SECTION – I

1. The decimal expansion of the number √2 is: 1

(a) a finite decimal (c) non terminating recurring
(b) non terminating non recurring (d) 1.41421
OR
An irrational number lie between 2 and 3 is :
(a) √2 (b) √3 (c) √6 (d) √10
2. The abscissa of point T ( 4,7) is 1
(a) 4 (b) 7 (c) -7 (d) any number

3. Find a point on y – axis from where graph of linear equation 2x = 1-5y will pass. 1
1 1 1 1
(a) (0 , ) (b) ( , 0) (c) (0 , ) (d) ( , 0)
2 2 5 5
4. If (2,0) is a solution of the linear equation 2x + 3y = k, then the value of k is : 1
(a) 4 (b) 6 (c) 5 (d) 2
5. 2.93 can be expressed as 1
97 93 97 93
(a) 99 (b) 99 (c) 33 (d) 33

6. In ∆PQR , ∠R =∠P and ∠R = 65⁰ then measure of ∠P is : 1

(a)50⁰ (b) 65⁰ (c) 40⁰ (d) 55⁰
OR
In triangles ABC and DEF, AB = DF and ∠A = ∠D. The two triangles will be congruent
by SAS axiom if
(a) BC = EF (b) AC = DE (c) AC = EF (d) BC = DE
7. What is the value is √4 × √81 ? 1
(a) 36 (b) 18 (c) 16 (d) 42

8. Euclid stated that things which are equal to the same thing are equal to one another in the 1
form of:
(a) an axiom (b) a definition (c) a postulate (d) a proof
OR
Euclid stated that all right angles are equal to each other in the form of
(a) an axiom (b) a definition (c) a postulate (d) a proof
9. The supplement of an angle is one – third of itself. The measure of the angle is: 1
1
(a) 672° (b) 65° (c) 90° (d) 135°
10. 1
Assertion: The angles of a triangle are in the ratio 2:3:4. The largest angle of the triangle
is 80°.
Reason: The sum of all the interior angles of a triangle is 180°
a) Both assertion (A) and reason (R) are true and reason (R) is the correct
explanation of assertion (A).
 b) Both assertion (A) and reason (R) are true but reason (R) is not the correct
explanation of assertion (A).
c) Assertion (A) is true but reason (R) is false.
d)Assertion (A) is false but reason (R) is true
11. Write the linear equation such that each point on its graph has an ordinate 3 times its 1
abscissa.
OR
Find the points where the graph of the equation 3x + 4y = 12 cuts the x-axis
12. How many rational numbers are there between 3/5 and 6/5 ? 1
(a) 2 (b) 1 (c) infinite (d) 0

13. The value of p(x) = (x – 1)(x + 1) for p(1) is: 1

(a) 1 (b) 0 (c) 2 (d) – 2

14. The point P(a,b) lies in third quadrant , then which of the following is true? 1
(a) a>0, b>0 (b) a>0, b<0 (c) a<0, b<0 (d) a<0, b>0
OR
A point lies on the positive side of X- axis. Its distance from origin is 2 units. Coordinates
of the point are:
(a) (0,2) (b) (0,-2) (c) (-2,0) (d) (2,0)
15. In a circle two chords AB and AC are present at distance of 3cm and 4.5cm from the 1
centre respectively.Which chord has greater length?

16. The sum of either pair of opposite angles of a cyclic quadrilateral is ______. 1

(a) 180o (b) 360o (c) 90o (d) none of these

17. If the area of an equilateral triangle is 36 √3 cm2, then its perimeter is 1
(a) 64 cm (b) 60 cm (c) 36 cm (d) none of these
18. In a trapezium ABCD, AB∥CD. Calculate ∠C and ∠D if ∠A = 55° and ∠B = 70° 1

19. In a parallelogram, the bisectors of any two consecutive angles intersects at __________ 1
angle.
20. Assertion: if 2S=( a+b+c)/2 where a,b,c are the sides of triangle then area =√s(s-a)(s- 1
b)(s-c)

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 Reason: the sides of triangle are 3cm,4cm,5cm it’s area is 6cm^2

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation
of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct
explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true
SECTION-II
Directions : (Qno 21-24) Case study based questions are compulsory . Attempt any four
sub-parts of each question. Each sub-part carries 1 mark.
21. Due to frequent robberies in the colony during night. The secretary with the members 4
together decides to attach more lights besides the street light set by municipality. There
are poles on which lights are attached.

These 4 poles are connected to each other through wire and they form a quadrilateral.
Light from pole B focus light on mid-point G of wire between pole C and B, from pole
C focus light on mid-point F of wire between pole C and pole D. Similarly pole D and
pole A focus light on the mid-point E and H respectively.

On the basis of the above information, solve the following questions:

Q 1. If BD is the bisector of ∠B then prove that I is the mid-point of AC.

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 Q 2. Prove that quadrilateral EFGH is a parallelogram.

Q 3. Is it true that every parallelogram is a rectangle?

Q4. Does BD bisects angle D ?
Q5. If the diagonals of a parallelogram are equal and perpendicular bisectors then it is
known as __________ .

22. Ankit visited in a mall with his father. He sees that three shops are situated at P, Q, R as shown 4
in the figure from where they have to purchase things according to their need. Distance between
shop P and Q is 8 m, that of between shop Q and R is 10 m and between shop P and R is 6 m.

Considering O as the centre of the circle, answer the following questions.

(i) Find the radius of the circle.

(ii) Measure of ∠QPR is ______

(iii) Area of ∆PQR is ________

(iv) Length of the longest chord of the circle is ________
(v) In figure, PSQR is known as
23. The following histogram shows the number of literate females in the age group of 10 to 4
40 years in a town:

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 (ii) What is the class width?

(ii) What is the lowest frequency?

(iii) What is the class marks of third class?

(iv) What is the total number of females ?
(v) In which age group literate females are the least?

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24. Once four friends Rahul, Arun, Ajay and Vijay went for a picnic at a hill station. Due 4
to peak season, they did not get a proper hotel in the city. The weather was fine so they
decided to make a conical tent at a park. They were carrying 300 m² cloth with them. As
shown in the figure they made the tent with height 10 m and diameter 14 m. The
remaining cloth was used for the floor.

1. How much Cloth was used for the floor?

a) 31.6 m² b)16 m² c)10 m² d)20 m²

2.What was the volume of the tent?

a)300 m³ b)160 m³ c)513.3 m³ d)500 m³

3.What was the area of the floor?

a)50 m² b)100 m² c)150 m² d)154 m²

4. What was the total surface area of the tent?

a)400 m² b)422.4 m² c)300 m² d)400 m

5.What was the latent height of the tent?

a. 12 m
b. 12.2 m
c. 15 m
d. 17 m

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 Section III

25. Calculate the x/ y form of 0.777 . . . . ., where x and y are integers 2

and y does not equal to zero.

OR
Simplify : 4
81 − 8( 3 216 ) + 15(5 32 ) + 225

26. If (x – 1/x) = 4, then evaluate (x2 + 1/x2 ) 2

27. Draw the graph of the equation represented by the straight line which is parallel to the x- 2
axis and is 4 units above it.

OR

Write the equation of the line parallel to x-axis and passing through point (-2,3) in the
standard form.

28. Plot the points A (4, 4) and B(–4, 4) on a graph sheet. Join the lines OA, OB and BA. 2
What figure do you obtain ?

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29. 2
If polynomials ax3+ 3x2– 3 and 2x3– 5x + a leaves the same remainder when each is divided
by x – 4, find the value of a.

30. Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars 2
from B to the arms of ∠A Show that ΔAPB ≅ ΔAQB.

31. 2
Draw histogram and frequency polygon for the following data:

Marks 10-20 20-30 30-40 40-50 50-60

No of students 10 12 13 11 9
Section IV

32. 1 3
If a = 9 - 14√5 and b = then what will be the value of a + b.
a

33. AB is a line segment and P is its mid-point. D and E are points on the same side of AB 3
such that∠BAD = ∠ABE and ∠EPA = ∠DPB . Show that
(i) ΔDAP ≅ ΔEBP
(ii) AD = BE

OR
AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.

34. 3
In fig, if AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE

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35. 3
Find three solutions of the linear equation 2x + y = 3.

36. 𝟏 3
If a point C lies between two points A and B such that AC = BC, then prove that AC = 𝟐
AB. Explain by drawing the figure.
OR
State Euclid”s fifth Postulate
37. 3
An umbrella is made by stitching 10 triangular pieces of cloth of two different colours
each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is
required for the umbrella?

Section V
38. Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden box 4
covered with coloured paper with picture of Santa Claus on it. She must know the exact
quantity of paper to buy for this purpose. If the box has length, breadth and height as 80
cm, 40 cm and 20 cm respectively how many square sheets of paper of side 40 cm would
she require?
OR
A cylindrical tube opened at both the ends is made of iron sheet which is 2 cm thick. If the
outer diameter is 16 cm and its length is 100 cm, find how many cubic centimeters of iron
has been used in making the tube ?
39. Find the value of a and b if 4
4+√5 4−√5
+ 4+ = a + b√5
4−√5 √5

40. Factorise: 4

(i) 16x2 + 40xy + 25y2.

(ii) x2 – 1 – 2a – a2.

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