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QHQ6NKR II, (2015-2016)

SUMMATIVE ASSESSMENT – II MATHEMATICS /

Class – X / X

3 90

Time allowed : 3 hours Maximum Marks : 90

(i)

(ii) 31 4

1 6 2 10

3 11 4

(iii)

(iv)

General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 31questions divided into four sections A, B, C and D.

Section-A comprises of 4 questions of 1 mark each, Section-B comprises of 6 questions of 2 marks each, Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11 questions of 4 marks each.

(iii) There is no overall choice. (iv) Use of calculator is not permitted.

/ SECTION-A

1 4 1

Question numbers 1 to 4 carry one mark each.

1 27

What is the 27th positive odd number ?

1

2

If the length of the ladder placed against a wall is twice the distance between the foot of the ladder and the wall. Find the angle made by the ladder with the horizontal.

1

3 1

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A pair of dice is thrown once, find the probability of getting an even number on the first die.

4 (6, 0) (0, 6)

Find the distance between the points (6, 0) and (0, 6)

1

/ SECTION-B

5 10 2

Question numbers 5 to 10 carry two marks each.

5 x210x390

Find the nature of the roots of the quadratic equation x210x390.

2

6 AP m am2bm

If the sum of first m terms of an AP is am2bm, find its common difference.

2

7

ABCD ABCD1

2 (ABCD

A circle is inscribed in a quadrilateral ABCD. Prove that ABCD

1

2 perimeter of ABCD.

2

8 2 1 : 2 1 ?

By geometrical construction, is it possible to divide a line segment in the ratio

2 1 : 2 1 . Give reason.

2

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9

PQPR QLRL

In the figure, if PQPR, prove that QLRL

2

10 14 cm

A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the remaining solid.

2

/ SECTION-C

11 20 3

Question numbers 11 to 20 carry 3 marks each.

11 50 5 175

The sum of the ages of a mother and her daughter is 50 years. Five years ago, the product of their ages (in years) was 175. Find their present ages.

3

12 200 1502 3

Find the sum of all natural numbers between 200 and 1502 which are exactly divisible by 3.

3

13

P A

A

3

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Two circles touch externally at point P. A is a point outside the circles, If tangents are drawn to the circles from A, show the position of the tangents and write a relation between them .

14 60 10 m

45

The angle of elevation of the top of a vertical tower from a point on the ground is 60. From another point 10 m vertically above the first, its angle of elevation is 45. Find the height of the tower.

3

15 100 65 15

A carton contains 100 bulbs out of which 65 are good one, 15 have minor defects and remaining have major defects. What is the probability that a man will pick up a bulb with major defect ?

3

16 10 (4, 5) P(10, 5) APB

APPB AB

The centre of a circle with radius 10 units is the point (4, 5). P(10, 5) is a point inside the circle and APB is a chord of the circle such that APPB. Calculate the length of AB.

3

17 A B (2, 3) (4, 5) P AP2BP2

8 x4y9

If A and B are the points (2, 3) and (4, 5) and P is a point such that AP2BP2

8, show that x4y9.

3

18 4 m 1408 m

22

7

A circular garden has a 4 m wide path around it. Find the radius of the garden, if the area of the path

is 1408 m2. (Use 22

7

)

3

19 10

18 cm15 cm8 cm

Some children playing with clay made 10 cubical dice from it. If they made it from the clay piece 18 cm by 15 cm by 8 cm, then what will be the edge of the die, assuming that there is no wastage ?

3

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20 4 cm 40

Find the area of the sector formulated by an arc, having length 4 cm, subtending an angle of 40 at the centre.

3

/ SECTION-D

21 31 4

Question numbers 21 to 31 carry 4 marks each.

21 k x2kx640 x2

8xk0

Find the positive value of k for which x2kx640 and x2

8xk0 will have real roots.

4

22 a, b, c, d e A.P. a4b6c4de0

If the numbers a, b, c, d and e are in an A.P. then prove that a4b6c4de0

4

23 (1m2)x22mcx(c2

a2)0 c2a2 (1m2)

If the equation (1m2)x22mcx(c2

a2)0 has equal roots, prove that

c2a2 (1m2).

4

24 AD O AB A

C DC B ABC=50 AOC

In the given figure, AD is a diameter of a circle with centre O and AB is a tangent at A . C is a

point on the circle such that DC produced intersects the tangent at B and ABC=50. Find

AOC.

4

25 ABC ABC 2.5

ABC 3 cm, 5 cm 6 cm

Construct a triangle similar to ABC whose sides are 2.5 times that of given ABC, where ABC has sides 3 cm, 5 cm and 6 cm.

4

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26 2 m

10

3 m

4

3 m

A person of height 2 m wants to get a fruit which is on the top of a tree of height 10

3 m. If he stands

at a distance of 4

3 m from the foot of the tree, find the angle at which he should throw the stone so

that it hits the fruit. Also find the distance travelled by the stone to reach the fruit.

4

27 4

152

5 10

A jar contains marbles of blue, white and red colours. The probability of selecting a blue

marble is 4

15and the probability of selecting a white marble is

2

5. If the jar contains 10 red

marbles find the total number of marbles in the jar.

4

28 (2, 0) (4, 0)

If two vertices of an equilateral triangle are (2, 0) and (4, 0), find the third vertex. Also, find the area of this equilateral triangle.

4

29 7m

22

7

Three cows owned by three farmers are tied at three corners of a triangular plot with ropes of 7m

length each. Find the area grazed by cows. What value is depicted by the farmers ? (Use 22

7

)

4

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30 5 cm 6 : 05 am 6 : 40 am

The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6 : 05 am and 6 : 40 am. Also, find the area does not covered by the minute hand.

4

31

3.5 cm 4 cm

5 cm 10.5 cm ( 22

7

Ice is formed in a container of the shape of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 3.5 cm and height of the cone is 4 cm. The ice is then put in a cylindrical glass full of juice such that on putting the ice the juice overflows. Find the volume

of juice left in the glass, if its radius is 5 cm and height 10.5 cm. (Use 22

7)

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