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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.
| 151. |
`{16-(4 + 18 divide 6 - bar(7-5)) xx 5]` |
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Answer» Correct Answer - -9 `{16-(4+17 divide 6 -bar(7-5)) xx 5}` `={16-(4 + 3 -2) xx 5} = {16-(7-2) xx 5}` `={16- 25} = -9` |
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| 152. |
Estimate the following to the nearest hundreds(a) 439 + 334 + 4317 (b) 1,08,734 – 47,599 (c) 8325 – 491 (d) 4,89,348 – 48,365 |
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Answer» (a) 439 + 334 + 4317 439 ⇒ 400 334 ⇒ 300 4317 ⇒ 4300 Sum = 5,000 (b) 1,08,734 – 47,599 1,08,734 ⇒ 1,08,700 47,599 ⇒ 47,600 Difference = 61,100 (c) 8325 – 491 8325 ⇒ 8300 491 ⇒ 500 Differences = 7,800 (d) 4,89,348 – 48,365 4,89,348 ⇒ 4,89,300 48,365 ⇒ 48,400 Difference = 4,40,900 |
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| 153. |
`4940 divide [{12 + 16 (48-(8-bar(15+6)))}]` |
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Answer» Correct Answer - 5 `4940 divide [12 + 16 {(48-(8-bar(15-6))}]` `=4940 divide [ 12 + 16 {48-(8-21)}]` `=4940 divide [12 + 16{48 + 13}]` ` = 4940 divide [12+16{61}]` `=4940 divide [12 + 976] = 4940 divide 988 = 5` |
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| 154. |
`52-[48 divide 12 xx 6 {6-(8 xx 3 - bar(6-4))}]` |
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Answer» Correct Answer - 436 `52-[48 divide 12 xx 6 {6-(8 xx 3-bar(6-4))}]` ` = 52-[ 4 xx 6 {6-(24-6 + 4)}]` `=52-[24.{6-22}] = 52-[24 xx (-16)]` `= 52 + 384 = 436` |
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| 155. |
In the same way, make different 4 digit numbers by exchanging the digits and check every time whether the number made is small or big.1432 < 4321 4321 > 32143214 > 2143 |
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| 156. |
India’s population has been steadily increasing from 439 million in 1961 to 1028 million in 2001. Find the total increase in population from 1961 to 2001. Write the increase in population in the Indian system of Numeration using commas suitably. |
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Answer» Population of India in 1961 = 439 millions = 439,000,000 Population of India in 2001 = 1028 millions = 1,028,000,000 Increase in population from 1961 to 2001 = Population in 2001 – Population in 1961 = 1028000000 – 439000000 = 589000000 = 589 million. Increase in population in Indian System = 58,90,00,000 |
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| 157. |
The population of a city was 43,43,645 in the year 2001 and 46,81,087 in the year 2011. Estimate the increase in population by rounding off to the nearest thousand. |
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Answer» Population in 2001 = 43,43,645 Population in 2011 = 46,81,087 Increase in population = 46,81,087 – 43,43,645 = 3,37,442 When rounded off to the nearest thousand = 3,37,000 |
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| 158. |
Arrange in descending order. 8461, 7535, 2943, 6214 |
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Answer» 8461 > 7535 > 6214 > 2943 |
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| 159. |
Arrange the following numbers in the descending order: 128435, 10835, 21354, 6348, 25840 |
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Answer» Place value chart is given by
The number with more digits is the greater number Step 1: 128435 is the larger number and 6348 is the least number Step 2: For the remaining 5 digit numbers we can compare the left-most digits and find 25840 > 21354 > 10835. The descending order: 128435 > 25840 > 21354 > 10835 > 6348 |
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| 160. |
Represent the following as integers. (a) Gain of Rs. 28 (b) Loss of Rs. 48 (c) 36 m below sea level (d) `12^(@)`C rise in temperature (e) `5^(@)`C fall in temperature |
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Answer» Correct Answer - (a) Rs. +28 (b) Rs.-48 `(c) -36m " " (d) 12^(@)C " " (e)-5^(@)C` `(a) "Gain of Rs." 28 to "Rs." + 28` `(b) "Loss of Rs." 48 to "Rs." - 48` `(c) 36 " m below sea level "to -36 m` (d) `12^(@)C " rise in temperature " to +12^(@)C` (e) `5^(@)C " fall in temperature " to -5^(@)C` |
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| 161. |
Write the following in descending order. (i) -8, 6, -9, 13, -23, 14, -16, 25 (ii) 42, -43, 64, -86, 120, -115 |
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Answer» Correct Answer - (i) 25, 14, 13, 6, -8, -9, -16, -23. (ii) 120, 64, 42, -43, -86, -115. (i) Descending order : 25, 14, 13, 6, -8, -9, -16, -23 (ii) Descending order: 120, 64, 42, -43, -86, -155 |
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| 162. |
Check whether the equation are identities. Write the patterns got from each, on taking x = 1, 2, 3, 4, 5 and x = -1, -2, -3, -4, -5.i. -x + (x + 1) = 1ii. -x + (x + 1) + (x + 2) – (x + 3) = 0iii. -x – (x + 1) + (x + 2) + (x + 3) = 4 |
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Answer» i. -x + (x + 1) = 1 If x = 1, -x + (x + 1) = -1 + (1 + 1) = -1 + 2 = 1 If x = 2, -x + (x + 1) = -2 + (2 + 1) = -2 + 3 = 1 If x = 3, -x + (x + 1) = -3 + (3 + 1) = -3 + 4 = 1 If x = 4 -x + (x + 1) = 4 + (4 + 1) = -4 + 5 = 1 If x = 5, -x + (x + 1) = -5 + (5 + 1) = -5 + 6 = 1 If x = -1, -x + (x + 1) = -(-1) + (-1 + 1) = 1 + 0 = 1 If x = -2, -x + (x + 1) = -(-2) + (-2 + 1) = 2 + (-1) = 1 If x = -3, -x + (x + 1) = -(-3) + (-3 + 1) = 3 + (-2) = 1 If x = -4, -x + (x + 1) = -(-4) + (-4 + 1) = 4 + (-3) = 1 If x = -5, -x + (x + 1) = -(-5) + (-5 + 1) = 5 + (-4) = 1 It is an identity. ii. -x + (x + 1) + (x + 2) – (x + 3) = 0 If x = 1, -x + (x + 1) + (x + 2) – (x + 3) = -1 + (1 + 1) + (1 + 2) – (1 + 3) = -1 + 2 + 3 – 4 = 0 If x = 2, -x + (x + 1) + (x + 2) – (x + 3) = -2 + (2 + 1) + (2 + 2) – (2 + 3) = -2 + 3 + 4 – 5 = 0 If x = 3, -x + (x + 1) + (x + 2) – (x + 3) = -3 + (3 + 1) + (3 + 2) – (3 + 3) = -3 + 4 + 5 – 6 = 0 If x = 4 -x + (x + 1) + (x + 2) – (x + 3) = -4 + (4 + 1) + (4 + 2) – (4 + 3) = -4 + 5 + 6 – 7 = 0 If x = 5, -x + (x + 1) + (x + 2) – (x + 3) = -5 + (5 + 1) + (5 + 2) – (5 + 3) = -5 + 6 + 7 - 8 = 0 If x = -1, -x + (x + 1) + (x + 2) – (x + 3) = -(-1) + (-1 + 1) + (-1 + 2) – (-1 + 3) = 1 + 0 + 1 – 2 = 0 If x = -2, -x + (x + 1) + (x + 2) – (x + 3) = 2 + (-2 + 1) + (-2 + 2) – (-2 + 3) = 2 + -1 + 0 – 1 = 0 If x = -3, -x + (x + 1) + (x + 2) – (x + 3) = 3 + (-3 + 1) + (-3 + 2) – (-3 + 3) = 3 + -2 + -1 – 0 = 0 If x = -4, -x + (x + 1) + (x + 2) – (x + 3) = 4 + (-4 + 1) + (-4 + 2) – (-4 + 3) = 4 + -3 + -2 – (-1) = 0 If x = -5, -x + (x + 1) + (x + 2) – (x + 3) = 5 + (-5 + 1) + (-5 + 2) – (-5 + 3) = 5 + -4 + -3 – (-2) = 0 It is an identity. iii. -x – (x + 1) + (x + 2) + (x + 3) = 4 If x = 1, -x – (x +1) + (x + 2) + (x + 3) = -1 – (1 + 1) + (1 + 2) + (1 + 3) = -1 – 2 + 3 + 4 = 4 If x = 2, -x – (x + 1) + (x + 2) + (x + 3) = -2 – (2 + 1) +(2 + 2) + (2 + 3) = -2 – 3 + 4 + 5 = 4 If x = 3, -x – (x + 1) + (x + 2) + (x + 3) = -3 – (3 + 1) + (3 + 2) + (2 + 3) = -3 – 4 + 5 + 6 = 4 If x = 4 -x – (x + 1) + (x + 2) + (x + 3) = -4 – (4 + 1) + (4 + 2) + (4 + 3) = -4 – 5 + 6 + 7 = 4 If x = 5, -x – (x + 1) + (x + 2) + (x + 3) = -5 – (5 + 1) + (5 + 2) + (5 + 3) = -5 – 6 + 7 + 8 = 4 If x = -1, -x – (x + 1) + (x + 2) + (x + 3) = -(-1) – (-1 + 1) + (-1 + 2) + (-1 + 3) = 1 – 0 + 1 + 2 = 4 If x = -2, -x – (x + 1) + (x + 2) + (x + 3) = 2 – (-2 + 1) + (-2 + 2) + (-2 + 3) = 2 – (-1) + 0 + 1 = 4 If x = -3, -x – (x + 1) + (x + 2) + (x + 3) = 3 – (-3 + 1) + (-3 + 2) + (-3 + 3) = 3 – (-2) + – 1 + 0 = 4 If x = -4, -x – (x + 1) + (x + 2) + (x + 3) = 4 – (-4 + 1) + (-4 + 2) + (-4 + 3) = 4 – (-3) + – 2 + (-1) = 4 If x = -5, -x – (x + 1) + (x + 2) + (x + 3) = 5 – (-5 + 1) + (-5 + 2) + (-5 + 3) = 5 – (-4) + -3 + (-2) = 4 It is an identity. |
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| 163. |
Take as x different positive numbers, negative numbers and zero, and compute x + 1, x – 1, 1 – x. Check whether the equations below hold for all numbers.i. (1 + x) + (1 – x) = 2ii. x – (x – 1) = 1iii. 1 – x = -(x – 1) |
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Answer» If x = 1 x + 1 = 1 + 1 = 2 x – 1 = 1 – 1 = 0 1 – x = 1 – 1 = 0 If x = 2 x + 1 = 2 + 1 = 3 x – 1 = 2 – 1 = 1 1 – x = 1 – 2 – 1 If x = 0 x + 1 = 0 + 1 x – 1 = 0 – 1 = -1 1 – x = 1 – 0 = 1 If x = -1 x + 1 = -1 + 1 = 1 – 1 = 0 x – 1 = -1 – 1 = -2 1 – x = 1 – (-1) = 1 + 1 = 2 If x = -2 x + 1 = -2 + 1 = -1 x – 1 = -2 – 1 = -3 1 – x = 1 – (-2) = 1 + 2 = 3 i. (1 + x) + (1 – x) In x = 1, (1 + x) + (1 – x) = 2 + 0 = 2 In x = 2, (1 + x) + (1 – x) = 3 + (-1) = 3 – 1 = 2 In x = 0, (1 + x) + (1 – x) = 1 + 1 = 2 In x = -1, (1 + x) + (1 – x) = 0 + 2 = 2 In x – 2, (1 + x) + (1 – x) – 1 + 3 = 3 – 1 = 2 (1 + x) + (1 – x) = 2 , for all values of x ii. x – (x – 1) In x = 1, x – (x – 1) = 1 – 0 = 1 In x = 2, x – (x – 1) = 2 – 1 = 1 In x = 0, x – (x – 1) = 0 – (-1) = 1 In x = -1, x – (x – 1) = -1 – (-2) = -1 + 2 = 1 In x = -2, x – (x – 1) = -2 – (-3) = -2 + 3 = 1 x – (x – 1) = 1, for all values of x iii. 1 – x In x = 1, 1 – x = o = -(x – 1) In x = 2, 1 – x = -1 = -(1) = -(x – 1) In x = o, 1 – x = 1 = -(-1) = -(x – 1) In x = -1, 1 – x = 2 = -(-2) = -(x – 1) In x = -2, 1 – x = 3 = -(-3) = -(x – 1) 1 – x = -(x – 1), for all values of x |
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| 164. |
Simplify \(\frac{-3}{2}+(\frac{-1}{2}\times\frac{-3}{4})+\frac{1}{2}\) |
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Answer» = \(\frac{-3}{2}+(\frac{-1}{2}\times\frac{-3}{4})+\frac{1}{2}\) = \(\frac{3}{2}+\frac{3}{8}+\frac{1}{2}\) = \(\frac{(-3\times4)+(3\times1)+(4\times1)}{8}\) = \(\frac{-12+3+4}{8}\) = \(\frac{-5}{8}\) |
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| 165. |
As per the census of 2001, the population of four states are given below. Arrange the states in ascending and descending order of their population.StatePopulationTamil Nadu72147030Rajasthan68548437Madhya Pradesh72626809West Bengal91276115 |
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Answer» All the four values have 8 digits Comparing the leftmost digits we have 91276115, 72626809, 72147030, 68548437 Descending order: 91276115 > 72626809 > 72147030 > 68548437 Ascending order: 68548437 < 72147030 < 72626809 < 91276115 Ascending order: Rajasthan < Tamil Nadu < Madhy Pradesh < West Bengal Descending order: West Bengal > Madhya Pradesh > TamilNadu > Rajasthan |
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| 166. |
Write the numbers in ascending order: 688, 9, 23005, 50, 7500. |
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Answer» Ascending order: 9, 50, 688,7500, 23005 9 < 50 < 688 < 7500 < 23005 |
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| 167. |
Arrange the following integers in ascending order. (i) 3, -5, 0, -2, -7, -1, 4 (ii) -15, -12, 11, -13, 10, 5, -9 |
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Answer» Correct Answer - (i) -7, -5, -2, -1, 0, 3, 4. (ii) -15, -13, -12, -9, 5, 10, 11. (i) Ascending order : -7, -5, -2, -1, 0, 3, 4 (ii) Ascending order : -15, -13, -12, -9, 5, 10, 11 |
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| 168. |
Find the units' digit in the expression 111.122.133.144.155.166 ? |
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Answer» Units' digit in the given expression = Units’ digit of 11 × Units’ digit of 22 × Units’ digit of 33 × Units’ digit of 44 × Units’ digit of 55 × Units’ digit of 66 = Units’ digit of (1 × 4 × 7 × 6 × 5 × 6) = Units' digit of 5040 = 0. |
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| 169. |
Write whether the answer got on doing the following operations are positive number or negative number.a. -8 x 9b. (-7) x (-8)c. (-7) ÷ 1d. (-9) ÷ (-3)e. 5 x 10f. 100 ÷ (-10)g. 10 x (-10) |
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Answer» a. Negative number (-8 x 9 = -72) b. Positive number (-7 x -8 = 56) c. Negative number (-7 ÷ 1 = -7) d. Positive number (\(\frac{-9}{-3}=3\)) e. Positive number (5 x 10 = 50) f. Negative number (\(\frac{100}{-10}=-10\)) g. Negative number (10 x -10 = -100) |
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| 170. |
Arrange the following in ascending order : -3,-8, 10, -2, 7, 15, -12, 6. |
| Answer» `-12, -8, -3, -2, 6, 7, 10, 15.` | |
| 171. |
What percent is the least rational number of the greatest rational number, if \(\frac{1}{2}\), \(\frac{2}{5}\), \(\frac{1}{3}\) and \(\frac{5}{9}\) are arranged in ascending order ? |
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Answer» Since LCM of 2, 5, 3, 9 = 270,\(\frac{1}{2}=\frac{135}{270}\), \(\frac{2}{5}=\frac{108}{270}\),\(\frac{1}{3}=\frac{90}{270}\),\(\frac{5}{9}=\frac{150}{270}\) \(\therefore\) Arranged in ascending order the numbers are \(\frac{90}{270}\),\(\frac{108}{270}\),\(\frac{135}{270}\),\(\frac{150}{270}\),i.e.,\(\frac{1}{2}\),\(\frac{2}{5}\),\(\frac{1}{2}\) and \(\frac{5}{9}\). \(\therefore\) Required percent =(\(\frac{1}{3}\)÷ \(\frac{5}{9}\)) x 100% = \((\frac{1}{3}\times \frac{9}{5}\times100)\)% = 60% |
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| 172. |
Write some properties of operations of rational numbers. |
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Answer» Properties of operations of rational numbers, For any rational numbers a, b, c.- (i) Rational numbers are closed under addition, multiplication and subtraction,i.e.,(a + b),(a x b) and (a - b) are also rational numbers. (ii) Rational numbers follow the commutative law of addition and multiplication, i.e., a + b = b + a and a × b = b × a. (iii) Rational numbers follow the associative law of addition and multiplication, i.e., (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c). (iv) Additive identity : 0 is the additive identity for rational numbers as a + 0 = 0 + a = 0. (v) Multiplicative identity : 1 is the multiplicative identity for rational numbers as a × 1 = 1 × a = a. (vi) Additive inverse : For every rational number 'a', there is a rational number '–a' such that a + (–a) = 0. (vii) Multiplicative inverse : For every rational number 'a' except 0, there is a rational number \(\frac{1}{a}\) such that a x \(\frac{1}{a}\)=1. (viii) Distributive property : Multiplication distributes over addition in rational numbers,i.e., a (b + c) = a × b + a × c. (ix) Between any two different rational numbers, there are infinitely many rational numbers. Rational numbers between any two given rational numbers a and b are q1 = \(\frac{1}{2}(a+b)\), q2= \(\frac{1}{2}(q_1+b)\), q3= \(\frac{1}{2}(q_2+b)\) and so on. |
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| 173. |
What is Rational number? |
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Answer» Numbers of the form \(\frac{p}{q}\), q ≠ 0 where p and q are integers and which can be expressed in the form of terminating or repeating decimals are called rational numbers. e.g.,\(\frac{7}{32}\)= 0.21875, \(\frac{8}{15}\)= 0.5\(\bar 3\) are rational numbers. |
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