Maharashtra SSC Geometry (Mathematics Part II) Board Paper March 2026

Q.1 (A)(1) Out of the following which is the Pythagorean triplet ?

Q.1 (A)(2) Two circles having radii 4 cm and 5 cm touch each other internally. Then the distance between the centres is .................... .

Q.1 (A)(3) Out of the following points ...................... lies to the right of the origin on X-axis.

Q.1 (A)(4) If the side of the cube is 5 cm, then the volume of that cube is ..................................... .

Q.1 (B)(1) The ratio of corresponding sides of similar triangles is 3 : 5, then find the ratio of their areas.

Q.1 (B)(2) Find the side of a square if its diagonal is \(10\sqrt{2}\) cm.

Q.1 (B)(3) If the measure of minor arc is 70º, then find the measure of corresponding major arc.

Q.1 (B)(4) Angle made by the line with the positive direction of X-axis is 45º, find the slope of line.

Q.2 (A)(1) In the following figure, seg PS is a tangent segment, line PR is a secant. If PQ = 3.6, QR = 6.4, find PS.

[Figure: a circle with an external point P; the secant through P cuts the circle at Q (nearer to P) and R (farther), and the tangent from P touches the circle at S.]

Activity :

PS² = ____ × PR (Tangent secant segment theorem)
= PQ × [PQ + QR]
= ____ × [3.6 + 6.4]
= 3.6 × ____
∴ PS² = 36
PS = ____

Q.2 (A)(2) If \(\sec\theta = \dfrac{25}{7}\), find the value of \(\tan\theta\).

Solution :

1 + tan² θ = ____
∴ 1 + tan² θ = ____²
∴ tan² θ = \(\dfrac{625}{49}\) – ____
= \(\dfrac{625 - 49}{49}\)
∴ tan² θ = \(\dfrac{576}{49}\)
∴ tan θ = ____

Q.2 (A)(3) In the following figure, side of square ABCD is 7 cm. With centre D and radius DA, sector D-AXC is drawn. Fill in the following boxes properly and find out the area of shaded region :

[Figure: square ABCD with A at the top left, D at the top right, B at the bottom left and C at the bottom right, side 7 cm. A quarter circle (sector D-AXC) with centre D and radius DA = 7 cm is drawn from A to C inside the square, passing through X. The region between the sides AB, BC and the arc AXC is shaded.]

Solution :

Area of square = (side)²
= (7)²
∴ Area of square = ____ cm²
If area of sector (D-AXC) = 38.5 cm², then
A (shaded region) = A ____ – A ____
= 49 cm² – 38.5 cm²
= ____ cm²

Q.2 (B)(1) Find QP using given information in the figure :

[Figure: Δ MNP with N at the lower left, M at the top and P at the lower right. Seg NQ is drawn to side MP, and the two angles at N are marked equal, so NQ bisects ∠MNP. MN = 25, MQ = 14, NP = 40.]

Q.2 (B)(2) In Δ RST, ∠S = 90º, ∠T = 30º, RT = 12 cm, then find RS and ST.

Q.2 (B)(3) In the following figure, chord MN and chord RS intersect at point D. If RD = 15, DS = 4, MD = 8, find DN.

[Figure: a circle with chords MN and RS intersecting at the point D inside the circle, so that R–D–S and M–D–N.]

Q.2 (B)(4) Find the co-ordinates of the midpoint of the line segment joining points P(0, 6) and Q(12, 20).

Q.2 (B)(5) Prove that : sin² θ + cos² θ = 1.

Q.3 (A)(1) In the following figure, seg XY || side AC. If 2AX = 3BX and XY = 9, complete the activity to find the value of AC.

[Figure: Δ ABC with A at the top, B at the lower left and C at the lower right; X lies on side AB and Y lies on side BC, and seg XY is parallel to side AC.]

Activity :

2AX = 3BX

∴ \(\dfrac{AX}{BX} = \dfrac{3}{2}\)

∴ \(\dfrac{AX + BX}{BX} = \dfrac{____ + ____}{2}\) .......... (By componendo)

\(\dfrac{AB}{BX} = \dfrac{____}{2}\)

Δ BCA ~ Δ BYX ............. (____ Test of similarity)

∴ \(\dfrac{BA}{BX} = \dfrac{AC}{XY}\) .............. (Corresponding sides of similar triangles)

∴ \(\dfrac{5}{____} = \dfrac{AC}{9}\)

∴ AC = ____

Q.3 (A)(2) For finding AB and BC with the help of information given in the following figure, complete the following activity :

[Figure: Δ ABC with ∠B = 90º; the sides AB and BC carry identical tick marks showing AB = BC, and the hypotenuse AC = \(\sqrt{8}\).]

Activity :

AB = BC .................... ____

∴ ∠BAC = ____

∴ AB = BC = ____ × AC

= \(\dfrac{1}{\sqrt{2}} \times\) ____

= \(\dfrac{1}{\sqrt{2}} \times 2 \times\) ____

AB = BC = ____

Q.3 (B)(1) Prove that : The tangent segments drawn from an external point to the circle are congruent.

[Figure: a circle with centre O and an external point P; tangent segments PA and PB touch the circle at A and B; seg OP, seg OA and seg OB are drawn.]

Q.3 (B)(2) 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.

Q.3 (B)(3) 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.

Q.3 (B)(4) A bucket is frustum shaped. Its height is 28 cm. Radii of circular faces are 12 cm and 15 cm. Find the capacity of the bucket in litres. \(\left(\pi = \dfrac{22}{7}\right)\)

Q.4 (1) Δ ABC ~ Δ ADE,

In Δ ABC, AB = 6.3 cm, ∠CAB = 50º, AC = 5.6 cm and \(\dfrac{AB}{AD} = \dfrac{7}{5}\).

Construct Δ ADE.

Q.4 (2) Surface area of sphere and total surface area of cube are same. Show that the ratio of the volume of the sphere to that of the cube is \(\sqrt{6} : \sqrt{\pi}\).

Q.4 (3) In Δ ABC, A-X-B and A-Y-C is such that segment XY || side BC. Segment XY divides Δ ABC in two equal areas, then find \(\dfrac{BX}{AB}\).

Q.5 (1) Seg PQ is a chord of a circle. Arc PXQ is a major arc and Arc PYQ is a minor arc. ∠POQ is central angle of the circle :

[Figure: a circle with centre O and a chord PQ; the major arc PXQ passes through the point X on the larger part of the circle and the minor arc PYQ passes through the point Y on the smaller part; ∠POQ is marked at the centre and the inscribed angles ∠PXQ and ∠PYQ are shown.]

(a) Draw the figure from given information.

(b) Find the measure of ∠PXQ, ∠PYQ and add m∠PXQ, m∠PYQ.

(c) Find the measure of ∠POQ. Write the relation between ∠PXQ and ∠POQ.

Q.5 (2) Two eagles are flying in the sky at height of \(10\sqrt{3}\) m above the ground. A boy standing at a point on the ground looks towards the eagles making angles of elevation of 60º and 30º respectively. Find the distance between these two eagles.