SSC (English Medium)
SSC (Marathi Semi-English)
Academic Year: 2023-2024
Date & Time: 24th July 2024, 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 MCQ's [Q. No. 1 (4)], only the first attempt will be evaluated and will be given credit.
- For every MCQ, the correct alternative (4), (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.
In ΔABC and ΔPQR, in a one to one correspondence of vertices, `(AB)/(QR) = (BC)/(PR) = (CA)/(PQ)`, then ______ statement is true.
ΔPQR ~ ΔABC
ΔPQR ~ ΔCAB
ΔCBA ~ ΔPQR
ΔBCA ~ ΔPQR
Chapter:
Two circles of radii 5.5 cm and 3.3 cm respectively, touch each other externally. Then the distance between their centres is ______.
4.4 cm
8.8 cm
2.2 cm
8.3 cm
Chapter:
Seg AB is parallel to Y-axis and coordinates of point A are (1, 3) then co–ordinates of point B can be ______.
(3, 1)
(5, 3)
(3, 0)
(1, –3)
Chapter:
The volume of a cube of side 10 cm is ______.
1 cm3
10 cm3
100 cm3
1000 cm3
10000 cm3
Chapter:
In ΔABC, ∠B = 90°, ∠C = 30°, AC = 12 cm, then find AB.
Chapter:
In the given figure, m(arc MN) = 70°, find ∠MLN.
Chapter:
If the radius of a circle is 4 cm and the length of an arc is 10 cm, then find the area of the sector.
Chapter:
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In the given figure, chord PQ and chord RS intersect at point T. Then complete the following activity to prove,
∠STQ = `1/2` [m(arc SQ) + m(arc PR)]
Activity:
∠STQ = ∠SPQ + `square` ...(Remote interior angles theorem of a triangle)
`1/2` m(arc PQ) + `square` ...(Inscribed angle theorem)
=`1/2 [square + square]`
Chapter:
If sec θ = `25/7`, complete the following activity to find the value of tan θ.
Activity:
We have, 1 + tan2θ = sec2θ
∴ 1 + tan2θ = `square`
∴ tan2θ = `625/49 - square`
∴ tan2θ = `(625 - 49)/(49)`
∴ tan2θ = `square/49`
∴ tan2θ = `square`
Chapter:
Complete the following activity to find the volume of a cone if the radius of its base is 7 cm and its perpendicular height is 6 cm.
Activity:
Here, radius (r) = 7 cm, height (4) = 6 cm
The volume of a cone = `square` ...(Formula)
= `1/3 xx 22/7 xx square xx 6`
= `1/3 xx 22/7 xx square xx 6`
∴ the volume of the cone = `square` cm3.
Chapter:
Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.
Chapter:
In ΔPQR, seg RS bisects ∠PRQ. If PR = 15, RQ = 20, and PS = 12, then find SQ.
Chapter:
Find the surface area of a sphere of diameter 14 cm.
Chapter:
In the given figure, ∠PQR = 90°, seg QN ⊥ seg PR, PN = 9, NR = 16, find QN.
Chapter:
Find the slope of the line passing through the points A(3, 3) and B(5, 7).
Chapter:
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In the given figure, AB || CD || EF. If AC = 12, CE = 9, BD = 8, then complete the following activity to find DF.
Activity:
AB || CD || EF
∴ `(AC)/square = square/(DF)` ...(Property of three parallel lines and their transversals)
∴ `12/square = square/(DF)`
∴ DF = `(8 xx 9)/square`
∴ DF = `square`.
Chapter:
A cylinder is having radius 7 cm and height 21 cm. Complete the following activity to calculate its volume and circumference of its base.
Activity:
Radius (r) = 7 cm, Height (h) = 21 cm.
The volume of a cylinder = `square` ...(Formula)
= `22/7 xx 7 xx 7 xx square`
= 154 × 21
= `square` cm3
The circumference of the base = `square` ...(Formula)
= `2 xx 22/7 xx square`
= `square` cm.
Chapter:
Prove that ‘Opposite angles of a cyclic quadrilateral are supplementary’.
Chapter:
Draw a circle with centre P and radius 3.5 cm. Take point Q at a distance 8 cm from the centre. Construct tangents to the circle from point Q.
Chapter:
Determine whether the points are collinear.
P(–2, 3), Q(1, 2), R(4, 1)
Chapter: [5] Co-ordinate Geometry
If ΔPQR ~ ΔLMN, 9 × A(ΔPQR) = 16 × A(ΔLMN) and QR = 20, then find MN.
Chapter:
ΔABC is an equilateral triangle. Point D is on seg BC such that BD = `1/5` BC. Then prove that `(AD^2)/(AB^2) = 21/25`.
Chapter:
ΔLMN ~ ΔLQP. In ΔLMN, LM = 3.6 cm, ∠L = 50°, LN = 4.2 cm and `("LM")/("LQ") = 4/7`. Construct ΔLQP.
Chapter:
To find the width of the river, a man observes the top of a tree, on the opposite bank making an angle of elevation of 60°. When he moves 24 metres backward from bank and observes the same top of the tree, his line of vision makes an angle of elevation of 30°. Find the height of the tree and width of the river. (`sqrt3 = 1.73`)
Chapter:
The diameter of a circular garden is 13 metres. The distance between two gates of the garden is 13 metres. An electric pole is to be erected on the circumference of the garden such that the difference between the distance of the pole from the gates is 7 metres. Can such a pole be erected? If yes, find the distance of the pole from each gate.
Chapter:
The line x – 6y + 11 = 0 bisects the join of (8, −1) and (0, k). Find the value of k.
Chapter:
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