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# Question Paper Solutions for Geometry Balbharati Model Question Paper Set 2 2018-2019 SSC (Marathi Semi-English) 10th

Geometry
Balbharati Model Question Paper Set 2
2018-2019 March
Marks: 40

[4]1
[4]1.A | Solve any four of the following.
[1]1.A.1

In the figure, line PQ || line RS. Using the information given
in the figure find the value of x.

Chapter: [4] Co-ordinate Geometry
Concept: General Equation of a Line
[1]1.A.2

In the figure, parts of the two triangles bearing identical marks are
congruent. State the test by which the triangles are congruent.

Chapter: [1] Similarity
Concept: Similarity of Triangles
[1]1.A.3

In Δ ABC, if ∠ A = 65° ; ∠ B = 40° then find the measure of ∠ C.

Chapter: [7] Mensuration
Concept: Length of an Arc
[1]1.A.4

squarePQRS is a parallelogram. Write the sum of measures of ∠P and ∠ Q.

Chapter: [3] Circle
Concept: Property of Sum of Measures of Arcs
[1]1.A.5

If hypotenuse of a right angled triangle is 5 cm, find the radius of
the circle passing through all vertices of the triangle.

Chapter: [2] Pythagoras Theorem
Concept: Apollonius Theorem
[1]1.A.6

Write the co-ordinates of the point of intersection of graphs of
equations x = 2 and y = -3.

Chapter: [4] Co-ordinate Geometry
Concept: Co-ordinates of the Midpoint of a Segment
[4]1.B | Solve any two of the following.
[2]1.B.1

Length of a rectangular tank is twice its breadth. If the
depth of the tank is 3 m and area of its four walls is 108 m2, find the
length of the tank.

Chapter: [7] Mensuration
Concept: Length of an Arc
[2]1.B.2

In right angled triangle PQR,
if ∠ Q = 90°, PR = 5,
QR = 4 then find PQ and hence find tan R.

Chapter: [2] Pythagoras Theorem
Concept: Similarity in Right Angled Triangles
[2]1.B.3

In Δ PQR, points S and T
are the midpoints of sides PQ
and PR respectively.
If ST = 6.2 then find the length of QR.

Chapter: [2] Pythagoras Theorem
Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle

In Δ PQR, points S and T
are the midpoints of sides PQ
and PR respectively.
If ST = 6.2 then find the length of QR.

Chapter: [1] Similarity
Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
[8]2
[4]2.A | Select the appropriate alternative and write it.
[1]2.A.1

Δ ABC ∼ Δ PQR. If A(Δ ABC)=25, A(ΔPQR)=16, find AB : PQ.
(A) 25:16
(B) 4:5
(C) 16:25
(D) 5:4

Chapter: [1] Similarity
Concept: Similar Triangles
[1]2.A.2

From the information given in the figure, find the measure of ∠ AEC.
(A) 42° (B) 30°
(C) 36° (D) 72°

Chapter: [3] Circle
Concept: Property of Sum of Measures of Arcs
[1]2.A.3

Point P is the midpoint of seg AB. If co-ordinates of A and B are (-4, 2) and (6, 2) respectively then find the co-ordinates of point P.
(A) (-1,2) (B) (1,2) (C) (1,-2) (D) (-1,-2)

Chapter: [4] Co-ordinate Geometry
Concept: Co-ordinates of the Midpoint of a Segment
[1]2.A.4

Find the ratio of the volumes of a cylinder and a cone having equal radius and equal height.
(A)1 : 2 (B) 2 : 1 (C) 1 : 3 (D) 3 : 1

Chapter: [7] Mensuration
Concept: Introduction of Surface Areas and Volumes
[4]2.B | Solve any two of the following.
[2]2.B.1

PQ ⊥ BC, AD ⊥ BC,
PQ = 4, AD = 6
Write down the following ratios.
(i)(A(ΔPQB))/(A(ΔADB))

(ii)(A(ΔPBC))/(A(ΔABC))

Chapter: [1] Similarity
Concept: Similar Triangles
[2]2.B.2

Diagonal of a square is 20 cm. Find the length and perimeter of the square.

Chapter: [7] Mensuration
Concept: Perimeter and Area of a Circle
[2]2.B.3

In the figure, point Q is the
point of contact. If PQ = 12,
PR = 8 then find PS.

Chapter: [3] Circle
Concept: Tangent to a Circle
[8]3
[4]3.A | Carry out any two activities of the following.
[2]3.A.1

In the following figure ‘O’ is the centre of the circle.

∠AOB = 1100, m(arc AC) = 450.

Use the information and fill in the boxes with proper numbers.

(i) m(arcAXB) =

(ii)m(arcCAB) =
(iv)∠COB =

(iv)m(arcAYB) =

Chapter: [3] Circle
Concept: Tangent Segment Theorem
[2]3.A.2

In the figure, c ABCD is a cyclic quadrilateral. Seg AB is a diameter. If ∠ ADC = 120˚, complete the following activity to find measure of ∠ BAC.

square ABCD is a cyclic quadrilateral.
∴ ∠ ADC + ∠ ABC = 180°
∴ 120˚ + ∠ ABC = 180°
∴ ∠ ABC =
But ∠ ACB = .......angle in semicircle In Δ ABC,
∠ BAC + ∠ ACB + ∠ ABC = 180°
∴ ∠BAC + = 180°
∴ ∠ BAC =

Chapter: [3] Circle
Concept: Cyclic Properties
[2]3.A.3

Complete the table below the graph with the help of the following graph.

 Sr. No. First point Second point Co-ordinates of first point (x1 , y1) Co-ordinates of second point (x2 , y2) (y_2 - y_2)/(x_2 - x_2) 1 C E (1, 0) (3,4) 4/2=2 2 A B (-1,-4) (0,-2) 2/1 = 2 3 B D (0,-2) (2,2) 4/2=2
Chapter: [4] Co-ordinate Geometry
Concept: Co-ordinates of the Midpoint of a Segment
[4]3.B | Solve any two of the following.
[2]3.B.1

If tanθ = 3/4 then find the value of secθ.

Chapter: [6] Trigonometry
Concept: Trigonometric Identities
[2]3.B.2

Find the length of an arc if measure of the arc is 90° and its radius
is 14 cm.

Chapter: [7] Mensuration
Concept: Length of an Arc
[2]3.B.3

Seg NQ is the bisector of ∠ N
of Δ MNP. If MN= 5, PN =7,
MQ = 2.5 then find QP.

Chapter: [1] Similarity
Concept: Property of an Angle Bisector of a Triangle
[9]4 | Solve any three of the following.
[3]4.A

∆ABC is an equilateral triangle. Point P is on base BC such that PC = $\frac{1}{3}$ BC, if AB = 6 cm find AP.

Chapter: [2] Pythagoras Theorem
Concept: Similarity in Right Angled Triangles
[3]4.B

seg XY || seg AC, If 3AX = 2BX
and XY = 9 then find the length of AC.

Chapter: [1] Similarity
Concept: Basic Proportionality Theorem Or Thales Theorem
[3]4.C

Show that square ABCD formed by the vertices A(-4,-7), B(-1,2), C(8,5) and D(5,-4) is a rhombus.

Chapter: [4] Co-ordinate Geometry
Concept: Concepts of Coordinate Geometry
[3]4.D

Two buildings are in front of each other on a road of width 15 meters. From the top of the first building, having a height of 12 meter, the angle of elevation of the top of the second building is 30°.What is the height of the second building?

Chapter: [6] Trigonometry
Concept: Heights and Distances
[4]5 | Solve any one of the following.
[4]5.A

Two circles intersect each other at points C and D. Their common tangent AB touches the circles at point A and B. Prove that :
∠ ADB + ∠ ACB = 180°

Chapter: [3] Circle
Concept: Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers
[4]5.B

Draw an isosceles triangle with base 5 cm and height 4 cm. Draw a triangle similar to the triangle drawn whose sides are 2/3 times the sides of the triangle.

Chapter: [1] Similarity
Concept: Basic Proportionality Theorem Or Thales Theorem
[3]6 | Solve any one of the following:
[3]6.A

Height of a cylindrical barrel is 50 cm and radius of its base is 20 cm. Anurag started to fill the barrel with water, when it was empty, by a cylindrical mug. The diameter and height of the mug was 10 cm and 15cm respectively. How many minium number of mugs will be required for the barrel to overflow?

Chapter: [3] Circle
Concept: Theorem - Converse of Tangent at Any Point to the Circle is Perpendicular to the Radius
[3]6.B

Draw Δ ABC such that, AB = 8 cm, BC = 6 cm and ∠ B = 90°. Draw seg BD
perpendicular to hypotenuse AC. Draw a circle passing through points
B, D, A. Show that line CB is a tangent of the circle.

Chapter: [3] Circle
Concept: Tangent to a Circle

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## Maharashtra State Board previous year question papers 10th Geometry with solutions 2018 - 2019

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