class x sa-ii mathematics sample paper 2016

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MOCK TEST PAPERMATHEMATICS

(class10th)

Boost your IIT-JEE / AIPMT Preparation

MATHS X TERM-II

MODEL TEST PAPER-2 (UNSOLVED)

[For Summative Assessment-2 (Term - II)]

[Based on the latest CBSE Sample Question Paper]

Time : 3 hours M.M. : 80

General Instructions : Same as in CBSE Sample Question Paper.

SECTION A

(Question numbers 1 to 10 carry 1 mark each. For each of the questions 1 to 10, four

alternative choices have been provided of which only one is correct. You have to select the

correct choice.)

1. If x = 2 is a root of the quadratic equation 3x2 – 2kx + 5 = 0, then k is equal to :

(a)4

17(b)

17

4(c)

1

17(d)

1

4

2. If the sum of n terms of an A.P. be 3n2 – n and its common difference is 6, then its

first term is :

(a) 2 (b) 3 (c) 1 (d) 4

3. PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter

of the circle such that ∠POR = 120°, ∠OPQ is :

(a) 50° (b) 40° (c) 30° (d) 25°

4. In the figure, ∆ABC is circumscribed touching the circle

at P, Q, R. If AP = 4 cm, BP = 6 cm, AC = 12 cm and

BC = x cm. Then, x = ?

(a) 10 cm (b) 6 cm

(c) 14 cm (d) 18 cm

5. The length of the tangent drawn from a point, whose distance from the centre of a

circle is 20 cm and radius of the circle is 16 cm, is :

(a) 12 cm (b) 13 cm (c) 17 cm (d) 25 cm

6. If four sides of a quadrilateral ABCD are tangential to a circle. Then :

(a) AC + AD = BC + DB (b) AC + AD = BD + CD

(c) AB + CD = AC + BC (d) AB + CD = BC + AD

7. A race track is in the form of a ring whose inner and outer circumferences are

437 m and 503 m respectively. The width of the track is :

(a) 10.5 m (b) 20.5 m (c) 21 m (d) 30 m

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2

8. The total surface area of a hemisphere of radius 7 cm is :

(a) 447 π cm2 (b) 239 π cm2 (c) 147 π cm2 (d) 174 π cm2

9. If the angle of elevation of a building from a distance of 100 m from its foot is 60°,

then the height of the building is :

(a) 100 3 m (b)100

3 m (c) 50 3 m (d)

200

3 m

10. The probability of selecting an even prime number from 1 to 50 is :

(a)1

50(b)

2

25(c)

1

25(d) none of these

SECTION B

(Question numbers 11 to 18 carry 2 marks each)

11. Find the roots of the following equation :

1 1 11; 4, 7

4 7 30x

x x− = ≠ −

+ −12. Find a, b and c such that the following numbers are in A.P. a, 7, b, 23, c.

13. In two concentric circles, prove that a chord of larger circle which is tangent to

smaller circle is bisected at the point of contact.

14. An arc of a circle is of length 5π cm and the sector it bounds has an area of 20π cm2.

Find the radius of the circle.

15. Determine the ratio of the volume of a cube to that of a sphere which will exactly

fit inside the cube.

16. If the points A(4, 3) and B(x, 5) are on the circle with centre O(2, 3), find the

value of x.

17. Find the value of k, if the points (7, –2), (5, 1) and (3, k) are collinear.

18. Two dice are thrown together. Find the probability of getting a total less than 6.

OR

Two coins are tossed simultaneously. Find the probability of getting atleast one head.

SECTION C


19. Solve for x : 4 3 2 1 1 3

10 3; – ,2 1 4 3 2 4

x xx x

x x

− + − = ≠ ≠ + −OR

A passenger train takes 2 hours less for a journey of 300 km, if its speed is increased

by 5 km/hr from its usual speed. Find the usual speed of the train.

t



3

20. Determine the A.P. whose 3rd term is 16 and 7th term exceeds the 5th term by 12.

21. In the figure, O is the centre of the circle, AB is a diameter and AD is a tangent. If

∠BOC = 120°, find ∠ADC.

OR

In ∆PQR, ∠Q = 90°, a circle with centre O and radius 2 cm has been inscribed in

the triangle. If QR = 6 cm, find the perimeter of ∆PQR.

22. Construct a ∆ABC in which BC = 6.5 cm, AB = 4.5 cm and ∠ABC = 60°. Construct

another triangle similar to ∆ABC such that each side of new triangle is 4

5of the

corrresponding sides of ∆ABC.

23. Four equal circles, each of radius 5 cm, touch each other, as shown in the figure below.

Find the area included between them. (Take π = 3.14)

24. Find the number of metallic discs with 1.5 cm base diameter and of height 0.2 cm, to be

melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

OR

Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively, are melted to form a

single solid sphere. Find the radius of the resulting sphere.



4



25. The shadow of a tower standing on ground level is found to be 45 m longer when

sun’s altitude is 30°, then when it was 60°. Find the height of the tower.

26. Prove that the points (0, 0), (5, 5) and (–5, 5) are the vertices of a right

isosceles triangle.

27. If the coordinates of the mid-points of the sides of a triangle are (1, 1), (2, –3) and

(3, 4). Find its centroid.

28. What is the probability that a number selected at random from the numbers

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, will be their average?

SECTION D


29. Show that the equation 2(a2 + b2) x2 + 2(a + b) x + 1 = 0 has no real roots, when

a ≠ b.

OR

By increasing the list price of a book by Rs 10 a person can buy 10 books less for

Rs 1200. Find the original list price of the book.

30. Find the sum of all natural numbers between 250 and 1000 exactly divisible by 3.

31. Prove that opposite sides of a quadrilateral circumscribing a circle subtend

supplementary angles at the centre of the circle.

32. A drain cover is made from a square metal plate of side 40

cm having 441 holes of diameter 1 cm each drilled in it. Find

the area of the remaining square plate.

OR

Find the area of the shaded region in the given figure, if

PQ = 24 cm, PR = 7 cm and O is the centre of the circle.

33. An oil funnel of tin sheet consists of a cylindrical portion 10 cm long attached to a

frustum of a cone. If the total height of the funnel be 22 cm, diameter of the

cylindrical portion be 8 cm and the diameter of the top of the funnel be 18 cm, find

the area of the tin required to make the funnel.

34. As observed from the top of a lighthouse, 100 m above sea level, the angle of

depression of a ship, sailing directly towards it, changes 30º to 45°. Determine the

distance travelled by the ship during the period of observation.

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class x sa-ii mathematics sample paper 2016

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