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

 Mathematics Sample paper

Section-I

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

1. If √3 tanø=1, then find the value of sin²∅-cos²∅.

2. Is this statement correct?

The tangents drawn at the extremities of the diameter of a circle are parallel.

3. Two poles of height 6m and 11 m stand vertically upright on a plane ground. If the distance between their foot is 12m, then find the distance between their tops.

4. A top is the shape of cone over a hemisphere and the radius of the hemisphere is 3.5cm. If the height of the top is 15.5cm, then find the total area of the top.

5. In the given figure, AB is a chord of circle, and PQ is a tangent at point B of the circle. If angle AOB=110°, then find angle ABQ.

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Or

Find the length of the tangent drawn from a point P, which is 8cm away from the centre of circle of radius 6cm.

6. If the nth term of an AP is 3n-8, then find it's 16th term.

7. If the distance between the points (4,p) and (1,0) is 5, then find the value of p.

8. A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, then find the probability that it bears a two-digits number.

Or

For grouped data, if sigma fi= 20, sigma fixi=2p+20 and mean of distribution is 12, then find the value of p.

9. In an isosceles right angled triangle, if the hypotenuse is 5√2 cm, then find the length of the sides of triangle.

10. If tan² 45° - cos² 30°= x sin 30° cos60°, then find the value of x.

Or

Find the simplified form of cos⁴∅-sin⁴∅ in terms of sin∅.

11. Check whether the following statement is true/false.

If a pair of linear equations in two variables is consistent, then the lines represented by two equations are coincident.

12. A solid sphere of radius r is melted and recast into the shape of a solid cone of height r, then find the radius of the cone.

13. If x=2 and x=0, are the zeroes of the polynomials f(x) =2x³-5x²+ax+b. Find the values of a and b.

Or

The graph of a polynomial p(x) is shown below. Find the number of zeroes of p(x).

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14. Find the value of k, for which one root of the quadratic equation kx²-14x+8=0 is six times the other.

15. Find the area of a sector of circle of radius 21cm and Central angle 90°.

(Take π= 22/7)

16. Evaluate sin45° cos60° +cos45° sin60°.

Or

Find angle A in the following figure 

Section-II

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

17. Case Study I

Science Exhibition 

For a science exhibition, Vikas presented a diagrammatic representation of rain water harvesting project. Through pipes AB and AC, each of 12m long are bringing water from the terrace of a building (as shown in figure).

a) A line drawn from centre of circle to the tangent line is

i. Parallel

ii. Perpendicular 

iii. Do not say anything

iv. None of the above

b) If two circles intersect each other at two points, then find the number of common tangents.

i. 1

ii. 2

iii. 3

iv. 0

c) If the radius of circle is 5cm, then find the length of OA.

i. 13cm

ii. 12cm

iii. 15cm

iv. 9cm

d) If we draw angle bisector line from intersection point of pair of tangents to the circle, then it always passes through

i. Centre

ii. Left side of centre

iii. Right side of centre

iv. None of the above

e) If a line OA makes an angle 60° from one of the tangent line, then find the length of OA.

i. 24cm

ii. 23cm

iii. 12cm

iv. 5m

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18. Case Study III

Morning Walk

In a morning walk, Nirmaljeet, Puneet and Raju step off together, their steps measuring 240cm, 90cm, 120cm respectively. They want to go for a juice shop for a health issue, which is situated near by them.

a) Find the minimum distance of shop from where they start to walk together, so that one can cover the distance in complete steps?

i. 720cm

ii. 700cm

iii. 620cm

iv. 740m

b) Find the number of common steps cover by all of them to reach the juice shop.

i. 20

ii. 30

iii. 40

iv. 35

c) If a and b are two number, then find the relation between LCM and HCF.

i. a/b=LCM (a,b) HCF(a,b)

ii. a×b =LCM (a,b)× HCF (a,b)

iii. a×LCM (a,b) = b× HCF (a,b)

iv. None of the above

d) A largest positive integer that divides given two positive integers is called

i. HCF

ii. LCM

iii. Coprime

iv. None of the above

e) Factor tree is a chain of factors, which is represented in the form of a 

i. Tree

ii. Division

iii. Flower

iv. None of these

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Posted by:- Anuranjan Gadekar

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