, y-2, 3; if the mean is 14. Find the value of y.
Q33. Find the mean of all the prime numbers lying between 20 & 30.
Q34. Find the median of first 11 multiples 0f 8.
Q35. Mean of 36 term is 12. One term 47 was misread as 74. Find the correct mean.
Q36. The mean age of 3 students is 21 years. If the ratio of their ages is 2:3:4, then find the age of the students.
Q37. The mean of a, b, c, d &e is 28. If the mean of a, c & e is 24. Find the mean of b & d.
Q38. The mean of seven numbers is 24. If out of these seven numbers, the mean of first four numbers is 23 &
the mean of last four numbers is 25.5, then find the fourth number.
X 5 6 7
8 9
Q39.calculate the mean of the given frequency distribution:
F 4 8 14
11 3
Q40.Find the mean & median of first ten prime numbers.
Q41. Find the mean &median of aii the factors of 108.
Q42. The mean of 200 items was 50. Later on, it was discovered that the two items were misread as 92 & 8
instead 0f 192 & 88. Find the correct mean.
xi
fi
Q43. The mean of the following distribution is 50. Find the value of p.
10
17
30
50
5p+3 32
70
7p-11
90
19
Q44. The following observations have been arranged in the ascending order : 29, 32,48,50,x-2, x, 72, 78, 84,
95.If the median of the data is 65, find the value of x &hence the mean of the data.
PROPBABILITY
Q45.In a kitchen , there are 54 utensils, consisting of bowls, plates & glasses. The ratio of bowls , plates &
glasses is 3:1:2. A utensil is picked at random. Find the probability that a) It is a plate b) It is not a bowl .
Q46.The following table gives the distance (in km0 that 40 students of s class have to travel from their
residences to their school. Find the probabilitythat randomly choosen student lives at a distance of:
Distance (in km)
No. of students
a) more than 35 km
b) atleast 25km
0-5
5
5-10
11
10-15
11
15-20
9
20-25
1
c) 15-25 km
25-30
1
30-35
2
d) 10-15 km
Q47. 1500 family with 2 children were selected randomly & the following data were recorded:
No. of girls in family
2
1
0
No. of family
475 814
211
Compute the probability of a family chosen at random having a) atmost 1 girl
CIRCLES
A
Q48. In fig. , O is the centre of the circle of radius 5cm.
If OP AB, OQ CD, AB॥ CD, AB = 6cm & CD = 8cm, Determine PQ
b) atleast 2 girls.
P
B
O
C
Q
D
Q49. Two congruent circles intersect each other at points A & B. Through A, a line segment PAQ is drawn so
that P & Q lie on the two circles. Prove that BP = BQ.
Q50. If two sides of a cyclic quadrilateral are parallel, prove that the remaining two sides are equal & diagonals
are also equal.
Q51. AC & BD are chords of a circle which bisect each other. Prove that i) AC & BD are diameters ii) ABCD
is a rectangle
A.
Q52. In fig, chord AB of a circle with centre O,is produced to C
such that BC = OB . CO is joined & produced to meet the circle at D.
If ACD = y &  AOD = x, show that x = 3y.
B
D
O
C
Q53.Two circles whose centres are O & O' intersect at P. Through P, a line l parallel to OO' intersecting the
circles at C & D Prove that CD = 2OO'.
A
Q54.In fig., AB is a diameter of the circle, CD is a chord equal
to the radius of the circle. AC & BC when extended intersect
at a point E. Prove that AEB = 600.
Q55.
B
C
D
A
C
O
E
In the fig., O is the centre &
E
AEC = 500 , then find i) CBE
B
D
AE is the diameter of the semi-circle ABCDE. If AB = BC &
ii) CDE
iii) AOB. Prove that BO॥CE.
Q56. The bisectors of the opposite A &C of a cyclic
quadrilateral ABCD intersect the circle at the points E & F,
respectively. Prove that EF is a diameter of the circle.
A
B
F
D
E
C
AREAS OF PARALLELOGRAMS & TRIANGLES
Q57.Diagonals AC & BD of a quadrilateral ABCD intersect at O in such a way that ar(AOD)=ar (BOC).
Prove that ABCD is a trapezium.
Q58. D is the mid-point of side BC of ABC & E is the mid-point of BD. If O is the mid-point of AE. then
1
prove that ar(BOE) = 8 ar(ABC).
Q59. In ABC, P & Q are respectively the mid-points of AB & BC and R is the mid-point of AP. Prove that
ar(PBQ) = ar(ARC).
Q60. O is any point on the diagonal BD of the parallelogram ABCD. Prove that ar(OAB) = ar(OBC).