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This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If x7y5 is exactly divisible by 3, then the least value of (x + y) is A. 6 B. 0 C. 4 D. 3 |
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Answer» We know that if sum of digits of a number is divisible by 3, then the number is divisible by 3. Here, x + 7 + y + 5 = multiple of 3 x + y + 12 = 0, 3, 6, 9, …. Hence, x + y + 12 = 12 ∴ x + y = 0 But x + y cannot be 0 because then x and y both will have to be 0.Since x is the first digit, it cannot be 0. ∴ x + y + 12 = 15 x + y = 3 ∴ the least value of (x + y) is 3 |
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| 2. |
If x4y5z is exactly divisible by 9, then the least value of (x + y + z) is A. 3 B. 6 C. 9 D. 0 |
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Answer» We know that if sum of digits of a number is divisible by 9, then the number is divisible by 9. Here, x + 4 + y + 5 + z = multiple of 9 x + y + z + 9 = 0, 9, 18, …. Hence, x + y + z + 18 = 18 But x + y + z cannot be 0 because then x, y and z will have to be 0.Since x is the first digit, it cannot be 0.∴ x + y + z + 18 = 27 x + y + z = 9 ∴ the least value of (x + y) is 9 |
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| 3. |
Check whether 876 and 345 are divisible by 3. Also check whether 3 divides the difference of 876 and 345? |
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| 4. |
Write some numbers which are divisible by 2,3,5,9 and 10 also. |
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Answer» 90, 180, 270. are divisible by 2, 3, 5, 9 and 10. [∵ The L.C.M. of 2, 3, 5, 9, 10 is 90] |
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| 5. |
If a number is divisible by ‘8’, then it also divisible by ‘4’. also Explain? |
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Answer» If a number is divisible by 8 it is also divisible by 4. ∴ If a number is divisible by 8, then it is also divisible by the factors of 8. Factors of 8 = 1, 2, 4, 8. ∴ The number which is divisible 8, is also divisible by 4. |
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| 6. |
If x48y is exactly divisible by 9, then the least value of (x + y) is A. 4 B. 0 C. 6 D. 7 |
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Answer» We know that if sum of digits of a number is divisible by 9, then the number is divisible by 9. Here, x + 4 + 8 + y = multiple of 9 x + y + 12 = 0, 9, 18, …. Hence, x + 11 = 18 ∴ x = 7 ∴ the least value of x is 7 |
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| 7. |
If 6x5 is exactly divisible by 9, then the least value of x is A. 1 B. 4 C. 7 D. 0 |
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Answer» We know that if sum of digits of a number is divisible by 9, then the number is divisible by 9. Here, 6 + x + 5 = multiple of 9 x + 11 = 0, 9, 18, …. Hence, x + 11 = 18 ∴ x = 7 ∴ the least value of x is 7 |
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| 8. |
If 7 × 8 is exactly divisible by 3, then the least value of x is A. 3 B. 0 C. 6 D. 9 |
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Answer» We know that if sum of digits of a number is divisible by 3, then the number is divisible by 3. Here, 7 + x + 8 = multiple of 3 x + 15 = 0, 3, 6, 9, …. Hence, x + 15 = 15 x = 0 ∴ the least value of x is 0 |
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| 9. |
If the 4-digit number x27y is exactly divisible by 9, then the least value of (x + y) is A. 0 B. 3 C. 6 D. 9 |
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Answer» We know that if sum of digits of a number is divisible by 9, then the number is divisible by 9. Here, x + 2 + 7 + y = multiple of 9 x + y + 9= 0, 9, 18, … Hence, x + y + 9 = 9 ∴ x + y =0 But x + y cannot be 0 because then x and y both will have to be 0.Since x is the first digit, it cannot be 0.∴ x + y + 9 = 18 x + y = 9 ∴ the least value of (x + y) is 9 |
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| 10. |
Find the value of z for which the number 471z8 is divisible by 9. Also, find the number. |
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Answer» Here, our given number is 471z8, which is divisible by 9. We know that if number is divisible by 9 only when sum of digits of given number is divisible by 9. Hence, if 471z8 is divisible by 9, then, 4 + 7 + 1 + z + 8 = 0, 9, 18,… ∴ 20 + z = multiple of 9. Hence, z = (multiple of 9) – 20 Here, possible values for multiples of 9 is 27 Hence, z = 7 ∴ Possible number is 47178 |
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| 11. |
If 56 x 32y is divisible by 18, find the least value of y. |
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Answer» It is given that, the number 56 x 32y is divisible by 18. Then, it is also divisible by each factor of 18. Now, the number is divisible by-2, its unit’s digit must be an even number that is 0, 2,4, 6, Therefore, the least value of y is 0. Again, the number is divisible by 3 also, sum of its digits is a multiple of 3. i.e. 5 + 6 + x + 3 + 2 + y is a multiple of 3 => 16 + x + y = 0, 3, 6, 9,… => 16+ x = 18 =>x = 2, which is the least value of x. |
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| 12. |
Which factors are not included in the prime factorisation of a composite number ? |
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Answer» 1 and the number itself. |
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| 13. |
The units digit of a two-digit number is 3 and seven times the sum of the digits is the number itself. Find the number. |
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Answer» It is given that the units place digit is 3. So, let tens place digit be y. ∴ Our number = (10y + 3) …(1) Our given condition is that seven times the sum of the digits is the number itself. ∴ By given condition, 7(y + 3) = (10 y + 3) 7 y + 21 = 10 y + 3 ∴ 10 y - 7y = 21 - 3 ∴ 3 y = 18 ∴ y = 6 Substituting the value of y in equation1, Number = 10 × 6 + 3 = 63 Hence, required number is 63. |
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| 14. |
Give five examples of numbers, each one of which is divisible by 4 but not divisible by 8. |
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Answer» Examples of numbers, such that each one of which is divisible by 4 but not divisible by 8, are 28, 36, 44, 52 and 60 |
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| 15. |
Give five examples of numbers, each one of which is divisible by 3 but not divisible by 9. |
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Answer» Examples of numbers, such that each one of which is divisible by 3 but not divisible by 9, are 21, 24, 30, 33 and 39. |
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| 16. |
In which of the following expressions, prime factorisation has been done?(a) 24 = 2 × 3 × 4(b) 56 = 7 × 2 × 2 × 2(c) 70 = 2 × 5 × 7(d) 54 = 2 × 3 × 9 |
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Answer» (a) 24 = 2 × 3 × 4 Since 4 is composite, prime factorisation has not been done. (b) 56 = 7 × 2 × 2 × 2 Since ail the factors are prime, prime factorisation has been done. (c) 70 = 2 × 5 × 7 Since all the factors are prime, prime factorisation has been done. (d) 54 = 2 × 3 × 9 Since 9 is composite, prime factorisation has not been done. |
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| 17. |
Write seven consecutive composite numbers less than 100 so that there is no prime number between them. |
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Answer» Between 89 and 97, both of which are prime numbers there are 7 composite numbers. They are 90, 91, 92, 93, 94, 95, 96, numbers factors 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 91 = 1, 7, 13, 91 92 = 1, 2, 4, 23, 46, 92 93 = 1, 3, 31, 93 94 = 1, 2, 47, 94 95 = 1, 5, 19, 95 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 |
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| 18. |
The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples. |
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Answer» 2 × 3 × 4 = 24, which is divisible by 6 9 × 10 × 11 = 990, which is divisible by 6 20 × 21 × 22 = 9240, which is divisible by 6 |
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| 19. |
Fill in the blanks to make the statement true.A number is divisible by 11 if the differences between the sum of digits at its odd places and that of digits at the even places is either 0 or divisible by ______. |
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Answer» 11 Explanation: Assume that the four digit number abcd Here, the digits at odd places are a and c and in even places are b and d Hence, (a+c) – (b+d) = 0 It follows that, (a+c) – (b+d) is divisible by 11, when (a+c) – (b+d) is not equal to 0. |
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| 20. |
Find the sum of integers which are divisible by 2 and 3 from 1 to 50. |
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Answer» Numbers which are divisible by 2 and 3 i.e., which are divisible by 6 from 1 to 50 are 6,12 …………….48. Sum of the numbers = 6 + 12 + ……..+ 48 = 6(1 + 2 +……… + 8) = 6 [\(\frac{8(8\,+\,1)}{2}\)] = 3 × 8 × 9 = 216 |
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| 21. |
The sum of two consecutive odd numbers is divisible by 4. Verily this statement with the help of some examples. |
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Answer» 3 + 5 = 8, which is divisible by 4 15 + 17 = 32, which is divisible by 4 19 + 21 = 40, which is divisible by 4 |
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| 22. |
What is the HCF of two consecutive(a) numbers?(b) even numbers?(c) odd numbers?Find the HCF of the following:(i) 24 and 36(ii) 15, 25 and 30(iii) 8 and 12(iv) 12, 16 and 28 |
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Answer» (i) 1 e.g., HCF of 2 and 3 is 1. (ii) 2 e.g., HCF of 2 and 4 is 2. (iii) 1 e.g., HCF of 3 and 5 is 1. |
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| 23. |
Sum of ‘n’ odd number of consecutive numbers is divisible by ‘n’. Explain the reason. |
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Answer» Sum of n’ consecutive odd numbers = n2 Since n is a factor of n2 , It Is divisible by ‘n’. |
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| 24. |
A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third and final day was respectively 1094,1812, 2050 and 2751. Find the total number of tickets sold on all the four days. |
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Answer» Tickets sold on 1st day = 1094 Tickets sold on 2nd day = 1812 Tickets sold on 3rd day = 2050 Tickets sold on 4th day = 2751 Total tickets sold = 1094 + 1812 + 2050 + 2751 = 7,707 |
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| 25. |
Insert commas suitably and write the names according to international system of numeration:a. 78921092b. 7452283c. 99985102d. 48049831 |
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Answer» a.Seventy eight million nine hundred twenty one thousand ninety two b. Seven million four hundred fifty two thousand two hundred eighty three c. Ninety nine million nine hundred eighty five thousand one hundred two d. Forty eight million forty nine thousand eight hundred thirty one. |
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| 26. |
Insert comas suitably and write the names according to indian system of numeration:a. 87595762b. 8546283c. 99900046d. 98432701 |
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Answer» a. Eight crore seventy five lakh ninty five thousand seven hundred sixty two. b. Eighty five lakh forty six thousand two hundred eighty three. c. Nine crore ninety nine lakh forty six. d. Nine crore eighty four lakh thirty two thousand seven hundred one |
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| 27. |
Place common correctly and write the numerals :a. Seventy three lakh seventy five thousand three hundred seven.b. Nine crore five lakh forty one.c. Seven crore fifty two lakh twenty one thousand three hundred two.d. Fifty eight million four hundred twenty three thousand two hundred two.e . Twenty three lakh thirty thousand ten. |
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Answer» a. 73,75,307 b. 9,05,00,041 c. 7,52,21,302 d. 58,423,202 e . 23,30,010 |
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| 28. |
इन्हें अंकों में लिखो-(क) पैंतालीस हजार अस्सी(ख) चौहत्तर हजार तीन सौ नौ(ग) तिरसठ हजार एक सौ उनतालीस(घ) अड़तालीस हजार एक |
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Answer» (क) 45080 (ख) 74309 (ग) 63139 (घ) 48001 |
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| 29. |
The LCM of two numbers is 495 and their HCF is 5. If the sum of the numbers is 100, then their difference is (a) 10 (b) 46 (c) 70 (d) 90 |
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Answer» (a) 10. Let one number = x. Then, Other number = 100 – x LCM = 495, HCF = 5 ⇒ x(100 – x) = 495 × 5 ⇒ 100x – x2 = 2475 ⇒ x2 – 100x + 2475 = 0 ⇒ x2 – 45x – 55x + 2475 = 0 ⇒ x (x – 45) – 55(x – 45) = 0 ⇒ (x – 45) (x – 55) = 0 ⇒ x = 45 or 55. ∴ The numbers and 45, 100 – 45 = 55 or 55, 100 – 55 = 45 Required difference = 55 – 45 = 10. |
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| 30. |
A room is 16 m long and 13.5 m broad. Find the cost of covering its floor with 75-m-wide carpet at ₹60 per metre. |
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Answer» Cost of covering room floor = ₹60 per metre. Length of room = 16 m Breadth of room = 13.5 m Breadth of carpet = 75 cm = 0.75 m We know, Area of room = Length × Breadth = 16 × 13.5 = 216 ⇨ Area of room is 216 m2 Length of carpet can be calculated by using below formula: Length of carpet = (area of room)/(Breadth of carpet) = 216/0.75 = 288 m Now, Cost of covering the floor = 288 m × ₹60 per meter = ₹17280 |
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| 31. |
A carpet is needed to cover the entire area of a room. If the length of the room is 16m and breadth 5m, find the area of the carpet required. |
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Answer» Area of the carpet = 1 × b = 16 × 5 = 80 Sq.cm |
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| 32. |
A room is 16 m long and 13.5 m broad. Find the cost of covering its floor with 75-m-wide carpet at ₹ 60 per metre. |
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Answer» As, the area of the floor = length x breadth = 16 x 13.5 = 216 m2 And, the width of the carpet = 75 m So, the length of the carpet required = \(\frac{Area\,of\,the\,floor}{Width\,of\,the\,carpet}\) = \(\frac{216}{75}\) = 2.88 m Now, the cost of the carpet required = 2.88 x 60 = 172.80 Hence, the cost of covering the floor with carpet is 172.80. Disclaimer: The answer given in the textbook is incorrect. The same has been rectified above. |
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| 33. |
Find the area of the square Whose side is 14 cm. |
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Answer» Side of the square = 14 cm Area of the square = side × side = (14 × 14) cm2 = 196 sq cm. |
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| 34. |
How many square metres of carpet will be required for a square room of side 6.5m to be carpeted. |
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Answer» Given, side of square room = 6.5 m So, area of square room = 6.52 = 6.5 × 6.5 = 42.25 m2 |
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| 35. |
List two characteristics of a good source of energy. |
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Answer» (i) Easily accessible and easy to store. (ii) Economical and eco-friendly. |
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| 36. |
Six square flower beds each of side 1 m are dug on a piece of land 8 m long 6 m wide. What is the area of the remaining part of the land? |
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Answer» Length of land = 8 m and b = 6 m Area of land = 8 × 6 = 48 sq. m Area of six squared flower beds each of sides 1 m = (side x side) × Number of flower beds = (1 × 1) × 6 = 6 sq. m remaining area = 48 – 6 = 42 sq. m Thus, Area of remaining land will be 42 sq. m. |
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| 37. |
List any three parameters, which categorizes any source of energy as a good source of energy. |
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Answer» (i) Does large amount of work per unit volume mass. (ii) Easy to store and transport. (iii) It should be economical and easily accessible. |
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| 38. |
There are four containers that are arranged in the ascending order of their heights. If the height of the smallest container given in the figure is expressed as 7/25 x =10.5 cm. Find the height of the largest container. |
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Answer» Correct answer is 37.5 |
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| 39. |
List two ways in which animal dung can be utilized as a fuel. Out of these two which one do you think is better ? Justify your answer. |
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Answer» Two ways : (i) as cow dung cakes (ii) as biogas Biogas is better than cow dung cakes because it has high heating capacity and is non-polluting as it burns without smoke and leaves no residue like ash. Slurry left in the biogas plant is a good manure for fields. |
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| 40. |
AB is a current-carrying conductor in the plane of the paper as shown in figure. What are the directions of magnetic fields produced by it at points P and Q? Given r1>r2, where will the strength of the magnetic field be larger? |
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Answer» Magnetic field at P is into the plane of paper and at Q it is out of the plane of paper. The strength of the magnetic field at Q will be larger as strength of the field ∝1/r. |
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| 41. |
PQ is a current carrying conductor producing magnetic field around it. A and B are two points at a distance r1 and r2 from it ll r1 > r2 where is the magnetic strength greater and why ? |
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Answer» At B, magnetic strength at B is greater as r2 is lesser than r1. |
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| 42. |
Why is biogas a better fuel than animal dung cakes? |
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Answer» Biogas is a better fuel than animal dung cakes because: |
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| 43. |
AB is a current-carrying conductor in the plane of the paper as shown in Figure. What are the directions of magnetic fields produced by it at points P and Q? Given r1 > r2, where will the strength of the magnetic field be larger? |
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| 44. |
Crosses ⊗ represent a uniform magnetic field directed into the paper. A conductor XY moves in the field toward right side. Find the direction of induced current in the conductor. Name the rule you applied. What will be the direction of current if the direction of field and the direction of motion of the conductor both are reversed ? |
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Answer» (i) Yto X (ii) Fleming's right-hand rule. (iii) The direction of induced current will still be the same i.e.,Y to X |
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| 45. |
Why is biogas considered an ideal fuel for domestic use ? |
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Answer» Biogas is considered an ideal fuel for domestic use because: (a) Biogas burns without smoke and hence does not cause air pollution. (b) Biogas has a high calorific value. That is, biogas produces a large amount of heat per unit mass. (c) Biogas is cheaper than most common fuels. (d) Biogas is a clean fuel since it burns completely without leaving any residue behind. |
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| 46. |
Name any one hydrocarbon fraction obtained during the fractional distillation of petroleum which is used as a domestic fuel. |
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Answer» used as a domestic fuel Kerosene. |
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| 47. |
What is overloading? State the causes of overloading. |
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Answer» Overloading: If the current drawn by the many electrical appliances connected to a single socket exceeds the current rating of the wire, the entire circuit or part of circuit gets heated and can even cause fire. This is known as overloading. It might be due to (i) accidental hike in supply voltage or (ii) connecting too many appliance to a single socket or (iii) damage in the insulation of wires or (iv) some fault in the appliances or (v) direct contact between a live wire and a neutral wire. |
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| 48. |
Why don’t two magnetic field lines intersect each other? |
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Answer» No two field-lines are found to cross each other. If they did, it would mean that at the point of intersection, the compass needle would point towards two directions, which is not possible. |
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| 49. |
Two magnetic field lines never intersect each other why ? |
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Answer» The intersection of magnetic field lines at a point means that the compass needle would point towards two directions at that point, which is not possible. |
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| 50. |
What are magnetic field lines? Justify the following statements (a) Two magnetic field lines never intersect each other. (b) Magnetic field lines are closed curves. |
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Answer» Magnetic field lines: It is defined as the path along which the unit North pole (imaginary) tends to move in a magnetic field if free to do so. (a) The magnetic lines of force do not intersect (or cross) one another. If they do so then at the point of intersection, two tangents can be drawn at that point which indicates that there will be two different directions of the same magnetic which field, i.e. the compass needle points in two different directions which is not possible. (b) Magnetic field lines are closed continuous curves. They diverge from the north pole of a bar magnet and converge its south pole. Inside the magnet they move from south pole to north pole. |
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