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

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1 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 If { (x, ), (, y) } represents an identity function, then (x,y) is (, ) (, ) (, ) (, ). For two sets A and B, A, B A if and only if A B B A. If A B, then A+ B is A+ B z A!B A B\A B A\B 5. Which one of the following is not true? A\B (A,B)+ Bl A\B (A,B)\B A\B A+Bl A\B A+B 6. If { (7, ), (5, a) } represents a constant function, then the value of a is If f :A " B is a bijective function and if n 5, then n is equal to For any three sets A, B and, A+^B,h is A,(B+) ^A,Bh+^B,h ^A,Bh,^B+h ^A+Bh,^A+h 9. For any three sets A,B and, B\^A,h is ^B\ Ah+^A\h ^A\Bh+^B\h ^A\Bh+^A\h ^B\ Ah+^B\h 0. For any two sets Aand B, {(A\B),(B\ A)}+(A+B) is A+B z Al +Bl A,B. For any two sets Pand Q, P+ Q is "x:x! Pand x! Q, "x:x b Pand x! Q, "x: x! Por x! Q, "x:x! Pand x b Q,. If the range of a function is a singleton set, then it is a bijective function an one-one function a constant function an identity function

2 . 5 D 6 5. Given f( x ) ^- f an one-one function an onto function x The given diagram represents not a function a constant function h is a function from N to Z. Then the range of f is {, -} Z { } N 5. If f(x) x+5, then f(-) If A { p, q, r, s }, B { r, s, t, u }, then A\B is { r, s } {p, q, r, s } { p, q } { t, u } 7. If n6p@ 6, then n^ah is Let A {,,, 7, }, B {,,, 5, 7, 9 } and f :A " B be given by f { (, ), (, ), (, ), (7, 5), (, 9) }. Then f is onto one-one not a function bijective 9. If A { 5, 6, 7 }, B {,,,, 5 }and f : A " B is deined by f(x) x -, then the range of f is {,, } {,, 5 } {,, 5 } {,,,, 5 } 0. If f { (6, ), (8, 9), (5, ), (, 6) }, then the pre-images of are 6 and 5 6 and 8 8 and 5 and -. TEST : 0. If a, b, c are in A.P. then a-b is equal to b - c a _ a b _ c b c. If the n th term of a sequence is 00 n +0, then the sequence is a constant sequence neither A.P. nor G.P.. In a G.P, t and t. Then the common ratio is an A.P. a G.P.. If a, b, c, l, m are in A.P, then the value of a-b+6c-l + m is 0

3 5. Which one of the following is not true? A sequence is a real valued function deined on N. A sequence may have ininitely many terms. A sequence may have a inite number of terms. Every function represents a sequence. 6. The next term of in the sequence,,,, g is If the sequence a,a,ag, is in A.P., then the sequence a 5, a 0,a 5, g is neither A.P nor G.P. a constant sequence a G.P. 8. The sequence,,,g is. If a, b, c are in G.P, then a-b is equal to b-c b c a b c b b a. 0 an A.P. an G.P. only a A.P. only both A.P. and G.P. neither A.P. nor G.P 9. If a a, a,a,a, gare in A.P. such that then the th term of the A.P. is 7 0 ( a a 0. If k+, k 6, k are the three consecutive terms of an A.P, then the value of k is 5. If the third term of a G.P is, then the product of irst 5 terms is 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 an A.P. a G.P neither A.P. nor G.P a constant sequence. If the n th term of an A.P. is t n -5n, then the sum of the irst n terms is n n n^-5nh ^+5 n n h n ^+ nh 5. If x, x+, x+,g are in G.P, then 5 x, 0x+0, 5x+5,g form a G.P. an A.P. neither A.P. nor a G.P. a constant sequence 6. The 8 th term of the sequence,,,, 5, 8, g is 5

4 7. If the product of the irst four consecutive terms of a G.P is 56 and if the common ratio is and the irst term is positive, then its rd term is If n k then + +g+ n is equal to k^ k+h ^ k+h k k 5 9. If x! 0, then + secx+ sec x+ sec x+ sec x+ sec x is equal to 5 (- secx)(secx+ sec x+ sec x) ( + secx)(+ sec x+ sec x) ( + secx)(sec x+ sec x+ sec x) (+ secx)(+ sec x+ sec x) 0. The common ratio of the G.P. am -n, am, am +n is -n a n a m a m a - TEST : 0 a+b. If and a a-b -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 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. The system of equations x y 8, x y has a unique solution has infinitely many solutions. The square root of x y 8 z 6 (l-m) is may or may not have a solution has no solution 6 x y z l-m x y z (l-m) x y z l-m 5. The remainder when x -x+7 is divided by x+ is The lowest form of the rational expression x +5x+6 x -x-6 is x+ x- x- x+ x- x+ x+ x- x y z (l-m)

5 7. A system of two linear equations in two variables is inconsistent, if their graphs cut the x-axis intersect only at a point 8. The GD of x -xy+y and x -y is x y x -y x+y 9. The LM of x -a and (x a) is (x -a )^x - ah (x -a )^x +ah x a ^ + h ^x +ax+a h ^x -ah ^x +ax+a h 50. 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 GD of ^x +h and x - is x + x- x - k k+ k+5 5. The LM of a,a,a where ken is k+6 k+5 k+9 k x -5x 6 0 x - 5x x 55.. The common x +bx-a 0 is c+a root of the equations -bx+c 0 and c-a a+b c+b b b c a 56. On dividing x - 5 by x+ 5 + is equal to x x - 9 (x +5)(x ) (x +5)(x+) (x 5)(x ) (x 5)(x+) do not intersect at any point coincide a a a a x + 5. The sum of two zeros of the polynomial f^xh x +(p+)x+5 is zero, then the value of p is A quadratic equation whose one root is is x +6x-5 0 x - 6x If b a + c, then the equation ax + bx+ c 0 has a c a - c a c a -c 58. The square root of 9 (x - xy+ y ) is 7 x- y 7^x+yh^x-yh 7( x - y) 7(x+y) 59. If aandb are the roots of ax +bx+c roots are and 0, then one of the quadratic equations whose a b, is cx +bx+a 0 cx+ax+b 0 ax +bx+c 0 bx+ax+c The square root of x + y + z - xy+ yz-zx x -y - z x- y+ z x+ y+ z x +y-z 5

6 6. The quotient when x -5x +7x- is divided by x is x - x+ x +x+ x +x- x -x- 6. If ax +bx+c 0 has equal roots, then c is equal - b - b b b a a a a 6. If x +5kx+6 0 has no real roots, then k 8 k 8 k b 5 k 5 6. If a is added with, then the new expression is a - b b- a a - ab+ b a + ab+ b a - b a + b 65.. If the system 6x y, kx y has a unique solution, then k k! k k! TEST : If A#c m^ h then the order of A is 0 # # # # 67. If a matrix is of order #, then the number of elements in the matrix is 6 5 b e a c -a o is such that A 68. If A I, then - a -bc 0 + a - bc 0 +a + bc 0 -a +bc If A c m and A B + e - - o then the matrix B c 0 0 m e 6 - o -8-8 e o e Which one of the following is true for any two square matrices A and B of same order?. (AB) 7. If A e - - BA (AB) B A T T T T o and A+ B O, then B is (AB) e o e o e o c T T T T T T T A B (A B) A B m o 6

7 8 7. If c m c m then the value of x is x 8 7. Which one of the following statements is not true? A scalar matrix is a diagonal matrix A diagonal matrix is a scalar matrix. A scalar matrix is a square matrix A diagonal matrix is a square matrix If x+ 7 5 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 -, -, 7 - p then A + B - 0 f0 p 0 not deined ^0 0 0h ^- h Multiplicative inverse matrix of A A - f 76. Matrix A 6 a is a square matrix if m# n m > n m < n m n m 77. 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 q n p m p 79. If A 6 and a i + j, then A ij # ij c m c m c 5 m c 6 If A e If A and B are square matrices such that AB I and BA I, then B is Unit matrix 80. If A is of order # and B is of order #, then the order of BA is # # # not deined 8. - o, then A is - 6 c 6 9 m e o e o e x 8. If c mc m c m, then the values of x and y respectively, are y 0,, 0 ), 0, - Null matrix 5 7 m - o - 7

8 8. 8. a 5 If c me oc m, then the value of a is a b 0 c mc 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 ^ 5 x hf- p ^ 0h, then the value of x is TEST : The point of intersection of the straight lines y 0 and x - is ^-, 0h ^0,-h ^, 0h ^0,,h 87. The straight line x+y- 0 intersects the y- axis at ^, h ^0, -h ^, 0h ^0, h 88. Area of the quadrilateral formed by the points ^,h, ^0,h, ^0,0h and ^,0h is sq. units sq. units sq. units sq. units 89. The equation of the straight line passing through the origin and perpendicular to the straight line x+y-7 0 is x+ y 0 x- y 0 y -5 0 y If a straight line y x+k passes through the point (, ), then the value of k is equal to The point P which divides the line segment joining the points A^,-h and B^-,9h internally in the ratio : is ^0,0h ^, h 5 `, j ^, -h 9. If the points (, 5), (, 6) and ^a,ah are collinear, then the value of a is equal to The point of intersection of the straight lines 9x-y- 0 and x+y-9 0 is ^,7h ^7,h ^-,7h ^-,-7h 9. If ^,h, ^,6h, ^x,6h and ^,h are the vertices of a parallelogram taken in order, then the value of x is The centroid of the triangle with vertices at ^-,-5h, ^-,h and ^0, -h is ^, h ^, h ^, h ^6,6h 96. The angle of inclination of a straight line parallel to x-axis is equal to 5c 90c 0c 60c 8

9 97. The slope of the straight line 7y-x is equal to If the line segment joining the points A^,h and B^,-h meets the x-axis at P, then the ratio in which P divides the segment AB is : : : : 99. The equation of a straight line passing through the point (, 7) and parallel to x-axis is x -7 x y y Slope of the straight line which is perpendicular to the straight line joining the points ^-, 6h and ^, 8h is equal to - 0. 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 0. The equation of a straight line parallel to y-axis and passing through the point ^-,5h is x + 0 x - 0 y -5 0 y The equation of a straight line having slope and y-intercept - is x-y- 0 x+ y- 0 x- y+ 0 x+ y The value of k if the straight lines x + 6y and x + ky 5 are perpendicular is The x and y-intercepts of the line x-y+6 0, respectively are 90c 5c 60c 0c Slope of the line joining the points ^,-h and ^-,ah is -, then the value of a is equal to - (0, 0) (-, ) (-9, 6) (-8, 0. The midpoint of the line joining ^a,-bh and ^a,5bh is ^a,bh ^a,bh ^-a,bh ^-a,-bh 05. Area of the triangle formed by the points (0,0), ^,0h and ^0,h is 8 sq. units sq. units sq. units sq. units,, -,, The angle of inclination of a straight line parallel to x-axis is equal to

10 TEST : 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 9 cm 6 cm cm cm.. In the adjoining figure, chords AB and D intersect at P. If AB 6 cm, PD 8 cm, P 6 and AP >PB, then AP cm 8 cm 6 cm cm A D P B.. The perimeter of two similar triangles DAB and DDEF are 6 cm and cm respectively. If DE 0 cm, then AB is 0 cm cm 8 cm 5 cm AB BD A D, +B 0c, and + 60c, then +BAD A. In igure, if 50c 0c 0c 80c 0c 60c. In the igure, the value x is equal to A B D x 56c $ $ D E 5ẇww.Padasalai.Net 8 56c 0 0$ 0$8 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 cm 8 cm 0 cm 0 cm 6. From the given igure, identify the wrong statement. A TADB + TAB TABD + TAB D TBD + TAB TADB + TBD 7. DAB is a right angled triangle where +B 90c and BD A. If BD 8 cm, AD cm, then D is 6 cm cm 8 cm B cm 8. The sides of two similar triangles are in the ratio :, then their areas are in the ratio : : 9: :9 9. Triangles AB and DEF are similar. If their areas are 00 cm and 9 cm respectively and B is 8. cm then EF 5.7 cm 5. 7 cm 6.7 cm 6.7 cm 0. If a straight line intersects the sides AB and A of a 9AB at D and E respectively and is parallel to B, then AE A AD AD DE AD AB DB B E 0

11 . AB and D are two chords of a circle which when produced to meet at a point P such that AB 5, AP 8, and D then PD 6 5. In triangles AB and DEF, +B +E, + +F, then AB DE A EF B EF AB FD AB DE B EF A FD AB EF B. In the igure, if +PAB 0c then +BPT 0c A 0 o 0 o 60 o 0 o In 9AB, DE is < to B, meeting AB and A at D and E. P T If AD cm, DB cm and AE.7 cm, then A is equal to.5 cm.5 cm.5 cm 6.5 cm 5. In the figure, PA and PB are tangents to A D the circle drawn from an external point P. Q P Also D is a tangent to the circle at Q. If PA 8 cm and Q cm, then P is equal to B 5 cm cm 8 cm cm 6. 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 cm.5 cm 6.5 cm 6 cm 7. 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 8. In 9PQR, RS is the bisector of +R. If PQ 6 cm, QR 8 cm, RP cm then PS is equal to cm 6 cm cm cm 6cm S P cm Q 8cm R 9. 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 60 m 75 m 50 m 0 m

12 TEST : tan i-9sec i. ^+tan ih^-sinih^+sinih. ^ - cosih^ + cotih 5. - sini + cosi coti cosec i cosi tan i 6. If tani a, then the value of x x a + x sec i cosec i sini cosi 7.. ^cos i-h^cot i+ h + 0 seci coti+ tani 00 m A 00 m B cosi- sini sini- cosi sini+ cosi 0. cos x- sin x sin x- cos x- + sin x - cos x. sin i 0 tan i + tani + coti sin i cot i cos i tan i coti sin i tan i coti 9. In the adjoining igure+ab 50c 0c 0. ^ + tanihsini cos i sin i cot i tan i. In the adjoining igure, sini 5. Then B 7 65 m 85 m. 75 m sin i+ + tani 60c 5c 95 m coseci+ coti coseci- coti cot i- cosec i sin i-cos i A 85 m i B

13 . sin^90c-ihcosi+cos^90c-ihsini 0 x aseci, y btani, then the value of x y. If a - b tan i cosec i 5.. 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 7 m 8.5 m 7.5 m 0 m 6. In the adjoining igure, A 5 m 5 m 5 60c m 5 m A 5 m 7. ^+cot ih^-cosih^+cosi h tani- seci sini- cosi seci- tani cosi-sini 8. ^- sinihseci 0 cos i tan i sin^90c -ihsini cos^90c -ihcosi 9. + tani coti sini tan i B TEST : If the radius of a sphere is half of the radius of another sphere, then their respective volumes are in the ratio : 8: : 8 : 5. The curved surface area of a right circular cylinder whose radius is a units and height is b units, is equal to ra bsq.cm rab sq.cm rsq.cm sq.cm 5. The surface areas of two spheres are in the ratio of 9 : 5. Then their volumes are in the ratio 79 : : 65 7 : 5 7 : 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 : 8 : 6 6 : 9 : 5. If the diameter and height of a right circular cone are cm and 8 cm respectively, then the slant height is 0 cm 96 cm 0 cm 0 cm

14 55. Base area of a right circular cylinder is 80 cm. If its height is 5 cm, then the volume is equal to cm 6 cm 00 cm cm 56. 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 8 cm 6 cm cm 0 cm 57. 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. 58. If the total surface area a solid right circular cylinder is 00r radius is 5 cm, then the sum of its height and radius is 5 cm 0 cm 5 cm 0 cm height h is equal to cm and its 59. 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 90 cm B) 0 cm 60 cm 00 cm 60. If the surface area of a sphere is 6r cm, then the volume of the sphere is equal to 7r cm 08r cm r cm 6r cm. 6. 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 6. If the radius of a sphere is cm, then the curved surface area of the sphere is equal to 6r cm 6 cm r cm 8r cm. 6. 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 80 cm 80 cm 0 cm 0 cm 6. The total surface area of a solid right circular cylinder whose radius is half of its r h sq. units rh sq. units rh sq.units r h sq.units 65. The total surface area of a solid hemisphere of diameter cm is equal to cm r cm r cm r cm. 66. If the volume of a sphere is 9 r cu.cm, then its radius is 6 cm cm cm cm. 67. 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

15 68. If the surface area of a sphere is 00r cm, then its radius is equal to 5 cm 0 cm 5 cm 00 cm. 69. 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. 70. The ratios of the respective heights and the respective radii of two cylinders are : an respectively. Then their respective volumes are in the ratio : : : : 7. urved 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 8 cm cm 8 cm 6 cm TEST : If the variance of, 8,, 6, 0 is, then the variance of 8, 6,,5,60 is Mean and standard deviation of a data are 8 and respectively. The coeficient of variation is For any collection of n items, (Rx) - x nx ( n- ) x ( n- ) x The variance of 0, 0, 0, 0, 0 is Standard deviation of a collection of data is. If each value is multiplied by, then the standard deviation of the new data is The range of the irst 0 prime numbers,, 5, 7,,, 7, 9,, 9 is For any collection of n items, R(x - x) R x x nx Variance of the irst natural numbers is / - and n. The coeficient of variation is 80. Given (x x) 8, x

16 8. The least value in a collection of data is.. The range of the collection is 8.. Then the greatest value of the collection is If the standard deviation of a set of data is.6, then the variance is For a collection of items, Rx, then the arithmetic mean is 8. 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 85. The greatest value of a collection of data is 7 and the least value is 8. Then the coeficient of range is If the variance of a data is.5, then the S.D is TEST : Probability of getting heads or tails in tossing a coin times 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 If A and B are two events such that P 0.5,P 0.05and P(A+B) 0., then P(A,B) The probabilities of three mutually exclusive events A, B and are given by,,and 5. Then P^A,B,h is The probability that a leap year will have 5 Fridays or 5 Saturdays is If S is the sample space of a random experiment, then P(S) Probability of sure event 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

17 95. If p is the probability of an event A, then p satisies 0 p 0 # p # 0 # p 0 p # 96. The probability that a non-leap year will have 5 Sundays and 5 Mondays is 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@ 98.. Two dice are thrown simultaneously. The probability of getting a doublet 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 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 z is an impossible event, then P^zh 0 0. If P 0.5,P 0.50,P(A+B) 0. then P(neither Anor B) The probability of selecting a queen of hearts when a card is drawn from a pack of 0. 5 playing cards is that he will not score centum is 5 5 The probability that a student will score centum in mathematics is 5 6. The probability 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 A fair die is thrown once. The probability of getting a prime or composite number is S.NANDHAKUMARM.Sc, B.Ed (Maths) Thannithasanur, Idappadi, Ph:

1. SETS AND FUNCTIONS

1. SETS AND FUNCTIONS . 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,