QBH507Z I, 2015-16 SUMMATIVE ASSESSMENT – I, 2015-16 / MATHEMATICS X / Class – X :3 hours Time Allowed: 3 hours

90 Maximum Marks: 90

1.

31

2.

4

1

6 3

2 11

10 4

3. 4.

General Instructions: All questions are compulsory. The question paper consists of 31 questions divided into four sections A, B, C and D. Section-A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11 questions of 4 marks each. 3. There is no overall choice in this question paper. 4. Use of calculator is not permitted. 1. 2.

/ SECTION-A 1

4

1

Question numbers 1 to 4 carry one mark each ABC  PQR

1

AB6.5 cm, PQ10.4 cm,

ABC

60 cm

PQR

If ABC  PQR, AB6.5 cm, PQ10.4 cm and perimeter of ABC60 cm, then find the perimeter of PQR.

Page 1 of 11

1

sec2Acosec (A36),

2

A

1

If sec2Acosec (A36), find A.

3

tan (45)cot (45)

1

Find the value of the tan (45)cot (45).

4

1 010 1020 2030 3040 4050 5060 6070 6

8

10

15

5

4

2

Find the median class of the following data : Class interval 010 1020 2030 3040 4050 5060 6070 Frequency

6

8

10

15

5

4

2

/ SECTION-B 5

10

2

Question numbers 5 to 10 carry two marks each. 8n

5

2

n

Check whether 8n can end with the digit 0 for any natural number n.

5

6

36

54

2

Find the least positive integer which on diminishing by 5 is exactly divisible by 36 and 54.

9t26t1

7

Find the zeroes of the quadratic polynomial 9t26t1 and verify the relationship between

Page 2 of 11

2

the zeroes and the coefficients.

8

ABCD

1 AB CD 3

ABCD

(AOB) 21 cm2

COD

2

1 In trapezium ABCD with ABCD, if AB CD and ar(AOB)21 cm2, find ar(COD). 3

x  p sec   q tan 

9

y  p tan   q sec 

x2 y2  p2  q2

2

If x  p sec   q tan  and y  p tan   q sec , then prove that x2 y2  p2  q2.

10

2 (cm )

Page 3 of 11

80-85

85-90

9095

95100

100105

105110

110115

33

27

85

155

110

45

15

The distribution of sale of shirts sold in a month in a departmental store is as under. Calculate the modal size of shirts sold. Size (in cm)

80-85

Number of 33 shirts sold

85-90

9095

95100

100105

105110

110115

27

85

155

110

45

15

Calculate the modal size of shirt :

/ SECTION-C 11

20

3

Question numbers 11 to 20 carry three marks each. 3m

11

3 m1

m

3

Show that the square of any positive integer is either of the form 3 m or 3 m1 for some integer m.

12

3 2x5y4 3x2y160 Solve using cross multiplication method : 2x5y4 3x2y160

f (x)

13 (x)6x313x2x2

g(x)

f 3

g(x)2x1

Using division algorithm, find the quotient and remainder on dividing f (x) by g(x) where f

Page 4 of 11

(x)6x313x2x2 and g(x)2x1

8

14

3

18 The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number.

EDAB, AB10 cm, BC6 cm, AC8 cm

15

GE3 cm

3

In given figure EDAB, AB10 cm, BC6 cm, AC8 cm and GE3 cm. List all similar triangles. How many pairs of similar triangles are possible ?

500

16 650

Page 5 of 11

3

From airport two aeroplanes start at the same time. If speed of first aeroplane due North is 500 km/h and that of other due East is 650 km/h, then find the distance between two aeroplanes after 2 hours.

 tan60 2 4 cos2 45 4cosec2 60 2cos2 90

17

2 cosec 30

Evaluate :

3

7 cot 2 30 3

3 sec 60

 tan60 2 4 cos2 45 4cosec2 60 2cos2 90 2 cosec 30

3 sec 60

7 cot 2 30 3

18

3 (1tan2 ). (1sin ) . (1sin)1 Prove that : (1tan2 ). (1sin ) . (1sin)1

19

3 58

x) 20-30

30-40

40-50

50-60

60-70

70-80

5

13

x

20

18

19

Following is the age distribution of cardiac patients admitted during a month in a hospital. Find the missing frequency, if the mode is given to be 58. Age (in years) Number patients

20-30 of 5

30-40

40-50

50-60

60-70

70-80

13

x

20

18

19

20

3 010 1020 2030 3040 4050

Page 6 of 11

7

12

13

10

8

Find the mean of the following frequency distribution, using step deviation method. Class interval 010 1020 2030 3040 4050 Frequency

7

12

13

10

8 / SECTION-D

21

31

4

Question numbers 21 to 31 carry four marks each. a

21

b

HCF

6, 9

LCM

4

15

What is the HCF and LCM of two prime numbers a and b ? Three alarm clocks ring at intervals of 6, 9 and 15 minutes respectively. If they start ringing together, after what time will they next ring together.

22

4

` 2100

3

5

` 1750

2

1

4

4 chairs and 3 tables cost ` 2100 and 5 chairs and 2 tables cost ` 1750. Find the cost of one chair and one table separately.

23

a

x4x38x2axb, x21

b

4

Find the values of a and b so that x4x38x2axb is divisible by x21.

24

XI

NCC) NCC

2x3x217x7 NCC

Page 7 of 11

XI

4 2x7 NCC

NCC Students of class XI of a school were motivated to apply for NCC. From each section equal number of students opted for NCC. If there are 2x7 sections of class XI and total number of students in all the sections is represented by 2x3x217x7, then find the number of students who opted for NCC from each section and how many did not opt for it. What is the importance of NCC in the life of a student ? 25

ABC

AC UYVZ

X

Y, Z, U

V

AX, XC, AB

BC

4

UVYZ

In ABC, X is any point on AC. If Y, Z, U and V are the middle points of AX, XC, AB and BC respectively, then prove that UYVZ and UVYZ.

BCDE

26

BCADCF, AC6 m

CF12 m

Find the length of the diagonal of the rectangle BCDE, if BCADCF, AC6 m and

Page 8 of 11

4

CF12 m.

27

m cotAn

m sinA n cosA n cosA m sinA

If m cotAn, find the value of

4

m sinA n cosA n cosA m sinA

28

4 (1  cotA  tanA). (sinA  cosA) 

secA 2

cosecA

cosec A

sec2 A

secA

cosecA

Prove the following indentity : (1  cotA  tanA). (sinA  cosA) 

2

cosec A

sec2 A

29

4

tan cot  sec 1 cosec

1

cosecsecsec. tan

Prove the following identity :

tan cot  sec 1 cosec

30

Page 9 of 11

1

cosecsecsec. tan

4

`

0-200

200400

400600

600800

8001000

10001200

12001400

33

74

170

88

76

44

25

Pocket expenses of the students of a class in a college are shown in the following frequency distribution : Pocket expenses (in `) Number students

of

0-200

200400

400600

600800

8001000

10001200

12001400

33

74

170

88

76

44

25

Find the mean and median for the above data.

31

4

`

400500

500600

600700

700800

800900

9001000

10001100

11001200

10

15

11

12

13

18

6

4

Consider the following distribution of daily wages of workers in a company : Daily wages (in `) Number workers

of

400500

500600

600700

700800

800900

9001000

10001100

11001200

10

15

11

12

13

18

6

4

Draw a ‘less than type’ ogive and a ‘more than type’ ogive for the above data.

Page 10 of 11

-o0o0o0o-

Page 11 of 11

B2YZ0XC I, 2015-16 SUMMATIVE ASSESSMENT – I, 2015-16 / MATHEMATICS X / Class – X :3 hours Time Allowed: 3 hours

90 Maximum Marks: 90

1.

31

2.

4

1

6 3

2 11

10 4

3. 4.

General Instructions: All questions are compulsory. The question paper consists of 31 questions divided into four sections A, B, C and D. Section-A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11 questions of 4 marks each. 3. There is no overall choice in this question paper. 4. Use of calculator is not permitted. 1. 2.

/ SECTION-A 1

4

1

Question numbers 1 to 4 carry one mark each 1

PQR

XY  QR

1 XY QR 3

PQ : PX

1 In PQR, XY  QR. If XY QR, then find PQ : PX. 3

Page 1 of 10

1

cotA2,

2

cosec2Acot2A

1

If cotA2, then find the value of cosec2Acot2A

cosec (3x15)2,

3

x

1

If cosec (3x15)2, then find the value of x.

4

1 14001550

1550-1700

1700-1850

1850-2000

8

15

21

8

From the following frequency distribution, find the median class : Cost of index

living 14001550

Number of weeks

8

1550-1700

1700-1850

1850-2000

15

21

8

/ SECTION-B 5

10

2

Question numbers 5 to 10 carry two marks each. 5

5 Prove that 5

6

120

2 2 is an irrational number

140

Find the HCF of 120 and 140 by Prime Factorisation method.

Page 2 of 10

2

2

7

2 4x2y9 3x4y4 Solve the following pair of linear equations : 4x2y9 3x4y4

ABDE

8

DC2CFAC

BDEF

2

In the given figure, ABDE and BDEF. Prove that DC2CFAC.

9

1 Prove that :

10

Page 3 of 10

1

1 sin A

1

1 sin A

1

x

1  2 sec2 A sin A

2

1 2 sec2 A sin A

 xi x 

2

If mean of set of observation is x , then evaluate

 xi x  .

/ SECTION-C 11

20

3

Question numbers 11 to 20 carry three marks each. 11

n

n3n, 6

3

Prove that n3n is divisible by 6 for any positive integer n.

12

1 10

` 600 1 6

3

` 1500

A man earns ` 600 per month more than his wife. One-tenth of the man’s salary and one-sixth of the wife’s salary amount to ` 1500, which is saved every month. Find their incomes.

13

1

20

3

Find a quadratic polynomial, the sum and product of whose zeroes are 1 and 20 respectively. Hence find the zeroes.

14

x

y

2x5y4 3x2y160 Solve for x and y : 2x5y4 3x2y160

Page 4 of 10

3

15

3 (a)

(b)

State whether the given pairs of triangles are similar or not. In case of similarity mention the criterion. (a)

(b)

Page 5 of 10

16

8

6

30 3

A vertical pole of length 8 m costs a shadow 6 m long on the ground and at the same time a tower casts a shadow 30 m long. Find the height of tower.

17

sin (2x3y)1; cos (2x3y)

If sin (2x3y)1; cos (2x3y)

3 2

x

3

y

3 , find the value of x and y. 2

18

3 sin

2 sin 3

2 cos3

cos

tan

Prove that : sin

2 sin 3

2 cos3

cos

tan

19

3 58

x) 20-30

Page 6 of 10

30-40

40-50

50-60

60-70

70-80

5

x

13

20

18

19

Following is the age distribution of cardiac patients admitted during a month in a hospital. Find the missing frequency, if the mode is given to be 58. Age (in years) Number patients

20-30 of 5

30-40

40-50

50-60

60-70

70-80

13

x

20

18

19

20

3 15-20

20-25

25-30

30-35

35-40

40-45

13

18

31

25

15

5

Draw a ‘less than type’ ogive for the following frequency distribution : Class 15-20 20-25 25-30 30-35 35-40 40-45 Frequency 13 18 31 25 15 5 / SECTION-D 21

31

4

Question numbers 21 to 31 carry four marks each. 360

21

4 360

Jenny and Sally bought a special 360 day joint membership of a tennis club. Jenny will use the club every alternate day and Sally will use the club every third day. They both use the club on the first day. How many days will neither person use the club in the 360 days ? 22

a

b

4

2x3y7, a(xy)b(xy)3ab2 For what values of a and b does the following pair of linear equations have infinite number of solutions ? 2x3y7, a(xy)b(xy)3ab2

23

Page 7 of 10

6x48x317x221x7

3x24x1

axb

a 4

b If the polynomial 6x48x317x221x7 is divided by another polynomial 3x24x1, the remainder comes out to be (axb), find a and b.

p(x)x2x2

24

(, 4

) 12

12

Rahul donated some money and books to a school for poor children. Money and books can be represented by the zeroes (i.e. , ) of the polynomial p(x)x2x2. Akash who is friend of Rahul, also got inspired by him and donated the money and books in the form of a polynomial whose zeroes are 12 and 12. Find the polynomial represented by Akash’s donation ? Why Akash got inspired by Rahul ? 25

4 Prove that the diagonals of a trapezium intersect each other in the same ratio AC

26 CDd

x

B h

ABADBCCD

ABx, BCh

d

In the right triangle, B is a point on AC such that ABADBCCD, If ABx, BCh and CDd, then find x (in terms of h and d)

Page 8 of 10

4

27

cos20cos21cos22cos23… cos288cos289

4

Evaluate cos20cos21cos22cos23… cos288cos289

28

4 cosecA cosecA

1 1

cosecA cosecA

1 1

2secA

1 1

cosecA cosecA

1 1

2secA

Prove that : cosecA cosecA

29

cosec  cot  q sin

cosec  cot 

1 q

sec

If cosec  cot  q, show that cosec  cot 

1 and hence find the values of sin and sec. q

200

30

4

10-20 20-30 30-40 40-50 50-60 60-70 40

22

35

50

23

30

The following are the ages of 200 patients getting medical treatment in a hospital on a

Page 9 of 10

4

particular day : Age (in years)

10-20 20-30 30-40 40-50 50-60 60-70

Number of Patients 40

22

35

50

23

30

Write the above distribution as less than type cumulative frequency distribution and also draw an ogive to find the median.

31

4 10

20

30

40

50

60

70

80

90

100

5

9

17

29

44

60

70

78

83

85

Find the mode of the data from the given information. Marks No. Students

of

Below 10

Below 20

Below 30

Below 40

Below 50

Below 60

Below 70

Below 80

Below 90

Below 100

5

9

17

29

44

60

70

78

83

85

-o0o0o0o-

Page 10 of 10