1. No category

JMMC RAMANUJAN MEMORIAL MTSE SAMPLE QUESTIONS
Class IX
CLASS - IX
1.
What is the value of
a)
c)
2.
3.
4.
1  1  1 ?
a  bc b  ca c  ab
a)
-2
-1
c)
0
d)
a)
(a2  b2) + (2ab)2
b)
(a2 + b2) – (2ab)2
c)
(a2  b2) + (2ab)2
d)
None of these.
1
Ratio of two numbers is 4 : 3 and the difference between the square of this two numbers is 28. Numbers are8,6
b)
8,6 ; -8,-6
c)
-8,-6
d)
None of these.
3
d)
4
a  2b = 5 and a2 + 4b2 = 37, then ab = ?
1
b)
2
What is the relation between
c)
8.
b)
Express (a2 + b2)2 as a sum of three square number :-
a)
7.
undefined
None of these.
then
a)
6.
b)
d)
If a + b + c = 1, ab + bc + ca = 2 and abc = 3
a)
5.
0
(a) or (b)
a
?
0


 
3  
c)

 
5 3 &

2
6 2

5 3 
6 2
b)

 
5
6
d)
None of these.
5 3 
6 2

What is the equation of parallel axis of x axis ?
a)
x =a, where a is constant
b) y = b where b in comtent
c)
x = a, y = a where a in constant d) None of these.
In the adjoining figure, DE | | BC Given AD = 3cm, DB = 5cm and AC = 4.8cm then AE = ?
a)
3.8cm
b)
2.8cm
c)
1.8cm
d)
0.8cm
A
D
E
B
C
9. O is a point inside ΔABC , then which of the followings is /are correct ?
10.
a)
2(OA + OB + OC) = (AB + BC + AC)
b)
2(OA + OB + OC) < (AB + BC + AC)
c)
2(OA + OB + OC) > (AB + BC + AC) d)
None of these.
Arrange in increasing order______
(3 : 5),(4 : 9),(5 : 11) and (9 : 13)
a)
b)
c)
d)
11.
(3 : 5) > (4 : 9) > (5 : 11) > (9 : 13)
(4 : 9) < (3 : 5) < (9 : 13) < (5 : 11)
(9 : 13) > (3 : 5) > (5 : 11) > (4 : 9)
(4 : 9) < (5 : 11) < (3 : 5) < (9 : 13)
If (a + b) : (a - b ) = 1 : 5, then (a2 - b2) : (a2 + b2 ) = ?
a)
2:3
b)
3:2
c)
5 : 13
d)
13 : 5
JMMC RAMANUJAN MEMORIAL MTSE SAMPLE QUESTIONS
Class IX
12.
In a filled container ther is 3 parts of water and 1 part of milk mixed together. What part of the mixture is replaced with that
part of milk so that the content of milk and water is equal in the container ?
a)
13.
14.
1
c)
2
d)
3
a

 cm
2 1

4a
b)

 cm
2 1

c)
4a

 cm
2 1

35%
b)
40%
c)
45%
d)
50%
9BC2 = 8CF2  8BE2 + 4AD2
9BC2 = 8CF2 + 8BE2 + 4AD2
9BC2 = 8CF2 + 8BE2  4AD2
None of these.
5
b)
7
c)
9
d) None of these.
Given 2A = 3B = 4C, then A : B : C = ?
2:3:4
b)
4:3:2
c) 6 : 4 : 3
d) 3 : 4 : 2
a 5  a 4  7 a 3  5a 2  a  ?
120 12 24 12 5
a
a)
(a + 1)(a + 2)(a + 4)(a + 5)
120
b)
a
(a + 1)(a + 2)(a + 3)(a + 4)
120
c)
a
(a + 1)(a + 3)(a + 4)(a + 5)
120
d)
21.
b)
By adding what value to 3 : 5 will it become 5 : 6 ?
a)
20.
0
AD,BE and CF are three medians of ΔABC . Which one is correct ?
a)
19.
None of these.
d)
None of these.
In an exam, 72% and 78% of examinees passed in mathematies and Bengali. If no examinees have failed in both the subjects
then what percentage of the examinees passed in both the subject ?
a)
b)
c)
d)
18.
d)
Difference between in-circle and circum-circle of a square is a cm. Find perimeter of that square ? (circum-circle goes
through the 4 vertices of the square)
a)
17.
1
part
6
c)
1
1
2x
+
=?
1+ x + x 2 1- x + x 2 1+ x 2 + x 4
a)
16.
1
part
4
b)
A(-3, 2), B(p, q) and C(–4, –3) are three vertices of an isosceles triangle. Which of the following is/are correct when AB = BC.
a)
p=1+q
b) p + q = 1
c) p = q
d) None of these.
a)
15.
1
3 part
None of these.
Chord of a circle with radius 14cm makes a right-angle with the centre of the circle. Find area of the shaded region.
O
A
a)
56cm2
B
b)
60cm2
c) 68cm2
d)
None of these.
JMMC RAMANUJAN MEMORIAL MTSE SAMPLE QUESTIONS
Class IX
Find G.C.M (22-33)
22.
2x2  x  1 & 4x2 + 8x + 3
a)
23.
(2x  1)
b)
(2x + 1)
c) 2x
d)
x  y
c) x2  y2
None of these.
(x4 - y4) & (x6  y6)
a)
x+y
b)
d)
None of these.
24.
If ab + bc + ca = 0, then find H.C.F of (a + b + c) and a + b + c3  3abc
a)
(a + b + c)
b) (a + b + c)2
3
c)
(a + b + c)
d) None of these.
25.
If (x  4) is the H.C.F of x2  x  12 and x2  mx  8 then m = ?
a)
0
b) 2
c) 4
d) None of these.
26.
H.C.F. and L.C.M of two expressions are (x + 3) and m3  7x + 6 respectively. If one of the expression is (x2 + 2x  3) then
the other expression is________
a)
x2 + x + 6
b) x2 + 2x + 6
2
c)
x  2x + 6
d) x2 + x – 6
27.
L.C.M of (a6  1),(a2  m)2 & a4 + a2 + 1 is (a + 1)2 (a –1)2 (a2 + a +1) (a2  a + 1), then m = ?
3
a)
28.
29.
2
b)
3
c)
3
1
d)
3
None of these.
Factorise- x3 + 7x2  21x  27
a)
(x + 1)(x + 9)(x  3) b)
(x  3)(x + 1)(x  2)
c)
d)
(x  3)(x2 + 3x – 7)
1
1
(x  3)(x2 + 2x + 7)
1
Given, a + b + c = 0 ( a  b)(b  c )   a  c  b  a    c  a  c  b   ?
a)
0
b) 1
c) 2
d)
None of these.
30.
Express (x + 1)(x + 2)(x + 6)(x + 7) + (x + 4) as a square number.
a)
(x2 + 8x +10)
b) (x2 + 8x  10)
c)
(x2 + 8x +10)2
d) (x2 + 8x  10)2
31.
(x  a) (x  b) (x  c)................(x  z) = ?
2
a)
32.
0
b)
1
c) x26 + abc...z....
d) None of these.
If A= {a,b}, B = {c,d}and A  B = {(a, c),(a, d),(b, c),(b, d)}then find A  B when A = {3, 5},
B = {5, 7}  a  b  c  d 
33.
a)
{(3,5),(3,7),(5,5),(7,5)}
b)
{(3,5),(3,7),(7,5),(5,5)}
c)
{(3,5),(3,7),(5,5),(5,7)}
d)
{(5,3),(5,5),(7,3),(7,5)}
In figure- 1, shaded region is A  B . Then what will be the shaded region in figure –2 ?
A
a)
34.
A
B
A+B
b)
A  B   A  B
c)
A  B   A  B
d) None of these.
What is the lowest value of (x  1)(x  3)(x  4)(x  6) + 10 ?
a)
35.
B
10
b)
3
c)
1
d)
–5
The ratio of the sum of the ages of father and mother to that of their two sons are 24 : 3 : 1. Elder brother is 6 year older than
younger brother. The ratio age of father & mother is 2 : 4. Then what is the age of two sons, father & mother ?
a)
Father - 40, Mother -32, elder brother-9, younger brother-2
b) F-38, M-34, EB-8, YB-3
c)
F-40, M-32, EB-9, YB-3
d) None of these.
JMMC RAMANUJAN MEMORIAL MTSE SAMPLE QUESTIONS
Class IX
36.
Solve :a)
x  a  x  b  x  3a  3b  0
b
a
ab
x=a
b)
x=b
c) x = a-b
d)
x=a+b
Passage for question number 37 to 41.
x  y expresses both the parts of x and y (excluding all repeatations) and x  y expresses the common parts between both
x and y.
If A = {1,2,3,4}, B = {2,5,7}, C ={1,2,9,11} the answeer the following
37.
 A  B  C  ?
a)
38.
39.
40.
c)
AB C
d)
None of these.
AB C  ?
 A  B   A  C 
a)
A B C
b)
c)
 A  B   A  C 
d)
None of these.
 A  B C
A   B  C  =?
a)
A B C
b)
c)
 A  B   A  C 
d)
None of these.
A B  ?
a)
41.
b) A  C
A B
b)
B A
B A
c)
A
d)
{1}
c)
{2}
d) None of these.
c)
0
d) None of these.
B
AC  ?
a)
{1,2}
b)
42.
For what value of n, O is undefined
a)
2
b)
-1
43.
For which condition (a – b)2 + (b  c)2 + (c  a)2 = 0
a)
a – b = 0,b – c = 0,c – a =0
b) a =b = c
c)
(a) and (b) both are correct
d) None of these.
44.
Express 4(2p + q)(p + 2q) as the difference of two square-
n
a)
c)
45.
2
1
b)
22
9
c)
23
9
d) None of these.
12 1 %
3
b)
12 2 %
3
c)
12 3 %
4
d)
12 1 %
2
In mixed ore the ratio of copper, xinc, and nickel is 4 : 3 : 5. What is the percentage of zinc.
a)
48.
22
7
(3p  3q)  (p  q)2
(3p + 3q)  (p  q)2
The ratio of principal and annual amout is 8 : 9. The annual rate of interest is a)
47.
3
b)
d)


2
If x  3  x   x ,then find x  2 ?
x


a)
46.
(3p + 3q)2 + (p  q)2
(3p + 3q)2  (p + q)2
24%
b)
25%
c)
26%
d)
27%
In a mathematics exam in the first paper a student scored 30% out of 180. What percentage should he score in the second
paper of 150 marks so that he score 50% in the overall.
a)
111
b)
113
c)
115
d)
117
JMMC RAMANUJAN MEMORIAL MTSE SAMPLE QUESTIONS
Class IX
49.
Two circles passes through the centre of both the each other, O and Q are the centre of two circles. Find the area of the shaded
portion if OQ = a cm.
O
50.
a)
22  7 3 sq.cm
7
b)
c)
22  7 3 sq.cm
7
d)
n
n
i
s
b
s

o
s
c
e
l
e
s
t
r
i
a
n

2 1
g
l
e
h
e
b2
b)
4
t
v
e

r
t
i
c
a
l
a
n
g

2 1
l
e
i
c)
4
s
4
5
b2
and the base is b, the area is -


2 1
4
d) None of these.
s(s + x)
b) s(s  x)
c) s2  x
d) None of these.
Centroid
incentre
b) Centre of gravity
d) None of these.
In a triangle ABC the three medians interesects at D, if E and F are mid points of BD and CD respectively the DEF
a)
54.
a
The point of intersection of three median of three sides of a triangle is called
a)
c)
53.
None of these.
In an equilateral triangle, semiperimeter is S and if the hypotenulse is x then the area of the triangle is a)
52.
22  7 3 sq.cm
28
0
I
a)
51.
Q
1 ΔABC
11
1 ΔABC
9
b)
c)
1 ΔABC
13
The ratio of areas of an equilateral triangle and a square is
d)
1 ΔABC
12
3 : 2 . The diagonal of a square is 60cm, then the perimeter of
the triangle isa)
55.
56.
172cm
d)
192cm.
b)
Equilateral triangle
c)
Isosceles triangle
d)
Impossible to determine.
In an isosceles triangle which of the following conditions holds:It can be acute angled triangel
it can be obtuse angled triangle
b)
d)
It can be right angle triangle
(a), (b) & (c)all are correct.
In a triangle if two angles are equal then the triangle isIsosceles
b)
equilateral
c) right angled
d) scalene
The lenght of a diagonal of a rhombus is twice the other. The area of the rhombus is 64 sq cm. Find the length of the
diagonals.
9cm, 18cm
b)
8cm, 16cm c) 7cm, 14cm
d) 6cm, 12cm
In a trapezium the length of the parallel sides are 16cm & 12cm. If the distance between them be 10cm find the are of the
trapezium.
a)
60.
c)
Right angled triangle
a)
59.
180cm
a)
a)
58.
b)
If an angle of a triangle is equal to the sum of other two angles then the triangle is-
a)
c)
57.
168cm
140sqcm
Factoirse : ––
b)
142sq cm
c)
144sq cm d) None of these.
a2b2  a2  b2 + 1
a)
(b + 1)(b  1)(a  1)2
b)
(b2  1)(a2  1)
c)
(b2  1)(a  1)
d)
None of these.