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Olympiad

UKMTIntermediateChallenge

UKMTSeniorChallenge
SCHOOL TOPICS
Real Numbers
Sample Question
Two tankers contain 371 litres and 189 litres of petrol respectively. A container with maximum capacity is used which can measure the petrol of either tanker in exact number of litres. How many containers of petrol are there in the first tanker.
A.
53
B.
7
C.
49
D.
54
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Linear Equations in Two Variables
Sample Question
A two digit number is 6 more than 4 times the sum of its digits. If 18 is added to the number, the digit interchange their places. Find the number.
A.
46
B.
55
C.
37
D.
64
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Quadratic Equations
Sample Question
Find a natural number whose square diminished by 59 is equal to 2 times of 20 more than the given number.
A.
10
B.
13
C.
11
D.
14
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Arithmetic Progressions
Sample Question
What is the first negative term in the arithmetic progression
140, 133, 126,...
?
A.
21
^{st}
B.
20
^{th}
C.
22
^{nd}
D.
23
^{rd}
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Trigonometry
Sample Question
3(sin
^{4}
θ + cos
^{4}
θ)  2(sin
^{6}
θ + cos
^{6}
θ) = ?
A.
sinθ cosθ
B.
1  sinθ cosθ
C.
1
D.
sinθ  cosθ
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Mean, Mode and Median
Sample Question
The distribution of IQ among a set of students is given below. What is their median IQ?
Class interval
8896
96104
104112
112120
120128
Frequency
12
10
25
20
29
A.
112.4
B.
107.4
C.
117.4
D.
122.4
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Probability
Sample Question
Ella draws one card from a shuffled deck of 52 cards. What is the probability that she drew a spade or a 5?
A.
1
52
B.
4
13
C.
1
13
D.
1
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Dice and Cubes
Sample Question
Faces of a cube are marked with A,B,C,D,E and F. If two views of cube are as shown below, what will be there on the face opposite to face F ?
A.
C
B.
E
C.
B
D.
Cannot be determined
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Venn Diagrams
Sample Question
Following chart shows number of students in a school who plays one of three sports. Find the number of students who plays exactly two sports.
A.
55
B.
51
C.
49
D.
52
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Number Series
Sample Question
Find the next term of given sequence ..
6, 13, 24, 39, 58, , ....
A.
73
B.
162
C.
89
D.
81
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Alphabet Problems
Sample Question
Which of the following choices would replace the blanks below
ab_aa_baab_aab_a
A.
bbbb
B.
bbab
C.
babb
D.
abbb
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NTSE_MAT
Sample Question
Find the next term of given sequence ..
1, 32, 103, 232, 437, , ....
A.
1472
B.
736
C.
744
D.
729
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Full Year 10th Grade Review
Sample Question
The HCF of 494 and 351 is
A.
13
B.
12
C.
16
D.
None of above
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Polynomials
Sample Question
If α and β are the zeros of polynomial
x
^{2}
+ 2
x
 3
, find a polynomial whose zeros are α
^{2}
/β
^{2}
and β
^{2}
/α
^{2}
.
A.
B.
C.
D.
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