Maharashtra Board Class 10 Maths Part 2 Geometry Guess Paper 2027
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A full practice paper on the official Maths Part 2 Geometry pattern, built from the most-likely questions by repetition analysis. Not an official or leaked paper.
Maharashtra Board Class 10 Maths Part 2 Geometry — Guess Paper 2027
Time: 2 hours · Maximum marks: 40 · Practice paper
Section 1Q1(A) MCQs (choose the correct alternative) and Q1(B) short one-mark subquestions
Q1.1 mark
Angle made by the line with the positive direction of X-axis is 30 degrees. Find slope of the line.
Why this question: Coordinate Geometry → Find the slope of a line making a given angle with the positive X-axis — appeared 5× Board 2024Board 2025Board 2026
Q2.1 mark
If the side of the cube is 5 cm, then the volume of that cube is ..................................... (A) 10 cm3 (B) 100 cm3 (C) 125 cm3 (D) 25 cm3
Why this question: Mensuration → Find the volume of a solid (cube/cuboid/cylinder/cone/sphere) given its dimensio — appeared 5× Board 2024Board 2025Board 2026
Q3.1 mark
Out of the following which is a Pythagorean triplet? (a) (1, 5, 10) (b) (5, 12, 13) (c) (2, 3, 4) (d) (5, 5, 2)
Why this question: Pythagoras Theorem → Identify which set of numbers forms a Pythagorean triplet — appeared 4× Board 2024Board 2025Board 2026
Q4.1 mark
Two circles having radii 4 cm and 5 cm touch each other internally. Then the distance between the centres is ..................... (A) 4 cm (B) 5 cm (C) 1 cm (D) 9 cm
Why this question: Circle → Find the distance between centres of two circles touching each other externally/ — appeared 4× Board 2024Board 2025Board 2026
Q5.1 mark
The ratio of corresponding sides of similar triangles is 3 : 5, then find the ratio of their areas.
Why this question: Similarity → Find the ratio of areas of two similar triangles given the ratio of correspondin — appeared 3× Board 2024Board 2025Board 2026
Q6.1 mark
Radius of a sector of a circle is 35 cm and length of its arc is 22 cm. What is the area of the sector? (a) 285 cm2 (b) 185 cm2 (c) 385 cm2 (d) 85 cm2
Why this question: Mensuration → Find the area of a sector given radius and arc length (A = l x r / 2) — appeared 3× Board 2024Board 2026
Q7.1 mark
Find the slope of the line passing through the points A(2, 3) and B(4, 7).
Why this question: Coordinate Geometry → Find the slope of a line passing through two given points — appeared 3× Board 2024Board 2025
Q8.1 mark
Find the diagonal of a square whose side is 5 cm.
Why this question: Pythagoras Theorem → Find the diagonal of a square given its side (45-45-90 relation, diagonal = side — appeared 2× Board 2025Board 2026
Section 2Q2(A) complete-the-activity (any two of three) and Q2(B) two-mark subquestions (any four of five)
Q9.2 marks
Find the co-ordinates of the midpoint of the line segment joining points P(0, 6) and Q(12, 20).
Why this question: Coordinate Geometry → Find the midpoint of the segment joining two given points — appeared 4× Board 2023Board 2025Board 2026
Q10.
2 marks
An observer at a distance of 10 m from a tree looks at the top of the tree, the angle of elevation is 60 degrees. To find the height of the tree complete the activity. (root 3 = 1.73) Activity: AB = h = height of tree, BC = 10 m; angle of elevation = angle BCA = 60 degrees; tan theta = AB/BC; tan 60 = AB/BC = root 3; AB = BC x root 3 = 10 root 3 = 10 x 1.73.
Why this question: Trigonometry → Find a height/length using a single angle of elevation/depression and a given di — appeared 4× Board 2023Board 2025Board 2026
Q11.2 marks
Find surface area of a sphere of radius 7 cm.
Why this question: Mensuration → Find the surface area of a solid (sphere/cone/cylinder/cube/cuboid) given its di — appeared 4× Board 2023Board 2024Board 2025
Q12.
2 marks
In the given figure, chord MN and chord RS intersect at point D. If RD = 15, DS = 4, MD = 8, find DN.
Why this question: Circle → Find an unknown chord segment using the internal intersecting-chords theorem — appeared 3× Board 2023Board 2025Board 2026
Q13.2 marks
If sin theta = 20/29, then complete the activity to find cos theta. Activity: sin2 theta + cos2 theta = 1; cos2 theta = 1 - sin2 theta; cos2 theta = 1 - 400/841; cos2 theta = 441/841; taking square roots, cos theta = 21/29.
Why this question: Trigonometry → Find one trigonometric ratio from another using a Pythagorean identity (sin2 + — appeared 3× Board 2022Board 2025Board 2026
Q14.
2 marks
In the given figure, seg PS is a tangent segment, line PR is a secant. If PQ = 3.6, QR = 6.4, find PS. Activity: PS2 = PQ x PR (Tangent secant segment theorem) = PQ x [PQ + QR] = 3.6 x [3.6 + 6.4] = 3.6 x 10; PS2 = 36; PS = 6.
Why this question: Circle → Find the tangent segment length from an external point using the tangent-secant — appeared 2× Board 2025Board 2026
Section 3Q3(A) three-mark activity (any one of two) and Q3(B) three-mark subquestions (any two of four)
Q15.3 marks
triangle ABC ~ triangle LMN. In triangle ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm. Construct triangle ABC and triangle LMN such that BC/MN = 5/4.
Why this question: Geometric Constructions → Construct a triangle similar to a given triangle with a given scale factor — appeared 7× Board 2022Board 2023Board 2024Board 2025Board 2026
Q16.3 marks
Draw a circle with centre O and radius 3.5 cm, take a point P at a distance 5.7 cm from the centre. Draw tangents to the circle from point P.
Why this question: Geometric Constructions → Construct tangents to a circle from an external point at a given distance — appeared 3× Board 2024Board 2025Board 2026
Q17.3 marks
Find the co-ordinates of point P, if P divides the line segment joining the points A(-1, 7) and B(4, -3) in the ratio 2 : 3.
Why this question: Coordinate Geometry → Find coordinates of the point dividing a segment in a given ratio (section formu — appeared 3× Board 2022Board 2025Board 2026
Section 4Q4 four-mark problems (any two of three)
Q18.
4 marks
In the given figure, line l intersects side AB and side AC of triangle ABC in points P and Q respectively. Show that A(triangle APQ)/A(triangle ABC) = (AP x AQ)/(AB x AC).
Why this question: Similarity → Prove the ratio of areas of two triangles sharing an angle equals the ratio of p — appeared 1× Board 2026
Q19.4 marks
In triangle ABC, A-X-B and A-Y-C is such that segment XY parallel side BC. Segment XY divides triangle ABC in two equal areas, then find BX/AB.
Why this question: Similarity → Find a segment ratio when a line parallel to a side divides a triangle into equa — appeared 1× Board 2026
Section 5Q5 three-mark challenge problem (any one of two)
Q20.
3 marks
In the given figure, seg XY parallel side AC. If 2AX = 3BX and XY = 9, complete the activity to find the value of AC. Activity: 2AX = 3BX; AX/BX = 3/2; (AX + BX)/BX = (3 + 2)/2; AB/BX = 5/2; triangle BCA ~ triangle BYX (AA test of similarity); BA/BX = AC/XY (corresponding sides); 5/2 = AC/9; AC = 22.5.
Why this question: Similarity → Find an unknown side using similar triangles (corresponding sides in proportion) — appeared 3× Board 2022Board 2025Board 2026