{"id":8270,"date":"2023-02-15T11:30:59","date_gmt":"2023-02-15T06:00:59","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=8270"},"modified":"2023-02-15T16:37:05","modified_gmt":"2023-02-15T11:07:05","slug":"mcq-questions-for-class-10-maths-chapter-1","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/mcq-questions-for-class-10-maths-chapter-1\/","title":{"rendered":"MCQ Questions for Class 10 Maths Chapter 1 Real Numbers with Answers"},"content":{"rendered":"

Students can access the NCERT MCQ Questions for Class 10 Maths Chapter 1 Real Numbers with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 10 Maths with Answers<\/a> during preparation and score maximum marks in the exam. Students can download the Real Numbers Class 10 MCQs Questions with Answers from here and test their problem-solving skills. Clear all the fundamentals and prepare thoroughly for the exam taking help from Class 10 Maths Chapter 1 Real Numbers Objective Questions.<\/p>\n

Real Numbers Class 10 MCQs Questions with Answers<\/h2>\n

Students are advised to solve the Real Numbers Multiple Choice Questions of Class 10 Maths to know different concepts. Practicing the MCQ Questions on Real Numbers Class 10 with answers will boost your confidence thereby helping you score well in the exam.<\/p>\n

Explore numerous MCQ Questions of Real Numbers Class 10 with answers provided with detailed solutions by looking below.<\/p>\n

Question 1.
\nIn a seminar, the number of participants in English, German and Sanskrit are 45,75 and 135. Find the number of rooms required to house them, if in each room, the same number of participants are to be accommodated and they should be of the same language.
\n(a) 45
\n(b) 17
\n(c) 75
\n(d) 135<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 17
\nSince, in each room, the same number of participants, of the same language, are to be accommodated, their number in each room
\nHCF of 45, 75 and 135.
\nHCF (45, 75,135) = 15
\nEach room accommodates 15 participants
\n=> Total no. of rooms required for English = 45\/15 = 3
\nTotal no. of rooms required for German = 75\/15 = 5
\nTotal no. of rooms required for Sanskrit= 135\/15 = 9
\nTotal no. of rooms = 3 + 5 + 9 = 17<\/p>\n<\/details>\n

\n

Find the Value of X<\/a> calculator is a free online tool that gives the value of x when two values are given.<\/p>\n

Question 2.
\nIf p = HCF (100,190) and q = LCM (100, 190); then p2<\/sup>q2<\/sup> is :
\n(a) 3.61 x 105
\n(b) 361 x 103
\n(c) 3.61 x 106
\n(d) 3.61 x 108<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer:
\npq = (HCF) (LCM) = Product of given numbers.
\n=> pq = 190×100 =19000
\n=> p2<\/sup>q2<\/sup> = 361 x 106<\/sup> = 3.61 x 108<\/sup><\/p>\n<\/details>\n

\n

The factors of 50<\/a> obtained this way are 1, 2, 5, 10, 25, and 50.<\/p>\n

Question 3.
\nA number \\(\\frac{p}{q}\\), when expressed in decimal form, terminates after 7 digits, then factors of q are of the form xm<\/sup> x yn<\/sup>; the value of x + y should be :
\n(a) 7
\n(b) 14
\n(c) 9
\n(d) 26<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 7
\n\\(\\frac{p}{q}\\) terminates after 8 digits
\nDecimal representation of \\(\\frac{p}{q}\\) is terminating
\n=> Factors of q should be of the form xm<\/sup> x yn<\/sup>
\nx+y=2+5=7<\/p>\n<\/details>\n

\n

What is the greatest common factor of 12 and 18<\/a>? Greatest Common Factor Calculator \/ Converter.<\/p>\n

Question 4.
\nThe condition to be satisfied by q, so that the rational number \\(\\frac{p}{q}\\) has a non terminating decimal expansion is:
\n(a) The prime factorisation of q is of the form 2m<\/sup> x 5n<\/sup>
\n(b) The prime factorisation of q is not of the form 2m<\/sup> x 5n<\/sup>
\n(c) The prime factorisation of q is of the form m2<\/sup> x n5<\/sup>.
\n(d) The prime factorisation of q is not of the form m2<\/sup> x 5n<\/sup>.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer:
\nThe prime factorisation is not of the form 2m<\/sup> x 5n<\/sup>“, where m and n are non-negative integers<\/p>\n<\/details>\n

\n

Question 5.
\nIf – 2 \u2264 x \u2264 2, which of the following is not true for x:
\n(a) x can take only 3 values if x is a natural number.
\n(b) if x is an irrational number, then only one value of x is possible.
\n(c) if x is a non-negative integer, then only 3 values of x are possible.
\n(d) if x is a rational number, infinite values of x are possible.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) if x is a rational number, infinite values of x are possible.
\n– 2 \u2264 x \u2264 2
\n\"MCQ<\/p>\n<\/details>\n

\n

Question 6.
\nThe largest positive integer which divides 434 and 539 leaving remainders 9 and 12 respectively is:
\n(a) 9
\n(b) 108
\n(c) 17
\n(d) 539<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 17
\nRequired number is the HCF of (434 – 9] and (539 -12)
\n= HCF of 425 and 527.
\n= 17<\/p>\n<\/details>\n

\n

Question 7.
\nThere is a circular path around a field. Reema takes 22 minutes to complete one round while her friend Saina takes 20 minutes to complete the same. If they both start at the same time and move in the same direction, after how many minutes will they meet again at the starting
\n(a) 220
\n(b) 3.4
\n(c) 440
\n(d) 4.4<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 220
\nLCM of 20 and 22 = 220 (question state: after how many minutes will they meet)<\/p>\n<\/details>\n

\n

365\/838<\/a> is already in the simplest form. It can be written as 0.435561 in decimal form (rounded to 6 decimal places).<\/p>\n

Question 8.
\nIf HCF (306, 657) = 9, then LCM of 306 and 657 is:
\n(a) 1
\n(b) 22338
\n(c) 9
\n(d) 12<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 22338
\nLCM (306, 657) = \\(\\frac{306 \u00d7 657}{9}\\)<\/p>\n<\/details>\n

\n

Question 9.
\nEuclid’s Lemma states that, for given positive integers a and b, there exist unique integers q and r, such that a = bq + r, where :
\n(a) 0 < r < b
\n(b) 0 \u2264 r < b
\n(c) 0 < r \u2264 b
\n(d) 0 \u2264 r \u2264 b<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 0 \u2264 r < b<\/p>\n<\/details>\n

\n

Question 10.
\nA number which can be expressed in the form \\(\\frac{p}{q}\\) where q \u2260 0 is a rational number is:
\n(a) p and q are co-prime numbers
\n(b) p and q are real numbers
\n(c) p and q are numbers
\n(d) p and q are integers<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) p and q are integers<\/p>\n<\/details>\n

\n

Question 11.
\nIn decimal expansion and representation, which of the following is not a rational numbers:
\n(a) terminating decimal
\n(b) terminates after 17 digits
\n(c) non-terminating repeating
\n(d) non-terminating non-repeating<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) non-terminating non-repeating
\nIn decimal representation, a rational number is either terminating or a non- terminating but repeating.<\/p>\n<\/details>\n

\n

Question 12.
\nIf a positive integer ‘a’ is divided by 2, what can be the remainder ?
\n(a) 0 or 1
\n(b) 0,1 or 2
\n(c) 1 or 2
\n(d) Any positive number<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 0 or 1
\n5. When a is divided by 2, the remainder is either 0 or 1 using Euclid’s Lemma<\/p>\n<\/details>\n

\n

Question 13.
\nFor some positive integer q, every even integer is of the form:
\n(a) q
\n(b) q + 1
\n(c)2q
\n(d)2q + l<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c)2q
\n(2q + r, 0\u2264r\u2264l but 2q +1 is odd)<\/p>\n<\/details>\n

\n

Question 14.
\nIf a non-zero rational number is multiplied to an irrational number, we always get:
\n(a) an irrational number
\n(b) a rational number
\n(c) zero
\n(d) one<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) an irrational number
\nThe product of a rational (non-zero) and m irrational number is always an irrational number.<\/p>\n<\/details>\n

\n

As seen on the calculation above, we have now obtained the LCM of 15 and 20<\/a>.<\/p>\n

Question 15.
\nHCF and LCM of two positive integers a and b satisfy a relationship, that:
\n(a) (HCF)(LCM) = \\(\\frac{a}{b}\\)
\n(b) (HCF) (LCM) = 1
\n(c) (HCF)(LCM) = ab
\n(d) No defined relation<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) (HCF)(LCM) = ab
\n7. (HCF) (LCM) = product of nos. a and b.<\/p>\n<\/details>\n

\n

Question 16.
\nIf we write 0.9 as a rational number, we get:
\n(a) \\(\\frac{9}{10}\\)
\n(b) 1
\n(c) \\(\\frac{1}{2}\\)
\n(d) \\(\\frac{1}{10}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 1
\n8. Let x = 0.9
\n10x =9.9
\n9x = 9
\nx = 1<\/p>\n<\/details>\n

\n

Question 17.
\nWrite an irrational number between 2 and 3.
\n(a) 2.5
\n(b) 2.001
\n(c) 2.1333333456…
\n(d) 2.13<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer:(c) 2.1333333456…
\nnon terminating non repeating<\/p>\n<\/details>\n

\n

Question 18.
\nWhich of the following are irrational whose sum and product are both rationals :
\n(a) \u221a2 + 3,\u221a2 – 3
\n(b) \u221a2 + \u221a3,\u221a2 – \u221a3
\n(c) 3 + \u221a2, 3 – \u221a2
\n(d) \u221a2 + 1,\u221a2 – 1<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 3 + \u221a2, 3 – \u221a2
\n3 + \u221a2 + 3 – \u221a2 = 6 and (3+\u221a2) (3-\u221a2) =7<\/p>\n<\/details>\n

\n

Question 19.
\nFind the value of x from the following such that x2<\/sup> is irrational but x4<\/sup> is rational:
\n(a) \u221a2
\n(b) 3\u221a2
\n(c) 4\u221a2
\n(d) 2<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 4\u221a2
\n\u221a2 is a irrational number.<\/p>\n<\/details>\n

\n

Question 20.
\nA rational number between 72 and 73 is:
\n(a) \\(\\frac{\u221a2 + \u221a3}{2}\\)
\n(b) \\(\\frac{\u221a2 – \u221a3}{2}\\)
\n(c) 1.5
\n(d) 1.8<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 1.5<\/p>\n<\/details>\n

\n

Question 21.
\nThe rational number that corresponds
\nto 0.6+0.\\(\\bar{7}\\)+0.4\\(\\bar{7}\\) is :
\n(a) \\(\\frac{83}{90}\\)
\n(b) \\(\\frac{7}{9}\\)
\n(c) \\(\\frac{43}{90}\\)
\n(d) \\(\\frac{167}{90}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) \\(\\frac{167}{90}\\)
\n0.7 = 7\/9
\n0.6 + 0.7 + 0.47
\n= 6\/10 + 7\/9 + 43\/90
\n= \\(\\frac{167}{90}\\)<\/p>\n<\/details>\n

\n

Question 22.
\nThe greatest number which divides 87 and 97, leaving 7 as remainder is :
\n(a) 10
\n(b) 1
\n(c) 87 x 97
\n(d) 6300<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 10
\nGreatest number which divides 87 and 97, leaving 7 as remainder = HCF of 80 and 90<\/p>\n<\/details>\n

\n

Question 23.
\nThe least number, which when divided by 10,14 and 18, leaves remainder 4, is :
\na) 630
\n(b) 634
\n(c) 252
\n(d) 496<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 634
\nRequired number is the LCM of 10, 14 and 18 (is 630) + 4
\n= 630 + 4
\n= 634<\/p>\n<\/details>\n

\n

Question 24.
\nThe greatest number which divides 17, 28 and 34 leaving remainders 2, 3 and 4 respectively is:
\n(a) 5
\n(b) 24
\n(c) 1
\n(d) 17<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 5
\nHere 17 – 2 = 15, 28 – 3 = 25, 34 – 4 = 30 Required number is the HCF of 15,25 and 30 = 5<\/p>\n<\/details>\n

\n

Question 25.
\n72 litres of liquid A and 108 litres of liquid B are to be packed in containers of the same size. The minimum number of containers required are:
\na) 36
\n(b) 18
\n(c) 5
\n(d) 10<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 5
\nFor minimum number of containers required, each container should contain the maximum liquid.
\nVolume of each container should be the HCF of 72 and 108, which is 36. Number of containers required for liquid
\nA = \\(\\frac{72}{36}\\) = 2
\nNumber of containers required for liquid
\nB = \\(\\frac{108}{36}\\) = 3
\ntotal = 5<\/p>\n<\/details>\n

\n

Question 26.
\nhe HCF of two consecutive rational numbers x and x +1 is :
\n(a) x
\n(b)x + 1
\n(c)1
\n(d) 0<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c)1
\nHCF of two consecutive numbers is always 1.<\/p>\n<\/details>\n

\n

Question 27.
\nThe HCF of a number which is neither prime nor composite and any other number x is:
\n(a) x
\n(b) x + 1
\n(c) 1
\n(d) Any number<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 1
\nAs, 1 is neither prime nor a composite number, thus, required number is the HCF of 1 and x, which is 1<\/p>\n<\/details>\n

\n

Question 28.
\nFind q and r, if 12560 = 215 q + r.
\n(a) q = 58, r = 0
\n(b) q = 58, r = 10
\n(c) q = 58, r = 4
\n(d) q = 58, r = 90<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) q = 58, r = 90
\nUsing Euclid’s Lemma, 12560 when divided by 215, gives quotient as 58 and remainder as 90.
\n=> 12560 = 215 (58) + 90
\n=>q = 58 and r = 90<\/p>\n<\/details>\n

\n

Question 29.
\nUsing Euclid’s Lemma, if d is the HCF of 1155 and 506, find ‘d’
\n(a) 11
\n(b) 143
\n(c) 77
\n(d) 66<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 11
\n1155=506×2 + 143
\n506 = 143 x 3 + 77
\n143 =77×1 + 66
\n77 =66 x 1 + 11
\n66 =11×6 + 0
\nLast divisor = 11 =>
\n11= HCF (66,11) =
\nHCF (1155,506)
\n=>d = 11<\/p>\n<\/details>\n

\n

Question 30.
\nAn army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups have to march in the same number of columns. Find the maximum number of columns in which they can march ?
\n(a) 32
\n(b) 60
\n(c) 40
\n(d) 8<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) 8
\nRequired number is the HCF of 616 and 32 616 = 32 x 19 + 8\u00a0 32 =8 x 4 + 0
\nHCF (616,32) = 8<\/p>\n<\/details>\n

\n

Question 31.
\nThe factor tree of a number has some unknowns, find the values of a, b, c, d, e,f and g.
\n\"MCQ<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: a = 277720, b = 6930, c = 3465, d = 3, e = 385, f = 77, g = 11<\/p>\n<\/details>\n

\n

Question 32.
\nWhich of the following is a rational number ?
\n(a) \"MCQ
\n(b) \"MCQ
\n(c) \"MCQ
\n(d) \"MCQ<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \"MCQ<\/p>\n

\"MCQ<\/p>\n<\/details>\n

\n

Question 33.
\n\\(\\frac{91}{625}\\) ,when written in decimal form 625 terminates; as factors of denominator are in the form m2<\/sup> x n5<\/sup>. This number will terminate after how many digits ?
\n(a) 3
\n(b) 2
\n(c) 1
\n(d) 4<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) 4
\n= 91 x 16\/104<\/sup>
\n= 1456\/104<\/sup> = 0.1456<\/p>\n<\/details>\n

\n

Question 34.
\nSelect the incorrect answer,
\n(2 + \u221a5)(2-\u221a5) is:
\n(a) a natural number
\n(b) a rational number
\n(c) a whole number
\n(d) an irrational number<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) an irrational number
\nwhich is a natural number, a whole number and also a rational number.<\/p>\n<\/details>\n

\n

Question 35.
\nWhich of the following rational numbers, in decimal form, terminates ?
\n(a) \\(\\frac{64}{455}\\)
\n(b) \\(\\frac{77}{210}\\)
\n(c) \\(\\frac{31}{200}\\)
\n(d) \\(\\frac{29}{343}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) \\(\\frac{31}{200}\\)
\n(a) \\(\\frac{64}{455}\\)
\n= \\(\\frac{64}{5 \u00d7 7 \u00d7 13}\\)
\n= non terminating
\n(b) \\(\\frac{77}{210}\\)
\n= \\(\\frac{77}{7 \u00d7 2 \u00d7 3 x 5}\\)
\n= non terminating
\n(c) \\(\\frac{31}{200}\\)
\n= 31\/23<\/sup> \u00d7 52<\/sup>
\n= terminating
\n(d) \\(\\frac{29}{343}\\)
\n= 29\/73<\/sup>
\n= non terminating<\/p>\n<\/details>\n

\n

Question 36.
\n\\(\\frac{91}{625}\\) ,when written in decimal form 625 terminates; as factors of denominator are in the form m2<\/sup> x n5<\/sup>. This number will terminate after how many digits ?
\n(a) 3
\n(b) 2
\n(c) 1
\n(d) 4<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) 4
\n= 91 x 16\/104<\/sup>
\n= 1456\/104<\/sup> = 0.1456<\/p>\n<\/details>\n

\n

Question 37.
\nSelect the incorrect answer,
\n(2 + \u221a5)(2-\u221a5) is:
\n(a) a natural number
\n(b) a rational number
\n(c) a whole number
\n(d) an irrational number<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) an irrational number
\nwhich is a natural number, a whole number and also a rational number.<\/p>\n<\/details>\n

\n

Question 38.
\nThe least positive integer divisible by 20 and 24 is
\n(a) 360
\n(b) 120
\n(c) 480
\n(d) 240<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 120<\/p>\n<\/details>\n

\n

Question 39.
\nThe HCF and LCM of two numbers is 9 and 459 respectively. If one of the numbers is 27, then the other number is
\n(a) 459
\n(b) 153
\n(c) 135
\n(d) 150<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 153<\/p>\n<\/details>\n

\n

Question 40.
\nThe largest number which divides 615 and 963 leaving remainder 6 in each case is
\n(a) 82
\n(b) 95
\n(c) 87
\n(d) 93<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 87<\/p>\n<\/details>\n

\n

Question 41.
\nThe product of three consecutive integers is divisible by
\n(a) 5
\n(b) 6
\n(c) 7
\n(d) none of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 6<\/p>\n<\/details>\n

\n

Question 42.
\nThe least number that is divisible by all the numbers from 1 to 8 (both inclusive) is
\n(a) 840
\n(b) 2520
\n(c) 8
\n(d) 420<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 840<\/p>\n<\/details>\n

\n

Question 43.
\nThe smallest composite number is:
\n(a) 1
\n(b) 2
\n(c) 3
\n(d) 4<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 3<\/p>\n<\/details>\n

\n

Question 44.
\nFor some integer p, every odd integer is of the form
\n(a) 2p + 1
\n(b) 2p
\n(c) p + 1
\n(d) p<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 2p + 1<\/p>\n<\/details>\n

\n

Question 45.
\nThe smallest composite number is:
\n(a) 1
\n(b) 2
\n(c) 3
\n(d) 4<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 3<\/p>\n<\/details>\n

\n

Question 46.
\nA lemma is an axiom used for proving
\n(a) other statement
\n(b) no statement
\n(c) contradictory statement
\n(d) none of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) other statement<\/p>\n<\/details>\n

\n

Question 47.
\nHCF of 8, 9, 25 is
\n(a) 8
\n(b) 9
\n(c) 25
\n(d) 1<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) 1<\/p>\n<\/details>\n

\n

Question 48.
\n\u221a7 is
\n(a) An integer
\n(b) An irrational number
\n(c) A rational number
\n(d) None of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) An irrational number<\/p>\n<\/details>\n

\n

Question 49.
\nThe product of a rational and irrational number is
\n(a) rational
\n(b) irrational
\n(c) both of above
\n(d) none of above<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) irrational<\/p>\n<\/details>\n

\n

Question 50.
\nA number when divided by 61 gives 27 as quotient and 32 as remainder. find the number
\n(a) 1967
\n(b) 1796
\n(c) 1679
\n(d) 1569<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 1679<\/p>\n<\/details>\n

\n

Question 51.
\nFor any two positive integers a and b, there exist (unique) whole numbers q and r such that
\n(a) q = ar + b , 0 = r < b.
\n(b) a = bq + r , 0 = r < b.
\n(c) b = aq + r , 0 = r < b.
\n(d) none of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) a = bq + r , 0 = r < b.<\/p>\n<\/details>\n

\n

Question 52.
\nTwo natural numbers whose difference is 66 and the least common multiple is 360, are:
\n(a) 120 and 54
\n(b) 90 and 24
\n(c) 180 and 114
\n(d) 130 and 64<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 90 and 24<\/p>\n<\/details>\n

\n

Question 53.
\nThe product of a non zero rational and an irrational number is
\n(a) Always irrational
\n(b) Always rational
\n(c) Rational or irrational
\n(d) One<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) Always irrational<\/p>\n<\/details>\n

\n

Question 54.
\nEvery positive even integer is of the form ____ for some integer \u2018q\u2019.
\n(a) 2q
\n(b) 2q \u2013 1
\n(c) 2q + 1
\n(d) none of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 2q<\/p>\n<\/details>\n

\n

Question 55.
\n\\(\\frac { 1 }{ \\sqrt { 3 } }\\) is –
\n(a) A rational number
\n(b) An irrational number
\n(c) A whole number
\n(d) None of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) An irrational number<\/p>\n<\/details>\n

\n

Question 56.
\nThe largest number which divides 60 and 75, leaving remainders 8 and 10 respectively, is
\n(a) 260
\n(b) 75
\n(c) 65
\n(d) 13<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) 13<\/p>\n<\/details>\n

\n

Question 57.
\np is
\n(a) a rational number
\n(b) an irrational number
\n(c) both (a) & (b)
\n(d) neither rational nor irrational<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) an irrational number<\/p>\n<\/details>\n

\n

Question 58.
\nThe largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively is
\n(a) 17
\n(b) 11
\n(c) 34
\n(d) 45<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 17<\/p>\n<\/details>\n

\n

Question 59.
\nWhich number is divisible by 11?
\n(a) 1516
\n(b) 1452
\n(c) 1011
\n(d) 1121<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 1452<\/p>\n<\/details>\n

\n

Question 60.
\nFor positive integers a and 3, there exist unique integers q and r such that a = 3q + r, where r must satisfy:
\n(a) 0 < r < 3
\n(b) 1 < r < 3
\n(c) 0 < r < 3
\n(d) 0 < r < 3<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 0 < r < 3<\/p>\n<\/details>\n

\n

Question 61.
\nThe decimal expansion of the rational number \\(\\frac { 47 }{ { 2 }^{ 3 }{ 5 }^{ 2 } }\\) will terminate after:
\n(a) one decimal place
\n(b) two decimal places
\n(c) three decimal places?
\n(d) more than three decimal places<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) three decimal places<\/p>\n<\/details>\n

\n

Question 62.
\nThe sum of a rational and an irrational number is
\n(a) Rational
\n(b) Irrational
\n(c) Both (a) and (c)
\n(d) Either (a) or (b)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) Irrational<\/p>\n<\/details>\n

\n

Fill in the blanks:<\/span><\/p>\n

1. Given any two positive integers a and b, there exist unique integers q and r satisfying a = bq + r and ______<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 0<r<b<\/p>\n<\/details>\n

\n

2. A rational number \\(\\frac{p}{q}\\) will have a terminating decimal representation, if prime factors of q are of the form _____<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: where m and n are positive integers.<\/p>\n<\/details>\n

\n

3. Rational number is a number which can be expressed in the form \\(\\frac{p}{q}\\), q and p, q are ______<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: integers<\/p>\n<\/details>\n

\n

4. If p is a prime number then \u221ap is ________<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: irrational number<\/p>\n<\/details>\n

\n

5. Every _________ can be expressed as a product of prime numbers.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: composite number<\/p>\n<\/details>\n

\n

Say true or false:<\/span><\/p>\n

Question 1.
\nHCF of two consecutive natural numbers n and n +1 is n.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: false
\nHCF of two consecutive natural numbers is 1<\/p>\n<\/details>\n

\n

Question 2.
\nEvery composite number can be expressed as a product of primes.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: true<\/p>\n<\/details>\n

\n

Question 3.
\nHCF of three numbers a, b, c; when multiplied by their LCM gives the product abc<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: false
\nthis property is true only for 2 numbers.<\/p>\n<\/details>\n

\n

Question 4.
\nThe number 6″ can never have a value which ends with the digit 0.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: true<\/p>\n<\/details>\n

\n

Question 5.
\nNon-terminating and Non-recurring decimals are called Irrational Numbers.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: true<\/p>\n<\/details>\n

\n

Match the following:<\/span><\/p>\n

Question 1.<\/p>\n\n\n\n\n\n\n
1. 4.37\\(\\bar{2}\\)<\/td>\na. \\(\\frac{1093}{250}\\)<\/td>\n<\/tr>\n
2. 4.3\\(\\bar{72}\\)<\/td>\nb. \\(\\frac{787}{180}\\)<\/td>\n<\/tr>\n
3. 4. \\(\\bar{372}\\)<\/td>\nc. \\(\\frac{1456}{333}\\)<\/td>\n<\/tr>\n
4. 4.372<\/td>\nd. \\(\\frac{4329}{990}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\nAnswer<\/span><\/summary>\n

Answer:<\/p>\n\n\n\n\n\n\n
1. 4.37\\(\\bar{2}\\)<\/td>\nb. \\(\\frac{787}{180}\\)<\/td>\n<\/tr>\n
2. 4.3\\(\\bar{72}\\)<\/td>\nd. \\(\\frac{4329}{990}\\)<\/td>\n<\/tr>\n
3. 4. \\(\\bar{372}\\)<\/td>\nc. \\(\\frac{1456}{333}\\)<\/td>\n<\/tr>\n
4. 4.372<\/td>\na. \\(\\frac{1093}{250}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/details>\n
\n

Question 2.<\/p>\n\n\n\n\n\n\n
a. it is the greatest positive integer which divides both the intergers.<\/td>\nRational number<\/td>\n4.37<\/td>\n<\/tr>\n
b. it is the lowest of their common multiples.<\/td>\nHCF<\/td>\nOf two consecutive numbers is 1<\/td>\n<\/tr>\n
c. terminating decimal expansion.<\/td>\nIrrational number<\/td>\nOf two consecutive numbers is their product.<\/td>\n<\/tr>\n
d. non terminating non repeating decimal expansion.<\/td>\nLCM<\/td>\n2.101001000110000\u2026\u2026.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\nAnswer<\/span><\/summary>\n

Answer:<\/p>\n\n\n\n\n\n\n
a. it is the greatest positive integer which divides both the intergers.<\/td>\nHCF<\/td>\nOf two consecutive numbers is 1<\/td>\n<\/tr>\n
b. it is the lowest of their common multiples.<\/td>\nLCM<\/td>\nOf two consecutive numbers is their product.<\/td>\n<\/tr>\n
c. terminating decimal expansion.<\/td>\nRational number<\/td>\n4.37<\/td>\n<\/tr>\n
d. non terminating non repeating decimal expansion.<\/td>\nIrrational number<\/td>\n2.101001000110000\u2026\u2026.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/details>\n
\n

Classify the following as Rational and Irrational:<\/span><\/p>\n

Question 1.
\n\u221a9<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: Rational<\/p>\n<\/details>\n

\n

Question 2.
\n2 + \u221a2<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: Irrational<\/p>\n<\/details>\n

\n

Question 3.
\n\\(\\frac { \u03c0 }{ 2 }\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: Irrational<\/p>\n<\/details>\n

\n

Question 4.
\n0.666………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: Rational<\/p>\n<\/details>\n

\n

Question 5.
\n1.7324<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: Rational<\/p>\n<\/details>\n

\n

Question 6.
\n\u221a4 + \u221a7<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: Irrational<\/p>\n<\/details>\n

\n

Question 7.
\n0.7347896……..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: Irrational<\/p>\n<\/details>\n

\n

Question 8.
\n4.363636……<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: Rational<\/p>\n<\/details>\n

\n

Question 9.
\n– 7 – \u221a3<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: Irrational<\/p>\n<\/details>\n

\n

Question 10.
\n– 3 + \u221a16<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: Rational<\/p>\n<\/details>\n

\n

We believe the knowledge shared regarding NCERT MCQ Questions for Class 10 Maths Chapter 1 Real Numbers with Answers Pdf free download has been useful to the possible extent. If you have any other queries regarding CBSE Class 10 Maths Real Numbers MCQs Multiple Choice Questions with Answers, feel free to reach us via the comment section and we will guide you with the possible solution.<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can access the NCERT MCQ Questions for Class 10 Maths Chapter 1 Real Numbers with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 10 Maths with Answers during preparation and score maximum marks in the exam. Students can …<\/p>\n

MCQ Questions for Class 10 Maths Chapter 1 Real Numbers with Answers<\/span> Read More »<\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[35],"tags":[],"yoast_head":"\nMCQ Questions for Class 10 Maths Chapter 1 Real Numbers with Answers - NCERT Solutions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ncertsolutions.guru\/mcq-questions-for-class-10-maths-chapter-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"MCQ Questions for Class 10 Maths Chapter 1 Real Numbers with Answers - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"Students can access the NCERT MCQ Questions for Class 10 Maths Chapter 1 Real Numbers with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. 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