2. The next term of. 3. If the n th term of an A.P is t n = 3-5n, then the sum of the first n terms is. (a)

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1 4. For a collection of data if x = 99, n = 9, (x 0) = 79 then find x and (x x) 44. A card is drawn from a deck of 5 cards. Find the probability of getting a King or a Heart or a Red card. 45. A circus tent is to be erected in the form of a cone surmounted on a cylinder. The total height of the tent is 49 m. Diameter of the base is 4 m and height of the cylinder is m. Find the total cost of canvas needed to make the tent, if the cost of canvas is Rs.50/m. (OR) Find the equations of the straight line segment whose end points is the point of intersection of the straight lines x-y+4=0, x-y+=0 and the midpoint of the line joining the points (,-) and (-5,8), Part - A I. CHOOSE THE CORRECT ANSWER 5 X = 5. IF {(x,),(4,y)} represent an identity function, then (x, y) is (,4) ( 4,) (c) (,) (d) (4,4). The next term of in the sequence,,,, is (c) (d) If the n th term of an A.P is t n = -5n, then the sum of the first n terms is n 5n n(-5n) (c) n + 5n (d) n ( + n) 4. The system of equation x- 4y = 8, x-y = 4 has infinitely many solutions has no solution (c) has a unique solution (d) may or may not have a solution 5. A quadratic equation whose one root is is x -6x-5=0 x +6x-5=0 (c) x -5x-6=0 (d) x -5x+6= If A = and A + B then B is PART D 4 0 (c) (d) ANSWER THE FOLLOWING QUESTIONS. X 0 = The angle of inclination of a straight line parallel to x-axis is equal to 46. a) Construct a ABC such that BC = 5.5cm, A = 60 and the median from A to BC is 0 60 (c) 45 (d) 90 of length 4.5cm (OR) Construct a cyclic quadrilateral PQRS with PQ = 4cm QR=6cmPR=7.5cm QS = 7cm 47. Draw the graph of XY = 0 x,y>0. Use the graph to find y when x= 5 and find x when y= 0.(OR) Solve graphically x -x-=0 8. The x and y- intercepts of the line x-y+6 = 0, respectively are,, (c) -, (d), - 9. Triangles ABC and DEF are similar triangles. If their areas are 00cm and 49 cm respectively and BC is 8.cm then EF = 5.47 cm 5.74 cm (c) 6.47 cm (d) 6.74 cm 0. The perimeter of two similar triangles ΔABC and ΔDEF are 6cm and 4cm respectively. If DE=0cm, then AB is cm 0cm (c) 5 cm (d) 8cm. cos 4 x sin 4 x = sin x cos x (c) +sin x (d) - cos x. ( + cot θ ) ( - cos θ ) ( + cos θ ) = tan θ - sec θ sin θ - cos θ (c) sec θ - tan θ (d) cos θ sin θ. If the surface area of a sphere is 00 πcm, then its radius is equal to 5cm 00 cm (c) 5 cm (d) 0cm

2 4. If standard deviation of a set of data is.6, then the variance is (c).96 (d) The probability of selecting a queen of hearts when a card is drawn from a pack of 5 playing cards is (c) PART B ANSWER ANY 0 QUESTIONS. Q.NO 0 IS COMPULSORY 0 X = 0 6. Draw Venn diagram AU(B C) 7. A function f:[,6) R is defined as follows f(x) = (ii) f() (d) 6 + x, x < x, x < 4 find (i) f() 9. If A is an event of a random experiment such that P(A): P(A ) = 7:, then find P(A). 0. Find the value of k if k =6084 (OR) Base area and volume of a solid right circular cylinder are.86 sq.cm and 69. cu.cm respectively. Find its height and radius. PART C ANSWER ANY 9 QUESTIONS. Q.NO 45 IS COMPULSORY 9 X 5 = 45. Using Venn diagram, verify following A\ (BUC) = (A\B) (A\C). Let A = {6,9,5,8,}; B= {,,4,5,6} and A B be defined by f(x) = x Represent f by (i) An arrow diagram A set of ordered pairs (c) a table (d) a graph 8. find a 5, a 8 if a n = (-) n n+ (n+) 9.Simplfy x 4 x a a a x +x 4. Find the sum of the series +4() +6(5) +8(7) +.+() 0. Show that the roots of the equation p x -pqx+q =0 are not real 5.Solve + 5 = 0 ; + 5 = 5 where x 0, y 0. If A= 4 x y xy x y xy 5 9 and B= 8 find 6A-B 6. If α and β are the roots of the equation x -x-=0, form a quadratic equation whose roots are and.. If A= B = then find (AB) T α+β αβ 4. Find the area of the triangle whose vertices are(5,)(,-5) and (-5,-) 4. Find the x and y intercept of the straight line 5x+y-5=0 5. In ABC, D and E are points on the sides AB and Ac respectively such that DE BC.If AD=6cm,DB=9cm and AE=8cm, then find AC 6. Prove that +cosθ sin θ sinθ (+cosθ ) = cotθ 7. A boy of height 5 feet away from the pillar of distance 00 feet saw the top of pillar with angle of elevation 45. Find the height of the pillar.. Find the first three consecutive terms in G.P whose sum is 7 and the sum of their reciprocals is 7/4. 7. A car left 0 min later than the scheduled time. In order to reach its destination 50 km away in time, it has to increase its speed by 5 km/hr from its usual speed. Find its usual speed. 8. If A = 0, B = and C = verify (AB)C = A(BC). 9. Find the value of k for which the given points are colinear (,-5),(,-4) and (9,k) 40. state and prove that angle bisector theorem 4. prove that =. cosecθ cotθ sinθ sinθ cosecθ +cotθ 8. The coefficient of variation of two series are 58 and 69. Their standard deviation is. and 5.6. What are their arithmetic means? 4. The TSA solid cylinder is 540 sq.cm. If the height is four times the radius of the base, then find the height of the cylinder

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4 4. A vertical wall and a tower are on the ground. As seen from the top of the tower, the angles of depression of the top and bottom of the wall are 45 and 60 respectively. Find the height of the wall if the height of the tower is 90m. ( =.7) 4. Radius and slant height of a solid right circular cone are in the ratio : 5. If the CSA is 60π sq.cm. then find TSA. 4. Find the C.V of the following data 8,0,5,,5 44. Three coins are tossed simultaneously. Find the probability that either exactly two tails or at least one head turn up. REVISION TEST 05-6 CLASS: X STD - A EX.NO : MARKS: 00 SUBJECT : MATHS TIME :.0 Hrs DATE : Part - A I.CHOOSE THE CORRECT ANSWER 5 X = 5. If f: A B is a bijective function and if n(a) = 5 then n(b) is equal to 0 4 (c) 5 (d) A right circular conical vessel whose internal radius is 5cm and height is 4cm is full of water. The water is emptied into an empty cylindrical vessel with internal radius 0cm.Find the height of the water level in the cylindrical vessel. (OR) If α and β are the roots of the equation x 6x + = 0 form an equation whose roots. If k+, 4k-6,k- are the three consecutive terms of an A.P then the value of k is (c) 4 (d) 5. If a,b,c are in an A.P then a b b c is equal to α + β, β + α. PART D 5.If α and β are the roots of ax +bx+c = 0 then one of the quadratic equations whose roots are and is α β ax +bx+c =0 bx +ax+c = 0 (c) cx +bx+a= 0 ANSWER THE FOLLOWING QUESTIONS. X 0 = 0 (d) cx +ax+b= Draw a circle of radius cm. From an external point 9 cm away from its centre, x construct the pair of tangents to the circle and measure their lengths.(or) 6. If y = then the values of x and y respectively are 4, 0 0, (c) 0, - (d), Construct a ABC such that BC = 5cm, A = 45 and the median from A to BC is of length 4cm. 7. The slope of the straight line 7y - x = -7/ 7/ (c) /7 (d) -/7 a b b c (c) a c (d) 4. If one zero of the polynomial p(x) = (k+4) x +x+k is reciprocal of the other, then k is equal to (c) 4 (d) Solve Graphically x +x-0=0 (OR) X Y Draw the graph for the above table and hence find (i) the value of y if x = 4 (ii) the value of x if y =. 8. The value of k if the straight lines x+6y+7 = 0 and x+ky = 5 are perpendicular is - (c) (d) / 9. The perimeter of two similar triangles is 4cm and 8 cm respectively. If one side of first triangle is 8cm, then the Corresponding side of the other triangle is 4 cm cm (c) 9cm (d) 6cm 0. ABC is a right angled triangle where B = 90 and BD AC. If BD = 8 cm, AD = 4 cm, then CD is 4 cm 6 cm (c) cm (d) 8 cm. sin θ = cos θ tan θ (c) cot θ (d) cosec θ +cosθ. secθ cotθ +tanθ = cotθ tanθ (c) sinθ (d) cotθ

5 . If the volume & the base area of a right circular cone are 48 πcm & cm respectively then the height of the cone is equal to 6 cm 8 cm (c) 0 cm (d) cm 4. Mean and standard deviation of a data are 8 and respectively. The coefficient of variation of 4 5 (c) 8 (d) If A and B are two events such that P(A)=0.5, P(B)=0.05 and P(A B) = 0.4,then P(A B)= (c) 0.4 (d) 0.6 PART B ANSWER ANY 0 QUESTIONS. Q.NO 0 IS COMPULSORY 0 X = 0 6. Given n(a)=85,n(b)=95,n(u)=500,n(a B)=40,find n(a B ). 7. A= { -,-,,} and f={(x,/x) : x A}.Write down the range of f. Is f a function? from A to A? 7. If the CSA of a solid sphere is cm, then find the radius of the sphere 8. If the C.V of a collection of data is 57. And its S.D is 6.84, and then finds the mean 9. If A and B are two events such that P(A) = ¼, P(B) = /5 and P(AUB) = / then find P(A B). 0. Find the equation of the straight line passing through the point (5,-4) with slope / Find a and b if a + b = 0 5. PART C ANSWER ANY 9 QUESTIONS. Q.NO 45 IS COMPULSORY 9 X 5 = 45. For A = {,,0,4,6,8,0}, B = {,,,4,5,6} and C = {,,,4,5,7} show that A B C = A B (A C). 8. The third term of the G.P is /. Find the product of its first five terms.. Let A= {4,6,8,0} and {,4,5,6,7} if f: A B is defined y f(x) = x + then represent f by a 9. Simplify + b (i) An arrow diagram (ii) a set of ordered pairs (iii) a table. a b b a. If a, b, c, d are in G.P then prove that (b-c) + (c-a) + (d-b) = (a-d). 0. If one of the equation x -0x+k=0 is, then find the other root and also value of k. 4. Find the sum to n terms of the following series Prove that and 5 are multiplicative inverse to each other 5. Factorize X +6(x+) -x. If the centroid of the triangle is at (,) and two of its vertices are(-7,6) and (8,5) then find the third vertex of the triangle.. Let PQ be a tangent to a circle at A and AB be chord. Let C be a point on the circle such that BAC = 54 and BAQ = 6 find ABC. 4. Prove the identity sinθ cosθ = cosecθ + cotθ 5. A girl of height 50cm stands in front of a lamp-post and casts a shadow of length 50 cm on the ground. Find the angle of elevation of the top of the lamp-post. 6. The radii of two right circular cylinders are in the ratio of : and their heights are in the ratio 5:. Find the ratio of their CSA. 6. A train covers a distance of 90km at a uniform speed. Had the speed been 5km/hr more, it would have taken0 minutes less for the journey. Find the original speed of the train. 7. If A = 0, B = and C = verify (AB)C = A(BC). 8. In what ratio is the line joining the points (-5,) and (,) divided by the y-axis? Also find the point of intersection. 9. The vertices of ABCare A(,) B(6,-) and C(4,). Find the equation of the straight line along the altitude from the vertex A. 40. State and prove that Tangent chord theorem.

6 8. Find the equation of straight line which passes through the point of intersection of 5x-8y+=0 and 7x+6y-7=0 and is perpendicular to the straight line 4x-y=. 9. The vertices of ABCare A(,-4) B(,) and C(-,5). Find the equation of the straight line along the altitude from the vertex B. 40. State and prove that Pythagoras theorem. 4. A vertical wall and a tower are on the ground. As seen from the top of the tower, the angles of depression of the top and bottom of the wall are 45 and 60 respectively. Find the height of the wall if the height of the tower is 90m. ( =.7) 4. The total surface area of a solid right circular cylinder is 540cm. If the height is four times the radius of the base, then find the height of the cylinder. 4. Calculate the S.D x 8 8 f If a die is rolled twice, find the probability of getting an even number in the first time or a total of 8. VIGHNESWAR VIDHYA MANDHIR MATRIC. HR. SEC. SCHOOL, SIRUKKALANDAI. REVISION TEST CLASS: X STD EX.NO : MARKS: 00 SUBJECT : MATHS TIME :.0 Hrs DATE : Part - A I.CHOOSE THE CORRECT ANSWER 5 X = 5. For any two sets A and B, {(A \ B) U (B \ A)} (A B) is A U B (c) A B (d) A B. If a, a, a are in A.P such that a 4 a 7 = then th term is 0 (c) a (d) 4a. If x 0 then +secx+sec x+sec x+sec 4 x+sec 5 x is equal to (+secx)( sec x+sec x+sec 4 x) (b ) (+secx)( sec x+sec 4 x) 45. If α and β are the roots of x -x-5=0, form a equation whose roots are α and β. (OR) (c) (-secx) (secx+sec x+sec 5 x) (d) (+secx)(+sec x+sec 4 x) A spherical solid material of radius 8cm is melted and recast into three small solid spherical 4. The system of equation x- 4y = 8, x-y = 4 has infinitely many solutions spheres of different sizes. If the radii of two spheres are cm and cm. Find the radius of the rd sphere. has no solution (c) has a unique solution (d) may or may not have a solution PART D 5. The common root of the equations x -bx+c=0 and x +bx-a=0 is ANSWER THE FOLLOWING QUESTIONS. X 0 = 0 c+a b c a b (c) c+b a (d) a+b c 46. Construct a ABC such that AB=6cm, C = 40 and the altitude from C to AB is length 4.cm.(OR) a b c d = 0 0 then the values of a, b, c and d respectively are Construct a cyclic quadrilateral ABCD when AB=6cm, BC=5.5cm, ABC = 80 and AD=4.5cm 47. Draw the graph of y=x +x- and hence find the roots of x -x-6=0. (OR) No of workers x No of days y Draw graph for the data given in the table. Hence find the number of days taken by workers to complete the work. -, 0, 0, -, 0, 0, (c) -, 0,, 0 (d), 0, 0, 0 7. Slope of the line joining the points (,-) and (-, a) is, then the value of a is equal to (c) (d) 4 8. If a straight line y = x+k passes through the point (,) then the value of k is equal to 0 4 (c) 5 (d) - 9. Triangles ABC and DEF are similar triangles. If their areas are 00cm and 49 cm respectively and BC is 8.cm then EF = 5.47 cm 5.74 cm (c) 6.47 cm (d) 6.74 cm

7 0. A point P is 6 cm away from the centre O of a circle and PT is the tangent drawn from P to the circle is 0 cm, then OT is equal to 6 cm 0 cm (c) 8 cm (d) 4 cm. If tanθ = a x, then the value of x a +x = cosθ sinθ (c) cosec θ (d) sec θ. Sin θ + = +tan θ cosec θ + cot θ cosec θ - cot θ (c) cot θ cosec θ (d) sin θ - cos θ. If the volume & the base area of a right circular cone are 48 πcm & cm respectively then the height of the cone is equal to 6 cm 8 cm (C) 0 cm (d) cm 4. Given (x x) = 48, x= 0 and n=.the coefficient of variation is 5 0 (C) 0 (d) 0 5. Prove the identity (sin 6 θ + cos 6 θ) = - sin θcos θ. 6. A ramp for unloading a moving truck has an angle of elevation of 0. If the top of the ramp is 0.9m above the ground level, then find the length of the ramp. 7. A rectangular sheet of metal foil with dimension 66cm x cm is rolled to form a cylinder of height cm. find the volume of the cylinder. 8. An iron right circular cone of diameter 8cm and height cm is melted and recast into spherical lead shots each of radius 4cm. how many lead shots can be made? 9. Three rotten eggs are mixed with good ones. One egg is chosen at random. What is probability of choosing a rotten egg? 0. Find the value of a if the straight lines 5x-y-9=0 and ay+x-=0 are perpendicular to each other. (OR) 5. If A and B are mutually exclusive events and S is the sample space such that P (A) = P(B) and S=A B, then P(A)= (C) (d) PART C PART B ANSWER ANY 9 QUESTIONS. Q.NO 45 IS COMPULSORY 9 X 5 = 45 ANSWER ANY 0 QUESTIONS. Q.NO 0 IS COMPULSORY 0 X = 0 6. If A B, then find A B and A\B(use Venn diagram). 7. Let A={,,,4} and B={-,,,4,5,6,7,9,0,,}.Let R={(,),(,6),(,0),(4,9)} A B be a relation.show that R is a function and find its domain, co-domain and the range of R. 8. Find the sum of the series A group of 00 candidates have their average height 6.8cm with coefficient of variation.. What is S.D of their heights?.in a village of 0 families, 9 families use firewood for cooking, 6 families use kerosene, 45 families use cooking gas, 45 families use firewood and kerosene, 4 families use kerosene and cooking gas, 7 families use cooking gas and firewood. Find how many use firewood,kerosene and cooking gas.. Let A = {5,6,7,8}; B={-,4,7,-0,-7,-9,-} and f={(x,y): y=-x, x A, y B} (i) Write down the elements of f (ii) What is the co-domain? (iii) what is range? (iv) Identify the type of function? 9. Find the quotient and remainder when x +4x -0x+6 is divided by x-. 0. Which rational number should be added to x. Solve:. Prove that y x = 6 x +4y 5 and 5 to get x +x +4? x + x + are multiplicative inverse to each other.. If the points (a,),(,) and (0,b+) are collinear, then show that a + b =. Find the sum up to n terms. 4. Find the total volume of 5 cubes whose edges are 6cm, 7cm, 8cm,.. 0cm respectively. 5. A fraction is such that if the numerator is multiplied by and the denominator is reduced by, we get 8/, but if the numerator is increased by 8 and the denominator is doubled, we get /5. Find the fraction. 6. If the equation (+m )x +mcx+c -a =0 has equal roots, then prove that c =a (+m ). 7. If A = a b c d and I = 0 0 then show that A -(a+d)a=(bc-ad) I 4. In PQR, AB QR. If AB is cm, PB is cm and PR is 6cm, then find the length of QR.

8 9. The vertices of a ABC are A(,), B(6,-) and C(4,). Find the equation of the straight line along the altitude from the vertex A. 40. In a quadrilateral ABCD, the bisector of B and Dintersects on AC at E. Prove that AB = AD BC DC 4. If tanθ+sinθ=m, tanθ-sinθ= n and m n then show that m -n = 4 mn I.CHOOSE THE CORRECT ANSWER 5 X = 5. Given f(x) = (-) x is a function from N to Z. Then the range of f is {} N (c) {, -} (d) Z. If the third term of a G.P is, then the product of first 5 terms is 5 5 (c) 0 (d) 5 4. The perimeter of the ends of a frustum of a cone are 44cm and 8.4π cm. If the depth is 4cm, then find its volume.. In a G.P t = 5 and t = 5 then the common ratio is 5 (c) (d) 5 4. A tent is in the shape of a right circular cylinder surmounted by a cone. The total height and the diameter of the base are.5m and 8m. If the height of the cylindrical portion is m, find the total surface of the tent. 4. The L.C.M of a k, a k+, a k+5 where k N a k+9 a k (c) a k+6 (d) a k+5 5. A quadratic equation whose one root is is 44. The probability that a new car will get an award for its design is 0.5, the probability that it will get an award for efficient use of fuel is 0.5 and the probability that it will get both x -6x-5=0 x +6x-5=0 (c) x -5x-6=0 (d) x -5x+6=0 the awards is 0.5. Find the probability that 6. Which one of the following is true for any two square matrices A and B of same order? (i) it will get at least one of the two awards (ii) It will get only one of the awards. (AB) T = A T B T (A T B) T = A T B T (c) (AB) T = AB (d) (AB) T = B T A T 45. Find the equation of the straight lines passing through the point (,) and the sum of 7. Slope of the line joining the points (,-) and (-, a) is, then the value of a is equal intercepts is 9 (OR) to (c) (d) 4 n Prove that the S.D of the first n natural numbers is PART D ANSWER THE FOLLOWIG QUESTIONS 0 X = Construct a ABC such that BC = 5 cm. A = 45 and the median from A to BC is 4cm. (OR) Construct a cyclic quadrilateral PQRS when PQ=4cm, QR=6cm, PR=7cm and QS=7cm 47. Draw the graph of y=x +x- and hence solve x -x-6=0 (OR) 8. If the point (,5), (4,6) and (a,a) are collinear, then the value the of a is equal to -8 4 (c) -4 (d) 8 9. Triangles ABC and DEF are similar triangles. If their areas are 00cm and 49 cm respectively and BC is 8.cm then EF = 5.47 cm 5.74 cm (c) 6.47 cm (d) 6.74 cm 0. ABC is a right angled triangle where B = 90 and BD AC. If BD = 8 cm, AD = 4 cm, then CD is 4 cm 6 cm (c) cm (d) 8 cm A bus travels at a speed of 40 km/hr. Write the distance-time formula and draw the graph of it. Hence, find the distance travelled in hours. ALL THE BEST secθ. cotθ +tanθ = cotθ tanθ (c) sinθ (d) cotθ

9 . Sin θ + = +tan θ cosec θ + cot θ cosec θ - cot θ (c) cot θ cosec θ (d) sin θ - cos θ. If the surface area of a sphere is 00 πcm, then its radius is equal to 5. Find the angular elevation (angle of elevation from the ground level) of the Sun when the length of the shadow of a 0m long pole is 0 m. 6. If the circumference of the base of a solid right circular cone is 6cm and its slant height is cm, find its CSA. (A) 5cm (B) 00 cm (C) 5 cm (D) 0cm 4. For any collection of n items,( x) x= (A) nx (B) (n-) x (C) (n-) x (D) 0 5. The probability that a non a leap year will have 5 Sundays and 5 Mondays is (A) 7 (B) 7 (C) 7 PART B (D) 0 ANSWER ANY 0 QUESTIONS. Q.NO 0 IS COMPULSORY 0 X = 0 7. The volume of a solid right circular cone is 498cu.cm. If its height is 4cm, then find its radius. 8. Find the standard deviation of the first 0 natural numbers. 9. Three coins are tossed simultaneously. Find the probability of getting at least two heads. 0. Prove that +secθ secθ 6. Let A={,,,4} and B={=,,,4,5,6,7,9,0,,}.Let R={(,),(,6),(,0),(4,9)} A B be PART C a relation. Show that R is a function and find its domain, co-domain and the range of R. ANSWER ANY 9 QUESTIONS. Q.NO 45 IS COMPULSORY 9 X 5 = Verify the commutative property of set intersection for A={l,m,n,o,,,4,7} and B={,5,,-,m,n,o,p}.. Let U = {-,-,0,,,, 0} A = { -,,,4,5} and B={,,5,8,9} verify DeMorgan s laws of complementation. 8.If the product of two consecutive positive even integers is 4,find the numbers.. If f : N N is defined by f(x) = x -, check whether f is a function. If f I not a function find 9. Solve x - 8 = for what choice of the co-domain, f will be a function? x = sin θ cosθ (OR) In an A.P 5 times of the fifth term is equal to 7 times of seventh term. Prove that th term is zero. 0. For the matrices A and B, the product AB exist but BA does not exist. What can you say about the order of A and B?. The ratio of the sums of first m and first n terms of A.P is m : n show that the ratio of the m th and n th term is (m-) : (n-).. If A= 9 6, then verify AI=IA=A, where I is the unit matrix of order. 4. The sum of first 0 terms of an A.P is 5 and common difference is twice of the first term. Find the 0 th term.. Find the equation of the straight line which passes through the mid - point of the line segment joining (4,) and (,) whose angle of inclination is The speed of a boat in still water 5 km/hr. it goes 0km upstream and returns downstream to the original point in 4hrs 0 min. Find the speed of the stream.. If the centroid of the triangle is at (,) and two of its vertices are(-7,6) and (8,5) then find the third vertex of the triangle. 6. Simplify a 6 a 8 x a a a a 4 a +9a+4 a +a+4 4. In ABC,the internal bisector AD of A meets the side BC at D. If BD =.5cm and AC = 4.cm, then find DC. 7. Find the G.C.D of the polynomials x 4 +x -x- and x +x -5x+. 8. If A = then show that A -4A+5I =0.

I. SETS AND FUNCTIONS. 3. Which of the following relations are function from A = { 1,4,9,16 } to B = { -1,2,-3,-4,5,6 }?.

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