10th maths full portions

8/20/2019 10th Maths Full Portions

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SSLC MATHEMATICS

100MARKS 2:30HRS

Section – I Choose the correct answer

1) Which one of the following is not true ?

(A) A \ B = A B’ B) A \ B = A B (C) A \ B = ( A B) B’ (D) A \ B=( A , B) \ B

2) The 8th term of the sequence 1, 1, 2, 3, 5, 8, g is (A) 25 (B) 24 (C) 23 (D)21

3) The sequence – 3, – 3, – 3,.. is

(A) an A.P. only (B) a G.P. only (C) neither A.P. nor G.P (D) both A.P. and G.P.

4) The GCD of x 2 + 2 xy +y 2 and x 4- y 4 – is (A) 1 (B) x+y (C) x – y (D) x 2 - y 2

5) Let b = a + c . Then the equation ax 2 + bx+ c=0 has equl roots, if

A) a = c (B) a = – c (C) a = 2c (D) a = – 2c

6) Matrix A=( aij )mxn is a square matrix if (A) m < n (B) m > n (C) m = 1 (D) m = n

7) If A and B are square matrices such that AB = I and BA = I , then B is (A) Unit matrix

(B) Null matrix (C) Multiplicative inverse matrix of A (D) – A

8) If the points (2, 5), (4, 6) and (a, a) are collinear, then the value of a is equal to

(a) -8 (b) 4 (c) -4 (d) 8

9) If the tangents PA and PB from an external point P to circle with centre O are inclined to

each other at an angle of 40o, then ∟POA = (A) 70o (B) 80o (C) 50o (D) 60o

10) The sides of two similar triangles are in the ratio 2:3, then their areas are in the ratio

(A) 9:4 (B) 4:9 (C) 2:3 (D) 3:2

11)

= (A)cot (B) tan (C) sin (D) – cot

12) man is 28.5 m away from a tower. His eye level above the ground is 1.5 m. The angle of

elevation of the tower from his eyes is 45c.Then the height of the tower is(A) 30 m (B) 27.5 m (C) 28.5 m (D) 27 m

13) The ratios of the respective heights and the respective radii of two cylinders are 1:2 and

2:1 respectively. Then their respective volumes are in the ratio

(A) 4 : 1 (B) 1 : 4 (C) 2 : 1 (D) 1 : 2

14) The variance of 10, 10, 10, 10, 10 is (A) 10 (B) √ (C) 5 (D) 0

15) There are 6 defective items in a sample of 20 items. One item is drawn at random. The

probability that it is a non-defective item is (A) (B) (C) (D) 0



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Section – II Answer any ten. Question no 30 is compulsory.

16) Verify the commutative property of set intersection for

A = { l m,n,o, 2, 3, 4, 7} and B = {2, 5, 3, - 2, m,n,o, p}.

17) ) Given n(A)= 200, n(B)=300, n(U) = 700, n =100, find

18) Find the LCM of the following 66a4 b2 c 3, 44a3 b4 c 2 , 24a2 b3 c 4

19) ( ) ( ) find(AB)T

20) Construct a 3x 2 matrix A =[aij ], whose elements are aij= ||

21) The centre of a circle is at (-6, 4). If one end of a diameter of the circle is at the origin,

then find the other end.

22) Find the angle of inclination of the line passing through the points(3 , 3) and(0 , 0)

23) Find the value of x in each of the above diagram.

24) Prove the identity

= cosec

25) A girl of height 150 cm stands in front of a lamp-post and casts a shadow of length 150√ cm on the ground. Find the angle of elevation of the top of the lamp-post .

26) The radii of two right circular cylinders are in the ratio of 3 : 2 and their heights are in the

ratio 5 : 3. Find the ratio of their curved surface areas.

27) Volume of a solid cylinder is 62.37 cu.cm. Find the radius if its height is 4.5 cm.

28) Calculate the standard deviation of the first 13 natural numbers.

29) Three dice are thrown simultaneously. Find the probability of getting the same number on

all the three dice.

30)a) Find the sum of the arithmetic series 5 + 11 + 17 +….+ 95. OR

b) Divide the following and write your answer in lowest terms.

Section – III Answer any nine. Question no 45 is compulsory.

31) Given that U = {a,b,c,d ,e, f , g ,h}, A = {a, b, f , g }, and B = {a, b, c}, verify De Morgan’s

laws of complementation.



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32) A function f : [-7,6)→R is defined as follows

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

(ii) f(-7)-f(-3) (iii)

33) The sum of three consecutive terms in an A.P. is 6 and their product is – 120. Find the

three numbers.

34) If S1 ,S2 and S3 are the sum of first n, 2n and 3n terms of a geometric series respectively,

then prove that S1(S3-S1) =(S2-S1)2 .

35) Factorize x 3-3x 2 - 10 x+ 24

36) A takes 6 days less than the time taken by B to finish a piece of work. If both A and B

together can finish it in 4 days, find the time that B would take to finish this work by himself.

37) Find the other polynomial q(x) of each of the following, given that LCM and GCD and

one polynomial p(x) respectively.

38) ( ) ( ), then show that A2-(a+d)A=(bc-ad)I.

39) Find the area of the quadrilateral whose vertices are (-4,5), (0,7), (5,-5) and (-4,-2)

40)State and prove Baudhayan theorem

41) The angles of elevation of an artificial earth satellite is measured from two earth stations,

situated on the same side of the satellite, are found to be 30o and 60o. The two earth stations

and the satellite are in the same vertical plane. If the distance between the earth stations is

4000 km, find the distance between the satellite and earth. ( √ = 1.732)

42) Using clay, a student made a right circular cone of height 48 cm and base radius

12 cm.Another student reshapes it in the form of a sphere. Find the radius of the sphere.

43) Given

∑ = 99 , n = 9 and

∑= 79. Find

∑ and

∑

44) A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are

rotten. If a person takes out one fruit at random, find the probability that the fruit is either an

apple or a good fruit.

45)a) Find the equation of the straight line which passes through the point of intersection of

the straight lines 5 x - 6y = 1 and 3 x + 2y + 5 = 0 and is perpendicular to the straightline 3 x- 5y + 11 = 0. OR

b) A mansion has 12 right cylindrical pillars each having radius 50 cm and height 3.5 m. Find

the cost to paint the lateral surface of the pillars at ` 20 per square metre.



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Section – IV Answer both choosing either of the alternative.

46)a) Construct a cyclic quadrilateral ABCD, given AB = 6 cm,

∟ ABC = 70o, BC = 5 cm and ∟ ACD = 30o.

or

b ) Construct a ∆ ABC such that AB = 6 cm, ∟C = 40o

and thealtitude from C to AB is of length 4.2 cm.

47) a) Draw the graph of y= x 2 - x-8 and hence solve x 2 - 2x -15 .Or b)

B ) N No. Of

workers x3 4 6 8 9 16

No of days

N No. Of days y 96 72 48 36 32 18

o. of wDraw graph for the data given in the table. Hence find the number

of days taken by 12 workers to complete the work.

Prepared by

R.Vinoth kumar M.sc., Genius Tuition Centre,

Coimbatore - 641 006.

Cell No. : 88702 49542, 95972 48278

10th maths full portions

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