Board Question Paper: July 2020: Maths - II
Board Question Paper: July 2020: Maths - II
Board Question Paper: July 2020: Maths - II
Notes:
i. All questions are compulsory.
ii. Use of calculator is not allowed.
iii. The numbers to the right of the questions indicate full marks.
iv. In case of MCQ’s [Q. No. 1(A)] only the first attempt will be evaluated and will be given credit.
v. For every MCQ, the correct alternative (A), (B), (C) or (D) with sub-question number is to be written
as an answer.
vi. Draw proper figures for answers wherever necessary.
vii. The marks of construction should be clear. Do not erase them.
viii. Diagram is essential for writing the proof of the theorem.
Q.1. (A) For each of the following sub-question four alternative answers are given. Choose the
correct alternative and write its alphabet: [4]
1. ΔABC ~ ΔPQR and ∠A = 45°, ∠Q = 87°, then ∠C = _______.
(A) 45° (B) 87° (C) 48° (D) 90°
2. ∠PRQ is inscribed in the arc PRQ of a circle with centre ‘O’.
If ∠PRQ = 75°, then m(arc PRQ) = _______.
(A) 75° (B) 150° (C) 285° (D) 210°
3. A line makes an angle of 60° with the positive direction of X-axis, so the slope of a line is
_______.
1 3 1
(A) (B) (C) 3 (D)
2 2 3
4. Radius of a sector of a circle is 5 cm and length of arc is 10 cm, then the area of a sector is _______.
(A) 50 cm2 (B) 25 cm2 (C) 25 m2 (D) 10 cm2
(B) Solve the following sub-questions: [4]
1. A
B C
D
In the above figure, seg AB ⊥ seg BC and seg DC ⊥ seg BC.
A( ABC)
If AB = 3 cm and CD = 4 cm, then find .
A( DCB)
1
D E
B C
In ΔABC, seg DE || side BC. If AD = 6 cm, DB = 9 cm, EC = 7.5 cm, then complete the
following activity to find AE.
Activity: In ΔABC, seg DE || side BC ….. (given)
AD AE
∴ .......
DB EC
6 AE
∴ =
9
6 7.5
∴ AE =
∴ AE =
2. A
C
B
In the above figure, chord AB and chord CD intersect each other at point E. If AE = 15, EB = 6,
CE = 12, then complete the activity to find ED.
Activity:
Chord AB and chord CD intersect each other at point E …… (given)
∴ CE × ED = AE × EB …..
∴ × ED = 15 × 6
∴ ED =
12
∴ ED =
3. If C(3, 5) and D(–2, –3), then complete the following activity to find the distance between
points C and D.
Activity:
Let C(3, 5) ≡ (x1, y1), D(–2, –3) ≡ (x2, y2)
x
2
y2 y1 …. (formula)
2
CD = 2
2
2
3 5
2
∴ CD =
22
∴ CD = 64
∴ CD =
Q S R
In ΔPQR, seg PS ⊥ side QR, then complete the activity to prove PQ2 + RS2 = PR2 + QS2.
Activity:
In ΔPSQ, ∠PSQ = 90°
∴ PS2 + QS2 = PQ2 ……. (Pythagoras theorem)
∴ PS2 = PQ2 – ……… (I)
Similarly,
In ΔPSR, ∠PSR = 90°
∴ PS2 + = PR2 ……… (Pythagoras theorem)
∴ PS2 = PR2 – ……… (II)
∴ PQ2 – = – RS2 …….. from (I) and (II)
∴ PQ2 + = PR2 + QS2
2. Measure of arc of a circle is 36° and its length is 176 cm. Then complete the following
activity to find the radius of circle.
Activity:
Here, measure of arc = θ = 36°
Length of arc = l = 176 cm
∴ Length of arc (l) = × ……. (formula)
360
36 22
∴ = ×2× ×r
360 7
1 44
∴ 176 = × ×r
7
176
∴ r=
44
∴ r= × 70
Radius of circle (r) = cm
3
2. Draw a circle with centre ‘O’ and radius 3.4 cm. Draw a chord MN of length 5.7 cm in it.
Construct tangents at points M and N to the circle.
3. Prove that:
1
= sec θ + tan θ.
sec tan
4. Radii of the top and base of frustum are 14 cm and 8 cm respectively. Its height is 8 cm. Find
its curved surface area.(π = 3.14)
B C
P D
In ΔABC, ∠BAC = 90°, seg AP ⊥ side BC, B-P-C. Point D is the mid-point of side BC, then
prove that 2AD2 = BD2 + CD2.
2. A
B D
E
In the above figure, chord AB ≅ chord AD. Chord AC and chord BD intersect each other at
point E. Then prove that:
AB2 = AE × AC.
3. A straight road leads to the foot of the tower of height 48 m. From the top of the tower the
angles of depression of two cars standing on the road are 30° and 60° respectively. Find the
distance between the two cars.( 3 =1.73)
Q.5. Solve the following sub-questions (Any one): [3]
i. Let M be a point of contact of two internally touching circles. Let line AMB be their common
tangent. The chord CD of the bigger circle touches the smaller circle at point N. The chord
CM and chord DM of bigger circle intersect the smaller circle at point P and R respectively.
a. From the above information draw the suitable figure.
b. Draw seg NR and seg NM and write the two pairs of congruent angles in smaller circle
considering tangent and chord.
c. By using the property which is used in (b) write the two pairs of congruent angles in
the bigger circle.
ii. Draw a circle with centre ‘O’ and radius 3 cm. Draw a tangent segment PA having length
40 cm from an exterior point P.
44