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Maths Olympiad 2023 Flashcards | StudBud
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Maths Olympiad 2023
Maths Olympiad 2023
80 terms
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Class 10 Total Chapters 8 2 chapters optional Total No of questions 80
Flashcards
80 cards
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Practice quiz
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Host live
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Questions
80
Answers
1
A tower is 100√3 m high. Find the angle of elevation of its top from a point 100 m away from its foot.
600
900
300
450
2
In figure if angle ATO = 40°, find angle AOB.
160 deg
120 deg
140 deg
100 deg
3
Identify a b and c in the std quad equation 7 = x
2
a = 1, b = 0 and c = 7
a = -1, b = 0 and c = -7
a = 1, b = 0 and c = -7
a = -1, b = 1 and c = 7
4
For the triangle below, decide which trigonometric ratio (i.e. sin, cos or tan) you would use?
Cos
Sin
Nat
Tan
5
Where were the fields of algebra and trigonometry developed?
the Islamic Middle East
classical Athens
Gupta India
Mayan city-states
6
If cos (40
0
+x) = sin 30
0
Find the value of x provided 40
0
+x is a acute angle
800
600
400
200
7
Find the value of k for which the polynomial x
4
+ 10x
3
+ 25 x
2
+ 15x + k is exactly divisible by (x + 7)
51
31
-41
-91
8
This is not a example of AP
5, 7, 9 ...
salary drawn by a person for 12 months
salary increment of 200 rupees every month in a year
8, 6, 4, ....
9
Which number is
NOT rational
?
3.14159
\sqrt{6}
\sqrt{49}
22/7
10
Divide 2x
2
+3x-4 by x - 3 will give the remainder
7
5
13
23
11
If the coefficients of two lines a
1
/ a
2
≠ b
1
/ b
2
we can say two lines are
intersecting
coincident
can't say
parallel
12
Write the rational number as
a decimal
: 4
1
/
6
4.16667
4.6
0.83333
0.10
13
A fraction becomes 1 /3 when 1 is subtracted from the num and it becomes 1/4 when 8 is added to its den. Find fraction.
3/2
4/14
5/12
8/13
14
Statements about π, which is correct?
π is an irrational number
π is infinity.
π = 22/7
π is a rational number.
15
Given the equation of lines 3x + 4y - 7 =0 and 9x + 12y + 19 = 0 these lines are
can't say
intersecting
parallel
coincident
16
Euclid's division lemma satisfies a=bq+r,then
0>r>b
0<r<b
0>=r>b
0\le r<b
17
Tick all rational numbers
3.676776777...
2.111...
√7
√5
18
The circumference of a circle equals _______.
2 times π times diameter
π times radius squared
radius length times 2
π times diameter
19
A pt. P is 26 cm from the centre of the circle. The "l" of the tangent drawn from P to the circle is 24 cm. Find radius
20 cm
30 cm
10 cm
5 cm
20
What are the GREEN and BLUE parts of the circle called?
G- Segment B- Arc
G- Sector B-Segment
G- Segment B- Pie
G-Pi B-Sector
21
Arithmetic Sequence
2
4
3
1
22
What is the angle of elevation of the sun, when the length of the shadow of a tree is equal to its vertical height?
450
600
300
00
23
In trigonometry, we learned that 180 degrees is equal to ________ radians.
π
2
3π
2π
24
If sin∅ = 1/2 Find the value of 3 cos∅ - 4 cos
3
∅
1
2
1/2
0
25
Find the discriminant of the quadratic equation: 3√3
x
2
+ 10
x
+ √3= 0.
64
54
104
34
26
If arithmetic mean of two numbers
a
and
b
is 8 and
ab
= 9, find a quadratic equation whose roots are
a
and
b
.
x2-16x+19
x2-16x+9
x2-8x+9
-x2-16x+9
27
Which sequence is arithmetic?
5, 8, 10, 11,...
27, 21, 15, 9,...
71, 91, 100, 111,...
99, 90, 80, 71,...
28
Find the 43
rd
term of the arithmetic sequence-124, -122, -120,…
-40
-210
-38
-208
29
If sin(A-B) = 1/2 , cos(A+B) = 1/2 Find A and B
A = 300 B = 300
A = 450 B = 450
A = 300 B = 150
A = 450 B = 150
30
A circle touches x-axis at A and y-axis at B. If O is origin and OA = 5 units, then diameter of the circle is
8 √2 units
8 units
10 √2 units
10 units
31
If value of tan∅ = √3 then value of sin∅ is
1/2
infinity
1
√3/2
32
Find the l of the tangent drawn from a pt whose dist. from the centre of a circle is 25 cm. Radius of circle = 7 cm
36 cm
can't be found out
24 cm
26 cm
33
Find the value of 'a' for which the following equations has infinitely many sols: 2x+3y-7=0 and (a-1)x+ (a+1)y= 3a-1
3
5
2
1
34
A quadrilateral ABCD is drawn to circumscribe a circle. If AB = 12 cm, BC = 15 cm and CD = 14 cm, then AD is equal to
10 cm
12 cm
11 cm
15 cm
35
Kite flying at a ht. of 75m from the ground, tied to string inclined at 60° to the horizontal. Find the l of the string
50/ √3 m
150/ √3 m
150 m
150√3 m
36
If the angle between two radii of a circle is 110º, then the angle between the tangents at the ends of the radii is:
40 deg
70 deg
90 deg
50 deg
37
What are the solutions to this quadratic?
x= 2 and 4
x= -2 and -4
x=-2 and 4
x=2 and -4
38
The solution of the quadratic equation x
2
+ 3x - 5 = 0 is
(-3 ∓√29)/2
(3 ∓√11)/2
(-3 ∓√11)/2
(3 ∓√29)/2
39
Solve 2x
2
+ 9x + 4 = 0 using the Quadratic Formula
x = 4 or x = 1/2
What's the Quadratic Formula??
x = −4 or x = − 1/2
x = (−9 ± √113)/4
40
What is a theodolite?
An instrument used to measure velocity aeroplane.
An instrument used to measure surface tension
A surveying instrument used to measure angles with rotating telescope
An instrument used to measure density of an object
41
A circle has a number of tangents equal to
2
3
1
infinite
42
Why we say that a equation with degree one ( ax + b = 0) is a linear equation
no reason in saying so
As its degree is one
When it is plotted on x y plane it a st line
It is a single equation
43
The number of polynomials having zeroes as –2 and 5 is
1
more than 3
3
2
44
Find the quadratic polynomial whose two zeroes are √2+1 and √2-1
x2 + √2 + 1
x2 - 2√2 + 1
x2 - √2 - 1
x2 + 2√2 - 1
45
What is true about sin 30
0
= 0.5
sine of 30 degree has the value of 1/2
Sine added with 30 deg becomes 0.5
Sine myltiply by 30 deg is 0.5
none of these
46
Applications of Trigonometry
v
None of the above
w
u
47
Find the sum of a+b, a-b, a-3b...... upto 22nd terms
22a - 440b
2a - 440b
can't find with given data
22a - 44b
48
Identify irrational number between 1 and 1.2
1.090909...
1.111.....
1.131313...
1.010010001...
49
Find the 20th term of AP 3,6,9,...
33
70
60
50
50
Is it a quadratic equation? x
2
- 2x + 1 = x
2
-3x +10
can be , can't be
No
Yes
can't say
51
Application of trigonometric ratios.
B
D
A
C
52
The shadow of a tower is √3 times its height. Find the angle of elevation of the top of the tower.
300
600
150
450
53
If tangents PA and PB from a pt P to a circle with centre O are inclined to each other at 80°, then ∠ POA is equal to
50 deg
70 deg
80 deg
60 deg
54
2x + 3y – 9 = 0 and 4x + 6y – 18 = 0 what is true about these lines
can't say
Parallel lines
coincident lines
intersecting lines
55
What is not true abount 5?
It is a ratinal number
It is a whole number
It is a irrational number
It is a natural number
56
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
24
20
8
16
57
Which sequence is NOT arithmetic?
10, 12, 15, 19,...
5, 10, 15, 20,...
3, 9, 15, 21,...
2, 4, 6, 8, ...
58
Find the area (in cm
2
) of ΔABC in which ∠ABC = 90°, ∠ACB = 45° and AC = 8 cm.
46
16
26
36
59
If you have the angle and the adjacent side, you can use all trigonometric functions
except
(a)
Arc Tan
Cos
Sin
Tan
60
Write the zeroes of polynomial
x
2
–
x
– 6.
-3, 2
1, 6
3, -2
6, -1
61
What is Irrational number?
A terminating decimal.
A number that can't be written as a fraction.
A number that can't be written as a decimal.
A repeating decimal.
62
Which of the following is a factor of the polynomial expression: 3x-12
x
(x-4)
(x+4)
3x
63
Two parallel lines touch the circle at points A and B respectively. If area of the circle is 25 π cm
2
, then AB is equals
10 cm
20 cm
can't be found
5 cm
64
What if the degree of constant polynomial '0'
2
0
1
can't be defined
65
Solve the following equations 3x + 4y = 10 and 2x – 2y = 2 Find the value if x and y?
2,1
3,1
3,2
2,2
66
Double the circumference of a circle is 88 cm. Area if the circle in cm square is
154
174
184
164
67
In the eqautions 3x+2y = 13xy and 4x-5y = 2xy Value of (x, y) satisfying the equations is
1/2 , 1/3
1/3,1/2
2,3
3,2
68
arithmetic progression
B
A
C
D
69
For what value of k, the roots of the equation x
2
+ 4x + k = 0 are real?
k < 4
k > 4
k ≥ 4
k ≤ 4
70
In a AP total no of terms are 100 first term is -18 and last term is 180 Find sum of all terms
1100
7100
9100
8100
71
The shape produced by a QUADRATIC is a _________.
Squared
v-shape
Line
Parabola
72
Find the value of x if 2x+1, x
2
+x+1, 3x
2
-3x+3 are all consecuive terms of an AP.
x = 1 or -2
x = 1 or 2
x = -1 or -2
x = -1 or 2
73
Two numbers are in the ratio 3:4. If 5 is subtrcted from each the ratio becomes 2:3 Find the smallest number?
15
20
18
24
74
Two zeroes of the polynomial p(z) = z
2
- 27
∓ √3
∓ 3
∓ 2√3
∓ 3 √3
75
Which definition of π is correct.
π terminates
π can be defined as ratio of circular length of a circle to its diameter.
π can be expressed a repeating decimal
π is a rational number
76
If zeroes of p(x) = 2x
2
– 7x + k are reciprocal of each other, then the value of k is __________.
7
2
1
5
77
A boat goes 16 km up and 24 km down in 6 hr. It also covers 12 km up and 36 km down in same time. Find its actual speed.
8 km/hr
none of these
12 km/hr
4 km/hr
78
What is the degree of the polynomial 5
7
x
4
+\sqrt{ }x-9
4
5
7
can't be defined
79
If tan∅ = 5/6 given θ + ∅ = 90
0
Find the value of cotθ
6/5
5/6
36/25
can't find out
80
Convert 1.777... into a rational number.
15/7
16/9
12/5
13/6
