# Class 10 Maths Sa-1

MATHEMATICS, SA - 1

Time allowed : 3 to 3½ hours General Instructions 1. 2. All questions are compulsory. The question paper consists of 34 questions divided into four sections A, B, C and D. Section A comprises of 10 questions of 1 mark each. Section B comprises of 8 questions of 2 marks each. Section C comprises of 10 questions of 3 marks each and Section D comprises of 6 questions of 4 marks each. Question numbers 1 to 10 in Section A are multiple choice questions where you are to select one correct option out of the given four. There is no overall choice. How ever, internal choice has been provided in 1 question of 2 marks 3 questions of three marks each and 2 questions of 4 marks each. You have to attempt only one of the alternatives in all such questions. Use of calculators is not permitted. Maximum Marks : 80

3. 4.

5.

SECTION A

Question number 1 to 10 are of 1 mark each 1. Euclid's Division Lemma states that for any two positive integers a and b, there exists unique integers q and r such that a = bq + r where r must satisfy : (a) (c) 2. 0 < r < b 0 < r b (b) (d) 0 r b 0 r b

In Fig. 1, the graph of a polynomial p(x) is shown. The number of zeroes of p(x) is: 65

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y p(x)

x´

x

y´ Fig. 1

(a) (c) 3.

1 3

(b) (d)

2 4

In Fig. 2, if DE || BC, then x equals :

A 3 cm D 2 cm B C 4 cm E

Fig. 2 (a) (c) 4. 3 cm 4 cm (b) (d) 2 cm

20 cm 3

If sin ( + 36°) = cos where and + 36° are acute angles, then value of is (a) (c) 36° 27° (b) (d) 54° 90° 4 sin – 3 cos is : 2 sin 6 cos

5.

If 3 cos = 2 sin then the value of

66

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(a)

1 8 1 2

(b)

1 3 1 4 4 . If AC = 15 cm the 3

(c)

(d)

6.

In fig. 3, ABC is right angled at B and tan A length of BC is : C

A

B

Fig.3 (a) (c) 7. 4 cm 12 cm (b) (d) 3 cm 9 cm

The decimal expansion of decimal? (a) (c) 1 3

21 will terminate after how many places of 24

(b) (d)

2 4

8.

The pair of linear equations x – 2y = 5 and 2x – 4y = 10 have : (a) (c) Many Solutions One Solution (b) (d) No Solution Two Solution

9.

If tan A cot B (a) (c) zero < 90°

15 then A + B is equal to : 7

(b) (d) 67

90° > 90°

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10.

For a given data with 50 observations 'the less than Ogive' and the 'more than Ogive' intersect at (38.5, 34). The median of the data is : (a) (c) 38.5 50 (b) (d) 34 4.5

SECTION B

Question number 11 to 18 are of 2 marks each 11. 12. 13. Is 7 × 11 × 13 + 11 a composite number? Justify your answer. Can (x + 2) be the remainder on division of a polynomial p(x) by (2x – 5). Justify your answer. In Fig. 4, ABCD is a rectangle. Find the value of x and y.

D

x+y

C

x –y

16

A

22

B

Fig. 4 14. If sin (A + B) = 1 and cos (A – B) = 1, 0° A + B 90°, find A and B. OR If cot 15.

7 1 sin 1 – sin , evaluate 8 1 cos 1 – cos

ABCD is a trapezium in which AB || DC and its diagonals intersect each AO CO : other at O. Prove that BO DO In Fig. 5, S 90 , PQ 10cm, QS 6 cm and RQ 6 cm. Calculate the length PR.

16.

68

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17.

The following table shows the distribution of the heights of a group of 50 factory workers. 150-155 8 155-160 14 160-165 20 165-170 4 170-175 3 175-180 1

Height (in cm) No. of Workers

Convert the distribution to a less than type cumulative frequency distribution. 18. Find the mode of the following distribution : 30-40 4

Height (in cm)

No. of Plants

40-50

3

50-60

8

60-70

11

70-80

8

SECTION C

Question number 19 to 28 carry 3 marks each 19. Show that the square of any positive integer is of the form 3q or 3q + 1 for some integer q : Prove that

20.

3 2 is irrational. 5

OR

Prove 21.

5

3 is irrational.

A person starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was Rs. 4500 after 4 years of service and Rs....

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