MATHEMATICS QUESTION BANK
CLASS IX
(Q.1) Given, 3x + 5y =11. Find the value of y in terms of x.
(Q.2) If x = 3 and 3x + 2y =11, find the value of y.
(Q.3) Find the value of x by the method of elimination: x + 3y =12 & 2x - 3y = 9
(Q.4) If x = -1 and y = 3 is the solution of the equation 7x + 4Py = 3P, then find P.
(Q.5) The ratio between a two-digit number and the sum of the digits of that number is
4:1. If the digit in the units place is 3 more than the digit in the tens place, then form a
system of linear equations to represent the relation between the digits.
(Q.6) The sum of the digits of a two-digit number is 8. If the digits are reversed, the
number is decreased by 54. Form a system of linear equations to represent the relation
between the digits.
(Q.7) Find the value of x by the method of elimination: 2x + y =1 & x + y = 9.
(Q.8) A collection of 105 coins consists of 1.00 coins and 5.00 coins. Find the number
of 5.00 coins in the collection if the total value is 205.00.
(Q.9) 4 chairs and 3 tables cost Rs. 21,000 and 5 chairs and 2 tables cost Rs.17,500.
Find the cost of a chair and a table, separately.
Q.10) A man starts his job with a certain monthly salary and earns a fixed increment
every year. If his salary was 15,000 after 4 years of service and 18,000 after 10 years of
service, what was his starting salary and what is the annual increment?
Q.11 Find the value of x, if log10 𝑥 + 5 = log10 10.
Q.12 Evaluate the following without using tables: 2log4 – 3log2.
Q.13 If log10 3 = a and log10 2 = b; express loglog10 12 in terms of a and b.
Q.14 If log(a + 1) = log( 4a – 5) – log3; find a.
(Q.15) Factorise 4x2-9.
(Q.16) Factorise 27y3-8.
(Q.17) Factorise 125z3+64.
(Q.18) Factorise 2a(x+2y)-3b(x+2y).
(Q19) Factorise a2+b2-4c2-2ab.
(Q.20) Factorise x2-2x-15.
(Q.21) Factorise 4x2-12x-7.
(Q.22) Factorise 5(a+b)2-6(a+b)-8.
(Q.23) Factorise 64z3+125.
(Q.24) Using the given table, find the following:
Class
Frequency
28 – 32
8
33 – 37
5
38 – 42
14
43 – 47
12
48 – 52
7
53 – 57
5
58 – 62
9
(i) upper and lower limits of fifth class.
(ii) true class limits of the fifth class
(iii) class boundaries of the third class
(iv) Class mark of the fourth class.
Q.25 Using class intervals 0 – 3, 4 – 7, 8 – 11, … construct the frequency distribution
for the following data: 13, 6, 10, 5, 11, 14, 2, 8, 15, 16, 9, 8, 14, 20, 16, 17, 11, 19, 5, 7,
12, 20, 21, 18, 1, 8.
Q.26 The class-marks of a distribution are 26,31,36,41,46,51,56,61,66,71 find the true
class limits.
Q.27 The weight of new born babies (in kg) in a hospital on a particular day is follows.
2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4
1. Determine the range.
2. How many babies weight is below 2.5kg?
3. How many babies weight is more than 2.8kg?
Q.28 The electric bills of 50 houses is given below:
146 210 315 120 108 129 114 216 232 251 328 524 152 614 736 668 335 329
324 468 762 185 349 495 728 754 675 449 286 564 632 624 766 369 267 669
450 652 255 275 418 617 826 523 746 643 441 512 152 213
(i) Taking a class interval of size 50, construct a frequency as well as
cumulative frequency table for the given data.
(ii) Which class has the largest frequency?
(Q.29) The monthly profits (in Rs.) of 100 shops are distributed as follows:
Profit per shop
No. of shops
0 – 50
12
50 –100
18
100 – 150
27
150 – 200
20
200 – 250
17
250 – 300
06
Draw a histrogram for the data and show frequency polygon also.
(Q.30) If the mean of observations x, (x+3), (x+5), (x+7) and (x+9) is 11, find value of x.
(Q.31) The mean of 15 observations is 32. Find the resulting mean, if each observation
is decreased by 7.
(Q.32) The mean of 40 observations was 160. It was detected that the value of 165 was
wrongly copied as 125. Find the correct mean.
(Q.33) The mean of 90 observations was found to be 30. If two observations were
wrongly taken as 32 and 12 instead of 23 and 11, find the correct mean.
(Q.34) Find mean of all factors of 21.
(Q.35) Find mean of prime factors of 144.
(Q.36) Find the value of x, if the median of given data is 31.
18, 25, 27, 30, x, 33, 36, 37, 39 and 40.
(Q.37) The data given has been arranged in ascending order 37, 53, 55, x, (x+2), 77, 83
and 100. If their median is 65, find the value of x.
(Q.38) Express 0.36363636 as a vulgar fraction.
(Q.39) ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal
sides AC and AB respectively. Show that these altitudes are equal
(Q.40) Show that in a right angled triangle, the hypotenuse is the longest side.
(Q.41) ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB,
BC, CD and DA. AC is a diagonal.
Show that :
(i) SR || AC and SR =
𝟏
𝟐
AC
(ii) PQ = SR
(iii) PQRS is a parallelogram.
(Q.42) ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC,
CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.
(Q.43) ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD
and DA respectively. Show that the quadrilateral PQRS is a rhombus.
(Q.44) ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point
of AD. A line is drawn through E parallel to AB intersecting BC at F. Show that F is
the mid-point of BC.
(Q.45) In a parallelogram ABCD, E and F are the mid-points of sides AB and CD
respectively. Show that the line segments AF and EC trisect the diagonal BD.
(Q.46) Show that the line segments joining the mid-points of the opposite sides of a
quadrilateral bisect each other.
(Q.47) ABC is a triangle right angled at C. A line through the mid-point M of
hypotenuse AB and parallel to BC intersects AC at D.
Show that
(i)
D is the mid-point of AC
𝟏
(ii)
(ii) CM = MA = AB
𝟐
(Q.48) Simplify the following:
(i)√ 45 – 3√20 +4√5
(iii)
(Q.49) If
3
8
7+ 5
7− 5
(Q,50) If x =
+
-
(ii)
1
7+ 5
9 +4 5
9 −4 5
=a+
7
11
and y =
3
81 - 8 216
(iv)
2
7− 5
4
24
8
+
54
9
5 b , find the values of a and b.
9− 4 5
9+4 5
, find the value of x2 + y2
5
+ 15 32
225