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Maharashtra SSC Class 10 Geometry March 2026 question paper

Maximum marks 40 · Time 2 hours

Try each question first, then open its model answer. Where the paper offers a choice, both questions are shown with OR between them.

Q.1 (A)

1 mark each

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

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  2. Q.1 (A) (2)1 mark
    Two circles having radii 44 cm and 55 cm touch each other internally. Then the distance between the centres is ________.

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

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  4. Q.1 (A) (4)1 mark
    If the side of the cube is 55 cm, then the volume of that cube is ________.

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Q.1 (B)

1 mark each

  1. Q.1 (B) (1)1 mark
    The ratio of corresponding sides of similar triangles is 3:53 : 5, then find the ratio of their areas.
  2. Q.1 (B) (2)1 mark
    Find the side of a square if its diagonal is 10210\sqrt{2} cm.
  3. Q.1 (B) (3)1 mark
    If the measure of minor arc is 70∘70^\circ, then find the measure of the corresponding major arc.
  4. Q.1 (B) (4)1 mark
    Angle made by the line with the positive direction of X-axis is 45∘45^\circ, find the slope of the line.

Q.2 (A)

2 marks each · attempt any 2

  1. Q.2 (A) (1)2 marks
    In the following figure, seg PS is a tangent segment and line PR is a secant. If PQ=3.6PQ = 3.6, QR=6.4QR = 6.4, complete the activity to find PS.
  2. Q.2 (A) (2)2 marks
    If sec⁡θ=257\sec\theta = \dfrac{25}{7}, complete the activity to find the value of tan⁡θ\tan\theta.
  3. Q.2 (A) (3)2 marks
    In the following figure, side of square ABCD is 77 cm. With centre D and radius DA, sector D-AXC is drawn. Complete the activity to find the area of the shaded region. (Area of sector D-AXC=38.5D\text{-}AXC = 38.5 cm2^2.)

Q.2 (B)

2 marks each · attempt any 4

  1. Q.2 (B) (1)2 marks
    Find QP using the given information in the figure. (In △MNP\triangle MNP, Q lies on side MP, seg NQ bisects ∠MNP\angle MNP, MN=25MN = 25, MQ=14MQ = 14, NP=40NP = 40.)
  2. Q.2 (B) (2)2 marks
    In △RST\triangle RST, ∠S=90∘\angle S = 90^\circ, ∠T=30∘\angle T = 30^\circ, RT=12RT = 12 cm, then find RS and ST.
  3. Q.2 (B) (3)2 marks
    In the following figure, chord MN and chord RS intersect at point D. If RD=15RD = 15, DS=4DS = 4, MD=8MD = 8, find DN.
  4. Q.2 (B) (4)2 marks
    Find the co-ordinates of the midpoint of the line segment joining the points P(0,6)P(0, 6) and Q(12,20)Q(12, 20).
  5. Q.2 (B) (5)2 marks
    Prove that: sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1.

Q.3 (A)

3 marks each · attempt any 1

  1. Q.3 (A) (1)3 marks
    In the following figure, seg XY ∥\parallel side AC. If 2AX=3BX2AX = 3BX and XY=9XY = 9, complete the activity to find the value of AC.
  2. Q.3 (A) (2)3 marks
    For finding AB and BC with the help of the information given in the following figure, complete the following activity. (In △ABC\triangle ABC, ∠B=90∘\angle B = 90^\circ, AB=BCAB = BC and hypotenuse AC=8AC = \sqrt{8}.)

Q.3 (B)

3 marks each · attempt any 2

  1. Q.3 (B) (1)3 marks
    Prove that: The tangent segments drawn from an external point to the circle are congruent.
  2. Q.3 (B) (2)3 marks
    Draw a circle with centre O and radius 3.53.5 cm, take a point P at a distance 5.75.7 cm from the centre. Draw tangents to the circle from point P.
  3. Q.3 (B) (3)3 marks
    Find the co-ordinates of point P, if P divides the line segment joining the points A(−1,7)A(-1, 7) and B(4,−3)B(4, -3) in the ratio 2:32 : 3.
  4. Q.3 (B) (4)3 marks
    A bucket is frustum shaped. Its height is 2828 cm. Radii of circular faces are 1212 cm and 1515 cm. Find the capacity of the bucket in litres. (π=227)\left(\pi = \dfrac{22}{7}\right)

Q.4

4 marks each · attempt any 2

  1. Q.4 (1)4 marks
    △ABC∼△ADE\triangle ABC \sim \triangle ADE. In △ABC\triangle ABC, AB=6.3AB = 6.3 cm, ∠CAB=50∘\angle CAB = 50^\circ, AC=5.6AC = 5.6 cm and ABAD=75\dfrac{AB}{AD} = \dfrac{7}{5}. Construct △ADE\triangle ADE.
  2. Q.4 (2)4 marks
    Surface area of a sphere and total surface area of a cube are same. Show that the ratio of the volume of the sphere to that of the cube is 6:π\sqrt{6} : \sqrt{\pi}.
  3. Q.4 (3)4 marks
    In △ABC\triangle ABC, A-X-B and A-Y-C is such that segment XY ∥\parallel side BC. Segment XY divides △ABC\triangle ABC in two equal areas, then find BXAB\dfrac{BX}{AB}.

Q.5

3 marks each · attempt any 1

  1. Q.5 (1)3 marks
    Seg PQ is a chord of a circle. Arc PXQ is a major arc and arc PYQ is a minor arc. ∠POQ\angle POQ is the central angle of the circle. (a) Draw the figure from the given information. (b) Find the measure of ∠PXQ\angle PXQ, ∠PYQ\angle PYQ and add m∠PXQ, m∠PYQm\angle PXQ,\ m\angle PYQ. (c) Find the measure of ∠POQ\angle POQ. Write the relation between ∠PXQ\angle PXQ and ∠POQ\angle POQ.
  2. Q.5 (2)3 marks
    Two eagles are flying in the sky at a height of 10310\sqrt{3} m above the ground. A boy standing at a point on the ground looks towards the eagles making angles of elevation of 60∘60^\circ and 30∘30^\circ respectively. Find the distance between these two eagles.