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Maharashtra SSC Class 10 Geometry July 2024 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
    In △ABC\triangle ABC and △PQR\triangle PQR, in a one to one correspondence of vertices, ABQR=BCPR=CAPQ\dfrac{AB}{QR} = \dfrac{BC}{PR} = \dfrac{CA}{PQ}, then ____ statement is true.

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  2. Q.1 (A) (2)1 mark
    Two circles of radii 5.5 cm and 3.3 cm respectively touch each other externally. Then the distance between their centres is ____.

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  3. Q.1 (A) (3)1 mark
    Seg AB is parallel to Y-axis and co-ordinates of point A are (1,3)(1, 3), then the co-ordinates of point B are ____.

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  4. Q.1 (A) (4)1 mark
    The volume of a cube of side 10 cm is ____.

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Q.1 (B)

1 mark each

  1. Q.1 (B) (1)1 mark
    In △ABC\triangle ABC, ∠B=90∘\angle B = 90^\circ, ∠C=30∘\angle C = 30^\circ, AC=12AC = 12 cm, then find AB.
  2. Q.1 (B) (2)1 mark
    In the above figure, m(arc MN)=70∘m(\text{arc } MN) = 70^\circ, find ∠MLN\angle MLN.
  3. Q.1 (B) (3)1 mark
    Find the value of sin⁡θ×cosec⁡θ\sin\theta \times \operatorname{cosec}\theta.
  4. Q.1 (B) (4)1 mark
    If radius of a circle is 4 cm and length of an arc is 10 cm, then find the area of the sector.

Q.2 (A)

2 marks each · attempt any 2

  1. Q.2 (A) (1)2 marks
    In the above figure, chord PQ and chord RS intersect at point T. Then complete the following activity to prove ∠STQ=12[m(arc SQ)+m(arc PR)]\angle STQ = \dfrac{1}{2}[m(\text{arc } SQ) + m(\text{arc } PR)].
  2. Q.2 (A) (2)2 marks
    If sec⁡θ=257\sec\theta = \dfrac{25}{7}, complete the following activity to find the value of tan⁡θ\tan\theta.
  3. Q.2 (A) (3)2 marks
    Complete the following activity to find the volume of a cone if the radius of its base is 7 cm and its perpendicular height is 6 cm.

Q.2 (B)

2 marks each · attempt any 4

  1. Q.2 (B) (1)2 marks
    Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.
  2. Q.2 (B) (2)2 marks
    In △PQR\triangle PQR, seg RS bisects ∠PRQ\angle PRQ. If PR=15PR = 15, RQ=20RQ = 20, PS=12PS = 12, then find SQ.
  3. Q.2 (B) (3)2 marks
    Find the surface area of a sphere of diameter 14 cm.
  4. Q.2 (B) (4)2 marks
    In the above figure, ∠PQR=90∘\angle PQR = 90^\circ, seg QN⊥QN \perp seg PR, PN=9PN = 9, NR=16NR = 16, find QN.
  5. Q.2 (B) (5)2 marks
    Find the slope of the line passing through the points A(3,3)A(3, 3) and B(5,7)B(5, 7).

Q.3 (A)

3 marks each · attempt any 1

  1. Q.3 (A) (1)3 marks
    In the given figure, AB∥CD∥EFAB \parallel CD \parallel EF. If AC=12AC = 12, CE=9CE = 9, BD=8BD = 8, then complete the following activity to find DF.
  2. Q.3 (A) (2)3 marks
    A cylinder is having radius 7 cm and height 21 cm. Complete the following activity to calculate its volume and circumference of its base.

Q.3 (B)

3 marks each · attempt any 2

  1. Q.3 (B) (1)3 marks
    Prove that, 'Opposite angles of a cyclic quadrilateral are supplementary'.
  2. Q.3 (B) (2)3 marks
    Draw a circle with centre P and radius 3.5 cm. Take point Q at a distance 8 cm from the centre. Construct tangents to the circle from point Q.
  3. Q.3 (B) (3)3 marks
    Show that points P(−2,3)P(-2, 3), Q(1,2)Q(1, 2), R(4,1)R(4, 1) are collinear.
  4. Q.3 (B) (4)3 marks
    If △PQR∼△LMN\triangle PQR \sim \triangle LMN, 9×A(△PQR)=16×A(△LMN)9 \times A(\triangle PQR) = 16 \times A(\triangle LMN) and QR=20QR = 20, then find MN.

Q.4

4 marks each · attempt any 2

  1. Q.4 (1)4 marks
    △ABC\triangle ABC is an equilateral triangle. Point D is on seg BC such that BD=15BCBD = \dfrac{1}{5} BC. Then prove that AD2AB2=2125\dfrac{AD^2}{AB^2} = \dfrac{21}{25}.
  2. Q.4 (2)4 marks
    △LMN∼△LQP\triangle LMN \sim \triangle LQP. In △LMN\triangle LMN, LM=3.6LM = 3.6 cm, ∠L=50∘\angle L = 50^\circ, LN=4.2LN = 4.2 cm and LMLQ=47\dfrac{LM}{LQ} = \dfrac{4}{7}. Construct △LQP\triangle LQP.
  3. Q.4 (3)4 marks
    To find the width of the river, a man observes the top of a tree, on the opposite bank making an angle of elevation of 60∘60^\circ. When he moves 24 meter backward from bank and observes the same top of the tree, his line of vision makes an angle of elevation of 30∘30^\circ. Find the height of the tree and width of the river. (3=1.73)(\sqrt{3} = 1.73)

Q.5

3 marks each · attempt any 1

  1. Q.5 (1)3 marks
    The diameter of circular garden is 13 meter. The distance between two gates of garden is 13 meter. An electric pole is to be erected on the circumference of the garden such that the difference between distance of the pole from each gate is 7 meter. Can such pole be erected? If yes, find the distance of the pole from each gate.
  2. Q.5 (2)3 marks
    The line x−6y+11=0x - 6y + 11 = 0 bisects the segment joining the points (8,−1)(8, -1) and (0,k)(0, k), then find the value of kk.