Maths sample question paper:- Q. 1Find HCF and LCM of following numbers 8, 9 and 25.
Q. 2 The decimal expansion of the rational number will terminate after how many places of decimal.
Q. 3 Prove that (5 + 3) is an irrational number.
Q. 4 Using Euclid's division algorithm, find HCF of 56, 96 and 404.
Q. 5 Write the denominator of the rational number in the form 2m x 5n, where m and n are non-negative integers. Hence write its decimal expansion without actual division.
Q. 6 On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
Q. 7 Show that the square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q.
Q. 8 Find the HCF and LCM of-
a2b2c9 and b2c5e3
Q. 9 Show that the cube of a positive integer of the for m 6q + r, q is an integer and r = 0, 1, 2, 3 is also of the form 6m + r
Q. 10 If x is an odd integer then show that x2 - 1 is divisible by 8.
Objective type questions:-
Q. 1 HCF of 8, 9, 25 is -
(a) 8 (b) 9
(c) 25 (d) 1
Q. 2 The product of rational and irrational number is (a) rational (b) irrational
(c) both of above (d) None of above
Q. 3 The sum of two irrational number is always -
(a) rational (b) irrational
(c) rational or irrational (d) one
Q. 4 Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.
(a) 98 Kg (b) 290 Kg
(c) 200 Kg (d) 350 Kg
Q.5 For some integer m, every even integer is of the form -
(a) m (b) m + 1
(c) 2m (d) 2m + 1
Q. 6 The decimal expansion of the rational  will terminate after.
(a) One decimal place (b) Two decimal place
(c) Three decimal place (d) Four decimal place
Q. 7 If the HCF of 408 and 1032 is expressible in the form [1032 X 2 + 408 X P], then the value of P is :
(a) 5 (b) -5
(c) 4 (d) -4
Q. 8 The number in the form of (4P + 3), where P is a whole number, will always be -
(a) Even (b) Odd
(c) Even or odd (d) Multiple of 3
Q. 9 The value of  is -
(a) Natural Number (b) Rational Number
(c) Irrational Number (d) Rational or irrational
Q. 10 Euclid's division lemma states that for two positive integers a and b, there exist unique integer q and r such that [a = bq + r], where r must satisfy :
(a) a < r < b (b) 0 < r  b
(c) 1 < r < b (d) 0  r < b
Q. 11 The ratio between the LCM and HCF of 5, 15, 20 is :
(a) 9 : 1 (b) 4 : 3
(c) 11 : 1 (d) 12 : 1
Q. 12 If A = 2x + 3, B = x + 7, where N is a natural number then HCF of A and B is :
(a) 2 (b) 1
(c) 3 (d) 4
Q. 13 If the HCF of 55 and 99 is expressible in the form 55m - 99, then the value of m is .............
(a) 1 (b) 2
(c) 3 (d) 4
Q.14 If two positive integers a and b are written as a = p3q2 and b = pq3, then HCF of a, b is-
(a) pq (b) pq2
(c) p3q3 (d) p2q2
Q. 15 If the HCF of 65 and 117 is expressible in the form 65m - 117, then the value of m is :
(a) 4 (b) 2
(c) 1 (d) 3
Q. 16 The values of the remainder r, when a positive integer a is divided by 3 are :
(a) 0, 1, 2, 3 (b) 0, 1
(c) 0, 1, 2 (d) 2, 3, 4
Q. 17
(d) will have -
(a) Terminating decimal expansion
(b) Non terminating Non repeating decimal expansion
(c) Non terminating repeating decimal expansion
(d) None of these
Q. 18 If n is a rational number, then [52n . 22n] is divisible by
(a) 3 (b) 7
(c) both 3 and 7 (d) None of these
Q. 19 What is the least number that must be added to 1056. so the number is divisible by 23?
(a) 0 (b) 2
(c) 3 (d) 1
Q. 20 (6 + 5 ) - (4 - 3 ) is -
(a) A natural number (b) Irrational Number
(c) Rational Number (d) Integer
Q. 21 LCM of given number 'x' and 'y' where 'y' is a multiple of x is given by -
(a) x (b) y
(c) xy (d) x/y
Q. 22 For some integer P, every even integer is of the form.
(a) 2P + 1 (b) 2P
(c) P + 1 (d) P
Q. 23 Represent as
(a) Terminating decimal
(b) Non terminating decimal
(c) Non terminating repeating decimal
(d) None of these
Q. 24 The product of three consecutive positive integers is divisible by -
(a) 4 (b) 6
(c) No common factor (d) 1 (only)
Q. 25 The decimal expansion of the rational number will terminate after.
(a) One decimal place (b) two decimal place
(c) three decimal place (d) More than 3 decimal place
Q. 26 A rational number in its decimal expansion is [327.7081], what world be the prime factors of q, when the number is expressed in the form :
(a) 2 and 3 (b) 3 and 5
(c) 2, 3 and 5 (d) 2 and 5
Q. 27 The least number that is divisible by all the numbers for 1 to 10 (both inclusive) is :
(a) 10 (b) 100
(c) 504 (d) 2520
Q. 28 For some integer q, every odd integer is of the form :
(a) q (b) q + 1
(c) 2q (d) 2q + 1
Q. 29 For some integer P and 5, there exist unique integers q and r such that [P = 5q + r] possible value of r are
(a) 0 or 1 (b) 0, 1 or 2
(c) 0, 1, 2 or 3 (d) 0, 1, 2, 3 or 4
Q. 30 Product of [98] is -
(a) 22 X 7 (b) 22 X 72
(c) 2 X 72 (d) 23 X 7
Q. 2 The decimal expansion of the rational number will terminate after how many places of decimal.
Q. 3 Prove that (5 + 3) is an irrational number.
Q. 4 Using Euclid's division algorithm, find HCF of 56, 96 and 404.
Q. 5 Write the denominator of the rational number in the form 2m x 5n, where m and n are non-negative integers. Hence write its decimal expansion without actual division.
Q. 6 On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
Q. 7 Show that the square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q.
Q. 8 Find the HCF and LCM of-
a2b2c9 and b2c5e3
Q. 9 Show that the cube of a positive integer of the for m 6q + r, q is an integer and r = 0, 1, 2, 3 is also of the form 6m + r
Q. 10 If x is an odd integer then show that x2 - 1 is divisible by 8.
Objective type questions:-
Q. 1 HCF of 8, 9, 25 is -
(a) 8 (b) 9
(c) 25 (d) 1
Q. 2 The product of rational and irrational number is (a) rational (b) irrational
(c) both of above (d) None of above
Q. 3 The sum of two irrational number is always -
(a) rational (b) irrational
(c) rational or irrational (d) one
Q. 4 Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.
(a) 98 Kg (b) 290 Kg
(c) 200 Kg (d) 350 Kg
Q.5 For some integer m, every even integer is of the form -
(a) m (b) m + 1
(c) 2m (d) 2m + 1
Q. 6 The decimal expansion of the rational  will terminate after.
(a) One decimal place (b) Two decimal place
(c) Three decimal place (d) Four decimal place
Q. 7 If the HCF of 408 and 1032 is expressible in the form [1032 X 2 + 408 X P], then the value of P is :
(a) 5 (b) -5
(c) 4 (d) -4
Q. 8 The number in the form of (4P + 3), where P is a whole number, will always be -
(a) Even (b) Odd
(c) Even or odd (d) Multiple of 3
Q. 9 The value of  is -
(a) Natural Number (b) Rational Number
(c) Irrational Number (d) Rational or irrational
Q. 10 Euclid's division lemma states that for two positive integers a and b, there exist unique integer q and r such that [a = bq + r], where r must satisfy :
(a) a < r < b (b) 0 < r  b
(c) 1 < r < b (d) 0  r < b
Q. 11 The ratio between the LCM and HCF of 5, 15, 20 is :
(a) 9 : 1 (b) 4 : 3
(c) 11 : 1 (d) 12 : 1
Q. 12 If A = 2x + 3, B = x + 7, where N is a natural number then HCF of A and B is :
(a) 2 (b) 1
(c) 3 (d) 4
Q. 13 If the HCF of 55 and 99 is expressible in the form 55m - 99, then the value of m is .............
(a) 1 (b) 2
(c) 3 (d) 4
Q.14 If two positive integers a and b are written as a = p3q2 and b = pq3, then HCF of a, b is-
(a) pq (b) pq2
(c) p3q3 (d) p2q2
Q. 15 If the HCF of 65 and 117 is expressible in the form 65m - 117, then the value of m is :
(a) 4 (b) 2
(c) 1 (d) 3
Q. 16 The values of the remainder r, when a positive integer a is divided by 3 are :
(a) 0, 1, 2, 3 (b) 0, 1
(c) 0, 1, 2 (d) 2, 3, 4
Q. 17
(d) will have -
(a) Terminating decimal expansion
(b) Non terminating Non repeating decimal expansion
(c) Non terminating repeating decimal expansion
(d) None of these
Q. 18 If n is a rational number, then [52n . 22n] is divisible by
(a) 3 (b) 7
(c) both 3 and 7 (d) None of these
Q. 19 What is the least number that must be added to 1056. so the number is divisible by 23?
(a) 0 (b) 2
(c) 3 (d) 1
Q. 20 (6 + 5 ) - (4 - 3 ) is -
(a) A natural number (b) Irrational Number
(c) Rational Number (d) Integer
Q. 21 LCM of given number 'x' and 'y' where 'y' is a multiple of x is given by -
(a) x (b) y
(c) xy (d) x/y
Q. 22 For some integer P, every even integer is of the form.
(a) 2P + 1 (b) 2P
(c) P + 1 (d) P
Q. 23 Represent as
(a) Terminating decimal
(b) Non terminating decimal
(c) Non terminating repeating decimal
(d) None of these
Q. 24 The product of three consecutive positive integers is divisible by -
(a) 4 (b) 6
(c) No common factor (d) 1 (only)
Q. 25 The decimal expansion of the rational number will terminate after.
(a) One decimal place (b) two decimal place
(c) three decimal place (d) More than 3 decimal place
Q. 26 A rational number in its decimal expansion is [327.7081], what world be the prime factors of q, when the number is expressed in the form :
(a) 2 and 3 (b) 3 and 5
(c) 2, 3 and 5 (d) 2 and 5
Q. 27 The least number that is divisible by all the numbers for 1 to 10 (both inclusive) is :
(a) 10 (b) 100
(c) 504 (d) 2520
Q. 28 For some integer q, every odd integer is of the form :
(a) q (b) q + 1
(c) 2q (d) 2q + 1
Q. 29 For some integer P and 5, there exist unique integers q and r such that [P = 5q + r] possible value of r are
(a) 0 or 1 (b) 0, 1 or 2
(c) 0, 1, 2 or 3 (d) 0, 1, 2, 3 or 4
Q. 30 Product of [98] is -
(a) 22 X 7 (b) 22 X 72
(c) 2 X 72 (d) 23 X 7