Pai.Net s Public Exam 2019 Model Question Paper 1 MATHEMATICS Time Allowed :2.30 hrs Maximum Marks : 100 t et SECTION I Note : (i) Answer all the 15 questions. 15x1 = 15 (ii) Choose the correct answer from the given four alternatives and write the option code and the corresponding answer. t et 1. If f ( x ) = x 2 + 5 then f( 4) = (a) 26 (b) 21 (c) 20 (d) 20 2. The 8 th term of the sequence 1, 1, 2, 3, 5, 8,, is t et (a) 25 (b) 24 (c) 23 (d) 21 3. If the n th term of an A.P is t n = 3 5n, then the sum of the first n term is t et (a) n 2 [ 1 5n ] (b) n ( 1 5n ) (c) n 2 [ 1 + 5n ] (d) n 2 [ 1 + n ] 4. If the system 6x 2y = 3, kx y = 2 has a unique solution, then t et (a)k = 3 (b) k 3 (c) k = 4 (d) k 4 5. The square root of 49 (x 2 2xy + y 2 ) 2 is (a)7 x y (b) 7 ( x + y ) ( x y ) (c) 7 ( x + y ) 2 (d) 7 ( x y ) 2 6. If A is of order 3 x 4 and B is of order 4 x 3, then the order of BA is (a) 3 x 3 (b) 4 x 4 (c) 4 x 3 (d) not defined 7. Area of the triangle formed by the points ( 0, 0 ), ( 2, 0 ) and ( 0, 2 ) is (a) 1 Sq.units (b) 2 Sq.units (c) 4 Sq.units (d) 8 Sq.units 8. The point of intersection of the straight lines y = 0 and x = 4 is (a) ( 0, 4 ) (b) ( 4, 0 ) (c) ( 0, 4 ) (d) ( 4, 0 ) 9. 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 10. In the figure, if PAB= 120 0 then BPT= (a)120 0 (b) 30 0 (c) 40 0 (d) 60 0 t et t et t et t et 11. ( 1 + tan 2 θ )Sin 2 θ = (a)sin 2 θ (b) Cos 2 θ (c) tan 2 θ (d) Cot 2 θ 12. 9tan 2 θ 9Sec 2 θ = (a) 1 (b) 0 (c) 9 (d) 9 13. The total surface area of a solid hemisphere of diameter 2 cm is equal to (a) 12cm 2 (b) 12πcm 2 (c) 4πcm 2 (d) 3πcm 2 14. For any collection of n items, ( x x )= (a) x (b) x (c) nx (d) 0 t et t et 15. If A and B are mutually exclusive events and S is the sample space such that P(A) = 1 P(B) and 3 S = A B, then P(A) = t et (a) 1 4 t w t t t t t t t t t t t t t t t t t t t t t t t t (b) 1 2 w t t t t t t t t t t t t t t t t t t t t t t t t (c) 3 4 w t t t t t t t t t t t t t t t t t t t t t t t t (d) 3 8
w SECTION II Note : (i) Answer 10 questions. 10x2 = 20 t et (ii) Question number 30 is compulsory. Select any 9 question from the first 14 questions. t t 16. If A = { 4, 6, 7, 8, 9 }, B = { 2, 4, 6 } and C = { 1, 2, 3, 4, 5, 6 } then find A ( BUC ) t et t t 17. Use Venn diagram to verify ( A B ) U ( A \ B ) = A 18. Find the sum of the first 75 positive integers t et t t 19. The sum of a number and its reciprocal is 65. Find the number. 8 20. Determine the nature of roots of the quadratic equation, x 2 8x + 12 = 0 t et t t 21. If A = ( 8 5 2 1 3 4 ), then find A T and ( A T ) T 22. Find the product of the matrices ( 3 2 5 1 ) (4 1 2 7 ) t et t t 23. The centre of a circle is at ( 6, 4 ).if one end of a diameter of the circle is at the origin, t et then find the other end. t t w t t t t t t t t t t t t 24. Show that the straight lines x + 2y + 1 = 0 and 3x + 6y + 2 = 0 are parallel. 25. In PQR, AB ǁQR. If AB is 3 cm, PB is 2cm and PR is 6 cm, then find the length of QR. 26. Find the angular elevation ( angle of elevation from the ground level ) of the Sun when the t et t t t t length of the shadow of a 30 m long pole is 10 3 m. 27. The total surface area of a solid right circular cylinder is 660 sq.cm. If its diameter of the base t et t t t t is 14 cm, find the height and curved surface area of the cylinder 28. Find the standard deviation of the first 13 natural numbers. t et t t t t 29. A bag contains 6 white balls numbered from 1 to 6 and 4 red balls numbered from 7 to 10. A t et ball is drawn at random. Find the probability of getting ( i ) an even-numbered ball ( ii ) a white ball. t t t t 30. (a) Prove the identity ( Sin θ + Cosec θ ) 2 + ( Cosθ + Sec θ ) 2 = 7 + tan 2 θ + Cot 2 θ t et t et t t t t (b) The ratio between the base radius and the height of a solid right circular cylinder is 2 : 5. t If its curved surface area is 3960 sq.cm, find the height and radius t t 7 t t w t t t t t t t t t t t t t t t t t t t t t t t t
SECTION III Note : (i) Answer 9 questions. 9x5 = 45 t et (ii) Question number 45 is compulsory. Select any 8 question from the 14 questions. 31. Let U = { -2, -1, 0, 1, 2, 3, 10 }, A = { -2, 2, 3, 4, 5 } and B = { 1, 3, 5, 8, 9 }. t et Verify De Morgan s laws of Complementation. 32. Let A = { 0, 1, 2, 3 } and B = { 1, 3, 5, 7, 9 } be two sets. Let f : A B be a function t et given by f(x) = 2x + 1. Represent this function as i ) a set of ordered pairs ii ) a table iii ) an arrow diagram and iv ) a graph 33. Find the sum of all 3 digit natural numbers, which are divisible by 9. 34. Find the total area of 14 squares whose sides are 11 cm, 12 cm, 24 cm respectively. t et 35. Factorize: x 3 5x 2 2x + 24 36. If αand βare the roots of the equation 2x 2 3x 5 = 0, form an equation whose roots are α 2 and β 2 t et w t t t t t t t t t t 37. If A = ( 1 1 2 3 ) then show that A2 4A + 5I 2 = O 38. In an isosceles PQR, PQ=PR. The base lies on the x-axis, P lies on the y-axis and t et t t 2x 3y+9 = 0 is the equation of PQ. Find the equation of the straight line along PR. 39. The vertices of a ABC are A ( 5, 7 ), B ( 4, 5 ) and C ( 4, 5 ).Find the slopes of the t et t t altitudes of the triangle. 40. The government plans to develop a new industrial t et t et Zone in an unused portion of land in a city. t t The shaded portion of the map shown on the Right, indicates the area of the new industrial zone. t t Find the area of the new industrial zone. 41. A vertical tree is broken by the wind. The top of the tree touches the ground and makes an t et angle 30 0 with it.if the top of the tree touches the ground 30 m away from its foot, then t t find the actual height of the tree. 42. The radii of two circular ends of a frustum shaped bucket are 15 cm and 8 cm. If its depth is t et t et t t 63 cm, find the capacity of the bucket in liters t t t w t t t t t t t t t t t t t t t t t t t t t t t t w t t t t t t t t t t t t t t t t t t t t t t t t
w 43. The following table shows the marks obtained by 48 students in a Quiz competition t et t et in Mathematics. Calculate the standard deviation. t t Data x 6 7 8 9 10 11 12 Frequency f 3 6 9 13 8 5 4 t t 44. A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that it will be a spade or a king. 45. (a) Solve the quadratic equation 5x 2 6x 2 = 0 by completing the square. t et t et t et t t (b) Water in a cylindrical tank of diameter 4 m and height 10 m is released through a to Cylindrical pipe of diameter 10 cm at the rate of 2.5 Km/hr. How much time will it t t take empty the half of the tank? Assume that the tank is full of water to begin with. t t SECTION IV Note : Answer both questions choosing either of the alternatives. 10x2 = 20 46. (a) Draw a circle of radius 3 cm. From an external point 7 cm away from its centre, t et t et t t construct the pair of tangents to the circle and measure their lengths. (b) Construct a cyclic quadrilateral ABCD with AB = 7 cm, A = 80, AD = 4.5 cm and t t BC = 5 cm. 47. (a) Draw the graph of y = 2x 2 and hence solve 2x 2 + x 6 = 0 t et t t (b) Draw the Graph of xy = 20, x, y > 0. Use the graph to find y when x = 5, and to find x when y = 10. t et t et t et t et t t t Prepared by, w t t t t t t t t t t t t t t t t -o0o- t t L.SURESH (PG Teacher) Kamalammal Matric Hr.Sec.School, Thanipadi-606708, Tiruvannamalai District Cell No : 9444333734 t t t t t t t t t t t t w t t t t t t t t t t t t t t t t t t t t t t t t
Pai.Net s Public Exam 2019 Model Question Paper 2 MATHEMATICS Time Allowed :2.30 hrs Maximum Marks : 100 SECTION I Note : (i) Answer all the 15 questions. 15x1 = 15 (ii) Choose the correct answer from the given four alternatives and write the option code and the corresponding answer. t et 1. If n[ P ( A ) ] = 64, then n(a) is (a) 6 (b) 8 (c) 4 (d) 5 2. If 1 + 2 + 3 + + n = k then 1 3 + 2 3 + 3 3 +. + n 3 is equal to t et t et (a) k 2 (b) k 3 (c) k ( k + 1 ) 2 (d) ( k + 1 ) 3 3. If a, b, c, l, m are in A.P., then 3a + 7, 3b + 7, 3l + 7, 3m + 7, 3n + 7 form (a) a G.P (b) an A.P (c) a constant sequence (d) neither A.P nor G.P 4. The system of equations x 4y = 8, 3x 12y = 24 (a) has infinitely many solutions (b) has no solution t et (c) has a unique solution (d) may or may not have a solution 5. The remainder when x 2 2x + 7 is divided by x + 4 is (a) 28 (b) 29 (c) 30 (d) 31 6. If ( 5 x 2 1) ( 1)= ( 20 ), then the value of x is 3 (a) 7 (b) 7 (c) 1 7 (d) 0 7. The value of k if the straight lines 3x + 6y + 7 = 0 and 2x + ky= 5 are perpendicular is (a) 1 (b) 1 (c) 2 (d) 1 2 8. The midpoint of the line joining ( a, b ), ( 3a, 5b ) (a) ( a, 2b ) (b) ( 2a, 4b ) (c) ( 2a, 2b ) (d) ( a, 3b ) 9. The perimeter of two similar triangles ABC and DEF are 36 cm and 24 cm respectively. If t et t et t et DE = 10 cm, then AB is (a) 12 cm (b) 20 cm (c) 15 cm (d) 18 cm 10. The perimeters of two similar triangles are 24 cm and 18 cm respectively. If one side of the first triangle is 8 cm, then the corresponding side of the other triangle is (a) 4 cm (b) 3 cm (c) 9 cm (d) 6 cm 11. (Cos 2 θ 1 )(Cot 2 θ + 1 ) + 1 = (a) 1 (b) 1 (c) 2 (d) 0 12. In the adjoining figure Sin θ = 15.Then BC = t et t et (a) 85 m (c) 95 m t et 17 (b) 65 m (d) 75 m 13. If the surface area of a sphere is 100 πcm 2, then its radius is equal to (a) 25 cm (b) 100 cm (c) 5 cm (d) 10 cm 14. The least value in a collection of data is 14.1. The range of the collection is 28.4.Then the greatest value of the collection is (a) 42.5 (b) 43.5 (c) 42.4 (d) 42.1 15. The probability that a leap year will have 53 Fridays or 53 Saturdays is t et t et (a) 2 7 t w t t t t t t t t t t t t t t t t t t t t t t t t (b) 1 7 w t t t t t t t t t t t t t t t t t t t t t t t t (c) 4 7 w t t t t t t t t t t t t t t t t t t t t t t t t (d) 3 7
SECTION II Note : (i) Answer 10 questions. 10x2 = 20 t et (ii) Question number 30 is compulsory. Select any 9 question from the first 14 questions. 16. Given A = { a, x, y, r, s }, B = { 1, 3, 5, 7, -10 } verify the commutative property of set union. t et 17. If R = { ( a, 2 ),( 5, b ),( 8, c ), ( d, 1 ) } represents the identify function, find the values of a, b, c and d. 18. If 9 th term of an AP is zero, prove that its 29 th term is double ( twice ) the 19 th term. t et 19. Find the quotient and remainder using synthetic division (3x 3 2x 2 + 7x 5) (x + 3) 20. Simplify 6x 2 + 9 3x 2 12x t et 21. A matrix consists of 30 elements. What are the possible orders it can have? 22. If A = ( 4 2 5 9 ) and B = ( 8 2 ) find 6A 3B 1 3 t et 23. If the area of the ABC is 68 sq.units and the vertices are A(6,7), B( 4,1) and C(a, 9) taken in order, then find the value of a. 24. In the figure,, DE ǁ BC and AD t et area of trapezium BCED area of ABC DB = 3 5, calculate the value of 25. If x = asecθ + btanθ and y = atanθ + bsecθ, then prove that x 2 y 2 = a 2 b 2 t et 26. A girl of height 150 cm stands in front of a lamp post and casts a shadow of length 150 3 cm on the ground. Find the angle of elevation of the top of the lamp post. 27. The total surface area of a solid right circular cylinder is 1540 cm 2. If the height is four times t et the radius of the base, then find the height of the cylinder. 28. Find the range and the coefficient of range of 43, 24, 38, 56, 22, 39, 45. 29. In tossing a fair coin twice, find the probability of getting t et ( i ) two heads ( ii ) atleast one head 30. (a) Find the equation of the straight line parallel to the line x 8y + 13 = 0 and passing t et t et through the points ( 2, 5 ) (b) If the curved surface area of a solid hemisphere is 2772 sq.cm, then find its total surface area. t et t w t t t t t t t t t t t t t t t t t t t t t t t t w t t t t t t t t t t t t t t t t t t t t t t t t w t t t t t t t t t t t t t t t t t t t t t t t t
SECTION III Note : (i) Answer 9 questions. 9x5 = 45 t et (ii) Question number 45 is compulsory. Select any 8 question from the 14 questions. 31. In a college, 60 students enrolled in chemistry, 40 in physics, 30 in biology, 15 in chemistry t et t et and Physics, 10 in physics and biology, 5 in biology and chemistry. No one enrolled in all the three. Find how many are enrolled in at least one of the subjects. 32. A function f [ 3,7 ) R is defined as follows t et 4x 2 1 ; 3 x < 2 f(x) = 3x 2 ; 2 x 4 2x 3 ; 4 < x < 7 f( 3 ) + f( 1) Find, i) f( 5 ) + f( 6 ) ii) f ( 1 ) f( 3 ) iii) f( 2 ) f( 4 ) iv) 2f(6) f(1) 33. The sum of three consecutive terms in an A.P is 6 and their product is 120. Find the three t et terms 34. Solve 3(2x + y) = 7xy ; 3(x + 3y) = 11xy using elimination method t et 35. If P = w t t t t t t t t t t t t x x + y, Q = y then find 1 2Q x + y P Q P 2 Q 2 36. The speed of a boat in still water is 15 km/hr. It goes 30 km upstream and return downstream t et to the original point in 4 hrs 30 minutes. Find the speed of the stream t t 37. Find X and Y if 2X + 3Y = ( 2 3 2 2 ) and 3X + 2Y = ( 4 0 1 5 ) 38. Find the equation of the straight line passing through the point of intersection of the lines t et t t 2x + y 3 = 0 and 5x + y 6 = 0 and parallel to the line joining the points ( 1, 2 ) and ( 2, 1 ) 39. Find the equation of the line passing through (22, 6) and having intercept on x-axis exceeds t et the intercept on y-axis by 5. t t 40. State and prove Basic proportionality theorem 41. A person in an helicopter flying at a height of 700 m, observes two objects lying opposite to t et each other on either bank of a river. The angles of depression of the objects are 30 0 and 45 0. t t Find the width of the river. (use 3 = 1.732) 42. Using clay, a student made a right circular cone of height 48 cm and base radius 12 cm. t et Another student reshapes it in the form of a sphere. Find the radius of the sphere. t t 43. Two dice are rolled simultaneously. Find the probability that the sum of the numbers on the t et faces is neither divisible by 3 nor by 4. t t t w t t t t t t t t t t t t t t t t t t t t t t t t w t t t t t t t t t t t t t t t t t t t t t t t t
44. The probability that a new car will get an award for its design is 0.25, the probability that it t et will get an award for efficient use of fuel is 0.35 and the probability that it will get both the awards is 0.15. Find the probability that ( i ) it will get atleast one of the two awards ( ii ) it will get only one of the awards. 45. (a) If a, b, c, d are in geometric sequence, then prove that, (b c) 2 + (c a) 2 + (d b) 2 = t et (a d) 2 t et t et t et (b) A cuboid shaped slab of iron whose dimensions are 55 cm x 40 cm x 15 cm is melted and recast into a pipe. The outer diameter and thickness of the pipe are 8 cm and 1 cm respectively. Find the length of the pipe. SECTION IV Note : Answer both questions choosing either of the alternatives. 10x2 = 20 t et 46. (a) Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 6 cm. t et t et (b) Construct a cyclic quadrilateral ABCD, where AB = 6.5 cm, ABC = 110 0, BC = 5.5 cm and AB CD 47. (a) Draw the graph of y = x 2 + 2x 3 and hence find the roots of x 2 x 6 = 0 t et t et (b) A bank gives 10% S.I on deposits for senior citizens. Draw the graph for the relation Prepared by, t et t et t w t t t t t t t t t t t t t t t t t t between the sum deposited and the interest earned for one year. Hence find ( i ) the interest on the deposit of `650 w t t t t t t t t t t t t t t t t t t ( ii ) the amount to be deposited to earn an interest of`45. t t t t -o0o- L.SURESH (PG Teacher) Kamalammal Matric Hr.Sec.School, Thanipadi-606708, Tiruvannamalai District Cell No : 9444333734 t t t t t t t t w t t t t t t t t t t t t t t t t t t t t t t t t
Pai.Net s Public Exam 2019 Model Question Paper 3 MATHEMATICS Time Allowed :2.30 hrs Maximum Marks : 100 t et SECTION I Note : (i) Answer all the 15 questions. 15x1 = 15 (ii) Choose the correct answer from the given four alternatives and write the option code and the corresponding answer. t et 1. If { ( x, 2 ), ( 4, y ) } represents an identity function, then ( x, y ) is (a) ( 2, 4 ) (b) ( 4, 2 ) (c) ( 2, 2 ) (d) ( 4, 4 ) 2. If a, b, c, l, m are in A.P, then the value of a 4b + 6c 4l + m is t et (a) 1 (b) 2 (c) 3 (d) 0 3. If a 1, a 2, a 3.. are in A.P. such that a 4 = 3 then the 13 th term of the A.P is a 7 2 (a) 3 (b) 0 (c) 12a 2 1 (d) 14a 1 4. If ax 2 + bx + c = 0 has equal roots, then c is equal to (a) b 2 (b) b 2 (c) b 2 (d) b 2 t et 2a w t t t t t t t t 4a 5. Let b = a + c, then the equation ax 2 + bx + c = 0 has equal roots, if (a) a = c (b) a = c (c) a = 2c (d) a = 2c 6. If A = ( 4 2 6 3 ), then A2 is (a)( 16 4 8 4 2 2 ) (b) ( ) (c) ( 4 ) (d) (4 36 9 12 6 6 3 6 3 ) 7. The centroid of the triangle with vertices at ( 2, 5 ), ( 2, 12 ) and ( 10, 1 ) is (a) ( 6, 6 ) (b) ( 4, 4 ) (c) ( 3, 3 ) (d) ( 2, 2 ) 8. The equation of a straight line having slope 3 and y-intercept 4 is (a) 3x y 4 = 0 (b) 3x + y 4 = 0 (c) 3x y + 4 = 0 (d) 3x + y + 4 = 0 9. In ABC, DE is to BC, meeting AB and AC at D and E. If AD = 3 cm, DB = 2 cm and AE = 2.7 cm then AC is equal to (a) 6.5 cm (b) 4.5 cm (c) 3.5 cm (d) 5.5 cm 10. AB and CD are two chords of a circle which when produced to meet at a point P such that AB = 5, AP = 8, and CD = 2 then PD = (a) 12 cm (b) 5 cm (c) 6 cm (d) 4 cm 11. If tan θ= a, then the value of x = x a 2 + x 2 (a) Cos θ (b) Sin θ (c) Cosec θ (d) Sec θ 12. ( 1 Cos 2 θ )( 1 + Cot 2 θ ) = (a)sin 2 θ (b) 0 (c) 1 (d) tan 2 θ 13. If the surface area of a sphere is 36πcm 2 then the volume of the sphere is equal to (a) 12πcm 3 (b) 36 πcm 3 (c) 72 πcm 3 (d) 108 πcm 3 14. If t is the standard deviation of x, y, z, then the standard deviation of x+ 5, y + 5, z + 5 is t et t et t et t et t et t et t et t t t t t t t t t t t t t t (a) t (b) t + 5 (c) t (d) xyz 3 15. A fair die is thrown once. The probability of getting a prime or composite number is t et (a) 1 (b) 0 (c) 5 6 t t t w t t t t t t t t 2a t t t t t t t t t t t t t t t t w t t t t t t t t (d) 1 6 4a t t t t t t t t t t t t t t t t
SECTION II Note : (i) Answer 10 questions. 10x2 = 20 t et (ii) Question number 30 is compulsory. Select any 9 question from the first 14 questions. 16. Let x = x if x 0 where x R. Does the relation { (x,y) y = x, x R } define a t et x if x<0, function? Find its range. 17. The following table represents a function from A = { 5, 6, 8, 10 } to B = { 19, 15, 9, 11 } t et where f(x) = 2x 1. Find the value of a and b. 18. Three numbers are in the ratio 2 : 5 : 7. If the first number, the resulting number on the t et subtraction of 7 from the second number and the third number form an A.P, then find the numbers. 19. Solve : x + 1 x = 26 5 t et 20. Form a quadratic equation whose roots are 3 + 7, 3 7 21. Construct a 2 x 3 matrix A = [a ij ] whose elements are given by a ij = 2i 3j t et 22. Let A = ( 3 2 1 ) and B = (8 ).Find the matrix C = 2A + B 5 1 4 3 23. If the points ( a, 1 ), ( 1, 2 ) and ( 0, b + 1 ) are collinear, then show that 1 + 1 = 1 a b t et 24. If the centroid of a triangle is at ( 1, 3 ) and two of its vertices are ( 7, 6 ) and ( 8, 5 ) then find third vertex of the triangle. 25. In the figure TP is a tangent to a circle. A and B are two points on the circle. If BTP = t et t et 72 0 and ATB = 43 0 find ABT. 26. Prove the identity 1 + Secθ Sec θ = Sin 2 θ 1 Cos θ 27. If Sinθ, Cosθ and tanθ are in G.P, then prove that Cot 6 θ Cot 2 θ = 1 t et 28. The volume of a solid right circular cone is 4928 cu. cm. If its height is 24 cm, then find the radius of the cone 29. A die is thrown twice. Find the probability of getting a total of 9. t et 30. (a) Radius and slant height of a cone are 20 cm and 29 cm respectively. Find its volume. t et (b) If the coefficient of variation of a collection of data is 57 and its S.D is 6.84, then find the mean. t w t t t t x 5 6 8 10 t t f(x) a 11 b 19 t t t t t t t t t t t t t t t t t t w t t t t t t t t t t t t t t t t t t t t t t t t w t t t t t t t t t t t t t t t t t t t t t t t t
SECTION III Note : (i) Answer 9 questions. 9x5 = 45 t et (ii) Question number 45 is compulsory. Select any 8 question from the 14 questions. 31. Use Venn diagram to verify De Morgan s law for set difference. A\(B C) = (A\B) U (A\C) t et 32. A function f: [ 1,6 ) R is defined as follows t et Find the value of t et 1+x, 1 x < 2 f(x) = 2x 1, 2 x < 4 3x 2 10, 4 x < 6 i) f(5) ii) f(3) iii) f(1) iv) f(2) f(4) v) 2f(5) 3f(1) 33. Find the sum of the first 2n terms of the following series. 1 2 2 2 + 3 2 4 2 + t et 34. The fifth term of a G.P is 1875. If the first term is 3, find the common ratio. 35. Simplify : t et 1 + 1 2 x 2 + 3 x + 2 x 2 + 5x + 6 x 2 + 4x + 3 36. If αand βare the roots of the equation x 2 3x 1 = 0, then form a quadratic equation t et whose roots 1 α 2and 1 β 2 37. If A = ( 5 2 2 1 ) and B = ( 7 3 1 1 ) verify that (AB)T = B T A T t et 38. Find the area of the quadrilateral whose vertices are ( 6, 9 ), ( 7, 4 ), ( 4, 2 ) and ( 3, 7 ) 39. Find the equation of the straight lines each passing through the point ( 2, 2 ) and whose sum t et of the intercepts is 9 w t t t t t t t t t t t t t t t t t t 40. A point O in the interior of a rectangle ABCD is joined to each of the vertices A, B, C and D. t et t t Prove that OA 2 + OC 2 = OB 2 + OD 2 w t t t t t t t t t t t t t t t t t t t t 41. If tan θ + Sin θ = m, tan θ Sin θ = n and m n then show that m 2 n 2 = 4 mn t et t t t t 42. A vessel is in the form of a frustum of a cone. Its radius at one end and the height are 8 cm t et and 14 cm respectively. If its volume is 5676 cm 3, then find the radius at the other end. t t t 3 t t w t t t t t t t t t t t t t t t t t t t t t t t t
w 43. Prove that the standard deviation of the first n natural numbers is σ = n2 1 t et t t 44. Two unbiased dice are rolled once. Find the probability of getting t et ( i ) a sum 8 ( ii ) a doublet ( iii ) a sum greater than 8. 45. (a) Find the GCD of the polynomials x 4 +3x 3 x 3 and x 3 +x 2 5x+3 t et t et t et t t (b) A circus tent is to be erected in the form of a cone surmounted on a cylinder. The total t t height of the tent is 49 m. Diameter of the base is 42 m and height of the cylinder is 21 m. Find the cost of canvas needed to make the tent, if the cost of canvas is Rs.12.50 / m 2 t t t t SECTION IV Note : Answer both questions choosing either of the alternatives. 10x2 = 20 46. (a) Take a point which is 9 cm away from a circle of radius 3 cm, and draw the two tangents t et t et t t to the circle from that point. (b) Construct a cyclic quadrilateral ABCD such that AB = 5.5 cm, ABC = 50 0, BAC = t t 60 0 and ACD = 30 0 47. (a) Draw the graph of y = 2x 2 + x 6 and hence solve 2x 2 + x 10 = 0 t et t et t et t et t et t t (b) The cost of the milk per litre is `15. Draw the graph for the relation between the quantity t and cost. Hence find t t (i) the proportionality constant. (ii) the cost of 3 litres of milk. t t Prepared by, w t t t t t t t t t t t t t t t t t t -o0o- t t L.SURESH (PG Teacher) Kamalammal Matric Hr.Sec.School, Thanipadi-606708, Tiruvannamalai District Cell No : 9444333734 t t t t t t t t w 12 t t t t t t t t t t t t t t t t t t t t t t t t
Pai.Net s Public Exam 2019 Model Question Paper 4 MATHEMATICS Time Allowed :2.30 hrs Maximum Marks : 100 t et SECTION I Note : (i) Answer all the 15 questions. 15x1 = 15 (ii) Choose the correct answer from the given four alternatives and write the option code and the corresponding answer. t et 1. If A B, then A B is (a) B (b) A\B (c) A (d) B\A 2. The common ratio of the G.P. a m n, a m, a m + n is t et (a) a m (b) a m (c) a n (d) a n 3. The next term of 1 (a) 1 t et 24 in the sequence 1, 1, 1, 1 is 20 2 6 12 20 (b) 1 (c) 1 4. If x 2 + 5kx + 16 = 0 has no real roots, then 22 30 (d) 1 (a)k > 8 (b) k > 8 (c) 8 < k < 8 (d) 0 < k < 8 5 5 5 5 5 5. The sum of two zeros of the polynomial f ( x ) = 2x 2 + ( p + 3 )x + 5 is zero, then the value of p is (a) 3 (b) 4 (c) - 3 (d) 4 6. If a matrix is of order 2 x 3,then the number of elements in the matrix is (a) 5 (b) 6 (c) 2 (d) 3 7. The equation of a straight line parallel to y-axis and passing through the point ( 2, 5 ) is (a) x 2 = 0 (b) x + 2 = 0 (c) y + 5 = 0 (d) y 5 = 0 8. The angle of inclination of a straight line parallel to x - axis is equal to (a) 0 0 (b) 60 0 (c) 45 0 (d) 90 0 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 of40 0, then POA = (a)70 0 (b) 80 0 (c) 50 0 (d) 60 0 10. ABC is a right angled triangle where B = 90 0 and BD AC. If BD = 8 cm, AD = 4 cm, the CD is (a) 24 cm (b) 16 cm (c) 32 cm (d) 8 cm 11. If = a Secθ, y = btanθ, then the value of x 2 y 2 = a 2 b 2 (a) 1 (b) - 1 (c) tan 2 θ (d) Cosec 2 θ t et t et t et t et t et 12. Sin (90 0 θ ) Sin θ t et tan θ w t t t t t t t t t t t t t t t t t t + Cos (90 0 θ ) Cos θ Cot θ t t w t t t t t t t t t t t t t t t t t t = t t w t t t t t t t t (a) tan θ (b) 1 (c) - 1 (d) Sin θ 13. Curved surface area of solid sphere is 24 cm 2. If the sphere is divided into two hemispheres, then the total surface area of one of the hemispheres is (a)12cm 2 (b) 8cm 2 (c) 16cm 2 (d) 18cm 2 14. If the variance of 14, 18, 22, 26, 30 is 32, then the variance of 28, 36,44,52,60 is t et t t t t (a) 64 (b) 128 (c) 32 2 (d) 32 15. Probability of sure event is t et t t t t (a) 1 (b) 0 (c) 100 (d) 0.1 t 18 t t t t t t t t t t t t t t t t
SECTION II Note : (i) Answer 10 questions. 10x2 = 20 t et (ii) Question number 30 is compulsory. Select any 9 question from the first 14 questions. 16. If A B, then find A B and A\B ( Use Venn diagram ) t et 17. A = { 2, 1, 1, 2 } and f = { ( x, from A to A? 18. How many two digits numbers are divisible by 13? t et 1 x ) x Є A }. Write down the range of f. Is f a function 19. Find a quadratic polynomial if the sum and product of zeros of it are 4 and 3 respectively. 20. Simplify : t et x 3 + 8 x 2 2 x 21. Prove that A = ( 5 2 3 2 ) and B = ( ) are inverse to each other under matrix 7 3 7 5 multiplication. t et 22. Solve for x and y if ( x2 y 2 ) + 3 ( 2x y ) = ( 9 4 ) 23. Find the centroid of the triangle whose vertices are A ( 4, 6 ), B ( 3, 2 ) and C ( 5, 2 ) t et 24. Find the equation of the straight line passing through the points ( 1, 1 ) and (2, 4) 25. If all sides of a parallelogram touch a circle, show that the parallelogram is a rhombus. t et 26. A ramp for unloading a moving truck, has an angle of elevation if 30 o.if the top of the ramp is 0.9 m above the ground level, then find the length of the ramp. 27. A cone, a hemisphere and cylinder have equal bases. If the heights of the cone and a cylinder t et are equal and are same as the common radius, then find the ratio of their respective volumes. 28. The standard deviation of 20 observations is 5. If each observation is multiplied by 2, find t et the standard deviation and variance of the resulting observations. 29. Three dice are thrown simultaneously. Find the probability of getting the same number on all t et the three dice. w t t t t t t t t t t t t t t t t t t t t 30. (a) Prove the identity Sec 2 θ + Cosec 2 θ = tan θ + Cot θ t et t et t t (b) Volume of a hollow sphere is t radius of the Sphere t t w t t t t t t t t t t t t t t t t t t t t 11352 7 t t w t t t t t t t t t t t t t t t t t t t t t t cm 3. If the outer radius is 8 cm, find the inner t t t t
SECTION III Note : (i) Answer 9 questions. 9x5 = 45 t et (ii) Question number 45 is compulsory. Select any 8 question from the 14 questions. 31. In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and t et hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games. Find the number of students in the group. 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, t et Represent f by, i) an arrow diagram ii) a set of ordered pairs and iii) a table iv) a graph 33. A TV manufacturer has produced 1000 TVs in the 7 th year and 1450 TVs in the 10 th year. t et Assuming that the production increases uniformly by a fixed number every year. Find the no of TVs produced in the first year and in the 15 th year. 34. Find the sum to n terms of the series 7 + 77 + 777 + 35. If m nx + 28x 2 + 12x 3 + 9x 4 is a perfect square, then find the value of m and n t et 36. If αand βare the roots of the equation 3x 2 5x + 2 = 0 then find the values of i ) α β + β α ii ) α β iii ) α 2 + β 2 β α 37. If the equation ( 1 + m 2 )x 2 + 2mcx + c 2 a 2 = 0, has equal roots, then prove that t et c 2 = a 2 (1 + m 2 ) a b 38. If A = ( c d ) and I 2 = ( 1 0 0 1 ), then show that A2 ( a + d )A = ( bc ad ) I 2 t et 39. Using the concept of slope show that the points ( 2, 1 ), ( 4, 0 ), ( 3, 3 ) and ( 3, 2 ) taken in order form a parallelogram. 40. A boy is designing a diamond shaped kite, as shown in the figure where t et t et AE = 16cm, EC = 81cm. He wants to use a straight cross bar BD. How long should it be? 41. From the top and foot of a 40 m high tower, the angles of elevation of the top of a lighthouse t et are found to be 30 0 and 60 0 respectively. Find the height of the lighthouse. Also find the distance of the top of the lighthouse from the foot of the tower. 42. A container with a rectangular base of length 4.4 m and breadth 2 m is used to collect rain t et water. The height of the water level in the container is 4 cm and the water is transferred into a cylindrical vessel with radius 40 cm. What will be the height of the water level in the cylinder? t et t w t t t t t t t t t t t t t t t t t t t t t t t t w t t t t t t t t t t t t t t t t t t t t t t t t w t t t t t t t t t t t t t t t t t t t t t t t t
43. Given x = 99, n = 9, (x 10 ) 2 = 79 then find x 2 and ( x x ) 2 44. If a die is rolled twice, find the probability of getting an even number in the first time or a t et total of 8 45. (a) The vertices of ABC are A ( 4, 4 ), B ( 8, 4 ) and C ( 8, 10 ).Find the equation of t et t et the straight line along the median from the vertex A. (b) 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) SECTION IV Note : Answer both questions choosing either of the alternatives. 10x2 = 20 t et 46. (a) Draw a circle of diameter 10 cm. From a point P, 13 cm away from its centre, draw t et t et the two tangents PA and PB to the circle, and measure their lengths. (b) Construct a cyclic quadrilateral PQRS with PQ = 4 cm, P = 100 0, PQS = 40 0 and SQR = 70 0 47. (a) Draw the graph of y = x 2 x 8 and hence find the roots of x 2 2 x 15 = 0 t et (b) t et t et Prepared by, t et t et t et t w t t t t t t t t t t t t t t No.of workers x t t No.of days y Draw graph for the data given in the table. Hence find the number of days taken by t t 12workers to complete the work. t t w t t t t t t t t t t t t t t 3 4 6 8 9 16 t t 96 72 48 36 32 18 t t -o0o- t t L.SURESH (PG Teacher) Kamalammal Matric Hr.Sec.School, Thanipadi-606708, Tiruvannamalai District Cell No : 9444333734 t t t t t t t t w t t t t t t t t t t t t t t t t t t t t t t t t