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Test: Real Numbers (Easy) - Class 10 MCQ


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15 Questions MCQ Test - Test: Real Numbers (Easy)

Test: Real Numbers (Easy) for Class 10 2024 is part of Class 10 preparation. The Test: Real Numbers (Easy) questions and answers have been prepared according to the Class 10 exam syllabus.The Test: Real Numbers (Easy) MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Real Numbers (Easy) below.
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Test: Real Numbers (Easy) - Question 1
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Use Euclid's division algorithm to find the HCF of 210 and 55.

Detailed Solution for Test: Real Numbers (Easy) - Question 1
Step 1: Given integers are 210 and 55 such as 210 > 55 By Euclid division lemma 210 = 55 x 3 + 45 (i)

Step 2 : Since remainder 45 ≠ 0. So for divisor 55 and remainder 45 By Euclid division lemma 55 = 45 x 1 + 10 (ii) Remainder ≠ 0

Step 3 : For division 45 and remainder 10 by Euclid division lemma 45 = 10 x 4 + 5 (iii) Remainder ≠ 0

Step 4 : For new divisor 10 and remainder 5 by Euclid division lemma 10 = 5 x 2 + 0 (iv)

Hence remainder = 0 So, HCF of 210, 55 is 5

Test: Real Numbers (Easy) - Question 2
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Three sets of English, Hindi and Mathematics books have to be stacked in such a way that all the books are stored topic-wise and the height of each stack is the same.The number of English books is 96, the number of Hindi books is 240 and the number of Mathematics books is 336. Assuming that the books are of the same thickness, determine the number of stacks of English, Hindi and Mathematics books.

Detailed Solution for Test: Real Numbers (Easy) - Question 2
In order to arrange the books as required, we have to find the largest number that divides 96, 240 and 336 exactly. Clearly, such a number is their HCF Computation of HCF of 96 and 240: Clearly, HCF of 96 and 240 is 48. Computation of HCF of 48 and 336: Thus, HCF of 96, 240 and 336 is 48. Hence, there must be 48 books in each stack. Now,

Number of stacks of English books = Number of English books / Number of books in each stack = 96 / 48 = 2

Number of stacks of Hindi books = Number of Hindi books / Number of books in each stack = 240 / 48 = 5

and, Number of stacks of Mathematics books = Number of Mathematics books / No. of books in each stack = 336 / 48 = 7

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Test: Real Numbers (Easy) - Question 3
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Classify the following number as rational and irrational

Detailed Solution for Test: Real Numbers (Easy) - Question 3

Test: Real Numbers (Easy) - Question 4
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Euclid's division lemma states that if a and b are any two +ve integers, then there exists unique integers q and r such that:
Detailed Solution for Test: Real Numbers (Easy) - Question 4
Division Algorithm : Euclid's division lemma states that if a and b are any two positive integers then there exist unique integers q and r such that, a = bq + r, 0 ≤ r < b
Test: Real Numbers (Easy) - Question 5
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If HCF 210 of and 55 is of the form 210(5) + 55y, then the value of y is:
Detailed Solution for Test: Real Numbers (Easy) - Question 5
HCF of 210 and 55 is 5.

210 x 5 + 55y = 5

55y = 5 - 1050

55y = 1045y

= -19

Test: Real Numbers (Easy) - Question 6
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Which of the following numbers are irrational?
Detailed Solution for Test: Real Numbers (Easy) - Question 6
An Irrational Number is a real number that cannot be written as a simple fraction.
Test: Real Numbers (Easy) - Question 7
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If 6370 = 2m.5n.7k.13p, then find m + n + k + p.
Detailed Solution for Test: Real Numbers (Easy) - Question 7
6370 = 2 × 3185

= 2 × 5 × 637

= 2 × 5 × 7 × 91

= 2 × 5 × 7 × 7 × 13m

= 1n

= 1k

= 2p

= 1m + n + k + p

= 1 + 1 + 2 + 1 = 5

Test: Real Numbers (Easy) - Question 8
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Assertion: n2 - n is divisible by for every positive integer.

Reason: √2 is not a rational number.
Detailed Solution for Test: Real Numbers (Easy) - Question 8
n2 - n = n(n - 1) If n is odd, n - 1 will be even.
Test: Real Numbers (Easy) - Question 9
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HCF of 95 and 152 is:
Detailed Solution for Test: Real Numbers (Easy) - Question 9
95 = 5 x 19 and 152 = 23 x 19 h.c.f = 19
Test: Real Numbers (Easy) - Question 10
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Use Euclid's division lemma to find the HCF of the following 27727 and 53124.
Detailed Solution for Test: Real Numbers (Easy) - Question 10
Here, a = 53124 and b = 27727

by using Euclid's division lemma,

a = bq + r ; 0 < r < b 53124

= (27727)(1) + 25397 + 27727

= (25397)(1) + 2330 + 25397

= (2330)(10) + 2097 + 2330

= (2097)(1) + 233 + 2097

= (233)(9) + 0

H.C.F is 233

Test: Real Numbers (Easy) - Question 11
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Find the H.C.F.of the following numbers using prime factorization method 106,159,265.
Detailed Solution for Test: Real Numbers (Easy) - Question 11
Prime factorisation method

106 = 2 × 53

159 = 3 × 53

265 = 5 × 53

Therefore , HCF (106, 159, 265) = 53

Test: Real Numbers (Easy) - Question 12
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Find the HCF of each set of numbers using prime factorisation method 51 and 85.
Detailed Solution for Test: Real Numbers (Easy) - Question 12

HCF of these numbers using prime factorization method 51, 85. Given 51 and 85. We need to find the hcf or highest common factor of the given numbers by prime factorization method. So factors are. 51 = 3 x 17 and. ... So the highest common factor of these numbers by prime factorization is 17.

Test: Real Numbers (Easy) - Question 13
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For some integer m, every even. integer is of the form :
Detailed Solution for Test: Real Numbers (Easy) - Question 13
Put m = 1, 2, 3, 4, 5, -1, -2,......

=> 2(1) = 2

=> 2(2) = 4

=> 2(-3) = -6

=> 2(-10) = -20

The above results are all even numbers.

So,For some integer m,every even integer is of the form 2m.

Test: Real Numbers (Easy) - Question 14
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If the HCF of 65 and 117 is expressible in the form 65 m - 117, them the value of m is:
Detailed Solution for Test: Real Numbers (Easy) - Question 14
65 = 5 × 13

117 = 3 × 3 × 13

Therefore, HCF of 65 and 117 is 13.

So, 65m − 117 = 13 or, 65m = 130

Therefore, m = 2

Test: Real Numbers (Easy) - Question 15
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HCF of 870 and 225 is:
Detailed Solution for Test: Real Numbers (Easy) - Question 15
870 = 225 × 3 + 195

225 = 195 × 1 + 30

195 = 30 × 6 + 15

30 = 15 × 2 + 0

Therefore, HCF = 15

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