SET - A

MT EDUCARE LTD.QUEST - II (Semi Prelim II)

(2017-18)Portion : Quadratic Equations, Arithmetic progression, Statistics, Circle, Constructions

Areas Related to circles and Surface Areas and Volumes

CBSE - X

• Please check that this question paper contains 6 printed pages.• Code number given on the right hand side of the question paper should be

written on the title page of the answer-book by the candidate.• Please check that this question paper contains 30 questions.• Please write down the serial number of the question before attempting it.

MATHEMATICS

General Instructions:i) All questions are compulsory.

ii) The question paper consists of 30 questions divided in four sections: A, B, C and D.

iii) Section A contains 6 questions of 1 mark each,

Section B contains 6 questions of 2 marks each,

Section C contains 10 questions of 3 marks each,

Section D contains 8 questions of 4 marks each.

iv) There is no overall choice. However, an internal choice has been provided in four

questions of 3 marks each and three questions of 4 marks each. You have to attempt

only one of the alternnatives in all such questions.

v) Use of calculator is not permitted.

Time allowed : 3 hours Maximum Marks : 80

Series RLH

Roll No. Code No. 31/1

SET - A

SECTION - AQuestion number 1 to 6 carry 1 marks each.

1. Is the following an AP? If it forms an AP, find the common difference d and writethree more terms3, 3 + 2 , 3 + 2 2 , 3 + 3 2 , ...

2. A tangent PQ at a point P of a circle of radius 5 cmmeets a line through the centre O at a point Qsuch that OQ = 12cm. Length PQ is ________.(A) 12cm (B) 13cm (C) 8.5cm (D) 119 cm.

3. The radii of two circles are 19 cm and 9 cm respectively. Find the radius of thecircle which has circumference equal to the sum of the circumferences of thetwo circles.

4. Check whether the following is quadratic equation :(x – 3) (2x + 1) = x (x + 5)

5. Curved surface area of a hemisphere is 90517 cm2. What is its volums.

6. Following due the lives in hours of 15 pieces of the components of aircraft engine.Find the median. 715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728,716, 705, 719.

SECTION - BQuestion number 7 to 12 carry 2 marks each.

7. Represent the following situation in the form of quadratic equation :The area of a rectangular plot is 528 m². The length of the plot (in metres) is onemore than twice its breadth. We need to find the length and breadth of the plot.

8. Draw a tangent at any point M on the circle of radius 2.9 and Centre ‘O’.

9. Check whether – 150 is a term of the AP : 11, 8, 5, 2, ...

... 2 ...

O

P Q

5 12

?

SET - A... 3 ...

10. O is the centre of circle. AB and AC are tangents drawnfrom A and seg BA seg CA.Prove that BACO is a square.

11. The length of the minute hand of a clock is 14 cm. Find the area swept by theminute hand in 5 minutes.

12. Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively, are melted to forma single solid sphere. Find the radius of the resulting sphere.

SECTION - CQuestion numbers 13 to 22 carry 3 marks each.

13. How many terms of the AP: 9, 17, 25, ... must be taken to give a sum of 636 ?

14. Draw a pair of tangents to a circle of radius 5cm which are inclined to eachother at an angle of 600.

15. Find the roots of the following quadratic equation, if they exist, by the method ofcompleting the square :2x2 – 7x + 3 = 0

16. In the adjoining figure, OACB is a quadrant of a circlewith centre O and radius 3.5 cm.If OD = 2 cm, find the area of the(i) quadrant OACB,(ii) shaded region.

OR

16. In the adjoining figure, a square OABC is inscribed in aquadrant OPBQ. If OA = 20 cm, find the area of the shadedregion. (Use = 3.14)

A

O

B

C

A

OB

DC

2cm

3.5 cm

Q

O P

BC

A20 cm

SET - A... 4 ...

17. Prove that the parallelogram circumscribing a circle is a rhombus.

18. The slant height of a frustum of a cone is 4cm and the perimeters (circumference)of its circular ends are 18cm and 6cm. Find the curved surface area of thefrustum.

OR

18. A fez, the cap used by the Turks, is shaped like the frustum ofa cone. If its radius on the open side is 10 cm, radius at theupper base is 4 cm and its slant height is 15 cm, find the areaof material used for making it.

19. A student noted the number of cars passing through a spot on a road for 100periods each of 3 minutes and summarised it in the table given below. Find themode of the data :

Number of cars 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

Frequency 7 14 13 12 20 11 15 8

20. A train travels 360km at a uniform speed. If the speed had been 5 km/hr more, itwould have taken 1 hour less for the same journey. Find the speed of the train.

21. The following figure depicts a racing track whose left and right ends aresemicircular.

The distance between the two inner parallel line segments is 60 m and they areeach 106 m long. If the track is 10 m wide, find :(i) the distance around the track along its inner edge(ii) the area of the track

22. A quadrilateral ABCD is drawn to circumscribea circle as shown in the fig.Prove that : AB + CD = AD + BC.

OR

A B

CD

106 m

B 60 cm

H 10 m

F

G

E

Q

R

S

D

C

BA P

SET - A... 5 ...

22. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chordof the larger circle which touches the smaller circle.

SECTION - DQuestion numbers 23 to 30 carry 4 marks each.

23. How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must bemelted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm ?

24. In fig. XY and XY are two parallel tangentsto a circle with centre O and anothertangent AB with point of contact Cintersecting XY at A and XY at B.Prove that AOB = 900.

25. A spiral is made up of successive semicircles, with centres alternately at A andB, starting with centre at A, of radii 0.5cm, 1.0cm, 1.5cm, 2.0cm, What is thetotal length of such a spiral made up of thirteen consecutive semicircles ?

22Take =7

26. The sum of the areas of two squares is 468m². If the difference of their perim-eters is 24m. Find the sides of the two squares.

OR

26. Solve :2

3x

x +1

2 3x + 3 93 2 3

x

x x = 0

27. A well of diameter 3m is dug 14 m deep. The earth taken out of it has beenspread evenly all around it in the shape of a circular ring of width 4m to forman embankment. Find the height of the embankment.

OR

27. A vessel is in the form of an inverted cone. Its height is 8 cm and the radius ofits top, which is open, is 5 cm. It is filled with water up to the brim. When leadshots, each of which is a sphere of radius 0.5 cm are dropped into the vessel,one-fourth of the water flows out. Find the number of lead shots dropped in thevessel.

X

X

O

P A

Q B

Y

C

Y

SET - A

28. Construct an isosceles triangle whose base is 8cm and altitude 4cm and then

another triangle whose sides are 112 times the corresponding sides of isosceles

triangle.

29. The wheels of a car are of diameter 80 cm each. How many complete revolu-tions does each wheel make in 10 minutes when the car is travelling at a speedof 66 km per hour ?

OR

29. A-BPC is a quadrant of a circle of radius 14cm and asemicircle is drawn with BC as diameter. Find the areaof the shaded region.

30. The following distribution gives the daily income of 50 workers of a factory.

Daily income (in Rs) 100 - 120 120 - 140 140 - 160 160 - 180 180 - 200

Number of workers 12 14 8 6 10

Convert the distribution above to a less than type cumulative frequencydistribution, and draw its ogive.

C

QP

B

A

14 cm

14 cm

All the Best

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