kendriya vidyalaya sangathan,chennai region practice test 2020 - 2021 class: 10 ... - kvs · 2021....

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KENDRIYA VIDYALAYA SANGATHAN,CHENNAI REGION

PRACTICE TEST 2020 - 2021

Class: 10 Std Max.Marks:80

Sub: Mathematics- Standard Time: 3 Hours +15 Min

General Instructions:

1. This question paper contains two parts A and B.

2. Both Part A and Part B have internal choices.

Part – A:

1. It consists two sections- I and II.

2. Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions.

3. Section II has 4 questions on case study. Each case study has5 case-based sub-parts.

An examinee is to attempt any 4 out of 5 sub-parts.

Part – B:

1. It consists of three sections III, IV and V.

2. In Section III,Question No 21 to 26 are Very short answer Type questions of

2 mark each.

3. In Section IV, Question No 27 to 33 are Short Answer Type questions of 3 marks each.

4. In Section V, Question No 34 to 36 are Long Answer Type questions of 5 marks each.

5. Internal choice is provided in 2 questions of 2 marks, 2 questions of 3 marks

and 1 question of 5 marks

PART – A

SECTION – I

Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions.

1) Find the quadratic polynomial whose zeroes are 5 and 8. (1)

2) If ‘’ and ‘’ are the zeroes of a quadratic polynomial 652 xx , then find the

value of + 2 .

(OR)

If both the zeroes of the quadratic polynomial cbxax 2 are equal and

opposite in sign, then find the value of ‘b’.

(1)

3) If the graph of a polynomial intersects the x-axis at exactly two points, is it

necessarily a quadratic polynomial?

(1)

4) Which term of the A.P. 27, 24, 21,…..is zero?

(OR)

In an Arithmetic Progression, if 4d , n = 7,n

a =4, then find a .

(1)

5) The first term of an A.P. is ‘p’ and its common difference is ‘q’. Find its 10th term. (1)

6) If (p – 1), (p + 3) and 11 are in A.P., then find the value of ‘p’. (1)

PT10MATHSTDSET3

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7) In the ∆ABC, D and E are points on side AB and AC respectively such that DE ║

BC. If AE=2cm, AD=3cm and BD=4.5cm, then find CE.

(1)

8) Two circles are always congruent. Why or Why not?

(OR)

Two squares are always similar. Why or Why not?

(1)

9)

A pair of triangles is given above. Write whether they are similar or not. If similar

write in symbolic form.

(1)

10) If 1cossin yx and 0cossin yx , find the value of ‘x’. (1)

11) Simplify )sin1)(sin1)(tan1( 2 AAA .

(OR)

Prove that 11cos1sec 22 ec .

(1)

12) If 30sin45cos45sintan x , find the value of ‘x’. (1)

13) PQ is a tangent to a circle with centre O at point P. If ∆OPQ is an isosceles

triangle, then find ∠OQP.

(1)

14) If two tangents are inclined at 60˚ are drawn to a circle of radius 3cm then find

length of each tangent.

(1)

15) Draw a circle and two lines parallel to a given line such that one is a tangent and

the other, a secant to the circle.

(OR)

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q

fromthe centre is 25 cm. Find the radius of the circle.

(1)

16) In the adjoining figure, if TP and TQ

are the two tangents to a circle with

centre O so that POQ = 110°,

then find PTQ.

(1)

SECTION – II

Case study based questions are compulsory. Attempt any four sub parts of each

question. Each sub part carries 1 mark.

17)

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Sylvia wants to organize her birthday party. She was happy on her birthday. She is

very health conscious, thus she decided to serve fruits only.

She has 36 apples and 60 bananas at home and decided to serve them. She want to

distribute fruits among guests. She does not want to discriminate among guests so

she decided to distribute equally among all.

a) How many maximum guests Sylvia can invite?

(i) 12 (ii) 120 (iii) 6 (iv) 180

(1)

b) How many apples and bananas will each guest get?

(i) 3 apple 5 banana (ii) 5 apple 3 banana

(iii) 2 apple 4 banana (iv) 4 apple 2 banana

(1)

c) Sylvia decide to add 42 mangoes also. In this case how many maximum guests

Sylvia can invite?

(i) 12 (ii) 120 (iii) 6 (iv) 180

(1)

d) How many total fruits will each guest get?

(i) 6 apple 5 banana and 6 mangoes (ii) 6 apple 10 banana and 7 mangoes

(iii) 3 apple 5 banana and 7 mangoes (iv) 3 apple 10 banana and 6 mangoes

(1)

e) If Sylvia decide to add 3 more mangoes and reduced 6 apples, in this case how

many maximum guests Sylvia can invite?

(i) 12 (ii) 30 (iii) 15 (iv) 24

(1)

18)

Type – A Type – B

Due to ongoing Corona virus outbreak, Raj Medical store has started selling masks

of decent quality.

The store is selling two types of masks currently type A and type B. The cost of

one type A mask is Rs.15 and of one type B mask is Rs.20. In the month of April,

2020, the store sold 100 masks for total sales of Rs.1650.

Due to great demand and short supply, the store has increased the price of each

type by Rs.5 from May 1, 2020. In the month of May, 2020, the store sold 310

masks for total sales of Rs.6875.

On the basis of the above information, answer any four of the following questions:

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a) How many masks of each type were sold in the month of April?

(i) 40 masks of type A, and 60 masks of type B

(ii) 60 masks of type A, and 40 masks of type B

(iii) 70 masks of type A, and 30 masks of type B

(iv) 30 masks of type A, and 70 masks of type B

(1)

b) If the store had sold 50 masks of each type, what would be its sales in the month of

April?

(i) Rs.550 (ii) Rs.560 (iii) Rs.1050 (iv) Rs.1750

(1)

c) How many masks of each type were sold in the month of May?

(i) 175 masks of type A, and 135 masks of type B

(ii) 200 masks of type A, and 110 masks of type B

(iii) 110 masks of type A, and 200 masks of type B

(iv) 135 masks of type A, and 175 masks of type B

(1)

d) If the store had sold 30 masks of each type, what would be its sales in the month of

May?


(1)

e) What extra profit did he earned by increasing price in May month.


(1)

19) RK Fabricators has got a order for making a frame for machine of their client. For

which, they are using a AutoCAD software to create a constructible model that

includes the relevant information such as dimensions of the frame and materials

needed.

The frame will have a solid base and will be cut out of a piece of steel The final

area of the frame should be 76 sq.m. The diagram of frame is shown below.

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In order to input the right values in the AutoCAD software, the engineer needs to

calculate some basic things. On the basis of the above information, answer any

four of the following questions:

a) What are the dimensions of the outer frame?

(i) (10 + x) and (5 + x) (ii) (10 – x) and (5 – x)

(iii) (10 + 2x) and (5 + 2x) (iv) (10 – 2x) and (5 – 2x)

(1)

b) A metal sheet of minimum area is used to make the frame. What should be the

minimum area of metal sheet before cutting?

(i) 50304 2 xx (ii) 55272 xx

(iii) 305 2 x (iv) 504 2 x

(1)

c) What is the area of required final metal frame?

(i) 50304 2 xx (ii) 55272 xx

(iii) xx 504 2 (iv) xx 304 2

(1)

d) If the area of the frame is 76 sq.m, what is the value of x?

(i) 1.5 m (ii) 3.0 m(iii) 2.0 m (iv) 1.8 m

(1)

e) What is the perimeter of the outer frame?

(i) 36 m (ii) 46 m (iii) 45 m (iv) 39 m

(1)

20) Students of a Kendriya Vidyalaya are standing in rows and columns in the

assembly ground for morning prayer. A, B, C, D are the positions of four students

as shown in the figure

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a) The co-ordinates of A and B are respectively

(i) (3, 5) and (7, 9) (ii) (5, 3) and (9, 7)

(iii) (3, 5) and (7, 9) (iv) (3, 5) and (7, 9)

(1)

b) The co-ordinates of C and D are respectively

(i) (5, 11) and (1, 7) (ii) (11, 5) and (7, 1)

(iii) (5, 11) and (1, 7) (iv) (5, 11) and (1, 7)

(1)

c) The distance between A and B is

(i) 24 units (ii) 23 units (iii) 25 units (iv) 22 units

(1)

d) The distance between C and D is

(i) 8 units (ii) 23 units (iii) 24 units (iv) 28 units

(1)

e) The co-ordinates of a point which is equidistant from each of the four students A,

B, C and D are

(i) (5, 7) (ii) (5, 7) (iii) (7, 5) (iv) (7, 5)

(1)

PART – B

SECTION – III

All questions are compulsory. In case of internal choices, attempt any one.

21) If one of the zeroes of the quadratic polynomial 3

2)1( kxxk is (3), then

find the value of ‘k’.

(2)

22) Find the value(s) of ‘k’ so that the pair of equations 52 yx and

0153 kyx has a unique solution.

(2)

23) Find the value of ‘k’ for which the quadratic equation

02)12(2 kxkx has real and equal roots.

(2)

24) In the adjoining figure,

TR

PT

SQ

PS and

PST = PRQ. Prove that PQR is an

isosceles triangle.

(2)

25) Find the ratio in which the point (3, x) divides the line-segment joining the points

(5, 4) and (2, 3).

(OR)

Find the point on x-axis which is equidistant from the points (2,-2) and (-4,2)

(2)

26) If cossin , then find the value of 2costan2 .

(OR)

If 0cossin3 , 0<< 90, find the value of .

(2)

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SECTION – IV


27) If HCF of 255 and 867 is expressible in the form 11583 n , find the value of ‘ n’.

(3)

28) Find the zeroes of 252 2 xx and verify the relationship between the zeroes

and the coefficients.

(3)

29) The sum of the squares of two consecutive multiples of 7 is 637. Find the

multiples.

(OR)

If sin and cos are the roots of the quadratic equation 02 cbxax ,

prove that 0222 acba .

(3)

30) The sum of the 5th and 9th terms of an AP is 30. If its 25th term is three times its 8th

term, find the AP.

(3)

31) In an equilateral triangle ABC, D is a point on the side BC such that BCBD

3

1 .

Prove that 22 79 ABAD .

(3)

(OR)

In the adjoining figure, E is a point on

side CB produced of an isosceles

triangle ABCwith AB = AC. If AD

BC and EF AC,prove that ABD ~

ECF.

32) Prove that the points (1, 7), (4, 2), (1, 1) and (4, 4) are the vertices of a square. (3)

33) Construct a tangent to a circle of radius 4 cm from a point on the concentric circle

of radius 6 cm and measure its length. Verify by actual calculation.

(3)

SECTION – V


34) Draw the graph of 02 yx and 2043 yx . Find the area of the triangle

formed these lines and y - axis.

(5)

35) “In a right triangle, the square of the hypotenuse is equal to the sum of the squares

of the other two sides” – Prove.Using the above theorem, solve the following:

A ladder 10 m long reaches a window 8 m above the ground. Find the distance of

the foot of the ladder from base of the wall.

(5)

36) Two poles of equal heights are standing opposite each other on either side of the

road, which is 80 m wide. From a point between them on the road, the angles of

elevation of the top of the poles are 60° and 30°, respectively. Find the height of

the poles and the distances of the point from the poles.

(OR)

The angles of depression of the top and bottom of a building 50 meters high as

observed from the top of a tower are 30˚ and 60˚ respectively. Find the height of

the tower, and also the horizontal distance between the building and the tower.

(5)

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kendriya vidyalaya sangathan,chennai region practice test 2020 - 2021 class: 10 ... - kvs · 2021....

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