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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 201. |
Add the following rational numbers:(i) \(\frac{-5}{7}\; and\; \frac{3}{7}\)(ii) \(\frac{-15}{4} \;and\;\frac{7}{4}\)(iii) \(\frac{-8}{11}\;and\;\frac{-4}{11}\)(iv) \(\frac{6}{13}\;and\;\frac{-9}{13}\) |
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Answer» All denominators are in positive numbers. We add it i) \(\frac{-5}{7} +\frac{3}{7}=\frac{(-5 + 3)}{7}=\frac{2}{7}\) ii) \(\frac{-15}{4} + \frac{7}{4}=\frac{(-15+7)}{4}=\frac{-8}{4}\) \(\frac{-8}{4}=-2\) (Dividing by 4 we get) iii) \(\frac{-8}{11}+\frac{-4}{11}= \frac{-8+(-4)}{11}=\frac{-12}{11}\) iv) \(\frac{6}{13} +\frac{-9}{13}= \frac{6+(-9)}{13}=\frac{-3}{13}\) |
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| 202. |
Add the following rational numbers:(i) \(\frac{3}{4}\) and \(\frac{-5}{8}\)(ii) \(\frac{5}{-9}\) and \(\frac{7}{3}\)(iii) -3 and \(\frac{3}{5}\)(iv) \(\frac{-7}{27}\) and \(\frac{11}{18}\)(v) \(\frac{31}{-4}\) and \(\frac{-5}{8}\)(vi) \(\frac{5}{36}\) and \(\frac{-7}{12}\) |
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Answer» i) The denominators are 4 and 8 . The LCM of 4 and 8 is 8. \(\frac{-3}{4}=\frac{(3\times2)}{(4\times2)}=\frac{6}{8}\) and \(=\frac{-5}{8}\) \(\frac{-5}{8}=\frac{(-5\times1)}{(8\times1)} \) Hence the denominators are same.Now, \(\frac{6}{8}+\frac{-5}{8} \) = \(\frac{6+(-5)}{8}=\frac{(6-5)}{8}\) = \(\frac{1}{8} \) ii) We convert the denominators in to positive numbers \(\frac{5}{-9} =\frac{(5\times-1)}{(-9\times-1)}\) = \(\frac{-5}{9}\) The denominators are 9 and 3.The LCM for 9 and 3 is 9 \(\frac{-5}{9}=\frac{(-5\times1)}{(9\times1)}\) = \(\frac{-5}{9}\) and \(\frac{7}{3}\) \(=\frac{(7\times3)}{(3\times3)}\) = \(\frac{21}{9}\) Since the denominators are same now we can add them directly.We get \(\frac{-5}{9}\) + \(\frac{21}{9}=\frac{(-5+21)}{9}\) = \(\frac{16}{9}\) iii) The denominators are 1 and 5.The L.C.M of 1 and 5 is 5. \(\frac{-3}{1}=\frac{(3\times5)}{(1\times5)}\) = \(\frac{-15}{5}\) and \(\frac{3}{5}\) \(=\frac{(3\times1)}{(5\times1)}\) = \(\frac{3}{5}\) Since the denominators are same now we can add them directly.We get \(\frac{-15}{5}+\frac{3}{5}=\frac{(-15+3)}{5}\) = \(\frac{-12}{5}\) iv) The denominators are 27 and 18. The L.C,M of 27 and 18 is 54. \(\frac{-7}{27}=\frac{(-7\times2)}{(27\times2)}\) = \(\frac{-14}{54}\) and \(\frac{11}{18}\) \(=\frac{(11\times3)}{(18\times3)}\) = \(\frac{33}{54}\) Since, the denominators are same we can add them directly \(\frac{-14}{54} + \frac{33}{54}=\frac{(-14+33)}{54}\) = \(\frac{19}{54}\) v) Firstly we convert the denominators to positive numbers. \(\frac{31}{-4}=\frac{(31\times-1)}{(-4\times-1)}\) = \(\frac{-31}{4}\) The denominators are 4 and 8. The L.C.M of 4 and 8 is 8 \(\frac{-31}{4}=\frac{(-31\times2)}{(4\times2)}\\=\frac{-62}{8}\) \(\frac{5}{8}=\frac{(-5\times1)}{(8\times1)}\\=\frac{-5}{8}\) Since the denominators are same we can add them directly as \(\frac{-62}{8}+\frac{(-5)}{8}=\frac{(-62+(-5))}{8}\\\frac{(-62-5)}{8}=\frac{-67}{8}\) vi) : The denominators are 36 and 12. The L.C.M of 36 and 12 is 36. \(\frac{-5}{36}=\frac{(5\times1)}{(36\times1)}\\=\frac{5}{36}\) \(\frac{-7}{12}=\frac{(-7\times3)}{(12\times3)}\\\frac{-21}{36}\) Now, the denominators are same we can add them directly.We get \(\frac{5}{36} + \frac{-21}{36}=\frac{(5+(-21))}{36}\\\frac{5-21}{36}=\frac{16}{36}\\\frac{-4}{9}\) |
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| 203. |
Keeping the place of 6 in the number 6350947 same, the smallest number obtained by rearranging other digits is (A) 6975430 (B) 6043579 (C) 6034579 (D) 6034759 |
| Answer» The correct option is (C) 6034579. | |
| 204. |
A submarine was situated 450 feet below sea level. If it descends 300 feet. What is its new position? |
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Answer» Position of submarine = -450 ft. Again it descends 300 feet ⇒ -300 feet ∴ New position = -450 + (-300) = -750 ft. ∴ It was 750 feet below sea level |
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| 205. |
Find the sum of the greatest and the least six digit numbers formed by the digits 2, 0, 4, 7, 6, 5 using each digit only once. |
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Answer» By using the digits 2, 0, 4, 7, 6, 5 The greatest number formed = 765420, and the least number formed = 204567 ∴ The required sum = 765420 + 204567 = 969987 |
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| 206. |
State whether the given statement are true (T) or false (F).Any non-zero whole number divided by itself gives the quotient 1. |
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Answer» True. Consider any non-zero whole number i.e. 5 5 is divided by itself = 5/5 = 1 |
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| 207. |
State whether the given statement are true (T) or false (F).Every number is a multiple of itself. |
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Answer» True. We know that, 1 is the identity for multiplication of whole numbers Therefore, any number is multiplied by 1 we get the number itself. Hence, every number is a multiple of itself. |
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| 208. |
State whether the given statement are true (T) or false (F).Every multiple of a number is greater than or equal to the number. |
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Answer» True. As per the standard rule, every multiple of a number is greater than or equal to the number. 2 × 1 = 2 2 × 3 = 6 |
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| 209. |
State whether the given statement are true (T) or false (F).The number of multiples of a given number is finite. |
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Answer» False. The number of multiples of a given number is infinite. Because, we know that numbers are infinite. |
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| 210. |
The sum of first three common multiples of 3, 4 and 9 is (A) 108 (B) 144 (C) 252 (D) 216 |
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Answer» The correct option is (D) 216. First we have to find out common multiples of 3 , 4 and 9, For that find L.C.M of 3 ,4 and 9 3 | 3 , 4 , 9 __________ 1 , 4 , 3 L. C.M ( 3 , 4 ,9 ) = 3 × 4 × 3 = 36 Now multiples of 36 = { 36 , 72 , 108, ....} Sum of first three common multiples of 3 , 4 , and 9 = 36 + 72 + 108 = 216 |
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| 211. |
Fill in the blanks to make the statements true.Length of river ‘Narmada’ is about 1290km. Its length in metres is_______. |
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Answer» We know that 1 km = 1000 m Length of river ‘Narmada’ is about 1290 km. Length of river ‘Narmada’ in metres = 1290 x 1000 m = 1290000 m |
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| 212. |
A rational number between 2 and 3 is(A) (√2+√3)/2(B) (√2. √3)/2(C) 1.5(D) 1.8 |
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Answer» (C) 1.5 Explanation: √2 =1.4142135…. and √3 =1.732050807…. (A) (√2+√3)/2 = 1.57313218497… is a non-terminating and non-recurring decimal and therefore is an irrational number. (B) (√2. √3)/2 = 1.22474487139… is a non-terminating and non-recurring decimal and therefore is an irrational number. (C) 1.5 is a terminating decimal and therefore is a rational number. (D) 1.8 is a terminating decimal and therefore is a rational number. Here both 1.5 and 1.8 are rational numbers. But, 1.8 does not lie in between √2 =1.4142135…. and √3 =1.732050807…. Whereas 1.5 lies in between √2 =1.4142135…. and √3 =1.732050807…. Hence, (C) is the correct option. |
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| 213. |
The value of 1.999… in the form p/q, where p and q are integers and q ≠ 0 , is(A) 19/10(B) 1999/1000(C) 2(D) 1/9 |
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Answer» (C) 2 Explanation: (A) 19/10 = 1.9 (B) 1999/1000= 1.999 (C) 2 (D) 1/9= 0.111…. Let x = 1.9999….. — ( 1 ) Multiply equation ( 1 ) with 10 10x = 19.9999….. — ( 2 ) Subtract equation (1) from equation(2) We get, 9x = 18 x = 18 / 9 x = 2 Therefore, x = 1.9999… = 2 Hence, (C) is the correct option. |
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| 214. |
The value of 2√3 + √3 is(a) 2√6(b) 6 (c) 3√3(d) 4√6 |
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Answer» (c) 3√3 2√3 + √3 = √3 (2 + 1) = 3√3 |
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| 215. |
Fill in the blanks to make the statements true.1 centimetre = _____ millimetres. |
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Answer» 1 centimetre = 10 millimetres. |
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| 216. |
Write each of the following in numeral form.i) Hundred crores hundred thousands and hundred.ii) Twenty billion four hundred ninety seven million pinety six thousands four hundred seventy two. |
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Answer» i) 100,01,00,100. ii) 20,497,096,472 |
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| 217. |
Fill in the blanks to make the statements true.1 kilometre = _____ millimetres. |
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Answer» 1 kilometre = 10,00,000 millimetres. We know that, 1 km = 1000 meters. 1 metre = 100 centimetre 1000 metre = 1000 × 100 = 1,00,000 centimetre 1 cm = 10 millimetres Then, 1,00,000 centimetre = 10 × 1,00,000 = 10,00,000 millimetres |
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| 218. |
Fill in the blanks to make the statements true.Height of a person is 1 m 65 cm. His height in millimetres is_______. |
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Answer» 1 m = 100 cm 1m 65 cm = 100cm + 65 cm = 165 cm 1cm = 10 mm 165cm = 165×10 = 1650 mm His height in millimeter is 1650mm |
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| 219. |
Express \(0.6 + 0.\overline7 + 0.4\overline7\) in the form p/q, where p and q are integers and q ≠ 0. |
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Answer» Let x = 0.6 Multiply by 10 on L.H.S and R.H.S, 10x = 6 x = 6/10 x = 3/5 So, the p/q form of 0.6 = 3/5 Let y = 0.77777… Multiply by 10 on L.H.S and R.H.S, 10y = 7.7777… 10y – y = 7.7777777……. – 0.7777777………….. 9y = 7 y = 7/9 So the p/q form of 0.7777… = 7/9 Let z = 0.47777… Multiply by 10 on L.H.S and R.H.S, 10z = 4.7777… 10z – z = 4.7777777… – 0.47777777… 9z = 4.2999 z ≈ 4.3/9 z = 43/90 So the p/q form of 0.4777… = 43/90 Therefore, p/q form of \(0.6 + 0.\overline7 + 0.4\overline7\) is, x+y+z = 3/5 + 7/9 + 43/90 = (54 + 70 + 43)/90 = 167/90 |
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| 220. |
Fill in the blanks to make the statements true.10 million = _____ crore. |
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Answer» 10 million = 1 crore We know that, 1 million = 10 lakh Then, 10 million = 10 × 10 = 100 lakh = 1,00,00,000 Therefore, 10 million = 1 crore. |
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| 221. |
Fill in the blanks to make the statements true.1 metre = _____ millimetres. |
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Answer» 1 metre = 1000 millimetres We know that, 1 metre = 100 centimetre 1 centimetre = 10 millimeter Then, 100 cm = 10 × 100 = 1000 millimetres |
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| 222. |
Fill in the blanks to make the statements true.100 thousands = _____ lakh |
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Answer» 100 thousands = 1 lakh |
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| 223. |
The number of factors of 36 is (A) 6 (B) 7 (C) 8 (D) 9 |
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Answer» The correct option is (D) 9. The answer is 9 factors which are 1,2,3,4,6,9,12,18 and 36. |
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| 224. |
Fill in the blanks to make the statements true.10 lakh = _____ million. |
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Answer» 10 lakh = 1 million. |
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| 225. |
State whether the given statement are true (T) or false (F).XXIX = 31 |
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Answer» False. Where, X = 10 IX = 9 So, XXIX = 10 + 10 + 9 = 29 |
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| 226. |
The product of the place values of two 2’s in 428721 is (A) 4 (B) 40000 (C) 400000 (D) 40000000 |
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Answer» The correct option is (C) 400000. The product of the place values of two 2’s in 428721 is There are two 2’s in the given number. So, the first 2 is in the tenth place, Then, the product is = 2 × 10 = 20 The other 2 is in place value of ten thousand. Then, = 2 × 10000 = 20000 Therefore, the product of place values = 20 × 20000 = 400000 |
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| 227. |
One million is equal to (A) 1 lakh (B) 10 lakh (C) 1 crore (D) 10 crore |
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Answer» (B) 10 Lakh One million is equal to ten lakh. 1,000,000 = 10,00,000 |
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| 228. |
Find whether the following statements are true or false.(i) Every real number is either rational or irrational.(ii) π is an irrational number.(iii) Irrational numbers cannot be represented by points on the number line. |
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Answer» (i) True: As we know that rational and irrational numbers taken form the set of real numbers. (ii) True: As, is ratio of the circumference of a circle to its diameter, it is an irrational number. π = \(\frac{2πr}{2r}\) (iii) False: Irrational numbers can be represented by point on the number line. |
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| 229. |
State whether the given statement are true (T) or false (F).532235 = 5 × 100000 + 3 × 10000 + 2 × 1000 + 2 × 100 + 3 × 10 + 5 |
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Answer» True. Left Hand Side = 532235 Right Hand Side = 5 × 100000 + 3 × 10000 + 2 × 1000 + 2 × 100 + 3 × 10 + 5 = 5,00,000 + 30,000 + 2000 + 200 + 30 + 5 = 5,32,235 Left Hand Side = Right Hand Side |
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| 230. |
3 × 10000 + 7 × 1000 + 9 × 100 + 0 ×10 + 4 is the same as (A) 3794 (B) 37940 (C) 37904 (D) 379409 |
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Answer» The correct option is (C) 37904. 3 × 10000 + 7 × 1000 + 9 × 100 + 0 × 10 + 4 = 30000 + 7000 + 900 + 0 + 4 = 37904 |
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| 231. |
If 1 is added to the greatest 7- digit number, it will be equal to (A) 10 thousand (B) 1 lakh (C) 10 lakh (D) 1 crore |
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Answer» The correct option is (D) 1 crore. Greatest 7 digit number is 9999999 When added with 1, 9999999 + 1 = 10000000 = 1 crore |
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| 232. |
Numbers having more than two factors are called __________ numbers. |
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Answer» Numbers having more than two factors are called Composite numbers. A number that has more factors than itself and 1 is called a composite number because '1' is neither prime nor composite , and its only factor is 1. |
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| 233. |
State whether the given statements are true or false:LXXV is greater than LXXIV. |
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Answer» True [LXXV = 75, LXXIV = 74] |
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| 234. |
Fill in the blanks to make the statements true.The population of Pune was 2,538,473 in 2001. Rounded off to nearest thousands, the population was __________. |
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Answer» The population of Pune was 2,538,473 in 2001. Rounded off to nearest thousands, the population was 2,538,000. |
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| 235. |
The expanded form of the number 9578 is (A) 9 × 10000 + 5 × 1000 + 7 × 10 + 8 × 1 (B) 9 × 1000 + 5 × 100 + 7 × 10 + 8 × 1 (C) 9 × 1000 + 57 × 10 + 8 × 1 (D) 9 × 100 + 5 × 100 + 7 × 10 + 8 × 1 |
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Answer» The correct option is (B) 9 × 1000 + 5 × 100 + 7 × 10 + 8 × 1. Consider the given number 9578, The place value of 8 is ones = 8 × 1 The place value of 7 is tens = 7 × 10 The place value of 5 is thousand = 5 × 100 The place value of 9 is ten thousand = 9 × 1000 |
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| 236. |
Numbers having more than two factors are called __________ numbers. |
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Answer» Numbers having more than two factors are called Composite numbers. |
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| 237. |
The number 58963 rounded off to nearest hundred is 58900. |
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Answer» False Given : Number 58963 rounded off to nearest hundred is 58900. To find : Is it true or false ? Solution : Rounded off to nearest hundred, 1) If tens number is greater than or equal to 5 then hundredth place increased by one and rest became zero. 2) If tens number is less than 5 then hundredth place remain same and rest became zero. In the number 58963, At tens place value is 6 > 5. So, the number became 59000. Therefore, it is false. |
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| 238. |
When rounded off to nearest thousands, the number 85642 is (A) 85600 (B) 85700 (C) 85000 (D) 86000 |
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Answer» The correct option is (D) 86000. When rounded off to nearest thousands, the number 85642 is 86000 |
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| 239. |
The number 58963 rounded off to nearest hundred is 58900. |
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Answer» The number 58963 rounded off to nearest hundred is 58900 is False. |
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| 240. |
When rounded off to nearest thousands, the number 85642 is (A) 85600 (B) 85700 (C) 85000 (D) 86000 |
| Answer» The correct option is (D) 86000. | |
| 241. |
State whether the given statements are true (T) or false (F).Estimated sum of 7826 and 12469 rounded off to hundreds is 20,000. |
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Answer» Estimated sum of 7826 and 12469 rounded off to hundreds is 20,000. True |
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| 242. |
State whether the given statement are true (T) or false (F).The numbers 4578, 4587, 5478, 5487 are in descending order. |
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Answer» False. In the question, the arrangement of the numbers in ascending order. Descending order of the given number = 5487, 5478, 4587, 4578. |
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| 243. |
Collect ‘5’ mobile numbers and arrange them in ascending and descending order. |
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Answer» Let the 5 mobile numbers are: 9247568320, 9849197602, 8125646682, 6305481954, 7702177046 Ascending order: 6305481954, 7702177046, 8125646682, 9247568320, 9849197602 Descending older: 9849197602, 9247568320, 8125646682, 7702177046, 6305481954 |
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| 244. |
Write the given numbers in ascending and descending order.S.No.NumbersDescending order1.75645,77845,24625,856902.6790,27895,16176,50000S.No.NumbersAscending order1.75645,77845,24625,856902.6790,27895,16176,50000 |
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| 245. |
Compare the numbers written in the following table by writing them in ascending order:54329722310629352237912318263454344782 |
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Answer» The given number in ascending order are as : 54344782 > 243182634 > 23106293 > 5432972> 5223791
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| 246. |
By making a suitable chart, compare:(i) 540276 and 369998(ii) 6983245 and 6893254 |
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Answer» (i) 540276 and 369998
Clearly, both the numbers have equal number of digits i.e. 6 And at the leftmost, the first number has 5 and the second number has 3. Since 5 > 3 540276 is greater. (ii) 6983245 and 6893254
Clearly, both the numbers have equal number of digits i.e. 7 And at the leftmost, both have the same digit i.e. 6 And at the second place from the left, the first number has 9 and the second number has 8. Since 9 > 8 6983245 is greater. |
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| 247. |
Find five rational numbers between 1 and 2. |
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Answer» We know, one rational number between two numbers m and n = (m+n)/2 Step 1: Rational number between 1 and 2 = (1+2)/2 = 3/2 Step 2: Rational number between 1 and 3/2 = (1+3/2)/2 = 5/4 Step 3: Rational number between 1 and 5/4 = (1+5/4)/2 = 9/8 Step 4: Rational number between 3/2 and 2 = 1/2 [(3/2) + 2)] = 7/4 Step 5: Rational number between 7/4 and 2 = 1/2 [7/4 + 2] = 15/8 Arrange all the results: 1 < 9/8 < 5/4 < 3/2 < 7/4 < 15/8 < 2 Therefore required integers are, 9/8, 5/4, 3/2, 7/4, 15/8. |
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| 248. |
Find five rational numbers between 3/5 and 4/5. |
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Answer» Steps to find n rational numbers between any two numbers: Step 1: Multiply and divide both the numbers by n + 1. In this example, we have to find 5 rational numbers between 3/5 and 4/5. Here n = 5 Multiply 3/5 and 4/5 by 6 3/5 x 6/6 = 18/30 and 4/5 x 6/6 = 24/30 Step 2: Choose 5 numbers between 18/30 and 24/30 3/5 = 18/30 < 19/30 < 20/30 < 21/30 < 22/30 < 23/30 < 24/30 = 4/5 Therefore, 5 rational numbers between 3/5 and 4/5 are 19/30, 20/30, 21/30, 22/30, 23/30. |
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| 249. |
Are the following statements true or false? Give reason for your answer. (i) Every whole number is a natural number.(ii) Every integer is a rational number.(iii) Every rational number is an integer.(iv) Every natural number is a whole number,(v) Every integer is a whole number.(vi) Every rational number is a whole number. |
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Answer» (i) False. As 0 is not a natural number. |
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| 250. |
Write the following in expanded form. i) 756723 ii) 60567234 iii) 8500756762 |
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Answer» i) 756723 Expanded form: 7 × 1,00,000 + 5 × 10,000 + 6 × 1,000 + 7 × 100 + 2 × 10 + 3 × 1 : 7 lakhs + 5 ten thousands + 6 thousands + 7 hundreds + 2 tens + 3 ones Word form: Seven lakh fifty six thousand seven hundred and twenty three. ii) 60567234 Expanded form: 6 × 1,00,00,000 + 5 × 1,00,000 + 6 × 10,000 + 7 × 1,000 + 2 × 100 + 3 × 10 + 4 × 1 : 6 crores + 5 lakhs + 6 ten thousands + 7 thousands + 2 hundreds + 3 tens + 4 ones Word form: Six crore five lakh sixty seven thousand two hundred and thirty four. iii) 8500756762 Expanded form: 8 × 1,00,00,00,000 + 5 × 10,00,00,000 + 7 × 1,00,000 + 5 × 10,000 + 6 × 1000 + 7 × 100 + 6 × 10 + 2 × 1 : 8 hundred crores + 5 ten crores + 7 lakhs & 5 ten thousands + 6 thousands + 7 hundreds + 6 tens + 2 ones Word form: Eight hundred and fifty crore seven lakh fifty six thousand seven hundred and sixty two. |
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