InterviewSolution
Saved Bookmarks
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.
| 51. |
If `x and y in R`, then `xcancel(gt) y` can also be written as ________. |
| Answer» Correct Answer - `x le y` | |
| 52. |
Solve for `x: |2x + 3| lt 2x + 4`A. `x gt -2`B. `x gt -(7)/(4)`C. `x lt -(7)/(4)`D. `x lt -2` |
|
Answer» Correct Answer - B (i) `|x| lt a rArr -a lt x lt a` (ii) `|x + a| = x + a " where " x gt -a and -(x +1)` when `x lt -a` |
|
| 53. |
By adding or subtracting any value to both sides of the inequality, inequality ______. (changes/does not change). |
| Answer» Correct Answer - Does not change | |
| 54. |
For all `x, y and z in R`, if ` x gt y and y gt z`, then `x gt z `. This property is known as __________. |
| Answer» Correct Answer - Transitive property | |
| 55. |
The number of ordered pairs of different prime numbers whose sum is not exceeding 26 and difference between second number and first number cannot be less than 10A. 8B. 9C. 10D. 11 |
|
Answer» Correct Answer - d Write the prime numbers up to 23, find the order pairs such that `x + y le 26 and y - x gt 10` |
|
| 56. |
Solve `|5x - 7| lt -18`. |
| Answer» The modulus of any number has to be 0 or positive. Thus, there are no values of `x` which satisfy the given inequality. The solution set is `varphi`. | |
| 57. |
Solve `|5x -7| lt -18` |
| Answer» The modulus of any number has to be 0 or positive. Thus, there are no values of x which satisfy the given inequality. The solution set is `phi` | |
| 58. |
Solve `|3x +2| ge 7` |
|
Answer» `|3x +2| ge 7` `3x + 2 ge 7 or 3x + 2 le -7` `3x ge 5 or 3x le -9` `x ge (5)/(3) or x le -3` `:.` Solution set is `{x//x ge (5)/(3) or x le -3} or (-oo, -3] uu [(5)/(3), oo)` |
|
| 59. |
Solve `|7 -2x| le 13`A. `3 le x le 10`B. `-3 lt x lt 10`C. `-10 le x le 3`D. `-3 le x le 10` |
|
Answer» Correct Answer - D `|x| le a rArr -a le x le a` |
|
| 60. |
Solve `|2x + 4| ge 14`. |
|
Answer» `2x + 4 ge 14 (or) 2x + 4 le -14` `rArr 2x ge 14 - 4 (or) 2x le -14 - 4` `rArr 2x ge 10 (or) 2x le -18` `rArr x ge 5 (or) x le -9` `therefore` Solution set `={x//x ge 5 or x le -9} (or) (-oo, -9) uu (5, oo)` |
|
| 61. |
Solve `|3x-2| le 5`. |
|
Answer» `|3x -2| le 5` `rArr -5 le 3x -2 le 5` `rArr -5 + 2 le 3x le 5 + 2` (adding 2 throughout the continued inequation) `rArr -3 le 3x le 7` `rArr (-3)/(3) le x le (7)/(3)` (dividing by 3 throughout the contiued inequation) `rArr -1 le x le (7)/(3)` `therefore ` Solution set `={ x //-1le x le (7)/(3)} (or) = [-1, (7)/(3)]`. |
|
| 62. |
Kiranmai pays ₹ 50 to shopkeeper in the denominations of one rupee coins and five rupee coins. She gives a total of 26 coins. Find the number of 5 rupee coins given to the shopkeeper.A. 12B. 6C. 10D. 4 |
|
Answer» Correct Answer - B Frame two simple equations in two variables and solve them. |
|
| 63. |
The system of equations `x+ y = 2, 4x+4y =8` is _________. (inconsistent/consistent) |
|
Answer» Correct Answer - Consistent answer is inconsistent |
|
| 64. |
If `(a_1)/(a_2) = (b_1)/(b_2) ne (c_1)/(c_2)`, then the equations `a_1x + b_1y + c_1 =0 and a_2x + b_2y + c_2=0` are _________. (consistent/inconsistent) |
| Answer» Correct Answer - Inconsistent | |
| 65. |
The least positive integer `x`, which satisfies `|x-2| gt 7` ?A. 9B. 10C. 7D. 5 |
|
Answer» Correct Answer - B Verify from the options. |
|
| 66. |
If `(2x+1)/(x) lt 2`, then what is the range of x ?A. `{x//x gt 2 or x lt 0}`B. `{x// -2 le x le 2}`C. `{x//x ge 2 or x le 2}`D. None of these |
| Answer» Correct Answer - D | |
| 67. |
If `(3)/(x-4) lt 0`, then what is the range of x ?A. `x lt 4`B. `x lt 5`C. `x lt 3`D. `x lt 2` |
|
Answer» Correct Answer - A Denominator must be less than 0. |
|
| 68. |
The least integral value of `x` that satisfies ` 2x + 4 + 3(x-5) gt 7` isA. 3B. 4C. 5D. 6 |
|
Answer» Correct Answer - B Solve the given inequation. |
|
| 69. |
Find the values of `x and y`, which satisfies the simultaneous equations `2006x = 2007y = 8024 and 2007x + 2006y = 8028`.A. `x=4, y =0`B. `x =0, y =4`C. `x=y =4`D. None of these |
|
Answer» Correct Answer - A Verify from the options. |
|
| 70. |
If the ordered pair (p, q) satisfies the simultaneous equations `(a + b)x + (b + c)y + (c + a) = 0` and `(b + c)x + (c +a)y + (a + b) = 0` such that p and q are in the ratio 1:2, then which of the following is correct?A. `a^(2) + 2ac + 3c^(2) = 2b^(2) + 3ab +bc`B. `a^(2) + b^(2) + c^(2)= ab + bc + ca`C. `a^(2) + 3ac + 3c^(2) = 3b^(2) + 3ab + bc`D. `a^(3) + b^(3) + c^(3) = 3 abc` |
|
Answer» Correct Answer - C (i) Apply the method of cross multiplication and get the desired condition. (ii) Two equation have more than one solution, it they represent a single line. (iii) Use, ratio of coefficients of `x `= ratio of coefficients of `y`= ratio of constants and find `a and b`. |
|
| 71. |
The solution set of the inequation `(1)/(5 + 3x) le 0` isA. `x in ((-5)/(3), oo)`B. `x in (-oo, (5)/(3))`C. `x in ((5)/(3), oo)`D. `x in (oo, (-5)/(3))` |
|
Answer» Correct Answer - D Multiple the numerator and denominator with `5 + 3x` and solve the inequator obtained |
|
| 72. |
If the ordered pair satisfying the equations `a_1 x+b_1 y +c_1 and a_2 x + b_2 y +c_2` has 1 as its first coordinate, then which of the following is correct?A. `(a_1+ b_1)/(a_2 + b_2) = (c_1)/(c_2)`B. `(b_1 + c_1)/(b_2 + c_2) = (a_1)/(b_2)`C. `(c_1 + a_1)/(c_2 + a_2) = (b_1)/(b_2)`D. All the above |
|
Answer» Correct Answer - C (i) Solve the given two equations. (ii) Equare x co-ordinate to 1. (iii) Substitute x = 1 in both the equations and solve for y. (iv) Equate the values of y and obtain the required relation. |
|
| 73. |
If `2|x| - |y| = 3 and 4|x| + |y| = 3`, then number of possible ordered pairs of the form (x,y) is |
|
Answer» Correct Answer - A (i) We cannot find a common solution (ii) Solve the two equations for `|x| and |y|` and write the possible values of x and y |
|
| 74. |
If sum of two numbers is 10 whereas their difference is 4, then the greater number is ____ |
| Answer» Correct Answer - 7 | |
| 75. |
The number of possible pairs of successive prime numbers, such that each of them is greater than 40 and their sum is utmost 100, isA. 3B. 2C. 4D. 1 |
|
Answer» Correct Answer - a (i) Write primes as per the given conditions (ii) Assume the prime numbers as x, y (iii) find the possible values of x and y such that `x + y lt 100`, where `x gt y gt 40` |
|
| 76. |
If the line `x+y =5` divides the plane into two half planes, then the region containing the origin is represented by __________. |
| Answer» Correct Answer - `x+y lt 5` | |
| 77. |
In an election the supporters of two candidates A and B were taken to polling booth in two different vehicles, capable of carrying 10 and 15 voters respectively. If at least 90 vehicles were required to carry a total of 1200 voters, then find the maximum number of votes by which the elections couble be won by the Candidate BA. 900B. 600C. 300D. 500 |
|
Answer» Correct Answer - b Find the value of x and y such that `x + y gt 90 and 10x + 15y = 1200` |
|
| 78. |
Three numbers are in the ratio `1:2:3` and their sum is 120. The numbers are __________. |
| Answer» Correct Answer - 20, 40 and 60 | |
| 79. |
Four years ago, age of a person was 4 times that of his son. Six years later, the age of the person will be 10 years less than thrice the age of his son. Find the present ages of the person and his son |
|
Answer» Let the present ages of the person and his son be x years and y years respectively. Given, `x - 4 = 4(y -4)` `rArr x -4 = 4y -16` `rArr x - 4y = -12` (1) And also given, `x + 6 = 3(y + 6) -10` `rArr x +6 = 3y + 8` `rArr x -3y = 2` (2) By solving the Eqs. (1) and (2), we get, `x = 44 and y = 14` |
|
| 80. |
There are some four-wheelers and six-wheelers in a garage. The total number of wheels of these vehicles is 120. The number of four-wheelers is `3//2` times the number of six-wheelers. Find the number of six-wheelers in the garage.A. `20`B. `5`C. `15`D. `10` |
|
Answer» Correct Answer - D Let the number of six-wheelers be x. `therefore `The number of four -wheelers = `(3)/(2) x`. Given `6x + (3)/(2) x xx 4 = 120` `6x + 6x = 120 rArr 12x = 120` `x = 10` `therefore` The number of six wheelers = 10. |
|