SSC (English Medium)
SSC (Marathi Semi-English)
Academic Year: 2024-2025
Date: March 2025
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General Instructions :
- All questions are compulsory.
- Use of a calculator is not allowed.
- The numbers to the right of the questions indicate full marks.
- In case of MCQs (Q. No. 1(A)) only the first attempt will be evaluated and will be given credit.
- For every MCQ, the correct alternative (A), (B), (C) or (D) with subquestion number is to be written as an answer.
- Draw proper figures for answers wherever necessary.
- The marks of construction should be clear. Do not erase them.
- Diagram is essential for writing the proof of the theorem.
Find the coordinates of the mid-point of the line segment with points A(– 2, 4) and B(–6, –6) on both ends.
(4, –1)
(–4, –1)
(4, 1)
(– 4, 1)
Chapter: [0.05] Co-ordinate Geometry
In the figure, line l is parallel to X-axis. Which of the following statement is true?
The slope is zero.
The slope cannot be determined.
The slope is positive.
The slope is negative.
Chapter: [0.05] Co-ordinate Geometry
If sec θ = `1/2`, what will be the value of cos θ?
2
1
3
5
Chapter: [0.06] Trigonometry
If ΔABC ∼ ΔDEF such that ∠A = 92° and ∠B = 40°, then ∠F = ?
52°
92°
40°
48°
Chapter: [0.01] Similarity
The coordinates of two points are P(4, 5) and Q(–1, 6). Find the difference between their abscissas.
Chapter: [0.05] Co-ordinate Geometry
In ΔABC, ∠ABC = 90° and ∠ACB = θ. Then write the ratios of sin θ and tan θ from the figure.
Chapter: [0.06] Trigonometry
The three angles of a quadrilateral are 100°, 60°, 70°. Find the fourth angle.
Chapter: [0.03] Circle
If the coordinate of point A on the number line is –1 and that of point B is 6, then find d(A, B).
Chapter: [0.05] Co-ordinate Geometry
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From the top of building AB, a point C is observed on the ground whose angle of depression is 60° and which is at a distance of 40 m from the base of the building. Complete the following activity to find the height of building AB.
From figure, BC = `square`, ∠ACB = `square`
In ΔACB,
tan `square = square/(BC)`
⇒ `square = square/square`
⇒ `square = square`
Hence, the height of the building AB is `square`.
Chapter: [0.06] Trigonometry
Find the total surface area of frustum, if its radii are 15 cm and 7 cm. Also, the slant height of the frustum is 14 cm.
Radii of the frustum = `square` cm and `square` cm
Slant height of the frustum = `square` cm
Total surface area = `π[(r_1^2 + r_2^2 + (r_1 + r_2)l]`
= `22/7 [square + square + (square + square) square]`
= `22/7 (square)`
= `square` cm2
Hence, the total surface area of the frustum is `square`.
Chapter: [0.07] Mensuration
If the length of the diagonal of a cube is `5sqrt(3)` cm, find the total surface area.
Length of the diagonal of the cube = `square`
So, `square` = `5sqrt(3)`
⇒ Side = `square`
Total surface area of cube = `square`
= `square` × `square` × `square`
= `square` cm2
Hence, the total surface area is `square`.
Chapter: [0.07] Mensuration
In the following figure, XY = 10 cm and LT = 4 cm. Find the length of XT.
Chapter: [0.03] Circle
Point C divides the line segment whose points are A(4, –6) and B(5, 9) in the ratio 2:1. Find the coordinates of C.
Chapter: [0.05] Co-ordinate Geometry
Find the slope of the line passing through given points G(3, 7) and K(–2, –3).
Chapter: [0.05] Co-ordinate Geometry
There is a ladder of length 32 m which rests on a pole. If the height of pole is 18 m, determine the distance between the foot of ladder and the pole.
Chapter: [0.02] Pythagoras Theorem
In ΔABC, AP ⊥ BC, BQ ⊥ AC. If AP = 7, BQ = 8 and BC = 12, then find AC.
Chapter: [0.01] Similarity
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Determine whether the following points are collinear. A(–1, –1), B(0, 1), C(1, 3)
Given: Points A(–1, –1), B(0, 1) and C(1, 3)
Slope of line AB = `(square - square)/(square - square) = square/square` = 2
Slope of line BC = `(square - square)/(square - square) = square/square` = 2
Slope of line AB = Slope of line BC and B is the common point.
∴ Points A, B and C are collinear.
Chapter: [0.05] Co-ordinate Geometry
Prove that: cot θ + tan θ = cosec θ·sec θ
Proof: L.H.S. = cot θ + tan θ
= `square/square + square/square` ......`[∵ cot θ = square/square, tan θ = square/square]`
= `(square + square)/(square xx square)` .....`[∵ square + square = 1]`
= `1/(square xx square)`
= `1/square xx 1/square`
= cosec θ·sec θ ......`[∵ "cosec" θ = 1/square, sec θ = 1/square]`
= R.H.S.
∴ L.H.S. = R.H.S.
∴ cot θ + tan θ = cosec·sec θ
Chapter: [0.06] Trigonometry
The angles of elevation of the bottom and the top of a flag fixed at the top of a 25 m high building are 30° and 60° respectively from a point on the ground. Find the height of the flag.
Chapter: [0.06] Trigonometry
In the figure with ΔABC, P, Q, R are the mid-points of AB, AC and BC respectively. Then prove that the four triangles formed are congruent to each other.
Chapter: [0.01] Similarity
Draw a line segment AB of length 10 cm and divide it internally in the ratio of 2:5 Justify the division of line segment AB.
Chapter: [0.04] Geometric Constructions [0.05] Co-ordinate Geometry
In the given figure, a rectangle ABCD is inscribed inside a semi-circle of radius 10 cm. Using the dimensions given in the figure, determine the area of the shaded region.
Chapter: [0.07] Mensuration
A tangent ADB is drawn to a circle at D whose centre is C. Also, PQ is a chord parallel to AB and ∠QDB = 50°. Find the value of ∠PDQ.
Chapter: [0.01] Similarity
In an equilateral triangle PQR, prove that PS2 = 3(QS)2.
Chapter: [0.02] Pythagoras Theorem
The radius of a metallic sphere is 8 cm. It was melted to make a wire of diameter 6 mm. Find the length of the wire.
Chapter: [0.07] Mensuration
In the given figure, triangle PQR is right-angled at Q. S is the mid-point of side QR. Prove that QR2 = 4(PS2 – PQ2).
Chapter: [0.02] Pythagoras Theorem
The perimeter of an arc of radius 4.2 cm is 12.8 cm. Determine the angle subtended by the arc at the centre of circle.
Chapter: [0.07] Mensuration
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