#### Public Exam Model Question Paper 2019 - 2020

10th Standard EM

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Maths

Time : 02:45:00 Hrs
Total Marks : 100

Part I

Answer all the questions.

Choose the most suitable answer from the given four alternatives and write the option code with the corresponding answer.

14 x 1 = 14
1. A={a,b,p}, B={2,3}, C={p,q,r,s} then n[(A U C) x B] is

(a)

8

(b)

20

(c)

12

(d)

16

2. Let n(A)= m and n(B) = n then the total number of non-empty relations that can be defined from A to B is

(a)

mn

(b)

nm

(c)

2mn-1

(d)

2mn

3. An A.P. consists of 31 terms. If its 16th term is m, then the sum of all the terms of this A.P. is

(a)

16 m

(b)

62 m

(c)

31 m

(d)

$\frac { 31 }{ 2 }$

4. For the given matrix A = $\left( \begin{matrix} 1 \\ 2 \\ 9 \end{matrix}\begin{matrix} 3 \\ 4 \\ 11 \end{matrix}\begin{matrix} 5 \\ 6 \\ 13 \end{matrix}\begin{matrix} 7 \\ 8 \\ 15 \end{matrix} \right)$ the order of the matrix AT is

(a)

2 x 3

(b)

3 x 2

(c)

3 x 4

(d)

4 x 3

5. If in triangles ABC and EDF,$\cfrac { AB }{ DE } =\cfrac { BC }{ FD }$ then they will be similar, when

(a)

$\angle B=\angle E$

(b)

$\angle A=\angle D$

(c)

$\angle B=\angle D$

(d)

$\angle A=\angle F$

6. How many tangents can be drawn to the circle from an exterior point?

(a)

one

(b)

two

(c)

infinite

(d)

zero

7. The area of triangle formed by the points (−5, 0), (0, −5) and (5, 0) is

(a)

0 sq.units

(b)

25 sq.units

(c)

5 sq.units

(d)

none of these

8. A tower is 60 m height. Its shadow is x metres shorter when the sun’s altitude is 45° than when it has been 30°, then x is equal to

(a)

41.92 m

(b)

43.92 m

(c)

43 m

(d)

45.6 m

9. The angle of elevation of a cloud from a point h metres above a lake is $\beta$. The angle of depression of its reflection in the lake is 45°. The height of location of the cloud from the lake is

(a)

$\frac { h\left( 1+tan\beta \right) }{ 1-tan\beta }$

(b)

$\frac { h\left( 1-tan\beta \right) }{ 1+tan\beta }$

(c)

h tan(45°-$\beta$)

(d)

none of these

10. If A is an assets angle of Δ ABC, right angle at 3, then the value of sin A T cos A is

(a)

=1

(b)

>1

(c)

<1

(d)

=2

11. The volume (in cm3) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

(a)

$\frac{4}{3}\pi$

(b)

$\frac{10}{3}\pi$

(c)

$5\pi$

(d)

$\frac{20}{3}\pi$

12. If S1 denotes the total surface area at a sphere of radius ૪ and S2 denotes the total surface area of a cylinder of base radius ૪and height 2r, then

(a)

S1=S2

(b)

S1>S2

(c)

S1<S2

(d)

S1=2S2

13. The sum of all deviations of the data from its mean is

(a)

Always positive

(b)

always negative

(c)

zero

(d)

non-zero integer

14. The standard deviation is the ____ of variance

(a)

cube

(b)

square

(c)

square root

(d)

cube root

15. Part II

Answer any 10 questions. Question no. 28 is compulsory.

10 x 2 = 20
16. Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
R= {(3,7), (4,10), (7,7), (7,8), (8,11), (8,7), (8,10)}

17. Find the first term of the G.P. whose common ratio 5 and whose sum to first 6 terms is 46872

18. Prove that $\sqrt { 3 }$ is irrational

19. Find the LCM of the given expressions.
4x2y, 8x3y2

20. Using quadratic formula solve the following equations.
9x2-9(a+b)x+(2a2+5ab+2b2)=0

21. If radii of two concentric circles are 4 cm and 5 cm then find the length of the chord of one circle which is a tangent to the other circle

22. In figure OA· OB = OC·OD
Show that $\angle A=\angle C\quad and\quad \angle B=\angle D$

23. Show that the given vertices form a right angled triangle and check whether its satisfies Pythagoras theorem
A(1, - 4) , B(2, - 3) and C(4, - 7)

24. If A (-5, 7), B (-4, -5), C (-1, -6) and D (4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

25. The horizontal distance between two buildings is 140 m. The angle of depression of the top of the first building when seen from the top of the second building is 30° . If the height of the first building is 60 m, find the height of the second building.($\sqrt { 3 }$=1.732)

26. The radius and height of a cylinder are in the ratio 5:7 and its curved surface area is 5500 sq.cm. Find its radius and height.

27. If the radii of the circular ends of a conical bucket which is 45 em high are 28 em and 7 em, find the capacity of the bucket. (Use π=$\frac{22}{7}$)

28. A and B are two events such that, P(A)=0.42, P(B)=0.48, P(A ∩ B)=0.16. Find (i) P(not A) (ii) P(not B) (iii) P(A or B)

29. The marks scored by 5 students in a test for 50 marks are 20, 25, 30, 35, 40. Find the S.D for the marks. If the marks are converted for 100 marks, find the S.D. for newly obtained
marks.

30. Part III

Answer any 10 questions. Question no. 42 is compulsory.

10 x 5 = 50
31. An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides as shown Fig. Express the volume V of the box as a function of x.

32. A functionf: [-7,6) $\rightarrow$ R is defined as follows.

find 2f(-4) + 3f(2)

33. Determine the general term of an A.P. whose 7th term is -1 and 16th term is 17.

34. If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.

35. Solve $\frac { x }{ 2 } -1=\frac { y }{ 6 } +1=\frac { z }{ 7 } +2$$\frac { y }{ 3 } +\frac { z }{ 2 } =13$

36. Prove that in a right triangle, the square of 8. the hypotenure is equal to the sum of the squares of the others two sides.

37. The graph relates temperatures y (in Fahrenheit degree) to temperatures x (in Celsius degree)
Write an equation of the line

38. Find the coordinates at the points of trisection (i.e. points dividing in three equal parts) of the line segment joining the points A(2, -2) and B(-7, 4).

39. prove the following identities.
$\frac { cot\theta -cos\theta }{ cot\theta +cos\theta } =\frac { cosec\theta -1 }{ cosec+1 }$

40. If tanθ+sinθ=P; tanθ-sinθ=q P.T P2-q2=4$\sqrt{pq}$

41. A solid consisting of a right circular cone of height 12 cm and radius 6 cm standing on a hemisphere of radius 6 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of the water displaced out of the cylinder, if the radius of the cylinder is 6 cm and height is 18 cm.

42. What is the ratio of the volume of a cylinder, a cone, and a sphere. If each has the same diameter and same height?

43. In a box there are 20 non-defective and some defective bulbs. If the probability that a bulb selected at random from the box found to be defective is $\frac{3}{8}$ then, find the number of defective bulbs.

44. C.V. of a data is 69%, S.D. is 15.6, then find its mean.

45. Part IV

Answer all the questions.

2 x 8 = 16
1. A functionf: (1,6) $\rightarrow$R is defined as follows:

Find the value of f(3),

2. xA spherical ball of iron has been melted and made into small balls. If the raidus of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?

1. Find two consecutive natural numbers whose product is 20.

2. Find the equation of a straight line
Passing through (-8, 4) and making equal intercepts on the coordinate axes
Passing through (-8, 4) and making equal intercepts on the coordinate axes