A.I.M.
Ed Maths Scholarship Eligibility Test-2017 Class IX
Class IX
2
x2 y 2 z 2
1. If x + y + z = 0 then ______
yz zx xy
1) 1 2) 0 3) 9 4) 3
2. Number of positive integer pairs (a, b) satisfying 2a + b = 8
1) 2 2) 3 3) 4 4) Infinity
3. In an equilateral triangle semi perimeter is equal to 1 + h. Where h is height of the triangle.
Then the side of the triangle must be____
3 2 1 2
1)1 2) 3) 3 4)
3 3 1 3 3 3 1
1 1 1
4. a a 1 a 1 a 2 a 2 a 3 ...........100 terms =______when a=2
45 25 101 41
1) 2) 3) 4)
91 51 198 95
5. Number of perfect square numbers in first 1000 natural numbers is x. Number of perfect
x y2
4th powers in the same set of 1000 natural numbers is y, then ____
x 3 y 10
1) 2 2) 3 3) 0 4) 1
6. Number of right angled triangles having sides in the ratio 3 : 4 : 5 is______
1) 1 2) 3 3) 9 4) infinity
7. If x x x...... x x x ...... then x = ______
1) 1 2) 2 3) 3 4) 4
8. Number of whole number triplets (x,y,z) satisfying x 2 y 3 z 5 0 is___
1) 0 2) 1 3) 3 4) infinity
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A.I.M.Ed Maths Scholarship Eligibility Test-2017 Class IX
9. Number of parallelograms formed when 4 parallel lines are cut by another set of three
parallel lines is_____
1)18 2)12 3)24 4)36
10. x 3 2, xy 1 Then x 4 y 4 _________
1)194 2)204 3)196 4)198
11. 2 2 2 ....... ________
1)2 2)1 3) 2 4) 4 2
12. If ax 2 bx c and bx 2 ax c have a common factor x 1 then ____
1) a = b and c 0 2) a = b and c = 0
3) a b and c = 0 4) None
13. If 5 x 3 y 8 0 has a solution (2k 1, k ) then k =_____
1) 1 2) 2 3) 3 4) -1
2
14. 2 x 2 3 y 2 7 , 3 x 2 2 y 2 3 then x y 2 xy =_______
1)2 2)3 3)7 4)5
2 2 1
15. If x 6 x 1 0 then x _____
x2
1)30 2)34 3)63 4)64
16. ________ was born on March 14th, 1879.
1) Archimedice 2) Rene Descartes
3) Albert Einstein 4) Pythogarus
A B
17. The adjascent figure AB|| CD, CD|| EF and X
y : z = 3:7 then x + y - z = C Y D
1) 720 2) 540 Z
E F
3) 126 0 4) 0 0
18. If (a+1) (b+1) (c+1)=24 then (a-1) (b-1) (c-1)=________
1)4 2)7 3)0 4)5
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A.I.M.Ed Maths Scholarship Eligibility Test-2017 Class IX
19. In a ABC a point p is joined to all the three vertices such that area’s of
PAB , PBC and PCA are equal. Number of such points p will be_____
1)1 2)3 3)2 4)0
20. Remainder when x 2 x 1 divides x 4 x 2 1 is R, then R 4 R 2 R 15 is not
divisible by
1)9 2)3 3)5 4)15
21 .The three points 8,5 0, 3 2, 1 always lie on the line _____
1) y + x + 3 = 0 2) -x + y + 3 = 0
3) 2x - y -1 = 0 4) 3x - y = 1
22. In a triangle ABC if an angular bisector of A bisects BC then it is _____ triangle
1) Euqilateral 2) Right angled 3) Isoceles 4) Congruent
23. Who is the first mathematician computed the Value of
1) Euclid 2) Archemedice 3) Bhaskaracharya 4) Ramanujan
1 1
24. If x 2 then x1024 1024 ___
x x
1) 21024 2) 1024 3) 1 4) 2
25. The sides of right angled triangle are connected by x + y + z = 24 and x < y < z are all
natural numbers then the area of triangle must be________
1)12 2)24 3)48 4)72
26 . A rectangle of dimensions l, b ( l > b) satisfing x 2 7 x 12 0 is inscribed in a circle of
area____
1) 6.25 2) 3.75 3)1.25 4) 5
n 3! An3 Bn2 Cn D
27. n ! =1x2x3x........xn then A+B+C+D=_________
n!
1)24 2)36 3)44 4)16
28. 1 x 1 x 2 1 x 4 1 x 8 A is a polynomial of degree 16. Then A can be
1 1 x
1)1 2) 3)1 x 4) 1 x 2
x x2
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A.I.M.Ed Maths Scholarship Eligibility Test-2017 Class IX
29. ABCD is a square of maximum area inscribed in the circle
of radius 7 Then area of shaded region is____(approxmately) D C
1)34 2)56
3)64 4)73
.
30. Co-ordinate Geometry was introduced by ____
1) Archemedice 2) Rene Descartes
3) Pythogarous 4) Euclid A B
31. In the adjecent figure ray OS stands on a line PQ.
Ray OR and ray OT are angle bisectors of V
R S
V
POS and SOQ respectively. Then ROT = _____ T
1) 450 2) 600
P O Q
3) 900 4) 1050
32. In a parallelogram ABCD, the angular bisectors of A and B are interseting at P then
APB =
1) 600 2) 900 3) 450 4) 300
33. Number of real solutions of the equation x 2 2 x 5 is______
1)2 2)4 3)5 4)0
34. Remainder when 5 400 is divided by 62550 is______
1)0 2)1 3)5 4)50
35. The angular bisectors of a parallelogram forms ______
1) Parallelogram 2) Rhombus 3) Rectangle 4) Square
36. The sum of base angle and vertex angle of a golden traiangle is ___
1) 720 2) 360 3) 1080 4) 900
37. Number of primes less than or equal to 99 is______
1)14 2)25 3)11 4)33
-
38. 2 x 2 x 3 x 3x 1 is satisfied by _____(number of values of x)
1) Exactly1 2) Exactly2
3) Almost 4 but atleast 2 4) zero
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A.I.M.Ed Maths Scholarship Eligibility Test-2017 Class IX
39. ABC is a right angled triangle with A as vertex of right angle. If AB = 3, AC = 4, then
length of perpendicular drawn from A on BC must be____units
1)4.2 2)3.6 3)2.4 4)1.8
40. Center of circle which passes through the points (3,4) (-3,4) and (-4,3) is_____
1)(1,1) 2)(0,0) 3)(-2,-3) 4)(-2,-2)
41.(x+1)(x-a)=1 is satisfied by integer values of x. then a2 2a 3 ________
1)1 2)0 3)2 4)-4
ab 2a b
42. 25 5b c 625c a 3125 Then _______
1c
5 6 11
1) 2) 3) 4)1
3 5 4
1 1 1 1 1 1 1 1 1 1
43. 2 2 2 ....... A; ..... B
2
1 2 3 4 2
2017 2018 2
2018 2 2017 2 2 2 12
1 1 1
Then ...... _____
12 22 10092
2A B A B BA
1) 2) 3) 4)2( B - A )
2 2 2
44. Number of orderd integer pairs (x,y) such that x y y x is_____
1)0 2)1 3)3 4)infinite
45. Which is wrong statement?
1)Sum of two prime numbers may be a prime number
2)Product of two prime numbers may be even number
3)Difference of two prime numbers may be a prime number
4)Ratio of two prime numbers may be an integer
2 2
46. If p2 1 q2 Then 3 p 4 p3 4q2 3 q2
1)0 2) 2 p 2 q 2 3)1 4) p3 q3 p2q
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A.I.M.Ed Maths Scholarship Eligibility Test-2017 Class IX
47.A new operation is defined by a b a b ab. [e.g 2 3 2 3 6 1
44 4 416 8 etc] then a(a 1) a(a 1) 0 has sum of roots_____
1)2 2)0 3)-2 4)-5
48. Two concentric circles are shown in the figure. A B
AB=8, radius of inner circle is 3. Area
between these circles is _____
1) 4 2) 8
.
3)16 4) 64
49. In which triangles corresponding parts are equal
1) Equilateral triangles 2) Right angled triangles
3) Isoceles triangles 4) Congruent triangles
1 1 1 1
50. 1 1 1 .............1 ______
2 3 4 2009
1005 2009
1) 2)2010 3)1005 4)
2 2
51. Number of circles that can be drawn through three mid points of sides of given triangle
is______
1)1 2)2 3)3 4)0
52.Sum of all positive integral divisors of 64 is______
1)164 2)127 3)128 4)256
53. The diagonal of a rectanglar field is 100m. Length and breadth are in the ratio 4:3. The
area of the field is____ sq.m
1)1400 2)6400 3)4800 4)8400
54. If all the multiples of 3 are deleted from first 100 natural numbers, then sum of the
remaining numbers is______
1)3980 2)3367 3)4163 4)4147
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A.I.M.Ed Maths Scholarship Eligibility Test-2017 Class IX
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55. 8 8 8 ............ x Then x _____
x
1 1
1)1 2) 3)4 4)
2 4
1 1 3 5
56. Missing term in the series , , , ______, ,
1001 504 1027 1125
1 4 1 3
1) 2) 3) 4)
266 1073 611 1107
x2 z 2 y 2
57. If x + y + z = 0 then 4 is_______number
yz xy zx
1) even 2) prime 3) square 4) odd cube
58. One factor of x3 23 x 2 142 x 120 is
1) (x-1) 2) x + 10 3) x - 10 4) x - 5
3 1 1
59. x y xy y z yz z x zx Then
2 5 3
1 x y z xy yz zx xyz ____
11 41
1) 2) 3) 4 4) 2
35 3
60. If the diaganal of a square is ‘a’ units. what is the diagonal of the square
whose area is double that of the 1st square.
a2
1) 2a 2) a 2 3) 2a 4)
2
