SSC (English Medium)
SSC (Marathi Semi-English)
Academic Year: 2024-2025
Date & Time: 7th March 2025, 11:00 am
Duration: 2h
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Note:
- 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.
- 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: [0.02] Pythagoras Theorem
∠ACB is inscribed angle in a circle with centre O. If ∠ACB = 65°, then what is the measure of its intercepted arc AXВ?
65°
230°
295°
130°
Chapter:
The distance of the point (3, 4) from the origin is ______.
25
5
7
1
−5
Chapter:
If the radius of the cone is 5 cm and its perpendicular height is 12 cm, then the slant height is ______.
17 cm
4 cm
13 cm
60 cm
Chapter:
In ∆ABC, B – D – C and BD = 7, BC = 20, then find the following ratio.
`(A(∆ABD))/(A(∆ABC))`
Chapter: [0.01] Similarity
In the given figure, ∠MNP = 90°, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.
Chapter: [0.02] Pythagoras Theorem
Angle made by a line with the positive direction of X-axis is 30°. Find slope of that line.
Chapter:
In cyclic quadrilateral ABCD m∠A = 100°, then find m∠C.
Chapter:
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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 by using the following activity. (π = 3.14)
Activity:
r = 10 cm, θ = 90°, π = 3.14
A(P − AXB) = `θ/360 xx square`
= `square/360 xx 3.14 xx 10^2`
= `1/4 xx square`
A(P − AXB) = `square` sq. cm
Chapter:
In the following figure, chord MN and chord RS intersect at point D. If RD = 15, DS = 4, MD = 8, find DN by completing the following activity:
Activity:
∴ MD × DN = `square` × DS ...(Theorem of internal division of chords)
∴ `square` × DN = 15 × 4
∴ DN = `square/8`
∴ DN = `square`
Chapter:
An observer at a distance of 10 m from a tree looks at the top of the tree; the angle of elevation is 60°. To find the height of the tree, complete the activity. `(sqrt3 = 1.73)`
Activity:
In the figure given above, AB = h = height of tree, BC = 10 m, distance of the observer from the tree.
Angle of elevation (θ) = ∠BCA = 60°
tan θ = `square/("BC")` ...(I)
tan 60° = `square` ...(II)
`("AB")/("BC") = sqrt3` ...(From (I) and (II))
AB = BC × `sqrt3` = `10sqrt3`
AB = 10 × 1.73 = `square`
∴ Height of the tree is `square` m.
Chapter:
In ΔABC, DE || BC. If DB = 5.4 cm, AD = 1.8 cm, EC = 7.2 cm, then find AE.
Chapter:
In the figure given below, find RS and PS using the information given in ΔPSR.
Chapter:
In the adjoining figure, circle with center D touches the sides of ∠ACB at A and B. If ∠ACB = 52°, find measure of ∠ADB.
Chapter: [0.03] Circle
Determine whether the points are collinear.
A(1, −3), B(2, −5), C(−4, 7)
Chapter: [0.05] Co-ordinate Geometry
If sinθ = `11/61`, find the values of cosθ using trigonometric identity.
Chapter: [0.06] Trigonometry
In the given fig, XY || seg AC. If 2AX = 3BX and XY = 9. Complete the activity to find the value of AC.
Activity:
2AX = 3BX ...(Given)
∴ `"AX"/"BX" = 3/square`
`("AX" +"BX")/"BX" = (3 + 2)/2` ...(by componendo)
`square/"BX" = 5/2` ...(I)
Now ΔBCA ~ ΔBYX ...`(square" test of similarity")`
∴ `"BA"/"BX" = "AC"/"XY"` ...(Corresponding sides of similar triangles)
∴ `square/square = "AC"/9` ...[From(I)]
∴ AC = `square`
Chapter:
Complete the following activity to prove that the sum of squares of diagonals of a rhombus is equal to the sum of the squares of the sides.
Given:
`square` PQRS is a rhombus. Diagonals PR and SQ intersect each other at point Т.
To prove: PS2 + SR2 + QR2 + PQ2 = PR2 + QS2
Activity:
Diagonals of a rhombus bisect each other.
In ΔPQS, PT is the median, and in ΔQRS, RT is the median.
∴ By Apollonius theorem,
PQ2 + PS2 = `square` + 2QT2 ...(I)
QR2 + SR2 = `square` + 2QT2 ...(II)
Adding (I) and (II),
PQ2 + PS2 + QR2 + SR2 = 2(PT2 + `square`) + 4QT2
= 2(PT2 + `square`) + 4QT2 ...(RT = PT)
= 4PT2 + 4QT2
= (`square`)2 + (2QT)2
∴ PQ2 + PS2 + QR2 + SR2 = PR2 + `square`
Chapter:
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Show that points P(1, –2), Q(5, 2), R(3, –1), S(–1, –5) are the vertices of a parallelogram.
Chapter: [0.05] Co-ordinate Geometry
Prove the following theorem:
Tangent segments drawn from an external point to the circle are congruent.
Chapter: [0.03] Circle
Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance 7.3 cm from the centre.
Chapter: [0.04] Geometric Constructions
How many solid cylinders of radius 10 cm and height 6 cm can be made by melting a solid sphere of radius 30 cm?
Chapter:
In the following figure, DE || BC, then:
- If DE = 4 cm, BC = 8 cm, A(ΔADE) = 25 cm2, find A(ΔABC).
- If DE : BC = 3 : 5, then find A(ΔADE) : A(`square`DBCE).
Chapter:
ΔABC ~ ΔPQR. In ΔABC, AB = 3.6 cm, BC = 4 cm, AC = 4.2 cm. The corresponding sides of ΔABC and ΔPQR are in the ratio 2 : 3. Construct ΔABC and ΔPQR.
Chapter:
The radii of the circular ends of a frustum of a cone are 14 cm and 8 cm. If the height of the frustum is 8 cm, find: (π = 3.14)
- Curved surface area of frustum.
- Total surface area of the frustum.
- Volume of the frustum.
Chapter:
`square`ABCD is a rectangle. Taking AD as a diameter, a semicircle AXD is drawn which intersects the diagonal BD at X. If AB = 12 cm, AD = 9 cm, then find the values of BD and BX.
Chapter:
Taking θ = 30° to verify the following trigonometric identity:
sin2θ + cos2θ = 1
Chapter:
Taking θ = 30° to verify the following trigonometric identity:
1 + tan2θ = sec2θ
Chapter:
Taking θ = 30° to verify the following trigonometric identity:
1 + cot2θ = cosec2θ
Chapter:
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