InterviewSolution
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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.
| 1. |
Four persons A, B, C and D have ₹ 110 among them. A has twice the amound D has. B has an amount equal to the sum of the amounts with A and C and C has ₹ 20 more than D, then the amounts with A, B, C and D respectively areA. ₹ 20, ₹ 50, ₹ 30, ₹ 10B. ₹ 20, ₹ 40, ₹ 40, ₹ 10C. ₹ 30, ₹ 20, ₹ 40, ₹ 10D. ₹ 20, ₹ 40, ₹ 30, ₹ 20 |
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Answer» Correct Answer - A (i) Frame the 4 equations from the given date and then solve. (ii) Let `D` has ₹ x, then A has ₹`2x`, C has ₹ (`x+20`) and B has ₹ `(2x + x + 20)`. (iii) Total amount with A, B, C, and D is ₹ 110. (iv) Frame equation in `x` and solve for `x`. |
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| 2. |
Machine A can produce 6 items per hour and machine B can produce 11 items per hours. If machine A works for x hours and B works for y hours in a day and both the machines produce at the most 200 items in a day, then frame an inequation to support the above data. |
| Answer» Correct Answer - `6x + 11y le 200` | |
| 3. |
Mahesh has certain number of problems with him. He can solve some fixed number of problems every hour. After solving for 5 hours, he is left with 384 problems. If he had solved for 10 hours, he is left with 144 problems to solve. Find the number of problems with Mahesh initially.A. 600B. 584C. 624D. 734 |
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Answer» Correct Answer - C (i) Form an equation using the given data and solve. (ii) Let Mahesh can solve x number of problems every hour. (iii) `5x + 384 = 10x + 144`. Solve for x. |
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| 4. |
In hour, A walks twice the distance that B walks in the same period. In 5 hours, A walks 6 miles more than what B walks in 8 hours. How many miles does B walk per hour ?A. 4B. 2C. 3D. 5 |
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Answer» Correct Answer - C (i) From the equations using the given data and solve. (ii) Let speed of A be x mph and speed of B be y mph. (iii) Take `x = 2y and 5x = 6 + 8y`. Solve for y. |
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| 5. |
Find the solution set of `(1)/(x+3) lt 0` |
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Answer» `(1)/(x+3) lt 0` `rArr x + 3 lt 0 rArr x lt -3` `therefore` Solution set `={x//x lt -3}`. |
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| 6. |
If we divide 180 into two parts such that second part is 12 more than the twice of the first part, then the two parts areA. 56, 124B. 54, 126C. 52, 128D. 50, 130 |
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Answer» Correct Answer - A Form the equations as per the conditions given and solve them. |
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| 7. |
For what values of k is the system of equations `3x -2 (k-1)y =30 and 4x -2y = 35` consistent. |
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Answer» Consider the equations `a_1x + b_1y + c_1=0 and a_2x +b_2y +c_2=0`. If this pair of equation is consistent, `(a_1)/(a_2) ne (b_1)/(b_2)`. For the above equations let `a_1 = 3, b_1=-2(k-1), a_2 =4 and b_2 =-2`. Now, `(3)/(4) ne (-2(k-1))/(-2)` `rArr 4(k-1) ne 3 rArr k ne 7//4` For all values of `k`, except `7//4`, the pair of equations is consistent. |
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| 8. |
Solve `4x+3y =11 and 3x +4y =10`. |
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Answer» `4x +3y =11" "`(1) `3x+4y =10" " `(2) Step 1: Adding both the equations, we get `7x+7y = 21` `rArr 7(x+y)= 7xx3` `rArr x +y =3" "` (3) Step 2: Subtracting the equation (2) from the equation (1) `(4x+3y) - (3x+4y)= 11 -10` `rArr x-y =1 " "` (4) Step 3: Adding the equations (3) and (4), we get `(x+y)+ (x-y)= 3+1` `2x =4 rArr x =2` `2+y =3` (from (3)) `y =1` Substituting `y =1` in any of the equations (1), (2), (3) or (4), we get `x =2`. The solution of the pair of equations is `x =2 and y =1`. |
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| 9. |
Machine X can pack 30 articles per hour and machine Y can pack 35 articles per hour. Machine X works for x hours per day and machine Y works for `y` hours per day and both the machines pack at least 2500 articles in a day. Frame and inequation to represent the above data. |
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Answer» Frome data, Machine X can pack 30 x articles in a day. Machine Y can pack 35 y articles in a day. Both machines can pack at least 2500 articles. `rArr 30 x + 35 y ge 2500` is the required inequation. |
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| 10. |
In a fraction, if unity is added to the numerator and subtracted from the denominator, it becomes `(2)/(3)`. Instead, if unity is subtracted from the numerator and added to the denominator, it becomes `(1)/(2)`. Find the fraction. |
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Answer» Let the fraction be `(x)/(y)`, applying the first conditions, we get, `(x +1)/(y-1) = (2)/(3)` `rArr 3x + 3 = 2y -2` `rArr 3x - 2y = -5` (1) Applying the second conditions, we get, `(x-1)/(y +1) = (1)/(2)` `rArr 2x -3 = 2y +1` `rArr 2x - y = 3` (2) By solving the Eqs. (1) and (2) using any of the methods discussed earlier, we get x = 11 and y = 19 `:.` The fraction is `(11)/(19)` |
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| 11. |
The sum of the digits of a two-digit number is 9. If 27 is subtracted from the number, the digits get reversed. Find the number.A. 81B. 72C. 36D. 63 |
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Answer» Correct Answer - D Assume two digit number as `10 x + y` when `x` is in tens place and `y` is in units place. |
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| 12. |
The sum of the digits of a two digit numbers is 9. If 9 is subtracted from the number, the resultant number is equal to the number obtained by reversing the digits of the original number. Find the original number. |
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Answer» Let the number be in the form of `10 x +y` , where x and y are the tens digit and the units digit respectively. Applying the first condition given in the problem, we get `x +y =9 to (1)` Applying the second condition givent the problem, we get `10 x +y -9 = 10 y +x` `rArr x-y =1 to (2)` Solving equations (1) and (2) We get `x = 5 and y =4` `therefore ` The number is 54. |
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| 13. |
Solve the equation `0.35 x - 0.025= 0.32x + 0.023`. |
| Answer» Correct Answer - `x= 16` | |
| 14. |
In a zoo, the total number of rabbits and peacocks is 50 and the total number of their legs is 140. Find the number of rabbits and number of peacocks. |
| Answer» Correct Answer - 20 and 30 | |
| 15. |
If a number is multiplied by 9 and 22 is subtracted from the product and the difference is divided by 5, the result is 2 more than the original number. Then, find the number. |
| Answer» Correct Answer - 8 | |
| 16. |
If `2a + 3b + 4c = 35 and 3a + 5b + 7c = 30`, then `a + b + c =` _____ |
| Answer» Correct Answer - 40 | |
| 17. |
If `a gt b, " then " ac gt bc` for all a, b and `c in R`, where `c gt 0`. (True/False) |
| Answer» Correct Answer - 1 | |
| 18. |
If `a gt b, " then " (a)/(c) lt (b)/(c)` for all a, b and `c in R`, where `c lt 0`. (True /False) |
| Answer» Correct Answer - 1 | |
| 19. |
A true statement which contains the symbol ` lt or gt` is called an _________. |
| Answer» Correct Answer - Inequation | |
| 20. |
The solution set formed by the inequations `x + y ge3, x + y le 4, x le 2` in the first quadrant represents aA. triangleB. parallelogramC. rectangleD. rhombus |
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Answer» Correct Answer - B (i) Draw the graph (ii) Draw the region according to the inequations given, then identify the common region formed by them |
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| 21. |
The intergral solution set of the inequations `x gt -3 and x lt 2` is __________. |
| Answer» Correct Answer - `{-2, -1, 0, 1}` | |
| 22. |
If the boundary line is inclined in the region, then the plane is called _______. |
| Answer» Correct Answer - Closed half plane | |
| 23. |
If `x + y le 7 and x - y le 3`, then `x le 5`. (True/False) |
| Answer» Correct Answer - 1 | |
| 24. |
The point (6, 2) belongs to `x+y le 0`. (True/False) |
| Answer» Correct Answer - False | |
| 25. |
If `x + y le 5`, then either `x le 5 or y le 5` or both (True/False) |
| Answer» Correct Answer - 1 | |
| 26. |
The number of positive integral solutions of he inequation `(x+2)/(x+3) gt 1` is __________.A. 4B. 3C. 0D. infinite |
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Answer» Correct Answer - C (i) `(x+2) /(x+3) -1 gt 0` (ii) Simplify LHS and find the positive integer values of x which satisfy the simplified inequation. |
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| 27. |
Solution set for the inequation `(1)/(x +1) gt 0` is ____ |
| Answer» Correct Answer - `{x//x gt -1}` | |
| 28. |
Solve the inequation `|x+5| gt -2`. |
| Answer» Correct Answer - for all `x in R` | |
| 29. |
Solve `6x - 5 gt 7x + 2`. |
| Answer» Correct Answer - `{x//x lt -7}` | |
| 30. |
The solution set of `6x -2 ge 3` is ______. |
| Answer» Correct Answer - `{x : x ge (5)/(6), x in R}` | |
| 31. |
If `3x - 2y = 12 and 6x + y = 9`, then find the values of x and y |
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Answer» `3x - 2y = 12` (1) `6x + y = 9` (2) Using this method, the two equations are reduced to a single variable equation by substituting the value of one variable, obtained from one equation, in the other equation Step1: Using the first equation, find x in terms of y, i.e., `3x - 2y = 12 rArr 3x = 12 + 2y` `rArr x = (12 + 2y)/(3)` (3) Step2: Substitute the value of x in the second equatio to find the value of y, i.e., `6x + y = 9` `rArr 6((12 + 2y)/(3)) + y = 9` Step 3: Simplify the equation in terms of y and find the value of y `2(12 + 2y) + y = 9` `rArr 24 + 4y + y = 9` `rArr 5y = 9 - 24` `rArr y = -3` Step4 : Substituting the value of y in Eq. (3) we get `x = 2` `:.` The solution for the given pair of equations is (x, y) i.e., `(2, -3)` |
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| 32. |
The total cost of a dozen apples and half a dozen oranges cannot exceed 180. The cost ofeach orange cannot exceed *5. Find the minimum possible cost of each apple. |
| Answer» Frame the inequations and solve them. | |
| 33. |
The total cost of a score of apples and a dozen of oranges is greater than or equal to ₹ 420. The cost of each apple cannot exceed ₹ 15. Find the minimum possible cost of each orange ( in ₹) ( 1 score = 20).A. 9B. 11C. 10D. 12 |
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Answer» Correct Answer - C Let the cost of each apple = ₹ x. Cost of each orange = ₹ `y` `20 x + 12y ge 420 ( therefore `1 score = 20) To get the minimum cost of orange, the apple cost must be maximum, i.e., ₹ 15 `therefore 20xx 15 + 12y ge 420` `12y le 420 - 300` `rArr 12y ge 120` `y ge 10` The minimum possible value is 10. |
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| 34. |
The total cost of 10 erasers and 5 sharpeners is at least Rs 65. The cost of each eraser cannot exceed Rs 4. Find the minimum possible cost of each sharpenerA. Rs6B. Rs 5.50C. Rs 5D. Rs 6.50 |
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Answer» Correct Answer - C Frame the inequatios and proceed |
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| 35. |
Find the value of x, if `2x + 3y + k = 12 and x + 6y + 2k = 18` |
| Answer» Correct Answer - 2 | |
| 36. |
If the cost of 2 pencils and 3 erasers is Rs 14. Wheras the cost of 3 pencils and 5 erasers is Rs 22, then find the cost of one pencil and one eraser |
| Answer» Correct Answer - Rs 6 | |
| 37. |
The length of a rectangle is 5 m more than its breadth and its perimeter is 6 times its breadth. Find the breadth of the rectangle. The following are the steps involved in solving the above problem. Arrange them in sequential order. (A) `x = 5` (b) Breadth be `x m` (C) `2x + 5 = 3x` (D) Length is `(x+5) m` (E) Now, perimeter is `2(x+x+5) = 6x`A. ABCDEB. BDCAEC. BDECAD. DBACE |
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Answer» Correct Answer - C (B), (D), (E), (C) and (A) is the sequential order. |
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| 38. |
If the perimeter of a rectangle is 10 cm and the difference between its length and breadth is 1 cm, then its length is ______ and its breadth is ______. |
| Answer» Correct Answer - 3 cm and 2 cm | |
| 39. |
Rahul is 7 years order than Ramu. The ratio of their ages is `4:3`. Find their ages. |
| Answer» Correct Answer - 28 years, 21 years | |
| 40. |
The number of common solutions for `3x + 2y = 18 and 5x+4y =3` is ______. |
| Answer» Correct Answer - One | |
| 41. |
Solve: `a + 2b =4, 2a +b =9`. |
| Answer» Correct Answer - `a = (14)/(3), b= (-1)/(3)` | |
| 42. |
If `2x -3 =7 -5x`, then x is ______. |
| Answer» Correct Answer - `(10)/(7)` | |
| 43. |
The cost of `3` Maths books and `4` Physics books is `31`, while that of `4` Maths books and `3` Physics books is ` 32.` Find the cost of `5` Maths books and `4` Physics books. |
| Answer» Correct Answer - 41 | |
| 44. |
The sum of two natural numbers is 20. If one numbers is one-fourth of the other, then the numbers are _______. |
| Answer» Correct Answer - 4 and 16 | |
| 45. |
If the cost of two pens and three books is ₹ 69 and that of three pens and two books is ₹ 66. Find the difference in the cost of each book and each pen. ( in ₹)A. 6B. 3C. 0D. None of these |
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Answer» Correct Answer - B Frame two differenct equations and solve. |
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| 46. |
The sum of five consecutive odd natural numbers is 65. Find the sum of the extreme numbers.A. 26B. 30C. 24D. 32 |
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Answer» Correct Answer - A Assume the odd consecutive natural as `2x+1, 2x+3, 2x+5, 2x+7 and 2x+9`. |
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| 47. |
When a number is divided by 7, it is diminished by 36. Then, the number are ________. |
| Answer» Correct Answer - 42 | |
| 48. |
If the sum of two consecutive odd numbers is 36, then the numbers are _______. |
| Answer» Correct Answer - 17 and 19 | |
| 49. |
24 less than five times a number is 26, then the numbers is ______. |
| Answer» Correct Answer - 10 | |
| 50. |
If `(x-3)/(2) gt 0` then the value of x is ________. |
| Answer» Correct Answer - `x gt 3` | |