SSC (English Medium)
SSC (Marathi Semi-English)
Academic Year: 2025-2026
Date & Time: 9th March 2026, 11:00 am
Duration: 2h
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- All questions are compulsory.
- Use ofa 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.
- Draw proper figures wherever necessary.
- The marks of construction should be clear. Do not erase them.
- Diagram is essential for writing the proof of the theorem.
Out of the following, which is the Pythagorean triplet?
(1, 5, 10)
(3, 4, 5)
(2, 2, 2)
(5, 5, 2)
Chapter: [2] Pythagoras Theorem
Two circles having radii 4 cm and 5 cm touch each other internally. Then the distance between the centres is ______.
4 cm
5 cm
1 cm
9 cm
Chapter:
Out of the following, points ______ lies to the right of the origin on X-axis.
(–2, 0)
(0, 2)
(2, 3)
(2, 0)
Chapter:
If the side of the cube is 5 cm, then the volume of that cube is ______.
10 cm3
100 cm3
125 cm3
25 cm3
Chapter:
The ratio of corresponding sides of similar triangles is 3 : 5; then find the ratio of their areas.
Chapter:
Find the side of a square whose diagonal is `10sqrt2` cm.
Chapter: [2] Pythagoras Theorem
If the measure of a minor arc is 70°, then find the measure of the corresponding major arc.
Chapter:
The angle made by the line with the positive direction of the X-axis is given. Find the slope of the line:
45°
Chapter:
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In the following figure, seg PS is a tangent segment, and line P is a secant. If PQ = 3.6, QR = 6.4, find PS.
Activity:
∴ PS2 = `square` × PR (Tangent sccant segment theorem)
= PQ × [PQ + QR]
= `square` × [3.6 + 6.4]
= 3.6 × `square`
∴ PS2 = 36
PS = `square`
Chapter:
If sec θ = `25/7`, then find the value of tan θ.
Solution:
1 + tan2 θ = `square`
∴ 1 + tan2 = `square^2`
∴ tan2 θ = `625/49 - square`
= `(625 - 49)/49`
tan2 θ = `576/49`
tan θ = `square`
Chapter:
In the following figure, the side of square ABCD is 7 cm, with centre D and radius DA. Sector D-AXC is drawn. Fill in the following boxes properly and find out the area of the shaded region:
Solution:
Area of square = (side)2
= (7)2
Area of square = `square` cm2
If the area of the sector (D-AХC) = 38.5 cm2, then
A (shaded region) = `A square - A square`
= 49 cm2 − 38.5 cm2
= `square` cm2
Chapter:
Find QP using given information in the figure.
Chapter: [1] Similarity
In ∆RST, ∠S = 90°, ∠T = 30°, RT = 12 cm, then find RS and ST.
Chapter: [2] Pythagoras Theorem
In the following figure, chord MN and chord RS intersect at point D. If RD = 15, DS = 4, and MD = 8, find DN.
Chapter:
Find the coordinates of the midpoint of the line segment joining P(0, 6) and Q(12, 20).
Chapter:
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In the following figure, seg XY || side AC. If 2AX = 3BX and XY = 9, complete the activity to find the value of AC.
Activity:
2AX = 3BX
∴ `"AX"/"BX" = 3/2`
∴ `(AX + BX)/"BX"` = `(square + square)/2` ...[By componendo]
∴ `"AX"/"BX" = square/2`
ΔBCA ~ ΔBYX ...[`square` test of similarity]
∴ `"BA"/"BX" = "AC"/"XY"` ....[corresponding sides of similar triangles]
∴ `5/square = "AC"/9`
∴ AC = `square`
Chapter:
For finding AB and BC with the help of the information given in the following figure, complete the following activity:
Activity:
AB = BС .....`square`
∴ ∠ BAC = `square`
∴ AB = BC = `square` × AC
= `1/sqrt2 xx square`
= `1/sqrt2 xx 2 xx square`
AB = BC = `square`
Chapter:
Prove that, tangent segments drawn from an external point to the circle are congruent.
Chapter:
Draw a circle with centre O and radius 3.5 cm. Take point P at a distance of 5.7 cm from the centre. Draw tangents to the circle from point P.
Chapter:
Find the coordinates of point P if P divides the line segment joining the points A(–1, 7) and B(4, –3) in the ratio 2 : 3.
Chapter:
A bucket is frustum-shaped. Its height is 28 cm. Radii of circular faces are 12 cm and 15 cm. Find the capacity of the bucket in litres. `(π = 22/7)`
Chapter:
Δ ABC ~ Δ ADE,
In Δ ABC, AB = 6.3 cm, ∠ CAB = 50°, AC = 5.6 cm, and `"AB"/"AD" = 7/5`,
Construct Δ ADE.
Chapter:
The surface area of a sphere and the total surface area of a cube are the same. Show that the ratio of the volume of the sphere to that of the cube is `sqrt6 : sqrtπ`
Chapter:
In ΔABC, A-X-B and A-Y-C are such that segment XY || side BC.
Segment XY divides Δ ABC into two equal areas, then find `"BX"/"AB"`.
Chapter:
Seg PQ is a chord of a circle. Arc PXQ is a major arc, and Arc PYQ is a minor arc. ∠POQ is the central angle of the circle:
- Draw the figure from the given information.
- Find the measure of ∠PXQ, ∠PYQ, and add m ∠PXQ, m ∠PYQ.
- Find the measure of ∠POQ. Write the relation between ∠PXQ and ∠POQ.
Chapter:
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