KENDRIYA VIDYALAYA(EMBASSY OF INDIA SCHOOL) TEHRAN SUMMER HOLIDAYS – HOME WORK : CLASS : X I – MATHS :2014 CHAPTER : SETS 1. Write the following sets in the roaster form : (i) A= (ii) B= x : x is a positive integer less than 10 and 2 x – 1 is an odd number x : x2 + 7 x – 8 = 0 , x  R 2. Out of 100 students , 15 passed in English, 12 passed in Mathematics, 8 passed in Science, 6 passed in English and Mathematics, 7 passed in Mathematics and Science, 4 passed in English and Science, 4 passed in all the three. Find how many passed (i) in English and Mathematics but not in Science (ii) in Mathematics and Science but not in English (iii) in Mathematics only . 3. In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows : French = 17, English = 13 , Sanskrit = 15, French and English = 09, English and Sanskrit = 4, French and Sanskrit = 5 , English, French and Sanskrit = 3. Find the number of students who study (i) French only (ii) English only (iii) Sanskrit only (iv)English and Sanskrit but not French (v) French and Sanskrit but not English (vi) French and English but not Sanskrit (vii) at least one of three languages (viii) none of three languages. 4. In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Find the number of students who play neither. 5. In a town of 840 persons, 450 persons read Hindi, 300 read English and 200 read both. Find the number of persons who read neither. 6. If A =  , find the number of elements in P ( A ). 7. If A and B are finite sets such that A  B , find n ( A  B ). 8. If U = and C = 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 2, 3, 4, 8 , find ( I ) , A = B  C  1 ,2 , 3 , 5 ( ii) C  A , B= 2, 4, 6, 7 . CHAPTER : RELATIONS AND FUNCTIONS 9. Let A = 1, 2, 3, 4 and B = 5, 7, 9 . Determine (i) A × B (ii) B × A (iii) Is A × B = B × A (iv) Is n ( A × B ) = n (B × A ). 10. Find x and y if (i) ( 4 x + 3 , y ) = ( 3 x + 5 , – 2 ) (ii) ( x – y , x + y ) = ( 6 , 10 ). 11. Find the domain and range of the relation R given by R= (x,y):y =x+ 6 ; where x , y  N and x < 6 x . 12. Is the following relation a function ? Justify your answer : R = (2,3) , ( 3,0) ,(2,7), (4,6) 13. Find the domain for which the functions f ( x ) = 2x2 – 1 and g ( x ) = 1 – 3 x are equal. 14. If f ( x ) = x3 – 1 , find f ( x ) + f ( 1/x ). x3 15. If f and g are real functions defined by f ( x ) = x2 + 7 and g ( x ) = 3 x + 5, find each of the following: (i) f(3)+g( –5) . (ii) f ( ½ ) × g ( 14 ) (iii) f ( – 2 ) + g ( – 1 ). 16. If f and g are two real valued functions defined as f ( x ) = 2 x + 1 , g ( x ) = x 2 + 1 , find (i) f + g (ii) f – g (iii) f g (iv) f/g . 17. Find the domain and range of the function f ( x ) = 18. Find the domain of the function f defined by f ( x ) = 1 x5 . x 2  2x  1 . x2  x  6 CHAPTER : TRIGONOMETRY 19. If tan θ = 3 and θ lies in third quadrant, find the value of sin θ. 20. Find the value of tan 750 – cot 750 . 21. Find the value of sin ( 450 + θ ) – cos ( 450 – θ ).     22. Find the value of cot     cot     . 4  4  23. If tan A = 24. Solve : 1 1 , tan B = , find tan ( 2 A + B ). 2 3 3 cos θ + sin θ = 2 . 25. If sin θ + cos θ = 1 , find the value of sin2 θ. 26. If α + β =  , then find the value of ( 1 + tan α ) ( 1 + tan β ) . 4 CHAPTER : COMPLEX NUMBERS 27. If ( x + i y )1/3 = a + i b , where x , y , a , b  R, show that 28. What is the value of x y   2(a 2  b 2 ) . a b i 4 n 1  i 4 n 1 ? 2 29. What is the smallest positive integer n for which ( 1 + I )2n = ( 1 – I )2n ? 30. If (1  i ) 2  x  iy , find the value of x + y . 2i 31. What is the conjugate of 2i ? (1  2i ) 2 32. Find (1  i )(2  i ) . 3i   2 33. Find the argument of 1  i 3 . 34. Evaluate : ( 1 + i )6 + ( 1 – i )3 35. What is the conjugate of 5  12i  5  12i . 5  12i  5  12i 36. Find the polar form of the complex number ( i25)3. 1 i 37. Write the complex number z = cos  3  i sin  . 3 38. If Z 1 = Z 2 , is it necessary that Z1 = Z2 ? 39. If (a 2  1) 2 = x + i y , what is the value of x2+y2 ? 2a  i 40. Find (1  i )(2  i ) . (3  i ) **********************************************************************************************