SSC (English Medium)

SSC (Marathi Semi-English)

Academic Year: 2021-2022

Date: March 2022

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**Note:**

- All questions are compulsory.
- Use of calculator is not allowed.
- Figures to the right of questions indicates full marks.
- Draw proper figures for answers wherever necessary.
- The marks of construction should be clear and distinct. Do not erase them.
- While writing any proof, drawing relevant figure is necessary. Also the proof should be consistent with the figure.

If the length of the segment joining point L(x, 7) and point M(1, 15) is 10 cm, then the value of x is ______

7

7 or – 5

–1

1

Chapter: [0.05] Co-ordinate Geometry

**Choose the correct alternative:**

If length of sides of a triangle are a, b, c and a^{2} + b^{2} = c^{2}, then which type of triangle it is?

Obtuse angled triangle

Acute angled triangle

Equilateral triangle

Right angled triangle

Chapter: [0.02] Pythagoras Theorem

In fig, seg DE || sec BC, identify the correct statement.

`"AD"/"DB" = "AE"/"AC"`

`"AD"/"DB" = "AB"/"AC"`

`"AD"/"DB" = "EC"/"AC"`

`"AD"/"DB" = "AE"/"EC"`

Chapter: [0.01] Similarity

**Choose the correct alternative answer for the following question.**

^{3}.

1 cm

10 cm

100 cm

1000 cm

Chapter: [0.07] Mensuration

**Choose the correct alternative:**

∆ABC ∼ ∆AQR. `"AB"/"AQ" = 7/5`, then which of the following option is true?

A–Q–B

A–B–Q

A-C–B

A–R–B

Chapter: [0.04] Geometric Constructions [0.05] Co-ordinate Geometry

The radius of a circle is 10 cm. The measure of an arc of the circle is 54^{°}. Find the area of the sector associated with the arc. (\[\pi\]= 3.14 )

Chapter: [0.07] Mensuration

ΔPQR ~ ΔSUV. Write pairs of congruent angles

Chapter: [0.01] Similarity

Draw seg AB of length 4.5 cm and draw its perpendicular bisector

Chapter: [0.04] Geometric Constructions

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In figure, chord EF || chord GH. Prove that, chord EG ≅ chord FH. Fill in the blanks and write the proof.

**Proof:** Draw seg GF.

∠EFG = ∠FGH ......`square` .....(I)

∠EFG = `square` ......[inscribed angle theorem] (II)

∠FGH = `square` ......[inscribed angle theorem] (III)

∴ m(arc EG) = `square` ......[By (I), (II), and (III)]

chord EG ≅ chord FH ........[corresponding chords of congruent arcs]

Chapter: [0.03] Circle

From the given figure, in ∆ABC, if AD ⊥ BC, ∠C = 45°, AC = `8sqrt(2)` , BD = 5, then for finding value of AD and BC, complete the following activity.

Activity: In ∆ADC, if ∠ADC = 90°, ∠C = 45° ......[Given]

∴ ∠DAC = `square` .....[Remaining angle of ∆ADC]

By theorem of 45° – 45° – 90° triangle,

∴ `square = 1/sqrt(2)` AC and `square = 1/sqrt(2)` AC

∴ AD =`1/sqrt(2) xx square` and DC = `1/sqrt(2) xx 8sqrt(2)`

∴ AD = 8 and DC = 8

∴ BC = BD +DC

= 5 + 8

= 13

Chapter: [0.02] Pythagoras Theorem

Find distance between point Q(3, – 7) and point R(3, 3)

**Solution:** Suppose Q(x_{1}, y_{1}) and point R(x_{2}, y_{2})

x_{1} = 3, y_{1} = – 7 and x_{2} = 3, y_{2} = 3

Using distance formula,

d(Q, R) = `sqrt(square)`

∴ d(Q, R) = `sqrt(square - 100)`

∴ d(Q, R) = `sqrt(square)`

∴ d(Q, R) = `square`

Chapter: [0.05] Co-ordinate Geometry

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

In the given figure, if A(P-ABC) = 154 cm^{2 }radius of the circle is 14 cm, find

(1) `∠APC`

(2) l ( arc ABC) .

Chapter: [0.07] Mensuration

ΔABP ~ ΔDEF and A(ΔABP) : A(ΔDEF) = 144:81, then AB : DE = ?

Chapter: [0.01] Similarity

Draw a circle of radius 3.4 cm, take any point P on it. Draw tangent to the circle from point P

Chapter: [0.04] Geometric Constructions

In the given figure, m(arc NS) = 125°, m(arc EF) = 37°, find the measure ∠NMS.

Chapter: [0.03] Circle

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From fig., seg PQ || side BC, AP = x + 3, PB = x – 3, AQ = x + 5, QC = x – 2, then complete the activity to find the value of x.

In ΔPQB, PQ || side BC

`"AP"/"PB" = "AQ"/(["______"])` ...[______]

`(x + 3)/(x - 3) = (x + 5)/(["______"])`

(x + 3) [______] = (x + 5)(x – 3)

x^{2} + x – [______] = x^{2} + 2x – 15

x = [______]

Chapter: [0.01] Similarity

Complete the following activity to draw tangents to the circle.

- Draw a circle with radius 3.3 cm and center O. Draw chord PQ of length 6.6 cm. Draw ray OP and ray OQ.
- Draw a line perpendicular to the ray OP from P.
- Draw a line perpendicular to the ray OQ from Q.

Chapter: [0.04] Geometric Constructions

Some plastic balls of radius 1 cm were melted and cast into a tube. The thickness, length and outer radius of the tube were 2 cm, 90 cm, and 30 cm respectively. How many balls were melted to make the tube?

Chapter: [0.07] Mensuration

If sec θ = `41/40`, then find values of sin θ, cot θ, cosec θ

Chapter: [0.06] Trigonometry

In Quadrilateral ABCD, side AD || BC, diagonal AC and BD intersect in point P, then prove that `"AP"/"PD" = "PC"/"BP"`

Chapter: [0.01] Similarity

**Prove the following theorems:**

Opposite angles of a cyclic quadrilateral are supplementary.

Chapter: [0.03] Circle

As shown in figure, LK = `6sqrt(2)` then

(i) MK = ?

(ii) ML = ?

(iii) MN = ?

Chapter: [0.02] Pythagoras Theorem

Show that points A(– 4, –7), B(–1, 2), C(8, 5) and D(5, – 4) are the vertices of a parallelogram ABCD

Chapter: [0.05] Co-ordinate Geometry

Prove that `"cot A"/(1 - tan "A") + "tan A"/(1 - cot"A")` = 1 + tan A + cot A = sec A . cosec A + 1

Chapter: [0.06] Trigonometry

If AB and CD are the common tangents in the circles of two unequal (different) radii, then show that seg AB ≅ seg CD.

Chapter: [0.03] Circle

In the given figure, square ABCD is inscribed in the sector A - PCQ. The radius of sector C - BXD is 20 cm. Complete the following activity to find the area of shaded region

Chapter: [0.07] Mensuration

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