SSC (English Medium)
SSC (Marathi Semi-English)
Academic Year: 2022-2023
Date & Time: 25th July 2023, 11:00 am
Duration: 2h
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Note:
- All the questions are compulsory.
- Use of a calculator is not allowed.
- The numbers to the right of the question 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.
The volume of a cube of side 10 cm is ______.
1 cm3
10 cm3
100 cm3
1000 cm3
10000 cm3
Chapter:
A line makes an angle of 30° with the positive direction of X-axis. So the slope of the line is ______.
`1/2`
`sqrt3/2`
`1/sqrt3`
`sqrt3`
Chapter: [0.05] Co-ordinate Geometry
∠ACB is inscribed in arc ACB of a circle with centre O. If ∠ACB = 65°, find m(arc ACB).
65°
130°
295°
230°
Chapter: [0.03] Circle
Find the perimeter of a square if its diagonal is `10sqrt2` cm:
10 cm
`40sqrt{2`cm
20 cm
40 cm
Chapter: [0.02] Pythagoras Theorem
In the following figure, ∠ABC = ∠DCB = 90°, AB = 6, DC = 8, then `("A"(\Delta"ABC"))/("A"(\Delta"DCB"))` = ?
Chapter:
In the following figure, find the length of RP using the information given in ΔPSR.
Chapter:
What is the distance between two parallel tangents of a circle having radius 4.5 cm? Justify your answer.
Chapter: [0.03] Circle
Find the co-ordinates of midpoint of the segment joining the points A(4, 6) and B(−2, 2).
Chapter:
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In the figure, circle with centre D touches the sides of ∠ACB at A. If ∠ACB = 52°, complete the activity to find the measure of ∠ADB.
Activity:
ln `square`ABCD,
∠CAD = ∠CBD = `square`° ........Tangent theorem
∴ ∠ACB + ∠CAD + ∠CBD + ∠ADB = `square`°
∴ 52° + 90° + 90° + ∠ADB = 360°
∴ ∠ADB + `square`° = 360°
∴ ∠ADB = 360° − 232°
∴ ∠ADB = `square`°
Chapter:
In the figure, side of square ABCD is 7 cm with centre D and radius DA, sector D-AXC is drawn.
Complete the following activity to find the area of square ABCD and sector D-AXC.
Activity:
Area of square = `square` ...formula
= (7)2
= 49 cm2
Area of sector (D-AXC) = `square` ...formula
= `square/360 xx 22/7 xx square`
= 38.5 cm2
Chapter:
Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
Activity:
L.H.S. = cotθ + tanθ
= `square/sin theta xx sin theta/cos theta`
= `(square + square)/(sin theta * cos theta)`
= `1/(sin theta * cos theta)` (∵ sin2θ + cos2θ = 1)
= `1/sin theta xx 1/cos theta`
= `square xx sec theta`
∴ L.H.S. = R.H.S.
∴ cotθ + tanθ = cosecθ × secθ
Chapter:
Find the slope of line EF, where co-ordinates of E are (−4, −2) and co -ordinates of F are (6, 3).
Chapter:
In the given figure, ray PQ touches the circle at point Q. PQ = 12, PR = 8, find PS and RS.
Chapter: [0.03] Circle
In the given figure, ∠MNP = 90°, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.
Chapter: [0.02] Pythagoras Theorem
In the figure, if AB || CD || EF, then find x and AE by using the information given in the figure.
Chapter:
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In the figure, X is any point in the interior of the triangle. Point X is joined to vertices of triangle. seg PQ || seg DE, seg QR || seg EF.
Complete the following activity to prove seg PR || seg DF.
Activity:
In ΔXDE, PQ || DE ...(given)
∴ `"XP"/square = square/"QE"` ...(I) Basic proportionality theorem
In ΔXEF, QR || EF ......(Given)
∴ `"XQ"/"QE" = square/"RF"` ...(II)`square`
∴ `"XP"/"PD" = square/square` ...From (I) and (II)
∴ seg PR || seg DF ....Converse of basic proportionality theorem
Chapter:
A, B, C are any points on the circle with centre O.
If m(arc BC) = 110° and m(arc AB) = 125°, complete the following activity to find m(arc ABC), m(arc AC), m(arc ACB) and m(arc BAC).
Activity:
m(arcABC) = m(arc AB) + `square`
= `square`° + 110° = 235°
m(arc AC) = 360° − m(arc `square`)
= 360° − `square`° = 125°
Similarly
m(arcACB) = 360° − `square` = 235°
and m(arc BAC) = 360 − `square` = 250°
Chapter:
The area of a sector of a circle of 6 cm radius is 15 π sq.cm. Find the measure of the arc and length of the arc corresponding to the sector.
Chapter: [0.07] Mensuration
If A(3, 5) and B(7, 9), point Q divides seg AB in the ratio 2 : 3, find the co-ordinates of point Q.
Chapter:
Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Chapter: [0.01] Similarity
∆PQR ~ ∆LTR. In ∆PQR, PQ = 4.2 cm, QR = 5.4 cm, PR = 4.8 cm. Construct ∆PQR and ∆LTR, such that `"PQ"/"LT" = 3/4`.
Chapter: [0.04] Geometric Constructions [0.05] Co-ordinate Geometry
A bucket is in the form of frustum of cone. It holds 28,490 litres of water. The radii of the top and the bottom are 28 cm and 21 cm respectively. Find the height of the bucket. `(pi = 22/7)`
Chapter:
Draw a circle with centre P and radius 3 cm. Draw a chord MN of length 4 cm. Draw tangents to the circle through points M and N which intersect in point Q. Measure the length of seg PQ.
Chapter:
In ΔPQR, bisector of ∠Q and ∠R intersect in point X. Line PX intersects side QR in point Y, then prove that `("PQ" + "PR")/"QR" = "PX"/ "XY"`
Chapter:
From the top of the building, Ramesh is looking at a bicycle parked at some distance away from the building on the road.
If AB → Height of the building is 40 m, C → Position of bicycle,
A → Position of Ramesh on the top of the building.
∠MAC is the angle of depression and m∠MAC = 30°, then:
- Draw a figure with the given information.
- Find the distance between building and the bicycle. (`sqrt3` = 1.73)
Chapter:
`square`ABCD is a cyclic quadrilateral where side AB ≅ side BC, ∠ADC = 110°, AC is the diagonal, then:
- Draw the figure using given information
- Find measure of ∠ABC
- Find measure of ∠BAC
- Find measure of (arc ABC).
Chapter:
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