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SECOND SHIFT, C.B.S.E. Board & Pre Foundation for Engg & Medical, , CLASS 10 - MATHEMATICS, REAL NUMBERS - DAILY PRACTISE PROBLEM (D.P.P.) - MCQ01-SET-01, , 1., , The smallest rational number by which, , 1, 3, , should be multiplied so that its decimal expansion, , [1], , terminates after one place of decimal, is, a), c), 2., , 3., , 4., , 5., , 6., , 7., , 8., , 3, , 3, , b), , 100, , 10, , d) 3, , 1, 10, , The HCF and the LCM of 12, 21, 15 respectively are:, , [1], , a) 3, 140, , b) 420, 3, , c) 12, 420, , d) 3, 420, , The decimal expansion of the rational number, , 33, 2, , 2 ⋅5, , will terminate after, , a) more than 3 decimal places, , b) two decimal places, , c) three decimal places, , d) one decimal place, , ¯, ¯¯¯, ¯, , 1.2348, , [1], , [1], , is, , a) a rational number, , b) a natural number, , c) an irrational number, , d) an integer, , If p is a prime number, then √–, p is, , [1], , a) Prime number, , b) Rational, , c) Integer, , d) Irrational, , The decimal expansion of the rational number, , 37, 2, , 2 ×5, , will terminate after, , a) two decimal places, , b) one decimal place, , c) four decimal places, , d) three decimal places, , The exponent of 3 in the prime factorization of 864 is:, a) 2, , b) 3, , c) 4, , d) 8, , A rational number can be expressed as a terminating decimal if the denominator has the, , [1], , [1], , [1], , factors, , 9., , a) 2, 3 or 5 only, , b) 2 or 5 only, , c) 2 or 3 only, , d) 2 only, , The difference between two distinct irrational numbers is always, , Second Shift Unit | Class 7 to 12 | C.B.S.E., , [1], , 1/6

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10., , a) a rational number, , b) an irrational number, , c) none of these, , d) both rational and irrational number, , The number of decimal places after which the decimal expansion of the rational number, , 23, 2, , 2 ×5, , [1], , will terminate, is, , 11., , 12., , a) 1, , b) 3, , c) 2, , d) 4, [1], , n2 – 1 is divisible by 8, if n is, a) an even integer, , b) a natural number, , c) an integer, , d) an odd integer, , A number when divided by 143 leaves 31 as remainder. What will be the remainder when the, , [1], , same number is divided by 13?, , 13., , a) 3, , b) 0, , c) 1, , d) 5, , Which of the following rational numbers have terminating decimal?, a), c), , 14., , b), , 7, 250, , d), , 5, 18, , [1], , 16, 225, 2, 21, , If the sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF,, , [1], , then the product of two numbers is, , 15., , 16., , a) 205400, , b) 203400, , c) 194400, , d) 198400, [1], , The least number n so that 5n is divisible by 3, where n is:, a) a whole number, , b) a real number, , c) a natural number, , d) no natural number, , The decimal representation of, , 71, 150, , is, , a) a non-terminating and non-repeating, , [1], b) none of these, , decimal, c) a non-terminating, repeating decimal, 17., , 18., , 19., , d) a terminating decimal, , Every positive odd integer is of the form ________ where ‘q’ is some integer., a) 2q + 2, , b) 5q + 1, , c) 3q + 1, , d) 2q + 1, , The HCF of 95 and 152, is, , [1], , [1], , a) 57, , b) 19, , c) 38, , d) 1, , If two positive integers ‘a’ and ‘b’ are written as a =, , pq, , 2, , and b =, , 3, , p q, , 2, , , where ‘p’ and ‘q’ are, , [1], , prime numbers, then LCM(a, b) =, , Second Shift Unit | Class 7 to 12 | C.B.S.E., , 2/6

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20., , a) pq, , b), , c) p2q3, , d) p2q2, , 3, , p q, , 2, , A rational number can be expressed as a non-terminating repeating decimal if the, , [1], , denominator has the factors, , 21., , a) none of these, , b) other than 2 or 5 only, , c) 2 or 5 only, , d) 2 or 3 only, [1], , If n is a natural number, then 92n - 42n is always divisible by, [Hint: 92n - 42n is of the form a2n - b2n which is divisible by both a - b and a + b., So, 9, , 2n, , 22., , 23., , 24., , 25., , 26., , is divisible by both 9 - 4 = 5 and 9 + 4 = 13.], , 2n, , − 4, , a) None of these, , b) 13, , c) both 5 and 13, , d) 5, , The product of a rational number and an irrational number is, , [1], , a) both rational and irrational number, , b) none of these, , c) an irrational number only, , d) a rational number only, −, −, , −, −, , If a and b are both positive rational numbers, then (√a + √b)(√a − √b) is, a) neither rational nor rational number, , b) a rational number, , c) an irrational number, , d) none of these, , 3.24636363... is, , [1], , a) an integer, , b) an irrational number, , c) a rational number, , d) none of these, , HCF of (23 × 32 × 5), (22 × 33 × 52) and (24 × 3 × 53 × 7) is, a) 60, , b) 48, , c) 30, , d) 105, , If n =, , 3, , 2, , 4, , × 3, , [1], , 4, , × 5, , × 7, , , then the number of consecutive zeros in n, where n is a natural, , [1], , [1], , number, is, , 27., , 28., , 29., , a) 2, , b) 3, , c) 7, , d) 4, , The total number of factors of a prime number is:, a) 2, , b) 1, , c) 3, , d) 0, , The decimal expansion of the rational number, , 14587, 1250, , [1], , will terminate after, , a) 4 decimal places, , b) 1 decimal place, , c) 3 decimal places, , d) 2 decimal places, , The number 1.732 is, a) a whole number, , [1], , [1], b) an integer, , Second Shift Unit | Class 7 to 12 | C.B.S.E., , 3/6

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c) a rational number, 30., , 31., , 32., , 33., , 34., , d) an irrational number, , What is a lemma?, , [1], , a) contradictory statement, , b) proven statement, , c) no statement, , d) None ot these, , 2.35 is, , [1], , a) an integer, , b) a rational number, , c) an irrational number, , d) a natural number, , The largest number which divides 245 and 1029 leaving remainder 5 in each case is, a) 8, , b) 12, , c) 4, , d) 16, , Which of the following is an irrational number?, , [1], , a) 3.141141114..., , b), , c), , d) 3.1416, , ¯, ¯¯¯, ¯, , 2.35, , 22, 7, , [1], , ¯, ¯¯¯¯¯¯¯¯, ¯, , 3. 1416, , [1], , is, , a) a terminating decimal number, , b) non terminating and non repeating, decimal, , c) an irrational number, 35., , 36., , 37., , (2+, , –, √5, , ) is, , [1], , a) an irrational number, , b) not real number, , c) a rational number, , d) an integer, , The HCF of 867 and 255 is, , [1], , a) 51, , b) 35, , c) 25, , d) 55, , Which of the following numbers has terminating decimal expansion?, a), c), , 38., , d) a rational number, , 3, 11, 3, 5, , b), , 3, , d), , 5, , [1], , 7, , 3, , For any two positive integers a and b, such that a > b. There exist (unique) whole numbers q, , [1], , and r such that, , 39., , a) a = bq + r, 0 ≤ r < b, , b) a = qbr, , c) b = aq + r, 0 ≤ r < b, , d) q = ar + b, 0 ≤ r < b, , If two positive integers m and n can be expressed as m = x2y5 and n = x3y2, where x and y are, , [1], , prime numbers, then HCF(m, n) =, , 40., , a) x2y2, , b) x2y3, , c) x3y2, , d) x3y3, , A number when divided by 61 gives 27 as quotient and 32 as the remainder, then the number, , Second Shift Unit | Class 7 to 12 | C.B.S.E., , [1], 4/6

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is:, , 41., , 42., , 43., , 44., , 45., , a) 1796, , b) 1569, , c) 1679, , d) 1967, , If two numbers do not have common factor (other than 1), then they are called, a) prime numbers, , b) co-prime numbers, , c) composite numbers, , d) twin primes, , 2.13113111311113...is, , [1], , a) a rational number, , b) an irrational number, , c) none of these, , d) an integer, , ________ is neither prime nor composite., , [1], , a) 4, , b) 1, , c) 2, , d) 3, , The product of a non-zero rational and an irrational number is, a) always irrational, , b) always rational, , c) one, , d) rational or irrational, , If n is any natural number, then 6n - 5n always ends with, [Hint: For any n ∈, , N, , [1], , [1], , [1], , , 6n and 5n end with 6 and 5 respectively. Therefore, 6n - 5n always ends, , with 6 - 5 = 1.], , 46., , a) 1, , b) 5, , c) 3, , d) 7, , Every point on the number line corresponds to a ________ number which may be either, , [1], , rational or irrational., , 47., , a) non-terminating, , b) decimal, , c) real, , d) terminating, , If two positive integers p and q can be expressed as p = ab2 and q = a3 b; a, b being prime, , [1], , numbers, then LCM (p, q) is, , 48., , 49., , 50., , a) a3 b3, , b) a3 b2, , c) a2 b2, , d) ab, , The decimal expansion of, , 987, 10500, , will terminate after:, , a) 2 decimal places, , b) 3 decimal places, , c) 1 decimal place, , d) None of these, , The decimal form of, , 5, 8, , is:, , [1], , [1], , a) 0.625, , b) 0.600, , c) 0.750, , d) 0.375, , The least positive integer divisible by 20 and 24 is, , Second Shift Unit | Class 7 to 12 | C.B.S.E., , [1], 5/6

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51., , 52., , a) 480, , b) 240, , c) 360, , d) 120, , a) 6, , b) 4, , c) 2, , d) 8, , If HCF of two numbers is 1, the two numbers are called relatively ________ or ________., a) composite, co-prime, , [1], , b) composite, prime, , c) prime, co-prime, 53., , [1], , For every positive integer n, n2 - n is divisible by, , d) twin primes, square numbers, , The decimal expansion of the number, , 441, 2, , 3, , 2 ×5 ×7, , a) None of these, , 2, , has, , [1], , b) non-terminating and non-repeating, decimal, , c) terminating decimal, 54., , 55., , d) non-terminating repeating decimal, [1], , If 9x + 2 = 240 + 9x, then the value of x is, a) 0.5, , b) 0.1, , c) 0.3, , d) 0.2, , If two positive integers a and b are written as, a = x3 y2 and b = xy3; x, y are prime numbers,, , [1], , then HCF (a, b) is, , 56., , 57., , 58., , a) xy, , b) xy2, , c) x3 y3, , d) x2 y2, , Every positive even integer is of the form ________ for some integer ‘q’., a) 2q + 1, , b) none of these, , c) 2q - 1, , d) 2q, , [1], , [1], , If p and q are co-prime numbers, then p2 and q2 are, a) even, , b) coprime, , c) not coprime, , d) odd, , If p1 and p2 are two odd prime numbers such that p1, , > p2, , , then p21, , a) an even number, , b) an odd prime number, , c) an odd number, , d) a prime number, , Second Shift Unit | Class 7 to 12 | C.B.S.E., , 2, , − p, , 2, , is, , [1], , 6/6

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