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Maharashtra SSC Class 10 Geometry March 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.

Q.1 (A)

1 mark each

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

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  2. Q.1 (A) (2)1 mark
    ∠ACB\angle ACB is an inscribed angle in a circle with centre O. If ∠ACB=65∘\angle ACB = 65^\circ, then what is the measure of its intercepted arc AXB?

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  3. Q.1 (A) (3)1 mark
    Distance of the point (3,4)(3, 4) from the origin is ________.

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  4. Q.1 (A) (4)1 mark
    If the radius of a cone is 5 cm and its perpendicular height is 12 cm, then the slant height is ________.

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Q.1 (B)

1 mark each

  1. Q.1 (B) (1)1 mark
    In the following figure △ABC\triangle ABC, B–D–CB\text{–}D\text{–}C and BD=7BD = 7, BC=20BC = 20, then find A(△ABD)A(△ABC)\dfrac{A(\triangle ABD)}{A(\triangle ABC)}.
  2. Q.1 (B) (2)1 mark
    In the following figure ∠MNP=90∘\angle MNP = 90^\circ, seg NQ⊥NQ \perp seg MPMP, MQ=9MQ = 9, QP=4QP = 4, find NQNQ.
  3. Q.1 (B) (3)1 mark
    The angle made by a line with the positive direction of the X-axis is 30∘30^\circ. Find the slope of that line.
  4. Q.1 (B) (4)1 mark
    In cyclic quadrilateral ABCD, m∠A=100∘m\angle A = 100^\circ, then find m∠Cm\angle C.

Q.2 (A)

2 marks each · attempt any 2

  1. Q.2 (A) (1)2 marks
    The radius of a circle with centre P is 10 cm. If chord AB of the circle subtends a right angle at P, find the area of the minor sector P-AXB by completing the activity. (π=3.14\pi = 3.14)
  2. Q.2 (A) (2)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 DNDN by completing the activity.
  3. Q.2 (A) (3)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∘60^\circ. Find the height of the tree by completing the activity. (3=1.73\sqrt{3} = 1.73)

Q.2 (B)

2 marks each · attempt any 4

  1. Q.2 (B) (1)2 marks
    In △ABC\triangle ABC, DE∥BCDE \parallel BC. If DB=5.4DB = 5.4 cm, AD=1.8AD = 1.8 cm, EC=7.2EC = 7.2 cm, then find AEAE.
  2. Q.2 (B) (2)2 marks
    In the figure given below, find RSRS and PSPS using the information given in △PSR\triangle PSR.
  3. Q.2 (B) (3)2 marks
    In the following figure, a circle with centre D touches the sides of ∠ACB\angle ACB at A and B. If ∠ACB=52∘\angle ACB = 52^\circ, find the measure of ∠ADB\angle ADB.
  4. Q.2 (B) (4)2 marks
    Verify whether the points A(1,−3)A(1, -3), B(2,−5)B(2, -5) and C(−4,7)C(-4, 7) are collinear or not.
  5. Q.2 (B) (5)2 marks
    If sin⁡θ=1161\sin\theta = \dfrac{11}{61}, find the value of cos⁡θ\cos\theta using a trigonometric identity.

Q.3 (A)

3 marks each · attempt any 1

  1. Q.3 (A) (1)3 marks
    In the following figure, XY∥XY \parallel seg 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
    Complete the activity to prove that the sum of the squares of the diagonals of a rhombus is equal to the sum of the squares of its sides. (□PQRS\square PQRS is a rhombus; diagonals PR and SQ intersect each other at point T.)

Q.3 (B)

3 marks each · attempt any 2

  1. Q.3 (B) (1)3 marks
    Show that the points P(1,−2)P(1, -2), Q(5,2)Q(5, 2), R(3,−1)R(3, -1), S(−1,−5)S(-1, -5) are the vertices of a parallelogram.
  2. Q.3 (B) (2)3 marks
    Prove that the tangent segments drawn from an external point to a circle are congruent.
  3. Q.3 (B) (3)3 marks
    Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance of 7.3 cm from the centre.
  4. Q.3 (B) (4)3 marks
    How many solid cylinders of radius 10 cm and height 6 cm can be made by melting a solid sphere of radius 30 cm?

Q.4

4 marks each · attempt any 2

  1. In the following figure DE∥BCDE \parallel BC, then:
    Q.4 (1) (i)4 marks
    If DE=4DE = 4 cm, BC=8BC = 8 cm, A(△ADE)=25A(\triangle ADE) = 25 cm2^2, find A(△ABC)A(\triangle ABC).
  2. Q.4 (1) (ii)
    If DE:BC=3:5DE : BC = 3 : 5, then find A(△ADE):A(□DBCE)A(\triangle ADE) : A(\square DBCE).
  3. Q.4 (2)4 marks
    △ABC∼△PQR\triangle ABC \sim \triangle PQR. In △ABC\triangle ABC, AB=3.6AB = 3.6 cm, BC=4BC = 4 cm and AC=4.2AC = 4.2 cm. The corresponding sides of △ABC\triangle ABC and △PQR\triangle PQR are in the ratio 2:32 : 3. Construct △ABC\triangle ABC and △PQR\triangle PQR.
  4. The radii of the circular ends of a frustum of a cone are 14 cm and 8 cm. The height of the frustum is 8 cm. (π=3.14\pi = 3.14)
    Q.4 (3) (i)4 marks
    Find the curved surface area of the frustum.
  5. Q.4 (3) (ii)
    Find the total surface area of the frustum.
  6. Q.4 (3) (iii)
    Find the volume of the frustum.

Q.5

3 marks each · attempt any 1

  1. Q.5 (1)3 marks
    □ABCD\square ABCD is a rectangle. Taking AD as a diameter, a semicircle AXD is drawn which intersects the diagonal BD at X. If AB=12AB = 12 cm, AD=9AD = 9 cm, then find the values of BD and BX.
  2. Taking θ=30∘\theta = 30^\circ, verify the following trigonometric identities:
    Q.5 (2) (i)3 marks
    sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1
  3. Q.5 (2) (ii)
    1+tan⁡2θ=sec⁡2θ1 + \tan^2\theta = \sec^2\theta
  4. Q.5 (2) (iii)
    1+cot⁡2θ=cosec⁡2θ1 + \cot^2\theta = \operatorname{cosec}^2\theta