1. SETS AND FUNCTIONS

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1 . SETS AND FUNCTIONS. For two sets A and B, A, B A if and only if B A A B A! B A + B z. If A B, then A + B is B A\ B A B\ A. For any two sets Pand Q, P + Q is " x : x! P or x! Q, " x : x! P and x b Q, " x : x! P and x! Q, " x : x b P and x! Q,. If A { p, q, r, s }, B { r, s, t, u }, then A\B is { p, q } { t, u } { r, s } {p, q, r, s } 5. If n6 p@ 6, then n^ah is For any three sets A, B and C, A +^B, Ch is ^A, Bh,^B + Ch A, (B + C) ^A + Bh,^A + Ch ^A, Bh +^B, Ch 7. For any two sets A and B, {(A \ B), (B \ A)} + (A + B) is z A, B A + B Al + Bl 8. Which one of the following is not true? A \ B A + Bl A \ B A + B A \ B (A, B) + Bl A \ B (A, B) \ B 9. For any three sets A, B and C, B \ ^A, Ch is ^A \ Bh +^A \ Ch ^B \ Ah +^B \ Ch ^B \ Ah +^A \ Ch ^A \ Bh +^B \ Ch 0. If n 0, n 0 and n(a, B) 0, then n(a + B) is equal to If { (x, ), (, y) } represents an identity function, then (x,y) is (, ) (, ) (, ) (, )

2 . If { (7, ), (5, a) } represents a constant function, then the value of a is Given f( x ) ^- x h is a function from N to Z. Then the range of f is { } N {, } Z. If f { (6, ), (8, 9), (5, ), (, 6) }, then the pre-images of are 5 and 6 and 8 8 and 6 and Let A {,,, 7, }, B {,,, 5, 7, 9 } and f : A " B be given by 6. f { (, ), (, ), (, ), (7, 5), (, 9) }. Then f is one-one onto bijective not a function C 5 f D 6 5 an onto function an one-one function The given diagram represents a constant function not a function 7. If A { 5, 6, 7 }, B {,,,, 5 }and f : A " B is defined by f(x) x -, then the range of f is {,, 5 } {,,,, 5 } {,, } {,, 5 } 8. If f(x) x + 5, then f(- ) If the range of a function is a singleton set, then it is a constant function an identity function a bijective function an one-one function 0. If f : A " B is a bijective function and if n 5, then n is equal to 0 5 5

3 . SEQUENCES AND SERIES OF REAL NUMBERS. Which one of the following is not true? A sequence is a real valued function defined on N. Every function represents a sequence. A sequence may have infinitely many terms. A sequence may have a finite number of terms.. The 8 th term of the sequence,,,, 5, 8, g is 5. The next term of in the sequence,,,, g is If a, b, c, l, m are in A.P, then the value of a - b + 6c - l + m is 0 5. If a, b, c are in A.P. then a - b is equal to b - c a b a b c c 6. If the n th term of a sequence is 00 n +0, then the sequence is an A.P. a G.P. a constant sequence neither A.P. nor G.P. a 7. If a, a, a, gare in A.P. such that, a then the th term of the A.P. is 7 0 a a 8. If the sequence a, a, a, g is in A.P., then the sequence a, a, a, g is a G.P. an A.P. neither A.P nor G.P. a constant sequence 9. If k+, k 6, k are the three consecutive terms of an A.P, then the value of k is 5 0. If a, b, c, l, m. n are in A.P., then a+7, b+7, c+7, l+7, m+7, n+7 form a G.P. an A.P. a constant sequence neither A.P. nor G.P. If the third term of a G.P is, then the product of first 5 terms is If a, b, c are in G.P, then a - b b - c is equal to a b b a b c c b

4 . If x, x+, x +, g are in G.P, then 5 x, 0x+ 0, 5x + 5, g form an A.P. a G.P. a constant sequence neither A.P. nor a G.P.. The sequence,,,gpage an A.P. only a G.P. only neither A.P. nor G.P both A.P. and G.P. 5. If the product of the first four consecutive terms of a G.P is 56 and if the common ratio is and the first term is positive, then its rd term is In a G.P, t 5 and t. Then the common ratio is If x! 0, then + sec x + sec x + sec x + sec x + sec x is equal to ( + sec x)( sec x + sec x + sec x) ( + sec x)( + sec x + sec x) 5 ( - sec x)( sec x + sec x + sec x) ( + sec x)( + sec x + sec x) 8. If the n th term of an A.P. is t - 5n, then the sum of the first n terms is n n n n^ - 5nh n n ^ + 5 h n n ^ + h 9. The common ratio of the G.P. a m- n, a m, a m+ n is a m a - m a n a -n 0. If n k then + + g + n is equal to k k k ^ k + h ^k + h

5 . If the system 6x y, kx y has a unique solution, then k k! k k!. A system of two linear equations in two variables is inconsistent, if their graphs coincide do not intersect at any point. The system of equations x y 8, x y has infinitely many solutions has a unique solution. ALGEBRA intersect only at a point cut the x-axis has no solution may or may not have a solution. If one zero of the polynomial p^xh (k +) x +x+k is reciprocal of the other, then k is equal to 5 5. The sum of two zeros of the polynomial f^xh x + (p + )x + 5 is zero, then the value of p is 6. The remainder when x - x + 7 is divided by x+ is The quotient when x - 5x + 7x - is divided by x is x + x + x - x + x - x - x + x - 8. The GCD of ^x + h and x - is x - x + x + x - 9. The GCD of x - xy + y and x - y is x+y x y x - y 0. The LCM of x - a and (x a) is (x - a ) ^x + ah (x - a ) ^x - ah x a ^ - h ^x + ax + a h. The LCM of k k+ k+5 a, a, a where ken is k+9 a ^x + ah ^x + ax + a h k a k+6 a k+5 a is. The lowest form of the rational expression x + 5x + 6 x - x - 6 x - x + x + x - x + x - x - x + and a - b are the two rational expressions, then their product is a + b a + ab + b a - ab + b a - ab - b a + ab + b a - ab + b a + ab + b a + ab + b a - ab - b. If a + b a - b

6 . On dividing x - 5 by x + x + 5 is equal to x - 9 (x 5)(x ) (x 5)(x+) (x +5)(x ) (x +5)(x+) b 5. If a a - is added with, then the new expression is b b - a a + ab + b a - ab + b a + b a - b 6. The square root of 9 ( x - xy + y ) is 7 x - y 7^x + yh^x - yh 7( x + y) 7( x - y) 7. The square root of x + y + z - xy + yz - zx x + y - z x - y + z x + y + z x - y - z 8. The square root of 8 6 x y z (l - m) is x y z l - m 6 x y z l - m x y z (l - m) x y z (l - m) 9. If ax + bx + c 0 has equal roots, then c is equal b b - b - b a a a a 0. If x + 5kx has no real roots, then k 8 k A quadratic equation whose one root is is x - 6x k k 5 x + 6x x - 5x x - 5x The common root of the equations x - bx + c 0 and x + bx - a 0 is c + a c b - a c b + b a a + b c. If a,b are the roots of ax + bx + c 0 a Y 0, then the wrong statement is a + b b - ac ab c a a a + b b a - b b - ac a a. If a and b are the roots of ax + bx + c 0, then one of the quadratic equations whose roots are and a b, is ax + bx + c 0 bx + ax + c 0 cx + bx + a 0 cx + ax + b 0 5. If b a + c, then the equation ax + bx + c 0 has real roots no roots equal roots no real roots

7 . MATRICES. Which one of the following statements is not true? A scalar matrix is a square matrix A diagonal matrix is a square matrix A scalar matrix is a diagonal matrix A diagonal matrix is a scalar matrix.. Matrix A 6 a is a square matrix if m # n m n m n m m n. If x e o e y + - x 8, 7. If A ^ - h and B y - o then the values of x and y respectively are 8 -, 7 ^0 0 0h f -, - p then A + B - 0 f 0 0 ^ - h not defined p -, 7 5. If a matrix is of order #, then the number of elements in the matrix is If c m c m then the value of x is x 8 7. If A is of order # and B is of order #, then the order of BA is # # # not defined 8. If A # c m ^ h then the order of A is 0 # # # # 9. If A and B are square matrices such that AB I and BA I, then B is Unit matrix Multiplicative inverse matrix of A A - Null matrix x 0. If c m c m c m, then the values of x and y respectively, are y, 0 0, 0, -,

8 -. If A e o and A + B O, then B is e o e o e o c If A e 6 - o, then A is - 6 c 6 9 m e o e o e m - - o. A is of order m # n and B is of order p # q, addition of A and B is possible only if m p n q n p m p, n q. If c a 5 m, e o - c m then the value of a is 0 8 a b 5. If A e c -a o is such that A I, then + a + bc 0 - a + bc 0 - a - bc 0 + a - bc 0 6. If A 6 a and a i + j, then A # ij c m c m c 5 m c a b 0 c m c m e o, then the values of a, b, c and d respectively are 0 c d 0 - -, 0, 0, -, 0, 0, -, 0,, 0, 0, 0, If A c m and A + B 0 e - - o then the matrix B c 0 0 m e 6 - o -8-8 e o e If ^ 5 x h f - p ^ 0 h, then the value of x is Which one of the following is true for any two square matrices A and B of same order?. ( AB) T T T A B ( A B) T T T T A B ( AB) T BA ( AB) 5 7 m 7 o T T T B A

9 5. COORDINATE GEOMETRY. The midpoint of the line joining ^a, - bh and ^a, 5bh is ^- a, bh ^a, bh ^a, bh ^- a, - bh. The point P which divides the line segment joining the points A^, - h and B^-, 9h internally in the ratio : is ^, h ^0, 0h 5 `, j ^, -. If the line segment joining the points A, then the ratio in which P divides the segment AB is h ^ h and B^, - h meets the x-axis at P, : (b) : (c) : (d) :. The centroid of the triangle with vertices at ^-, - 5h, ^-, h and ^0, - h is ^6, 6h ^, h ^, h ^, h 5. If ^, h, ^, 6h, ^x, 6h and ^, h are the vertices of a parallelogram taken in order, then the value of x is 6 (b) (c) (d) 6. Area of the triangle formed by the points (0,0), ^, 0h and ^0, h is sq. units (b) sq. units (c) sq. units (d) 8 sq. units 7. Area of the quadrilateral formed by the points ^, h, ^0, h, ^0, 0h and ^, 0h is sq. units (b) sq. units (c) sq. units (d) sq. units 8. The angle of inclination of a straight line parallel to x-axis is equal to 0c 60c 5c 90c 9. Slope of the line joining the points ^, - h and ^-, ah is -, then the value of a is equal to (b) (c) (d) 0. Slope of the straight line which is perpendicular to the straight line joining the points ^-, 6h and ^, 8h is equal to -. The point of intersection of the straight lines 9x y and x y is ^-, 7h ^7, h ^, 7h ^-, - 7h. The straight line x + y - 0 intersects the y- axis at ^, 0h ^0, h ^, h ^0, - h. The slope of the straight line 7y - x is equal to The equation of a straight line passing through the point (, 7) and parallel to x-axis is x x - 7 y - 7 y

10 5. The x and y-intercepts of the line x - y + 6 0, respectively are, (b), (c) -, (d), - 6. The centre of a circle is (-6, ). If one end of the diameter of the circle is at (-, 8), then the other end is at (-8, ) (b) (-9, 6) (c) (-, ) (d) (0, 0) 7. The equation of the straight line passing through the origin and perpendicular to the straight line x + y is x + y 0 x - y 0 y y The equation of a straight line parallel to y-axis and passing through the point ^-, 5h is x - 0 x + 0 y y If the points (, 5), (, 6) and ^a, ah are collinear, then the value of a is equal to If a straight line y x + k passes through the point (, ), then the value of k is equal to The equation of a straight line having slope and y-intercept - is x - y - 0 x + y - 0 x - y + 0 x + y + 0. The point of intersection of the straight lines y 0 and x - is ^0, - h ^-, 0h ^0, h ^, 0h. The value of k if the straight lines x + 6y and x + ky 5 are perpendicular is (b) (c) (d)

11 6. GEOMETRY. If a straight line intersects the sides AB and AC of a 9ABC at D and E respectively and is parallel to BC, then AE AC AD AD DE AD DB AB BC EC. In 9ABC, DE is < to BC, meeting AB and AC at D and E. If AD cm, DB cm and AE.7 cm, then AC is equal to 6.5 cm.5 cm.5 cm 5.5 cm. In 9PQR, RS is the bisector of +R. If PQ 6 cm, QR 8 cm, RP cm then PS is equal to cm cm cm 6 cm 6cm S P cm Q 8cm R. In figure, if AB BD, +B 0c, and +C 60c, then +BAD AC DC 0c 50c 80c 0c 5. In the figure, the value x is equal to $ $ 0 $ 8 0 $ A x 56c D E 8 56c 0 B C 6. In triangles ABC and DEF, +B +E, +C +F, then A 0c 60c B D C AB CA BC AB AB DE EF EF FD DE 7. From the given figure, identify the wrong statement. BC EF A CA FD AB EF TADB + TABC TABD + TABC D TBDC + TABC TADB + TBDC B C 8. If a vertical stick m long casts a shadow 8 m long on the ground and at the same time a tower casts a shadow 0 m long on the ground, then the height of the tower is 0 m 50 m 75 m 60 m 9. The sides of two similar triangles are in the ratio :, then their areas are in the ratio 9: :9 : : 0. Triangles ABC and DEF are similar. If their areas are 00 cm and 9 cm respectively and BC is 8. cm then EF 5.7 cm 5.7 cm 6.7 cm 6.7 cm

12 . The perimeters of two similar triangles are cm and 8 cm respectively. If one side of the first triangle is 8 cm, then the corresponding side of the other triangle is cm cm 9 cm 6 cm. 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 then PD 5 6. In the adjoining figure, chords AB and CD intersect at P. If AB 6 cm, PD 8 cm, PC 6 and AP >PB, then AP 8 cm cm cm 6 cm A C P D B. 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 8 cm cm 5. In the figure, if +PAB 0c then +BPT C 0c B A 0 o 0 o 0 o 60 o P T 6. 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 0 o, then +POA 70 o 80 o 50 o 60 o 7. In the figure, PA and PB are tangents to the circle drawn from an external point P. Also CD is a tangent to the circle at Q. If PA 8 cm and CQ cm, then PC is equal to A B D Q C P cm 5 cm cm 8 cm 8. DABC is a right angled triangle where +B 90c and BD AC. If BD 8 cm, AD cm, then CD is cm 6 cm cm 8 cm 9. The areas of two similar triangles are 6 cm and 6 cm respectively. If the altitude of the first triangle is cm, then the corresponding altitude of the other triangle is 6.5 cm 6 cm cm.5 cm 0. The perimeter of two similar triangles DABC and DDEF are 6 cm and cm respectively. If DE 0 cm, then AB is cm 0 cm 5 cm 8 cm

13 7. TRIGONOMETRY. ^ - sin ih sec i 0 tan i cos i. ^ + tan ih sin i sin i cos i tan i cot i. ^ - cos ih^ + cot ih sin i 0 tan i. sin^90c - ih cos i + cos^90c - ih sin i sin i + cos i cos i tan i cot i cosec i 6. cos x - sin x sin x - cos x - + sin x - cos x. 7. If tan i a, then the value of x x a + x cos i sin i cosec i sec i 8. If x a sec i, y b tan i, then the value of x y a - b tan i cosec i sec i cot i + tan i cot i tan i sin i cot i sin^90c - ihsin i cos^90c - ihcos i + tan i cot i tan i sin i. In the adjoining figure, AC 5 m 5 m 5 m 5 m C. In the adjoining figure+ ABC C A 60c 5 m B 5c 0c 60c 50c 00 m A 00 m B

14 . A man is 8.5 m away from a tower. His eye level above the ground is.5 m. The angle of elevation of the tower from his eyes is 5c. Then the height of the tower is 0 m 7.5 m 8.5 m 7 m. In the adjoining figure, sin i 5. Then BC 7 85 m 65 m 95 m 75 m 5. ^ + tan ih^ - sin ih^ + sin ih cos i - sin i sin i - cos i sin i + cos i 0 6. ^ + cot ih^ - cos ih^ + cos ih tan i - sec i sin i - cos i sec i - tan i cos i - sin i A 85 m i C B 7. ^cos i - h^cot i + h tan i + cot i cos i tan i sin i cot i sin i + + tan i cosec i + cot i cosec i - cot i cot i - cosec i sin i - cos i 0. 9 tan i - 9 sec i 0 9 9

15 8. MENSURATION. The curved surface area of a right circular cylinder of radius cm and height cm is equal to r cm r cm r cm cm. The total surface area of a solid right circular cylinder whose radius is half of its height h is equal to r h sq. units rh sq. units rh sq.units r h sq.units. Base area of a right circular cylinder is 80 cm. If its height is 5 cm, then the volume is equal to 00 cm 6 cm 00 cm 00 cm. If the total surface area a solid right circular cylinder is 00r cm and its radius is 5 cm, then the sum of its height and radius is 0 cm 5 cm 0 cm 5 cm 5. The curved surface area of a right circular cylinder whose radius is a units and height is b units, is equal to ra b sq.cm rab sq.cm rsq.cm sq.cm 6. Radius and height of a right circular cone and that of a right circular cylinder are respectively, equal. If the volume of the cylinder is 0 cm, then the volume of the cone is equal to 00 cm B) 60 cm 0 cm 90 cm 7. If the diameter and height of a right circular cone are cm and 8 cm respectively, then the slant height is 0 cm 0 cm 0 cm 96 cm 8. If the circumference at the base of a right circular cone and the slant height are 0r cm and 0 cm respectively, then the curved surface area of the cone is equal to 00r cm 600r cm 00r cm 600 cm 9. If the volume and the base area of a right circular cone are 8r cm and r cm respectively, then the height of the cone is equal to 6 cm 8 cm 0 cm cm 0. If the height and the base area of a right circular cone are 5 cm and 8 sq. cm respectively, then the volume of the cone is equal to 0 cm 0 cm 80 cm 80 cm

16 . The ratios of the respective heights and the respective radii of two cylinders are : and : respectively. Then their respective volumes are in the ratio : : : :. If the radius of a sphere is cm, then the curved surface area of the sphere is equal to 8r cm 6 cm r cm 6r cm.. The total surface area of a solid hemisphere of diameter cm is equal to cm r cm r cm r cm.. If the volume of a sphere is cu. cm 6 cm cm cm cm. 5. The surface areas of two spheres are in the ratio of 9 : 5. Then their volumes are in the ratio 8 : : : 75 7 : The total surface area of a solid hemisphere whose radius is a units, is equal to r a sq.units ra sq.units ra sq.units a sq.units. 7. If the surface area of a sphere is 00r cm, then its radius is equal to 5 cm 00 cm 5 cm 0 cm. 8. If the surface area of a sphere is 6r cm, then the volume of the sphere is equal to r cm 6r cm 7r cm 08r cm. 9. If the total surface area of a solid hemisphere is r cm then its curved surface area is equal to 6r cm r cm 6r cm 8r cm. 0. If the radius of a sphere is half of the radius of another sphere, then their respective volumes are in the ratio : 8 : : 8 :. Curved surface area of solid sphere is cm. If the sphere is divided into two hemispheres, then the total surface area of one of the hemispheres is cm 8 cm 6 cm 8 cm. Two right circular cones have equal radii. If their slant heights are in the ratio :, then their respective curved surface areas are in the ratio 6 : 9 8 : 6 : :

17 . STATISTICS. The range of the first 0 prime numbers,, 5, 7,,, 7, 9,, 9 is The least value in a collection of data is.. The range of the collection is 8.. Then the greatest value of the collection is The greatest value of a collection of data is 7 and the least value is 8. Then the coefficient of range is For a collection of items, R x, then the arithmetic mean is 5. For any collection of n items, R( x - x) R x x nx 0 6. For any collection of n items, ( Rx) - x nx ( n - ) x ( n - ) x 0 7. If t is the standard deviation of x, y. z, then the standard deviation of x + 5, y + 5, z + 5 is t t + 5 t x y z 8. If the standard deviation of a set of data is.6, then the variance is If the variance of a data is.5, then the S.D is Variance of the first natural numbers is The variance of 0, 0, 0, 0, 0 is If the variance of, 8,, 6, 0 is, then the variance of 8, 6,,5,60 is 6 8

18 . Standard deviation of a collection of data is. If each value is multiplied by, then the standard deviation of the new data is 6 9. Given /( x - x) 8, x 0 and n. The coefficient of variation is Mean and standard deviation of a data are 8 and respectively. The coefficient of variation is 5 8 8

19 .PROBABILITY. If z is an impossible event, then P^z h 0. If S is the sample space of a random experiment, then P(S) 0 8. If p is the probability of an event A, then p satisfies 0 p 0 # p # 0 # p 0 p #. Let A and B be any two events and S be the corresponding sample space. Then P( A + B) P( B) - P( A + B) P( A + B) - P( B) P( S ) P6 ^A, Bhl@ 5. The probability that a student will score centum in mathematics is 5. The probability that he will not score centum is If A and B are two events such that 5 5 P( A) 0.5, P( B) and P( A + B) 0., then P( A, B) There are 6 defective items in a sample of 0 items. One item is drawn at random. The probability that it is a non-defective item is If A and B are mutually exclusive events and S is the sample space such that P P and S A, B, then P 8 9. The probabilities of three mutually exclusive events A, B and C are given by,, and 5. Then P^A, B, Ch is If P 0.5, P 0.50, P(A + B) 0. then P(neither A nor B)

20 . A bag contains 5 black balls, white balls and red balls. If a ball is selected at random, the probability that it is not red is 5. Two dice are thrown simultaneously. The probability of getting a doublet is 6 6. A fair die is thrown once. The probability of getting a prime or composite number is Probability of getting heads or tails in tossing a coin times is A card is drawn from a pack of 5 cards at random. The probability of getting neither an ace nor a king card is 8 6. The probability that a leap year will have 5 Fridays or 5 Saturdays is The probability that a non-leap year will have 5 Sundays and 5 Mondays is The probability of selecting a queen of hearts when a card is drawn from a pack of 5 playing cards is Probability of sure event is The outcome of a random experiment results in either success or failure. If the probability of success is twice the probability of failure, then the probability of success is 0

21 Answers. SetS and FunctionS A C C A A B A B B B A B C D A D D B A C. SequenceS and SerieS of real numbers A D C D D A B B B B B A B D A B B A C A. algebra B C A A C D B C C C D B A A A D D D B C 5 D A C C A. matrices D D A D B D B C C A B D D B C B A C B D 5. coordinate geometry C B A D A B D A D C C B C C C D B B D A A B B

22 6. geometry A B A D B C B D B B D D C D D A B B D C 7. trigonometry B C C A A B A A C B B C A D C C D B B D 8. mensuration B C A A B C A B D C C D D B D B C B D A D C. StatiSticS D A C B D C C B A B 5 D B C D B. probability C D B A A B A A D A D C C B B C D A A B

K.R.P.MATRIC HIGHER SECONDARY SCHOOL - PACHAMPALAYAM TENTH MATHS ONE MARK TEST

K.R.P.MATRIC HIGHER SECONDARY SCHOOL - PACHAMPALAYAM TENTH MATHS ONE MARK TEST K.R.P.MATRI HIGHER SEONDARY SHOOL - PAHAMPALAYAM TENTH MATHS ONE MARK TEST TEST : 0 S.NO:. If n 0, n 0 and n(a,b) 0, then n(a+b) is equal to 0 70 50 0... If { (x, ), (, y) } represents an identity function,