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Class: XthSTD

Subject: MATHEMATICS

Marks: 100 Time: 2:30 hrs.

SECTION - A (i) 1. 2.

3. 4.

5. 6.

(15 x 1 = 15)

Answer all the questions. (ii) Choose and write the correct answer. If f = {(6, 3), (8, 9),(5, 3),(-1, 6)}, then the pre-images of 3 are (A) 5 and -1 (B) 6 and 8 (C) 8 and -1 (D) 6 and 5 If the sequence a1, a2, a3,… is in A.P., then the sequence a5, a10, a15,… is (A) a G.P. (B) an A.P. (C) neither A.P. nor G.P (D) a constant sequence The 8th term of the sequence 1, 1, 2, 3, 5, 8, … is (A) 25 (B) 24 (C) 23 (D) 21 The system of equations x – 4y = 8, 3x – 12y = 24 (A) has infinitely many solutions (B) has no solution (C) has a unique solution (D) may or may not have a solution If 𝛼+ 𝛽 = 14 and 𝛼 - 𝛽 = 2 3 , then 𝛼𝛽 = (A) 42 (B) 44 (C) 46 (D) 48 A is of order of m x n and B is of order p x q, addition of A and B is possible only if (A) m = n (B) n = q (C) n = p (D) m = p, n = q The centre of a circle is (-6, 4). If one end of the diameter of the circle is at (-

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12, 8), then the other end is at (A) (-18, 12) (B) (-9, 6)

(C) (-3, 2)

(D) (0, 0)

8. The angle of inclination of a straight line parallel to x – axis is equal to (A) 0o (B) 60o (C)45o (D) 90o 9. The sides of two similar triangles are in the ratio 2 :3, then their areas in the ratio (A) 9 : 4 (B) 4 : 9 (C) 2: 3 (D) 3 : 2 10. A point P is 26 cm away from the centreO of a circle and PT is the tangent drawn from P to the circle is 10 cm, then OT is equal to (A) 36 cm (B) 20 cm (C) 18 cm (D) 24 cm 2 2 11. (1- sin 𝜃) sec 𝜃 (A) 0 (B) 1 (C) tan2𝜃 (D) cos2𝜃 𝑥2

𝑦2

12. If x = a sec 𝜃, y = b tan 𝜃, then the value of 2 - 2 = 𝑎 𝑏 2 (A) 1 (B) -1 (C) tan 𝜃 (D) cosec2𝜃 13. The total surface area of the solid hemisphere whose radius is a units, is equal to (A) 2𝜋a2sq.units (B) 3𝜋a2sq.units (C) 3𝜋asq.units (D) 3a2sq.units 14. For any collection of n items ,(∑x) - 𝑥 = (A) n𝑥 (B) (n -2)𝑥 (C) (n -1)𝑥 (D) 0

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15. The probability that a leap year will have 53 Fridays or 53 Saturdays is 2 1 4 3 (A) (B) (C) (D) 7 7 7 7 SECTION-B (10x2=20) (i)

Answer any 10 questions. (ii) Question no.30 is compulsory and choose any 9 questions from the remaining. (iii) Each question carries 2 marks. 16. P = {a,b,c},Q = {g, h, x, y} and Q = {a, e, f, s} Find R\ (P∩Q) 17. For any three sets A, B and C if n(A) = 17, n(B) = 17, n(C) = 17, n(A∩ B) = 7, n(B∩ C) = 6, n(A∩ C) = 5, and n(A∩B ∩ C) = 2, find n(A∪B∪C). 18. Factorize x3 – 3x2 – 10x + 24 19. Find the value of k, if 13 + 23 + 33 + ... +k3 = 4356 4 −2 8 2 20. If A = and B = find 6A – 3B. 5 −9 −1 −3 𝑥 1 0 21. Solve (x 1) = (0) −2 −3 5 22. If (7 ,3), (6 , 1), (8, 2) and (p, 4) are the vertices of a parallelogram taken in order, then find the value of p. 𝑦 23. If the straight lines = x – p and ax + 5 = 3y are parallel, then find a.

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24. Prove the identity (sin6 𝜃 + cos6𝜃) = 1 -3 sin2 𝜃cos2𝜃. 25. Find the value of the x in each of the following diagrams.

26. A ladder leaning against a vertical wall, makes an angle of 60o with the ground. The foot of the ladder is 3.5m away from the wall. Find the length of the ladder. 27. Radius and slant height of a solid right circular cone are 35 cm and 37 cm respectively. Find the curved surface area and total surface of the 22

cone. (Take 𝜋= ) 7

28. Calculate the standard deviation (S.D.) of the first 13 natural numbers. 29. If A is an event of a random experiment such that P(A) : P(𝐴) = 7:12, then find P(A).

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30. (a) 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 Rs. 20 per sq.m. [OR] (b) Solve

6 7𝑥−21

-

1 𝑥 2 −6𝑥+9

+

1 𝑥 2 −9

=0

SECTION-C

(9 x 5 = 45)

(i)

Answer any 9 questions. (ii) Question no.45 is compulsory and choose any 8 questions from the remaining. (iii) Each question carries 5 marks. 31. Using Venn diagrams to verify De Morgan’s law for set difference A\ (B∩ C) = (A \ B) ∪ (A \ C). 32. Let A = {6,9,15,18,21}; B = {1,2,4,5,6} and f : A→ B be defined by f (x) =

𝑥−3 3

. Represent f by (i) an arrow diagram (ii) a set of ordered

pairs(iii) a table (iv) a graph. 33. If a,b,c, d are in geometric sequence, then prove that (b - c)2 + (c - a)2 + (d - b)2 = (a - d)2 34. The first term of geometric series is 375 and the fourth term is 192. Find the common ratio and the sum of the first 14 terms. 35. If a + b x + 25 x2 - 24x3 + 16x4 is a perfect square, then find a and b

www.asiriyar.com 36. Find a quadratic equation whose roots are the reciprocal of the roots of the equation 4x2 – 3x -1 = 0.

2 3 2 −2 and 3X + 2Y = 4 0 −1 5 38. A straight line cuts the coordinate axes at A and B. If the midpoint of AB is (3,2), then find the equation of AB. 39. Find the equation of the straight line segment whose end points are the points of the intersection of the straight lines 2x – 3y +4 = 0,x - 2y +3 = 0 and the midpoint of the line joining the points (3,-2) and (5,-8). 40. If tan𝜃 + sin𝜃 = m, tan𝜃 - sin𝜃 = n and m≠n, then show that m2 - n2= 4 𝑚𝑛 41. The radius and height of a right circular cone are in the ratio 2 : 3. Find the slant height if its volume is 100.48 cu.cm. (Take 𝜋 = 3.14) 42. A circus tent is to be erected in the form of a cone surmounted on a cylinder. The total height of tent is 49 m. Diameter of the base is 42 m and height of the cylinder is 21 m. Find the cost of the canvas needed to 37. Find X and Y if 2X + 3Y =

make the tent, if the cost of canvas is Rs.12.50/m2. (Take 𝜋=

22 7

)

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43. Length of 40 bits of wire, correct to the nearest centimetre are given below. Calculate the variance. Length cm 1-10 11-20 21-30 31-40 41-50 51-60 61-70 No. of bits 2 3 8 12 9 5 1 44. A two digit number is formed with the digits 2, 5, 9 (repetition is allowed). Find the probability that the number is divisible by 2 or 5. 45. State and prove Thales theorem.[OR] (b)A car left 30 minutes later than the scheduled time. In order to reach its destination 150km away in time, it has to increase its speed by 25km/hr from its usual speed. Find its usual speed. SECTION-D (2 x 10 = 20) (i) This section contains 2 questions, each with two alternatives. (ii) Answer both the questions choosing either of the alternatives. (iii) Each question carries 10 marks. 46. (a) Draw a circle of radius 3 cm. From an externalpoint 7 cm away from Its centre, construct the pair of tangents to the circle and measure their length. [OR] (b) Construct a ∆PQR such that PQ = 4 cm,
www.asiriyar.com From R to PQ is 4.5 cm. 47. (a) Draw the graph of y = 2x2+ x - 6 and hence solve 2x2+ x - 10 = 0.

[OR] (b) The cost of the milk per litre is Rs.5. Draw the graph for the relation between the quantity and cost. Hence find (i) the proportionality constant, (ii) the cost of 3 litres of milk.