Mathematics Sample paper 8, Part- A for class 10th

 Mathematics Sample paper

Part- A

Section- I

Directions (Q.nos. 1-16 are of 1 marks each)

1. ∆ABC~∆DEF such that AB= 9.1cm and DE=6.5cm. If the perimeter of ∆DEF is 25cm, then what is the perimeter of ∆ABC?

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2. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then find angle POA.

Or

Check whether the following statement is true/false.

In two concentric circle, if chords are drawn in the outer circle which touch the inner circle, then all chords are of same length.

3. A cylindrical vessel 32cm high and 18cm as the radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24cm, then find the radius of it's base.

4. If one of the zeroes of the quadratic polynomial (k-1)x² +kx +1=0 is -3, then find the value of k.

Or

If 2 is a zero of polynomial p(x)= 4x² +2x -5a, then find the value of a.

5. If tan (∅1 +∅2)=√3 and sec (∅1 - ∅2)=2/√3, then find the sin 2∅1 + tan 3∅2.

6. If the first three terms of an AP are x-1, x+1, 2x+3, then find the value of x.

7. In ∆ABC, AD is the bisector of angle A. Then, prove that ar(∆ABD)/ar(ACD) = AB/AC.

Or

Write the area of sector of a circle with radius r and angle measure ∅.

8. Find the ratio, in which point P(1,2) divides the join of A(-2,1) and B(7,4).

9. If the perimeter of a circle is numerically half of the area of the circle, then find the radius of circle.

10. In the following figure, find angle F.

11. If the median of the data: 6,7, x-2, x, 17, 20 written in ascending order is 16, then find the value of x.

Or

If sigma fi is the sum of frequency of first 10 natural numbers and sigma fixi=120, then find the mean.

12. Find the minimum value of secA and cosecA.

13. Find the smallest number by which 891/3500 must be multiplied to make it a terminating decimal.

Or

Factorise the number 98 through factor tree.

14. The coefficient of x and the constant term in a linear polynomial are 5 and -3, respectively. Find it's zero.

15. From a point P which is at distance of 13cm from the centre O of radius 5cm, the pair of tangents PQ and PR to the circle are drawn. Then, find the area of quadrilateral PQOR.

16. A tower stands near an airport. The angle of elevation∅ of the tower from a point on the ground is such that it's tangent is 5/12. Find the height of the tower, if the distance of the observer from the tower is 120m.

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Section- II

Directions (Q.nos. 17-20 are of 4 marks each)

17. Case Study I

Eco friendly Week

For the inauguration of the ECO friendly week in DAV public school, badges were given to volunteers.

Organiser purchase these badges from Rashmi, who made these badges in the shape of a triangle with a circle inscribed in it. A message "SUPPORTING TREE PLANTATION" was written in the circles. Suppose BD=6cm, CD= 8cm and AE= 3cm.

a) Find the length of AB and AC

i. 9cm, 11cm

ii. 11cm, 9cm

iii. 9cm, 13cm

iv. 9cm, 10cm

b) Find the perimeter of ∆ABC.

i. 34cm

ii. 33cm

iii. 35cm

iv. 31cm

c) Find the radius of the circle.

i. 12√17

ii. 12/√17

iii. 10/√17

iv. 15/√17

d) Find the area between the triangle and the circle. 

i. 12(19√17-264)/17

ii. 12/17(119√17+264)

iii. 12/7(119√17-264)

iv. None of the above

e) An arc which makes an angle less than 180°, is called 

i. Major arc

ii. Minor arc

iii. Both i and ii

iv. None of these

18. Case Study II 

Electricity Problem

In a summer nagar area, there was a electricity problem. Mangal Singh complaint about this problem in JVVNL. In response to complain, company sent an electrician to solve the issue. In order to climb on the pole, the electrician put a ladder 9.5m away from the pole at the angle of 60°. (As shown in figure)

a) Given problem is based on the concept of 

i. Elevation and Depression

ii. Trignometric ratio

iii. Coordinate Geometry

iv. None of the above

b) Find the length of the ladder.

i. 18m

ii. 19m

iii. 17m

iv. 16m

c) If the foot of ladder is move any from the wall, then angle of ∅ is

i. 60°

ii. <60°

iii. >60°

iv. None of the above

d) The angles of elevation and depression are always

i. Acute

ii. Obtuse

iii. Right angle

iv. None of the above

e) The angle of ....... of an object viewed, is the angle formed by the line of sight with the horizontal.

i. Elevation

ii. Depression

iii. Both i and ii

iv. None of these

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Posted by :- Anuranjan Gadekar

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