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BELTHANGADY TALUK MATHS TEACHERS WORKSHOP
MINIMUM STUDY LEVEL QUESTION PAPER
Time: 2hour
TOTAL:
SUBJECT: MATHEMATICS
50
1x7=7
I . Choose the best alternative from following options
1) If Tn = 5n + 1 , the value of S2 ---(A)
18
(B)
(C) 19 (D) 20
n
2) The value of Cn is---(A) n
(B)
n!
(C)
1
(D) 0
3) If a coin is tossed once, the probability of head occurs.
2
(B)
(A)
(C)
(D)
4
4) The formula to find coefficient of variation.
∑
(A)
(B)
∑
(C) .
(D)
∑
5) The value of sin 60 ------
(B)
√
(D)
√3
6) The two lines are mutually perpendicular, then, the product of their slop is -------(A) 0
(B)
1
(C)
2
(D) −
7) The degree of the polynomial 3x2 - 4x4 + 2x3 + 7x - 8.
(A) 2
(B) 4
(C) 3
( D) 1
II. Answer the following
1x5=5
8) If A and B is a non – empty sets, write the relation between n (A), n (B), n (A∩B),
n (AUB).
n(AUB) = n(A) +n(B) – n(A∩B)
9) State Thales Theorem.
If a straight line is drawn parallel to a side of a triangle,then it divides the
(A)
√
(C)
other two sidesproportionally.
10) Write the relation between Dividend, Quotient, Reminder and Divisor.
a = bq + r [ 0≤ <q] where a=Dividend,b=Divisor,q=Quotient, R=Reminder
11) What is the distance between the circles of radius R and r touch each other
Internally?
d =R+r
12) Write the formula to find the Volume of a Cone.
V=
r 2h
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III. Answer the following
2x 10 = 20
13) In a circle of radius 4.5cm draw two radii such that the angle between them is700
Construct tangents at the non-centre ends of the radii.
14) Construct a pair of tangents to a circle of radius 3cm, such that the angle between
them is 1000.
15) Rationalize the denominator and simplify
√
√
=
=
=
=
√
√
√
√
√
√
√
√
x
√
√ √
√ √
√
√
√
√
− √
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16) Find the product. √2 x √3
√2
= 2 = 2 = √2
√3 = 3 = 3 = √3
√2 x3
√4x27
√108
17) In a group of 50 students, 30 like tea, 25 like coffee and 16 like both. In a Venn
diagram show how many like only tea.
18) How many 3 digit numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 without
repeating any digit.
The number of 3 digit numbers can be formed using the digits 1,2,3,4,5,6
Hundreds
Tens
ones
6
5
4
P1
P1
P1
6
5
4
=6x5x4 = 120
OR
How many diagonals can be drawn in a hexagon?
Formula - nC2 - n
6
C2 – 6
!
= ( )! - 6
!
=(
!
)! !
- 6
=
- 6
= 15 - 6
=
9
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19) Solve by using the formula. x2 + 12 = 7x
a = 1, b = -7 , c = 12
−(−7) ± (−7) − 4x1x12
=
2x1
7 ± √49 − 48
=
2
7 ± √1
=
2
7±1
=
2
=
or
=
= or
=
or
20) If cot A =
=
=
and sinA =
, Find cos A.
cotA =
cosA = cotA.sinA
cosA =
=
21) Calculate the slope of a line joining the points (3,-2) and (4, 5).
m=
5−(−2)
4−3
5+2
m= 1
m= 7
22) Verify Euler’s formula for the given graph
N = 6, R = 5, A = 9
N+R = 6+ 5 = 11
A+2 = 9 + 2 = 11
∴ N+R = A+2
22) Sketch out the field to the following notes from the field book
(1 cm = 50m.)
To D
100 To C
50To B
350
300
250
150
50
150 To E
100To F
From A
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1cm = 50m
50m =1cm, 150m = 3cm, 250m = 5cm, 300m = 6cm, 350m = 7cm, 100m = 2cm
IV. Answer the following
23) Calculate the standard deviation of the following data
X
0-10
10-20
20-30
f
7
10
15
3 x 2= 6
30-40
8
40-50
10
CI
X
f
d=x-25
fd
d2
fd2
0-10
10-20
20-30
30-40
40-50
5
15
25
35
45
7
10
15
8
10
-20
-10
0
10
20
-140
-100
0
80
200
400
100
0
100
400
2800
1000
0
800
4000
50
=
∑
−
=
−
=
– .
= √
.
=
40
8600
∑
.
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23) prove that “If two circles touch each other externally, the centers and the point of
contact is collinear”
If two circles touch each other externally, thecentres and the point of contact are
collinear.
Given:A and B are the centres of touching circles. P is the point of contact.
To prove : A,P,and B are collinear.
Construction: Draw the tangent XPY.
Proof:In the figure
∠APX = 900……………..(1) ∵Radius drawn at the point of contact is
∠BPX = 900 ………… ..(2) perpendicular to the tangent
∠APX + ∠BPX = 900 +900 [ by adding (1) and (2)
∠APB = 1800
[ APB is a straight line
∴ APB is a straight line
∴ A, P andB are collinear.
V. Answer the following
4 x 3= 12
24) Draw transverse common tangents to two circles of radii 4.5cm and 2.5cm having
Their Centers 10cm apart and measure their lengths.
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25) Draw a graph of y = x2 and find the value of√5.
5 = ±2.2
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27) Prove that “If two triangles are equiangular, then their corresponding sides are
Proportional”
Theorem: “ If two triangles are equiangular,then their corresponding sides are
proportional”.
Given: In ∆ABC and ∆DEF,
( i). ∠BAC = ∠EDF
(ii). ∠ABC = ∠DEF
To prove:
AB
DE
BC
=
EF
=
CA
FD
Construction: i) Mark points G’ and H’ on AB and AC such that.
Proof:In ∆AGH and ∆DEF,
[ ∵ Construction
AG = DE
∠BAC = ∠EDF
[ ∵ Given
[ ∵ Construdtion
AH = DF
∴ ∆AGH ≡ ∆DEF [ ∵ S.A.S. postulates
∴ ∠AGH = ∠DEF
[∵ Corresponding angles]
ಆದ ೆ∠ABC = ∠DEF [ ∵ Given
⇒
∴
∴
∴
∠AGH = ∠ABC [ ∵ Axioms
GH ॥ BC
AB
AG
=
=
BC
GH
=
=
CA
HA
[∵ converse of thales Theorem
[∵∆AGH ≡ ∆DEF
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