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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.
| 301. |
997 का घन क्या है?A. 991026973B. 991029673C. 991029773D. 991027273 |
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Answer» Correct Answer - A (a) `999=(1000-3)^(3)` `1000000000-27` `-3xx1000xx3(1000-3)` `=1000000000-27-9000000` `+27000=99102673` |
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| 302. |
Find two irrational number between 0.3030030003..... and 0.3010010001 ....... |
| Answer» 0.302020020002...... 0.302030030003.... etc. | |
| 303. |
Give two rational numbers lying between 0.232332333233332 . . . and 0.212112111211112. |
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Answer» Let, a = 0.212112111211112 And, b = 0.232332333233332... Clearly, a < b because in the second decimal place a has digit 1 and b has digit 3 If we consider rational numbers in which the second decimal place has the digit 2, then they will lie between a and b. Let, x = 0.22 y = 0.22112211... Then, a < x < y < b Hence, x, and y are required rational numbers. |
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| 304. |
Find a rational number and also an irrational number lying between the numbers 0.3030030003 ... and 0.3010010001 ... |
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Answer» Let, a = 0.3010010001 And, b = 0.3030030003... We observe that in the third decimal place a has digit 1 and b has digit 3, therefore a < b . in the third decimal place a has digit 1. so, if we consider rational and irrational numbers x = 0.302 y = 0.302002000200002..... We find that a < x < b And, a < y < b Hence, x and y are required rational and irrational numbers respectively. |
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| 305. |
Give two rational numbers lying between 0.515115111511115 ... and 0.5353353335 ... |
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Answer» Let, a = 0.515115111511115... And, b = 0.5353353335... We observe that in the second decimal place a has digit 1 and b has digit 3, therefore, a < b . So if we consider rational numbers x = 0.52 y = 0.52052052... We find that, a < x < y < b Hence x, and y are required rational numbers |
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| 306. |
Define an irrational number. |
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Answer» A number which can neither be expressed as a terminating decimal nor as a repeating decimal is called an irrational number.For example, 1.01001000100001… |
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| 307. |
Complete the following sentences: (i) Every point on the number line corresponds to a ______ number which many be either ______ or ______ (ii) The decimal form of an irrational number is neither ______ nor ______ (iii) The decimal representation of a rational number is either ______ or ______(iv) Every real number is either ______ number or ______ number. |
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Answer» (i) Every point on the number line corresponds to a Real number which may be either rational or irrational. (ii) The decimal form of an irrational number is neither terminating nor repeating (iii) The decimal representation of a rational number is either terminating, non-terminating or recurring. (iv) Every real number is either a rational number or an irrational number. |
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| 308. |
A number is a _____ of each of its factor. |
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Answer» A number is a multiple of each of its factor. |
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| 309. |
Fill in the blanks to make the statements true.786 × 3 + 786 × 7 = _____ |
| Answer» 786 × 3 + 786 × 7 = 7860 | |
| 310. |
Fill in the blanks to make the statements true.32 × (27 × 19) = (32 × _____ ) × 19 |
| Answer» 32 × (27 × 19) = (32 × 27 ) × 19 | |
| 311. |
Fill in the blanks to make the statements true.24 × 35 = 24 × 18 + 24 × _____ |
| Answer» 24 × 35 = 24 × 18 + 24 × 17 | |
| 312. |
Fill in the blanks to make the statements true.19 × 12 + 19 = 19 × (12 + _____) |
| Answer» 19 × 12 + 19 = 19 × (12 + 1) | |
| 313. |
Fill in the blanks to make the statements true.2916 × _____ = 0 |
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Answer» 2916 × 0 = 0 |
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| 314. |
Fill in the blanks to make the statements true.8925 ×1 = _____ |
| Answer» 8925 ×1 = 8925 | |
| 315. |
Fill in the blanks to make the statements true.125 + (68+17) = (125 + _____ ) + 17 |
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Answer» 125 + (68+17) = (125 + 0 ) + 17 |
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| 316. |
In 2001, the populations of Tripura and Meghalaya were 3,199,203 and 2,318,822, respectively. Write the populations of these two states in words. |
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Answer» Tripura-Three million, one hundred ninty-nine thousand, two hundred three; Meghalaya-Two million, three hundred eighteen thousand, eight hundred twenty two |
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| 317. |
Radius of the Earth is 6400 km and that of Mars is 4300000 m. Whose radius is bigger and by how much? |
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Answer» Earth, 2100000 m. |
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| 318. |
Express each of the following decimals in the form p/q :(i) 0. 4̅ (ii) bar 0.37 |
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Answer» (i) Let x = bar 0.4 Now, x = bar 0.4 = 0.444.... ---(1) Multiplying both sides of equation (1) by 10, we get, 10x = 4.444.... --- (2) Subtracting equation (1) by (2) 10x - x = 4.444... -0.444... => 9x = 4 => x = 4/9 Hence, bar 0.4 = 4/9 (ii) Let x = bar 0.37 Now, x = 0.3737... .....(1) Multiplying equation (1) by l0. 10x = 3.737.... .......(2) 100 37.3737... ........(3) Subtracting equation (1) by equation (3) 100x - x = 37 => 99 x = 37 => x = 37/ 99 Hence,bar 0.37 = 37/ 99 |
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| 319. |
Express each of the following decimals in the form`p/q :`(i)`0. bar(35) `(ii) `0. bar(585) ` |
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Answer» 1)`0.overline(35)` Let `x=0.overline_(35)-(1)` multiplying by 100 `100x=35.overline(35)-(2)` `99x=35` `x=35/99` 2)`0.overline(585)` Let `x=0.overline(585)-(1)` multiplying both side by 1000 `1000x=585.overline(585)-(2)` Subtracting equation 1 from 2 `999x=585` `x=585/999`. |
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| 320. |
Recall, `pi` is defined as the ratio of the circumference (say `c`) of a circle to its diameter (say `d`). That is, `pi=c/d`. This seems to contradict the fact the `pi` is irrational How will you resolve this contradiction? |
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Answer» When we measure a length with a scale or any other device, we only get an approximate rational value. So we may not realise that either c or d is irrational. `:.` Therefore, there is no contradiction. |
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| 321. |
If `x=(sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)-sqrt(a-2b))`, then prove that `b ^2-ax+b=0` |
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Answer» We have, `x=(sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)-sqrta-2b)=(sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)-sqrta-2b)xx(sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)-sqrta-2b)` `=((sqrt(a+2b)+sqrt(a-2b))^(2))/((sqrt(a+2b)-sqrta-2b)^(2))=(a+2b+a-2b+2sqrt((a+2b)(a-2b)))/((a+2b)-(a-2b))` `(2a+2sqrt(a^(2)-4b^(2)))/(4b)rArr" "x=(a+sqrt(a^(2)-4b^(2)))/(2b)` `rArr" "2bx=a+sqrt(a^(2)-4b^(2))" "rArr2bx-a=sqrt(a^(2)-4b^(2))` Squaring both sides, we get `=(2bx-a)^(2)=a^(2)-4b^(2)` `=4b^(2)x^(2)+a^(2)-4abx=a^(2)-4b^(2)` `=4b^(2)x^(2)-4abx+4b^(2)=0` `rArr" "4b(bx^(2)-ax+b)=0` `:." either "b=0orbx^(2)-ax+b=0` But b cannot be zero as it will not give the real value of x. `:." "bx^(2)-ax+b=0` |
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| 322. |
Find the decimal representation of `8/3dot` |
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Answer» decimal representation of `8/3=2.666666...` `8/3=2.overline6`. |
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| 323. |
Give an example of each, of two irrational numberswhose:difference is a rational number.difference is an irrational number.sum is a rational number.sum is an irrational number.product is a rational number.product is an irrational number.quotient is a rational number.quotient is an irrational number. |
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Answer» 1. `sqrt(2)-sqrt(2)=0` 2. `3sqrt(7)-1sqrt(7)=2sqrt(7)` 3.. `sqrt(3)+(-sqrt(3))=0` 4.`3sqrt(7)+1sqrt(7)=4sqrt(7) `5. `sqrt(2) xx sqrt(2)=2` 6. `sqrt(3) xx sqrt(2)=sqrt(6)` 7. `sqrt(18) / (sqrt(2))=3` 8.. `sqrt(18) / (sqrt(3))=sqrt(6)` |
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| 324. |
Express each of the following numbers in the form `p/q`15.75(ii) 8.0025 (iii) `-25. 6875` |
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Answer» `(a)1575/100=63/4` `(b)80025/10000=3201/400` `(c)-256875/10000=411/16` |
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| 325. |
100 से 600 के बीच ऐसे पूर्णांकों की संख्या कितनी है जो 4 तथा 6 दोनो अकं से विभाजित हो?A. 40B. 42C. 41D. 50 |
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Answer» Correct Answer - C 4 तथा 6 का ल0स0प लें जिससे संख्या 12 से विभाजित होनी चाहिए पहली संख्या after `100=108` अंतिम संख्या Less than `600=588` पूर्णांकों की संख्या `=(“Last term”-“first term”)/(“difference”)+1` `=(588-108)/12+1=480/12+1` `40+1=41` |
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| 326. |
Give an example of each, of two irrational numbers whose:(i) difference is a rational number.(ii) difference is an irrational number. (iii) sum is a rational number.(iv) sum is an irrational number.(v) product is a rational number.(vi) product is an irrational number.(vii) quotient is a rational number. (viii) quotient is an irrational number. |
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Answer» (i) √3 is an irrational number. Now, (√3) - (√3) = 0 0 is the rational number. (ii) Let two irrational numbers are 5√2 and√2 Now, (5√2) - (√2) = 4√2 4√2 is the rational number. (iii) Let two irrational numbers are√11 and -√11 Now, (√11) + (-√11) = 0 0 is the rational number. (iv) Let two irrational numbers are 4√6 and√6 Now, (4√6) + (√6) = 5√6 5√6 is the rational number. (v) Let two irrational numbers are 2√3 and √3 Now, 2√3 x √3 = 2 x 3 = 6 6 is the rational number. (vi) Let two irrational numbers are √2 and √5 Now, √2 x √5 = √10 √10 is the rational number. (vii) Let two irrational numbers are 3√6 and √6 Now, 3√6 /√6 = 3 3 is the rational number. (viii) Let two irrational numbers are√ 6 and √2 Now,√6/√2 = √3 + 2/√2 =√3 x √2/ √2 = √3 √3 is an irrational number |
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| 327. |
एक कार्यालय में 108 मेजें और 132 कुसिंयां हैं, प्रत्येक व्यक्ति को एक मेज और एक कुर्सी की आवश्यकता हो तो कितने लोग कार्य कर सकते हैं?A. 86B. 90C. 92D. 99 |
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Answer» Correct Answer - B टूटी हुई कुर्सियां `=132xx1/4=33` टूटी हुई मेंजें `=108xx1/6=18` शेष मेज `implies108-18=90` शेष कुर्सियां `implies132-33=99` प्रत्येक व्यक्ति को एक मेज तथा एक कुर्सी की आवश्यकता है इसीलिए कार्यालय में 90 व्यक्ति कार्य कर सकते हैं। |
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| 328. |
`’**’` का न्यूनतम कितना मूल्य रखा जाए कि `451**603`संख्या 9 से पूरी तरह विभाजित हो जाए?A. 7B. 8C. 5D. 9 |
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Answer» Correct Answer - B `451**603` to divide by 9 must be `(4+5+1**+6+0+3)` exactly divide by 9 to `(19+**)` divide by 9 `**` must be equal to `=8,17,……` For min. value `=8` |
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| 329. |
Test the divisibility of following numbers by 11 (a) 5335 (b) 9020814 |
| Answer» Both the numbers are divisible by 11. | |
| 330. |
Using divisibility tests, determine which of the following numbers are divisible by 4? (a) 4096 (b) 21084 (c) 31795012 |
| Answer» All the three number are divisible by 4. | |
| 331. |
Using divisibility test. determine which of the following numbers are divisible by 9? (a) 672 (b) 5652 |
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Answer» (b) 5652 number are divisible by 9. |
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| 332. |
`5.bar76` और `2.bar3` का अंतर ज्ञात कीजिए ।A. `2.bar54`B. `3.bar73`C. `3.bar46`D. `3.bar43` |
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Answer» Correct Answer - D `5.76767………` `-2.33333…………` `3,43434……..` `3.bar43` |
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| 333. |
एक संख्या को 6 से विभाजित करने पर 2 शेष बचता है, तो इसी संख्या के वर्ग को 6 से विभाजित करने पर शेषफल क्या होगा ? |
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Answer» Correct Answer - D Short Method Let number is 9 (Gives remainder 3 when divided by 6) Now `(9^(2))/6=81/6` `implies` Remainder `=3` |
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| 334. |
जब एक संख्या 893 से विभाजित की जाती है तो शेष 193 आता है, तो इसी संख्या को 47 से विभाजित करने पर शेषफल क्या आएगा?A. 3B. 5C. 25D. 33 |
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Answer» Correct Answer - B `("Remainder of no")/47=193/47` `implies` remainder `=5` |
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| 335. |
जब एक संख्या को 5 से विभाजित किया जता है तो उसका शेष 3 आता है जब उस संख्या के घन और वर्ग के योग को 5 से विभाजित किया जाएगा तो शेष क्या होगा?A. 1B. 2C. 3D. 4 |
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Answer» Correct Answer - A कोई ऐसी संख्या जो 5 से विभाज्य हो और शेष तीन बचें। मान यह 8 है। So, now `((8)^(2)+(8)^(3))/5=(64+512)/5` `=576/5=1` (remainder) |
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| 336. |
इनमें से कौन-सी संख्या किसी भी प्राकृत संख्या का वर्ग नहीं है?A. 17956B. 18225C. 63592D. 53361 |
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Answer» Correct Answer - C 63592 किसी भी प्राकृत संख्या का वर्ग नहीं है। `:.` कोई संखया जिसकि इकाई का अंक 2,3,7,8 हो तो वह संख्या पूर्ण वर्ग नहीं होती है। |
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| 337. |
जब एक पूर्णांक `K` को 3 से विभाजित किया जाता है, तो शेषफल 1 प्राप्त होता है और जब `K+1` को 5 से विभाजित किया जता है तो शेषफल 0 प्राप्त होता है तो निम्न में से `K` का संभावित मान क्या होगा?A. 62B. 63C. 64D. 65 |
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Answer» Correct Answer - C इस प्रकार के प्रश्नों को हमेशा समय बचाने के लिए विकल्प की सहायता से हल करें। प्रश्नों को ध्यान में रखते हुये विकल्प की सहायता ले। विकल्प `c` लेने पर 64 को 3 से विभाजित करने पर शेषफल 1 आता है। 64 में 1 जोड़ने पर शेषफल 0 इसे संतुष्ट करता है इसीलिए `k=64` सही उत्तर है। |
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| 338. |
इनमें से कौन सी संख्या 18 से विभाजित नहीं है ?A. 54036B. 50436C. 34056D. 65043 |
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Answer» Correct Answer - D एक संख्या 18 से तभी विभाजित होगी जब वह 2 तथा 9 से विभाजित होती हो। स्पष्तः देखा जा सकता है कि संख्या 65043,2 से विभाजित नहीं है क्योंकि संख्या 65043 का इकाई का अंक 3 है। इसलिए यह 18 से विभाजित नहीं होगी। |
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| 339. |
यदि `n` एक पूर्णांक है तो `(n^(3)-n)` किससे विभाजित होगी?A. 4B. 5C. 6D. 7 |
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Answer» Correct Answer - C `[(n^(3)-n)]` तथा `n` कोई पूर्णांक है। put `n=2` so `2^(3)-2=6` `(n=2,3,4…………..)` रखने पर यह हमेशा 6 से विभाजित होगी। |
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| 340. |
तीन अंकों की कितनी संख्याएं 6 से विभाजित हो जायेगी?A. 140B. 150C. 160D. 170 |
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Answer» Correct Answer - B `100……………………………999` First no. `=102`, last no `=996` no of terms `=("Last term" - "First term")/("Difference")+1` `implies(996-102)/6+1` `implies148+1+1` |
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| 341. |
`1 1/2` 67 और 101 के बीच कितनी संयुक्त संख्याएं हैं?A. `64:81`B. `8:9`C. `81:64`D. `9:8` |
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Answer» Correct Answer - A `1 1/2=3/2,1 1/3=4/3` Square `=9/4,16/9` Reciprocul ratio `4/9:9/16` |
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| 342. |
यदि दो संख्याओं का योग 80 हो, एवं उनके बीच `3:5` का अनुपात हो तो संख्या क्या होगी?A. `50,30`B. `60,20`C. `20,60`D. `30,50` |
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Answer» Correct Answer - D Let no are `a,b=3x,5x` so, `3x+5x=8x=80` `x=10` So no. `=3xx10,5xx10=30,50` |
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| 343. |
यदि `root(3)(9),root(4)(20),root(6)(25)`, को आरोही क्रम में रखा जाता है तो सही व्यवस्था क्या होगी?A. `root(6)(25)ltroot(4)(20)ltroot(3)(9)`B. `root(3)(25)ltroot(4)(20)ltroot(6)(25)`C. `root(6)(25)ltroot(3)(9)ltroot(4)(20)`D. `root(4)(20)ltroot(3)(9)ltroot(6)(25)` |
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Answer» Correct Answer - C `root(3)(9), root(4)(20), root(6)(25)` Taking L.C.m of 3,4 and 6. `root(12)(9^(4)),root(12)(20^(3)),root(12)(25^(2))` `root(12)(6561), root (12)(8000), root(12)(625)` so, ascending order `=root(6)925) lt root(3)(9), lt root(4)(20)` |
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| 344. |
`1/3, 4/7` और `2/5` को आरोही क्रम में लिखें ?A. `4/7 lt 1/3 lt 2/5`B. `2/5lt 4/7 lt 1/3`C. `1/3lt 2/5lt4/7`D. `4/7lt1/3lt2/5` |
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Answer» Correct Answer - C `1/2,4/7,2/5` `1/3=.33, 4/7=0.5, 2/5=0.4` `1/3lt2/5lt4/7` |
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| 345. |
50 दो भागों में विभाजित करें जिससे उनके व्युत्क्रमों का योगफल `1/12` हो।A. 35,15B. 20,30C. 24,36D. 28,22 |
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Answer» Correct Answer - B Short cut method हमेशा इस प्रकार के प्रश्नों को विकल्प की सहायता से हल करें। माना दो संख्याऐं 20 तथा 30 हैं। प्रश्नानुसार `1/20+1/30=1/12` `implies(3+2)/60=1/12` Matched Alternate: `x+y=50`………….i `1/x+1/y=1/12implies(x+y)/(xy)=12` `impliesxy=600`……..ii समीकरण i तथा ii से `x=30,y=20` |
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| 346. |
`(2153)^(167)` के गुणनफल में इकाई स्थान पर कौन सा अंक होगा ?A. 1B. 3C. 7D. 9 |
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Answer» Correct Answer - C `(2153)^(167)` Unit digit `=3^(167)` unit digit `3^(1)to3to3` `3^(2)to9to9` `3^(3)to27to7` `3^(4)to81to1` यह चक्र लगातार चलेगा। `implies` divide the power of 3 by 4 `167/4implies` remainder is 3 `3^(3)implies7` unit digit `=1xx7=7` |
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| 347. |
वह सबसे बड़ा अंक भरें जो 236953_876 को 11 से भाज्य बना दें?A. 7B. 8C. 9D. 3 |
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Answer» Correct Answer - C `x` (let) 236953…………..876 11 द्वारा विभाज्य विषम स्थानों के अंकों का योग और सम स्थानों के अंकों का अंतर 0 अथवा 11 का गुणज होगा। विषम स्थानों के अंकों का योग `=2+6+5+x+7=20+x` सम स्थानों के अंकों का योग `=3+9+3+8+6=29` सम स्थानों के अंकों का योग – विषम स्थानों के अंकों का योग `29=20+x` `x=9` |
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| 348. |
वह छोटे से छोटा अंक 935856_294 में भरें ताकि संख्या 9 से पूर्णतः विभाज्य हो जाए? |
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Answer» Correct Answer - D अंकों का योग 9 द्वारा विभाज्य होना चाहिए। `(9+3+8+5+6+x+2+9+4)/9` `=(46+x)/9=(45+(1+x))/9` तब `(1+x)` से अवश्य विभाज्य होगा। Hence value of `x=8` |
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| 349. |
`3^(50), 4^(40), 5^(30)` और `6^(20)` में सबसे बड़ी संख्या कौन सी है?A. `4^(40)`B. `5^(30)`C. `6^(20)`D. `3^(50)` |
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Answer» Correct Answer - A `3^(50)to (3^(5))^(10)to(243)^(10)` `4^(40)to(4^(4))^(10)to(256)^(10)larr` Largest `5^(30)to (5^(3))^(10)to(125)^(10)` `6^(20)to(6^(2))^(10)to(36)^(10)` |
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| 350. |
एक विद्यार्थी से किसी संख्या का `5/16` ज्ञात करने के लिए कहा गया। गलती से उस संख्या का `5/6` ज्ञात कर लिया। उसका उत्तर सही उत्तर से 250 अधिक था। दी हुई संख्या ज्ञात कीजिएA. 388B. 480C. 450D. 500 |
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Answer» Correct Answer - B Let the number of `x` According to question `5/6 x-5/16x=250` `(40x-15x)/48=250` `25x=250xx48` `x(25xx48)/25=480` |
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