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. |
For 20 Student, the mess bill for 12 days is Rs 7000. In how many days will the mess charges to Rs 4900 for 8 students?A. 20 daysB. 21 daysC. 22 daysD. 23 days |
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Answer» Correct Answer - B `(M_(1)D_(1))/(B_(1))=(M_(2)D_(2))/(B_(2))` where `B_(1) and B_(2)` are the mess bills. |
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| 2. |
if (2x+1):(5x-1) is the triplicate ratio of 3:4, then find the value of x. the following are the steps involved in solving the above problem. Arrange them in sequential order. (A) `(2x+1):(5x-1)=3^(3):4^(3)` (B) `135x-27=128x+64` (C) `27(5x-1)=64(2x+1)` (D) `7x=91impliesx+(91)/(7)=13`A. ACBDB. ABCDC. BCADD. CABD |
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Answer» Correct Answer - A (A),(C),(B) and (D) is the required sequential order. |
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| 3. |
In a bag, the numbers of Re 1 coins, 50 paise coins and 25 paise coins are in the ratio 3:2:4. the total value of the coins in it is Rs 50. Find the number of 50 paise coins in it.A. 10B. 20C. 30D. 40 |
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Answer» Correct Answer - B Let the number of Rs 1 coins be 3x. Number of 50 paise coins and 25 paise coins are 2x an 4x respectively. total value of coins `=(100)(3x)+(50)(2x)` `+(25)(4x)=500x=(50)(100)` paise `x=10` Required number of coins `=2x=20` |
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| 4. |
Given that a varies directly with the cube of b. When a is 3,b is also 3. find b when a is 24. |
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Answer» Since a varies directly with cube of b, then `a=kb^(3)` Given that, a=3,b=3 `3=k(3)^(3)` `k=3//27=1//9` Now, `a=kb^(3)` `implies24=1//9b^(3)` `b^(3)=24xx9` `b^(3)=216` `thereforeb=6`. |
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| 5. |
Raja divided 35 sweets among his daughters Rani and Sita in the ratio 4:3. How many sweets did Rani get?A. 16B. 24C. 28D. 20 |
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Answer» Correct Answer - D Number of sweets that Rani got ltBrgt `=(4)/(7)(35)=20`. |
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| 6. |
The flow of current through a resistor varies directly with the voltage (V) across it. When voltage across the resistor is 30 volts, the flow of current through it is 5A. What is the flow of current when the voltage across it is 60 volts?A. 10AB. 2.5AC. 5AD. 20A |
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Answer» Correct Answer - A (i) Use the direct variation concept ltBrgt (ii) Given, I is directly proportional to V. `implies(I_(1))/(I_(2))=(V_(1))/(V_(2))` |
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| 7. |
Frequency of vibration of a wire varies inversely with its length. The frequency is 220 Hz when the length of the wire is 120m. Find the frequency of the wire when its length is 100 m.A. 261B. 262C. 280D. 264 |
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Answer» Correct Answer - D (i) Use inverse variation concept. (ii) given, F is inversely proportional to l. `implies(F_(1))/(F_(2))=(l_(2))/(l_(1))` |
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| 8. |
A diamond worth Rs 640000 breaks into two pices whose weights are in the ratio 5:3. if the value of the diamond varies directly with square of its weight, then find loss incurred due to breakage (in Rs).A. 320000B. 300000C. 360000D. none of these |
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Answer» Correct Answer - B (i) diamond is of 8 parts. `therefore64x^(2)=640000` (ii) `(25x^(2)+9x^(2))=34x^(2)` is the value of diamond, when it is broken into the parts whose weights are in the ratio of 5:3 (iiI) Loss incurred `=64x^(2)-34x^(2)=30x^(2)` |
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| 9. |
If `x=(4sqrt(2))/(sqrt(2)+1)`, then find the value of `(x+2)/(x-2)-(x+2sqrt(2))/(x-2sqrt(2))`.A. 2B. `12+8sqrt(2)`C. `12-8sqrt(2)`D. `-2` |
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Answer» Correct Answer - B (i) Find `(x)/(2) and (x)/(2sqrt(2))` from the given data and then apply componendo-dividendo rule in both cases. (ii) Add the result obtained in the abvoe cases. |
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| 10. |
if `p=(8ab)/(a+b)`, then find the value of `((p+4a)/(p-4a)+(p+4b)/(p-4b))`.A. 4B. 2C. 1D. 3 |
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Answer» Correct Answer - B (i) Find `(P)/(4a) and (P)/(4b)` from the given data. (ii) Apply componendo-dividendo rule in both the cases. (iii) Then add the obtained equations. |
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| 11. |
if `x:y=3:2` then find `(2x+y)/(4x-3y)` |
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Answer» `(x)/(y)=(3)/(2)impliesx=(3y)/(2)` `(2x+y)/(4x-2y)=(2((3y)/(2))+y)/(4((3y)/(2))-3y)implies(3y+y)/(6y-3y)=(4y)/(3y)=(4)/(3)`. |
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| 12. |
The present ages of Aruna and Karuna are in the ratio 6:5. if the difference between their ages is 5 years, then what will be the sum of their ages after 20 years? (in years)A. 75B. 60C. 95D. 100 |
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Answer» Correct Answer - C (i) let the present ages of Aruna and Karuna be 6x annd 5x in years. (ii) Given, `(6x-5x)=5` then find 6x and 5x. |
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| 13. |
A question paper consist of questions, each carrying `(1)/(2)` mark, 1 mark and 2 marks ini the ratio 2:2:1. if the maximum mark in the exam is 100, then find the number of questions of each type. |
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Answer» Ratio of marks allotted for each type of question `=(1)/(2)xx2:1xx2:2xx1=1:2:2` Sum of the ters of the ratio is 1+2+2, i.e., 5 Given total marks in the paper=100 `implies` Marks allotted for `(1)/(2)` mark questions `=100xx(1)/(5)=20` `implies`Marks allotted for 1 mark questions`=100xx(2)/(5)=40` `implies`Marks allotted for 2 mark questions `=100xx(2)/(5)=40` `therefore` Number of `(1)/(2)` mark questions `=(20)/(((1)/(2)))=2xx20=40` Number of 1 mark questions `=(40)/(1)=40` Number of 2 mark question`=(40)/(2)=20` |
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| 14. |
Ther atio of marks obtained by Rajesh, rakesh annd Ramesh in an exam is 2:4:9. find the marks obtained by Rakesh and Ramesh, if Rajesh scored30 marks in the exam. |
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Answer» Let us assume that the marks secured by Rajesh, Rakesh and Ramesh to be 2x,4x and 9x respectively. Given that Rajesh scored 230 marks in the exam. `implies2x=30` `impliesx=15` marks scored by Rakesh `=4x=60` Marks scored by Ramesh`=9x=135` |
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| 15. |
A mixture contains milk and water in the atio of 5:6. on adding 8 litres of water, the ratio of milk and water becomes 1:2. find the quantity of the milk in the mixture. (in litres)A. 12B. 10C. 14D. 8 |
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Answer» Correct Answer - B (i) Form the linear equation from the given data (ii) Let the quantity of milk and water in the mixture be 5x and 6x. (iii) On adding 8 litres of water, they will become 5x and 6x+8. (iv) Given 5x:(6x+8)=1:2 |
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| 16. |
if `(2a+3b+4c+5d)/(2a-3b-4c-5d)=(2a-3b+4c-5d)/(2a-3b-4c+5d)`, then show that a,3b,2c and 5d are in proportion. |
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Answer» Given, `(a+3b+4c+5d)/(2a+3b-4c-5d)=(2a-3b+4c+5d)/(2a-3b-4c+5d)` `implies((2a+3b)+(4c+5d))/((2a+3b)-(4c+5d))=((2a-3b)+(4c-5d))/((2a-3b)-(4c-5d))` `implies(2a+3b)/(4c+5d)=(2a-3b)/(4c-5d)implies(2a+3b)/(2a-3b)=(4c+5d)/(4c-5d)` Using componendo and dividendo rule, `((2a+3b)+(2a-3b))/((2a+3b)-(2a-3b))=((4c+5d)+(4c-5d))/((4c+5d)-(4c-5d))` `implies(4a)/(6b)=(8c)/(10d)implies(a)/(3b)=(2c)/(5d)` `thereforea:3b: :2c:5d` So, a,3b, 2c and 5d are in proportion |
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| 17. |
Express 75:87 in its simplest form. |
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Answer» The HCF of 75 ad 87 is 3 We divide each term by 3 Then, 75:87`=(75)/(3):(87)/(3)=25:29` `therefore` the ratio 75:87 in its simplest form is 25:29. |
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| 18. |
Compare the ratios 3:4 and 17:24 |
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Answer» `3:4=(3)/(4)=0.75` `17:24=(17)/(24)=0.708` As, `0.708 lt 0.75implies17:24 lt 3:4` |
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| 19. |
Divide Rs 360 in the ratio 4:5 |
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Answer» Sum of the terms of the ratio=4+5=9. First part=`Rs(360xx(4)/(9))=Rs160` Second part`=Rs(360xx(5)/(9))=Rs200`. |
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| 20. |
If A:B=2:3 and B:C=4:17, then find A:B:C |
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Answer» Given `A+B=2:3 and B:C=4:17` Now multiply each ter of the ratio 4:17 by `(3)/(4)` to make its first ter equal to 3. `impliesB:C=3xx(3)/(4):17xx(3)/(4)=3:(51)/(4)` `thereforeA:B:C=2:3:(51)/(4)=8:12:51` |
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| 21. |
if A=2B and B=3C, then find A:C. |
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Answer» Given A=2B and B=3C A=2B=2(3C)=6C `impliesA=6C` `implies(A)/(C)=(6)/(1)impliesA+C=6:1` |
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| 22. |
If `x:y:z=3:3:5 and x^(3)+y^(3)+z^(3)=1728`, then find `(x-y+z)` |
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Answer» let x=3a, y=4a and z=5a Given `x^(3)+y^(3)+z^(3)=1728` `(3a)^(3)+(4a)^(3)+(5a)^(3)=1728` `216a^(3)=1728` `a^(3)=8` `a=2` `x-y+z=3a-4a+5a` `=4a=4(2)=8`. |
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| 23. |
If `(3a+5b):(3a-5b): :(3c+5d):(3c-5d)`, then show that a,b,c and d are in proportion. |
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Answer» Given `(3a+5b)/(3a-5b)=(3c+5d)/(3c-5d)` ltbRgt Using componendo and dividendo rule `implies((3a+5b)+(3a-5b))/((3a+5b)-(3a-5b))=((3c+5d)+(3c-5d))/((3c+5d)-(3c-5d))` `implies(6a)/(10b)=(6c)/(10d)implies(a)/(b)=(c)/(d)` `thereforea,b,c and d` are in proportion. |
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| 24. |
If `9:12(2)/(3)=81:(x+2)` ,then what is the value of x?A. 112B. 102C. 108D. 120 |
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Answer» Correct Answer - A (i) Convert `12(2)/(3)` into simple fraction. (ii) Apply (product of extremes)=(product of means) and find x. |
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| 25. |
Determine the fourth proportional to the numbers 5,6 and 8. |
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Answer» let us assume that x is the fourth proportional to 5,6 and 8. `implies5:6::8:x` product of means=Product of extremes `implies5xx x=6xx8impliesx=(48)/(5)=9.6` `therefore` The fourth proportional to 5,6 and 8 is 9.6. |
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| 26. |
If x:y=3:7, then find (7x+3y):(9x-3y)A. `7:1`B. `1:7`C. `7:3`D. `3:7` |
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Answer» Correct Answer - A (i) Divide numerator and denominator by y and then substitute the value of x/y. (ii) `x=(3y)/(7)` (iii) Substitute the value of x in the requried ratio. |
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| 27. |
if `x=(a-b)/(a+b+c+d)=(b-c)/(a+b+c+d)=(c-d)/(a+b+c+d)` `=(d-a)/(a+b+c+d)`, then find `x^(3)`.A. 1B. 8C. 0D. 27 |
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Answer» Correct Answer - C If `a=(p)/(q)=(r)/(s)=(t)/(u)`, then a `=(p+r+t)/(q+s+u)` Apply the sae in the problem. |
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| 28. |
If `(x)/(2),(7)/(x),(3x)/(2) and (7)/(3)` are in proportion, then the value of x is ______A. 3B. 6C. 9D. 10 |
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Answer» Correct Answer - C Apply "product of means=Producot of extremes" |
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| 29. |
Which of the following will result in 10,20,x and 40 being in proportion?A. Add one to 10B. Add one to 20C. Add one to 19D. Add one to 40 |
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Answer» Correct Answer - C Verify from the options one by one. |
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| 30. |
Verify whether 2,3,4 and 6 are in proportion |
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Answer» Ratio between 2 and 3=2:3 Ratio between 4 and 6=4:6=`(4)/(6)=(2)/(3)=2:3` `implies2:3=4:6` or `2:3::4:6` hence, the values 2,3,4 and 6 are in proportion. |
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| 31. |
Runs scored by Ramu an Raju are in the ratio 4:5. Runs scored by Raju and Ramesh are in the ratio 3:2. How many runs did Raju score, if Ramesh scored 120 runs less than that of Ramu?A. 800B. 850C. 900D. 950 |
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Answer» Correct Answer - C (i) Find the ratio of runs scored by Ramu, Raju and Ramesh and then find their scores in terms of one variable. ltBrgt (ii) Difference between runs scored by Ramu and Ramesh is 120. |
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| 32. |
the incomes of Rajesh and Mahesh are in the ratio 7:9 and their savings are in the ratio 5:7. what is the ratio of their expenditures in the same order, if Mahesh saves two third of his income? |
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Answer» 9a) the ratio of their expenditures is to be calculated. (b) Let the incomes of Rajesh and Mahesh be 7x and 9x, and their savings be 5y and 7y. (c) Given `7y=(2)/(3)(9x)` find `(x)/(y)` (d) Ratio of their expenditures`=(7x-5y):(9x-7y)` `=[7((x)/(y))-5]:[9((x)/(y))-y]` |
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| 33. |
If `(x)/(a)=(y)/(b)=(z)/(c)`, then prove that each ratio is equal to `((3x^(3)-11y^(3)+13z^(3))/(3a^(3)-11b^(3)+13c^(3)))^((1)/(3))` |
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Answer» Lwet `(x)/(a)=(y)/(b)=(z)/(c)=k` `impliesx=ak,y=bk and z=ck` `therefore((3x^(3)-11y^(3)+13z^(3))/(3a^(3)-11b^(3)+13c^(3)))^((1)/(3))=((3(ak)^(3)-11(bk)^(3)+13(ck)^(3))/(3a^(3)-11b^(3)+13c^(3)))^((1)/(3))=((k^(3)(3a^(3)-11b^(3)+13c^(3)))/((3a^(3)-11b^(3)+13c^(3))))^((1)/(3))=k` Hence, proved. |
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