9th 2022-2023 IPM Final Paper
1) If 2��+3
2��−1=2��−1
3��+1, then find value of (1/x)
a) 8
b) -8
c) -3/8
d) -8/3
2) The LCM and HCF of two polynomials is (��3 +6��2 − ��− 30) and (��− 2) respectively. If
one of the polynomials is (��2 + 3��− 10). Find the other polynomial
a) (��2 + ��− 6)
b) (2��2 + 3��−6)
c) (��2 − 3��+6)
d) (��2 + 2��−6)
3) In the given figure, if C is the centre of the circle and angle MNC = 25 oand angle MPC = 15o.
Find measure angle of PCN =?
a) 75o
b) 60o
c) 120o
d) 80o
2
2
4) Find the value of a +b , if 2��−3��= 12 and 5��+7��= 1. (b≠0)
a) 9.75
b) 9.50
c) 9.25
d) 8.50
5) Find the product of the root of the given quadratic equation:
(2x+3) (x-4) + (2x+3) (x-5) = 0
a) -7.5
b) -3.5
c) -9.5
d) -8
6) State the test of congruence by which the given triangles are congruent:
a) H-S
b) SAS
c) ASA
d) SSS
7) Reduce to lowest form: ��3−19��+30
��2−3��−40
a) (��−2)(��−3)
(��+8)
b) (��+2)(��+3)
(��+8)
c) (��+2)
(��2+2��+4)
d) (��−2)(��−3)
(��−8)
8) XY is drawn parallel to the base BC of triangle ABC, cutting AB at X and AC at Y. If
AB=5BX, and YC=3cm, then AY=?
a) 12cm
b) 8cm
c) 15cm
d) None of these
9) Raunak’s age is five times the age of Shail. Fifteen years hence, Raunak’s age will be 2.5
times than Shail. Find present age of Raunak?
a) 60 years
b) 45 years
c) 50 years
d) None of these
10) On of the factors of ��4 + ��2��2 +��4 is:
a) ��2 −��2
b) ��2 −��2 − ����
c) (��+ ��)2
d) ��2 +��2 − ����
11) If ��+1��= 2, then find
a) 4
b) 3
c) 1
d) None of these
��7 +1��7=?
3, ��= √5
2��������= √8
12) Arrange the given surds in Descending order: ��= √6
4
a) A, B, C
b) C, A, B
c) B, C, A
d) None of these
13) Simplify: ������135+ ������16
26− ������32
60=?
a) log 4
b) log 3
c) log 5
d) log 6
14) If (x-1) and (x-2) are factors of ��3 + ����2 + ����− 2. Then the value of
a2+b2=? a) 41
b) 25
c) 34
d) 61
15) If the product of two consecutive off natural numbers is 483. Then which of the
following is a multiple of the greater number?
a) 126
b) 231
c) 161
d) 210
16) The ratio of the interior angle to the exterior angle of a regular polygon is 8:1. If the
side of the polygon is 12cm. Find the perimeter of the polygon.
a) 228cm
b) 180cm
c) 240cm
d) 216 cm
17) What will be the angle between the hour hand and the minute hand at 4:33am? a)
57.5o
b) 61.5o
c) 71o
d) 68.5o
18) Find the square root of: 15+ 4√14.
a) (√6+ √9)
b) (√7+ √8)
c) None of these
d) (√5+ √3)
19) If Q=60o, find the value of tan��
sin��+tan (90−��)
sin��=?
a) 7/3
b) 8/3
c) 1/3
d) √2/3
20) The area of a rhombus is 720 sq.cm. If one of its diagonal is 18cm, find the perimeter of the
rhombus?
a) 164 cm
b) 72 cm
c) 144 cm
d) 176 cm
21) The quadrilateral formed by four angle bisectors of a parallelogram is:
a) Trapezium
b) Square
c) Rectangle
d) Rhombus
22) If 7 tan ��= 4, find the value of 14 sin ��−3 cos ��
21 sin ��+cos ��
a) 6/7
b) 5/13
c) 7/13
d) 4/5
23) If the side of the square is decreased by 7cm the area decreases by 553 cm.sq. Find
Perimeter of the original square?
a) 184 cm
b) 160 cm
c) 144 cm
d) 172 cm
24)��=3
√8−√11; ��=3
√8+√11Find value of: (x-y)2
a) 32
b) 36
c) 44
d) 54
25) If ������102 = 0.3010 find value of ������10160
a) 2.3010
b) 2.2401
c) 1.2040
d) 2.2040
26) The total number of subsets of the set {1,3,5,7} is?
a) 4
b) 16
c) 32
d) 12
27) Divide Rs.6940 in such a way that Ajinkya gets (2/3)rd of what Nirav gets and Nirav
gets (3/5)th of what Raunak gets. What is share of Ajinkya and Raunak together? a)
Rs.4858
b) Rs.5148
c) Rs.4625
d) Rs.3470
28) If 2����������× ��������25 = 3 find value of a.
a) k3
b) 243
c) √125
d) None of these
29) The ratio of the complementary angle to the supplementary angle of a given angle is 3:8.
Find ratio of the angle to its supplementary angle?
a) 2:5
b) 1:4
c) 1:3
d) 3:5
30) If (P+2Q) = 45, find the value of ��5+2��3+2��5+��3=?
a) 24
b) 27
c) 18
d) 30
31) Find the value 4������260 + 3������245 − 3������230
a) 0.5
b) 0.25
c) 0.33
d) 0.75
32) ABCD is an isosceles trapezium. ∠��= 74.5��. Which of the following shows all the angles
of ABCD.
a) 74.5o, 105.5o, 74.5o, 105.5o
b) 74.5o, 115.5o, 74.5o, 115.5o
c) 65.5o, 105.5o, 65.5o, 105.5o
d) None of these
33) In a class of 94 students 56 students like Maths and 48 students like English. Find how
many students like Maths as well as English?
a) 14
b) 8
c) 12
d) 10
34) 14x + 6y = 168; 6x + 14y = 152. Find value of y3-x3
a) None of these
b) -426
c) -512
d) 386
35) What is the cardinal number of the following set:
A= {x:x is a natural three digit multiple of 16}
a) 64
b) 62
c) 56
d) 58
36) A box contains a collection of triangular and square tiles. There are 49 tiles in the box
containing 175 edges in all. How many more square tiles are there than triangular tiles? a) 4
b) 8
c) 6
d) 7
37) Find x if (x-4), (x+28), (2x-6) & (5x-4) are in proportion.
a) 15
b) 14
c) 16
d) 12
38) Given that n(Q) = 148, n(C) = 107 and n(Q∪C) = 126 find n(Q∩C) =? a)
139
b) 131
c) None of these
d) 119
39) When ��3 + ����2 − 2��− 19 is divided by (x-2), the remainder is 5. Find the value
of a a) 4
b) 3
c) 5
d) 2
40) A regular pentagon has side as shown in figure. Find the value of c+d? given that b=2a-1
a) None of these
b) 4
c) 3
d) 6