SSC (English Medium)
SSC (Marathi Semi-English)
Academic Year: 2024-2025
Date & Time: 2nd July 2025, 11:00 am
Duration: 2h
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Note:
- All questions are compulsory.
- Use of 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.
If ΔABC ~ ΔDEF, m∠B = 60°, then m∠E = ______.
30°
60°
90°
45°
Chapter:
Two circles of radii 5.5 cm and 4.2 cm touch each other externally then distance between their centres is ______.
9.7 cm
1.3 cm
5.5 cm
4.2 cm
Chapter:
A line makes an angle of 45° with the positive direction of X-axis. So the slope of the line is ______.
`1/2`
`sqrt(3)/2`
1
`sqrt(3)`
Chapter:
The volume of a cube of side 2 cm is ______.
4 cm3
2 cm3
6 cm3
8 cm3
Chapter:
Find the diagonal of a square whose side is 10 cm.
Chapter:
The ratio of corresponding sides of similar triangles is 3 : 5; then find the ratio of their areas.
Chapter:
Find the slope of the line passing through the points A(2, 3) and B(4, 7).
Chapter:
If sin θ = `7/25`, then find the value of cosec θ.
Chapter:
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In the given figure, AR ⊥ BC, AR ⊥ PQ, then complete the activity for finding `(A(ΔABC))/(A(ΔAPQ))`.
Activity:
`(A(ΔABC))/(A(ΔAPQ)) = (square xx AR)/(PQ xx square)`
∴ `(A(ΔABC))/(A(ΔAPQ)) = square/square`
Chapter:
In the following figure, seg PS is a tangent segment, line PR is a secant. If PQ = 3.6, QR = 6.4, then find PS by completing the following activity.
Activity:
∴ PS2 = PQ × `square` (tangent secant segments theorem)
∴ PS2 = PQ × (PQ + `square`)
∴ PS2 = 3.6 × (3.6 + `square`)
∴ PS2 = 3.6 × 10
∴ PS2 = 36
∴ PS = `square`
Chapter:
Measure of an arc of a circle is 90° and its radius is 14 cm. Complete the following activity to find the length of an arc.
Activity:
Length of an arc = `θ/360 xx square` ...(Formula)
= `90/360 xx 2 xx 22/7 xx square`
= `1/4 xx square`
Length of an arc = `square` cm
Chapter:
In the following figure
In ΔLMN, ray MT bisects ∠LMN.
If LM = 6, MN = 10, TN = 8, then find LT.
Chapter:
In the following figure, m(arc NS) = 125°, m(arc EF) = 37°. Find m∠NMS.
Chapter:
Find the co-ordinates of midpoint of the segment joining the points P(22, 20) and Q(0, 16).
Chapter:
Find the volume of a cone if radius of its base is 7 cm and its perpendicular height is 15 cm.
Chapter:
If tan θ = 1, then find the value of `(sin θ + cos θ)/(sec θ + "cosec" θ)` by completing the following activity.
Activity:
tan θ = 1
but tan `square` = 1
∴ θ = `square`
∴ `(sin θ + cos θ)/(sec θ + "cosec" θ) = (sin 45^circ + cos 45^circ)/(sec 45^circ + "cosec" 45^circ)`
= `(1/square + 1/sqrt(2))/(sqrt(2) + square)`
= `(2/sqrt(2))/square`
`(sin θ + cos θ)/(sec θ + "cosec" θ) = 1/square`
Chapter:
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In the following figure, point O is the centre of the circle and length of chord AB is equal to the radius of the circle. Find the measures of:
a. ∠AOB
b. arc AB
c. ∠ACB
by completing the activity.
Activity:
In ΔAOB,
AO = OB = AB
∴ ΔAOB is an `square` triangle.
∴ m∠AOB = `square`
∴ m∠AOB = m(arc AB) = `square` ...(Definition of measure of an arc)
m∠ACB = `1/2 xx square` ...`square`
= `1/2 xx 60^circ`
m∠ACB = `square`
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:
Draw a circle with radius 3.4 cm. Draw a chord MN of length 5.7 cm in it. construct tangents at point M and N to the circle.
Chapter:
A storm broke a tree and the treetop rested 20 m from the base of the tree, making an angle of 60° with the horizontal. Find the height of the tree.
Chapter:
Prove that, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of remaining two sides.
Chapter: [2] Pythagoras Theorem
ΔABC has sides of length 4 cm, 5 cm and 6 cm while ΔPQR has perimeter of 90 cm. If ΔABC is similar to ΔPQR, then find the length of corresponding sides of ΔPQR.
Chapter:
ΔABC ∼ ΔPBR, BC = 8 cm, AC = 10 cm, ∠B = 90°, `"BC"/"BR" = 5/4`, then construct ΔPBR.
Chapter:
In the following figure ΔABC is an isosceles triangle with perimeter 44 cm. The base BC is of length 12 cm. Side AB and AC are congruent. A circle touches the three sides of triangle as shown. Find the length of tangent segment from A to circle.
Chapter:
Draw right-angled ΔABC of lengths of sides are 3 cm, 4 cm and 5 cm. Draw median on the hypotenuse of ΔABC.
Then:
- Measure the length of median and write it.
- By observing lengths of median and hypotenuse write your observations.
Chapter:
Observe the given figure and answer the following questions:
- How many surfaces does a solid cone have?
-
What are the names of slant height and perpendicular height in the given figure?
- If slant height of solid cone is 10 cm and perpendicular height is 8 cm, then find diameter of base of solid cone?
Chapter:
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