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Maharashtra SSC Class 10 Geometry March 2023 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
    If a,b,ca, b, c are sides of a triangle and a2+b2=c2a^2 + b^2 = c^2, name the type of triangle:

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  2. Q.1 (A) (2)1 mark
    Chords AB and CD of a circle intersect inside the circle at point E. If AE=4AE = 4, EB=10EB = 10, CE=8CE = 8, then find ED:

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  3. Q.1 (A) (3)1 mark
    Co-ordinates of the origin are ________.

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  4. Q.1 (A) (4)1 mark
    If the radius of the base of a cone is 7 cm and its height is 24 cm, then find its slant height:

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Q.1 (B)

1 mark each

  1. Q.1 (B) (1)1 mark
    If △ABC∼△PQR\triangle ABC \sim \triangle PQR and A(△ABC)A(△PQR)=1625\dfrac{A(\triangle ABC)}{A(\triangle PQR)} = \dfrac{16}{25}, then find AB:PQAB : PQ.
  2. Q.1 (B) (2)1 mark
    In △RST\triangle RST, ∠S=90∘\angle S = 90^\circ, ∠T=30∘\angle T = 30^\circ, RT=12RT = 12 cm, then find RS.
  3. Q.1 (B) (3)1 mark
    If the radius of a circle is 5 cm, then find the length of the longest chord of the circle.
  4. Q.1 (B) (4)1 mark
    Find the distance between the points O(0,0)O(0, 0) and P(3,4)P(3, 4).

Q.2 (A)

2 marks each · attempt any 2

  1. Q.2 (A) (1)2 marks
    In the given figure, points L, M, N lie on a circle and ∠L=35∘\angle L = 35^\circ. Complete the activity to find (i) m(arc MN)m(\text{arc } MN) and (ii) m(arc MLN)m(\text{arc } MLN).
  2. Q.2 (A) (2)2 marks
    Show that cot⁡θ+tan⁡θ=csc⁡θ×sec⁡θ\cot\theta + \tan\theta = \csc\theta \times \sec\theta.
  3. Q.2 (A) (3)2 marks
    Complete the activity to find the surface area of a sphere of radius 7 cm. (π=227)\left(\pi = \dfrac{22}{7}\right)

Q.2 (B)

2 marks each · attempt any 4

  1. Q.2 (B) (1)2 marks
    In trapezium ABCD, side AB ∥\parallel side PQ ∥\parallel side DC, with P on side AD and Q on side BC. AP=15AP = 15, PD=12PD = 12, QC=14QC = 14. Find BQ.
  2. Q.2 (B) (2)2 marks
    Find the length of the diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.
  3. Q.2 (B) (3)2 marks
    In the given figure, points G, D, E, F lie on a circle with centre C. ∠ECF=70∘\angle ECF = 70^\circ and m(arc DGF)=200∘m(\text{arc } DGF) = 200^\circ. Find (i) m(arc DE)m(\text{arc } DE) and (ii) m(arc DEF)m(\text{arc } DEF).
  4. Q.2 (B) (4)2 marks
    Show that the points A(−1,−1)A(-1, -1), B(0,1)B(0, 1), C(1,3)C(1, 3) are collinear.
  5. Q.2 (B) (5)2 marks
    A person is standing at a distance of 50 m from a temple looking at its top. The angle of elevation is 45∘45^\circ. Find the height of the temple.

Q.3 (A)

3 marks each · attempt any 1

  1. Q.3 (A) (1)3 marks
    In △PQR\triangle PQR, seg PM is a median. The angle bisectors of ∠PMQ\angle PMQ and ∠PMR\angle PMR intersect side PQ and side PR in points X and Y respectively. Complete the activity to prove that XY ∥\parallel QR.
  2. Q.3 (A) (2)3 marks
    Find the co-ordinates of point P, where P is the midpoint of the line segment AB with A(−4,2)A(-4, 2) and B(6,2)B(6, 2).

Q.3 (B)

3 marks each · attempt any 2

  1. Q.3 (B) (1)3 marks
    In △ABC\triangle ABC, seg AP is a median. If BC=18BC = 18 and AB2+AC2=260AB^2 + AC^2 = 260, find AP.
  2. Q.3 (B) (2)3 marks
    Prove that, "Angles inscribed in the same arc are congruent."
  3. Q.3 (B) (3)3 marks
    Draw a circle of radius 3.3 cm. Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at points P and Q.
  4. Q.3 (B) (4)3 marks
    The radii of the circular ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its curved surface area. (π=3.14)(\pi = 3.14)

Q.4

4 marks each · attempt any 2

  1. Q.4 (1)4 marks
    In △ABC\triangle ABC, seg DE ∥\parallel side BC. If 2A(△ADE)=A(□DBCE)2A(\triangle ADE) = A(\square DBCE), find AB:ADAB : AD and show that BC=3 DEBC = \sqrt{3}\, DE.
  2. Q.4 (2)4 marks
    △SHR∼△SVU\triangle SHR \sim \triangle SVU. In △SHR\triangle SHR, SH=4.5SH = 4.5 cm, HR=5.2HR = 5.2 cm, SR=5.8SR = 5.8 cm and SHSV=35\dfrac{SH}{SV} = \dfrac{3}{5}. Construct △SVU\triangle SVU.
  3. Q.4 (3)4 marks
    An ice-cream pot has a right circular cylindrical shape. The radius of the base is 12 cm and the height is 7 cm. This pot is completely filled with ice-cream. The entire ice-cream is given to students in the form of right circular ice-cream cones having diameter 4 cm and height 3.5 cm. If each student is given one cone, how many students can be served?

Q.5

3 marks each · attempt any 1

  1. Q.5 (1)3 marks
    In the given figure, a circle touches side BC of △ABC\triangle ABC at point P from outside the triangle. Lines AC and AB, when extended, are tangents to the circle at points N and M respectively. Prove that AM=12(Perimeter of △ABC)AM = \dfrac{1}{2}(\text{Perimeter of } \triangle ABC).
  2. Q.5 (2)3 marks
    Eliminate θ\theta if x=rcos⁡θx = r\cos\theta and y=rsin⁡θy = r\sin\theta.