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Maharashtra SSC Class 10 Geometry July 2025 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.

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Q.1 (A)

1 mark each

  1. Q.1 (A) (1)1 mark
    If △ABC∼△DEF\triangle ABC \sim \triangle DEF, m∠B=60∘m\angle B = 60^\circ, then m∠E=m\angle E = ________.

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  2. Q.1 (A) (2)1 mark
    Two circles of radii 5.5 cm and 4.2 cm touch each other externally then distance between their centres is ________.

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  3. Q.1 (A) (3)1 mark
    A line makes an angle of 45∘45^\circ with the positive direction of X-axis. So the slope of the line is ________.

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  4. Q.1 (A) (4)1 mark
    The volume of a cube of side 2 cm is ________.

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Q.1 (B)

1 mark each

  1. Q.1 (B) (1)1 mark
    Find the diagonal of square whose side is 10 cm.
  2. Q.1 (B) (2)1 mark
    The ratio of corresponding sides of similar triangles is 3:53 : 5, then find the ratio of their areas.
  3. Q.1 (B) (3)1 mark
    Find the slope of the line passing through the points A(2,3)A(2, 3) and B(4,7)B(4, 7).
  4. Q.1 (B) (4)1 mark
    If sin⁡θ=725\sin\theta = \dfrac{7}{25}, then find the value of cosec⁡θ\operatorname{cosec}\theta.

Q.2 (A)

2 marks each · attempt any 2

  1. Q.2 (A) (1)2 marks
    In the given figure, AR⊥BCAR \perp BC, AR⊥PQAR \perp PQ, then complete the activity for finding A(△ABC)A(△APQ)\dfrac{A(\triangle ABC)}{A(\triangle APQ)}.
  2. Q.2 (A) (2)2 marks
    In the following figure, seg PS is a tangent segment, line PR is a secant. If PQ=3.6PQ = 3.6, QR=6.4QR = 6.4, then find PS by completing the following activity.
  3. Q.2 (A) (3)2 marks
    Measure of an arc of a circle is 90∘90^\circ and its radius is 14 cm. Complete the following activity to find the length of an arc.

Q.2 (B)

2 marks each · attempt any 4

  1. Q.2 (B) (1)2 marks
    In the following figure, in △LMN\triangle LMN, ray MT bisects ∠LMN\angle LMN. If LM=6LM = 6, MN=10MN = 10, TN=8TN = 8, then find LT.
  2. Q.2 (B) (2)2 marks
    Find surface area of sphere of radius 7 cm.
  3. Q.2 (B) (3)2 marks
    In the following figure, m(arc NS)=125∘m(\text{arc } NS) = 125^\circ, m(arc EF)=37∘m(\text{arc } EF) = 37^\circ. Find m∠NMSm\angle NMS.
  4. Q.2 (B) (4)2 marks
    Find the co-ordinates of midpoint of the segment joining the points P(22,20)P(22, 20) and Q(0,16)Q(0, 16).
  5. Q.2 (B) (5)2 marks
    Find the volume of a cone if radius of its base is 7 cm and its perpendicular height is 15 cm.

Q.3 (A)

3 marks each · attempt any 1

  1. Q.3 (A) (1)3 marks
    If tan⁡θ=1\tan\theta = 1, then find the value of sin⁡θ+cos⁡θsec⁡θ+cosec⁡θ\dfrac{\sin\theta + \cos\theta}{\sec\theta + \operatorname{cosec}\theta} by completing the following activity.
  2. Q.3 (A) (2)3 marks
    In the following figure, point O is the centre of the circle and length of chord AB is equal to the radius of the circle. Find the measures of: (i) ∠AOB\angle AOB (ii) arc AB (iii) ∠ACB\angle ACB by completing the activity.

Q.3 (B)

3 marks each · attempt any 2

  1. Q.3 (B) (1)3 marks
    Find 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.
  2. Q.3 (B) (2)3 marks
    Draw a circle with centre O of radius 3.4 cm. Draw a chord MN of length 5.7 cm in it. Construct tangents at point M and N to the circle.
  3. Q.3 (B) (3)3 marks
    A storm broke a tree and the treetop rested 20 m from the base of the tree, making an angle of 60∘60^\circ with the horizontal. Find the height of the tree.
  4. Q.3 (B) (4)3 marks
    Prove that, 'In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of remaining two sides'.

Q.4

4 marks each · attempt any 2

  1. Q.4 (1)4 marks
    △ABC\triangle ABC has sides of length 4 cm, 5 cm and 6 cm while △PQR\triangle PQR has perimeter of 90 cm. If △ABC\triangle ABC is similar to △PQR\triangle PQR, then find the length of corresponding sides of △PQR\triangle PQR.
  2. Q.4 (2)4 marks
    △ABC∼△PBR\triangle ABC \sim \triangle PBR, BC=8BC = 8 cm, AC=10AC = 10 cm, ∠B=90∘\angle B = 90^\circ, BCBR=54\dfrac{BC}{BR} = \dfrac{5}{4}, then construct △PBR\triangle PBR.
  3. Q.4 (3)4 marks
    In the following figure △ABC\triangle ABC is an isosceles triangle with perimeter 44 cm. The base BC is of length 12 cm. Side AB and AC are congruent. A circle touches the three sides of triangle as shown. Find the length of tangent segment from A to circle.

Q.5

3 marks each · attempt any 1

  1. Draw right-angled △ABC\triangle ABC of lengths of sides are 3 cm, 4 cm and 5 cm. Draw median on the hypotenuse of △ABC\triangle ABC. Then:
    Q.5 (1) (i)3 marks
    Measure the length of median and write it.
  2. Q.5 (1) (ii)
    By obeserving lengths of median and hypotenuse write your observations.
  3. Observe the given figure and answer the following questions:
    Q.5 (2) (i)3 marks
    How many surfaces does a solid cone have?
  4. Q.5 (2) (ii)
    What are the names of slant height and perpendicular height in the given figure?
  5. Q.5 (2) (iii)
    If slant height of solid cone is 10 cm and perpendicular height is 8 cm, then find diameter of base of solid cone?