CBSE 10 Math Test ( Real Numbers -1)

Benjamin Academia 1 CBSE 10 Mathematics Assessment Real Numbers April,16, 2011 MM 50 Time 90 minutes You are required to attempt all questions. Q 1. State whether true or false : ( a ) All of the following are natural numbers : -2, -1, 0, 1, 2 ( T/F ) ( b ) All of the following real numbers are integers : 0.5, -2, 5, 2.5 ( T/F ) ( c ) All of the following real numbers are irrationals : 3 , 4, -2 ( T/F ) ( d ) Non-terminating non-recurring decimal numbers are irrationals. ( T/F ) ( e ) Sum of a rational and an irrational number is always irrational. ( T/F ) ( f ) Sum of two irrational numbers is always a rational number. ( T/F ) ( g ) Difference of two irrational numbers is always an irrational. ( T/F ) ( h ) Quotient of an irrational and a rational number is an irrational. ( T/F ) ( i ) Quotient of a rational and an irrational is always a rational. ( T/F ) ( j ) Real numbers include all rational and all irrational numbers. ( T/F ) [ 10 ] Q 2. State Euclid’s Division Lemma. [ 3 ] Q 3. Show that every positive even integer is of the form 2m, and every positive odd integer is of the form 2 1 m+ , where m is some integer. [ 3 ] Q 4. Show that any positive odd integer is of the form 4 1 m+ or 4 3 m+ , where m is some integer. [ 3 ] Benjamin Academia 2 Q 5. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3q or 3 1 q + for some integer q . [ 4 ] Q 6. State Fundamental Theorem of Arithmetic. Prove that 3 5 11 11 × × + is a composite number. [ 5 ] Q 7. Udit finds that two brands of chocolates are available in packets containing 12 and 15 chocolates respectively. He wants to buy an equal number of chocolates of each kind spending minimum amount of money. How many packets of each kind must he purchase ? [ 4 ] Q 8. Show that following real numbers are irrational : ( a ) 3 ( b ) 7 5 − ( c ) 5 3 ( d ) 35 [ 8 ] Q 9. Following real numbers have decimal expansions as given below. In each case decide whether the number is rational or not. ( a ) 23.123456789 ( b ) 23.5151151115…… ( c ) 23.123456789 [ 6 ] Q 10. Can part ( c ) of question number 9 be expressed in the form pq , where p and q are integers. What are prime factors of q ? [ 4 ]