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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. |
. . Erwhen the price of petrol is increased by 3%, it becomes49.44 per litre. Find theoriginal price of petrol. |
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| 2. |
Rachel, an engineering student, was asked to make a model shaped like a cylindertwo cones attached at its two ends by using a thin aluminium sheet. The diametermodel is 3 crn and its length is 12 cm. Ifeach cone has a height of2 cm, find the vol theof air contained in the model that Rachel made. (Assume the outer and inner dimensof the model to be nearly the same.)2.WiumeSI |
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| 3. |
MATHEMATICS2242 cm is cut out from a square piece of an aluminium sheet ofi. A circle of radius6cm What is the area of the left over aluminium sheet?(Take3.14) |
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| 4. |
If the mth term of an AP is-and nth term isthen show that its (mn)th term is 1.12 |
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| 5. |
28. If the mth term of an A.P. be and nth term beshow that its (mn |
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| 6. |
4.If mth term of an A.P. is and nth term is 1, then show that its (m /n)th term is 1. |
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| 7. |
28. If the mth term of an AP is 7 and nth term is m, then show that its (mn)th term is 1. |
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| 8. |
: If m times the mth term of an A.P. is n times its nth term, show thatthe (m+n)th term of the A.P. is 0. |
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Answer» Let the first term of AP = acommon difference = dWe have to show that (m+n)th term is zero ora + (m+n-1)d = 0 mth term= a + (m-1)dnth term = a + (n-1) d Given thatm{a +(m-1)d} = n{a + (n -1)d}⇒am +m²d -md = an + n²d - nd⇒am - an +m²d - n²d -md + nd = 0⇒a(m-n) + (m²-n²)d-(m-n)d = 0⇒a(m-n) + {(m-n)(m+n)}d -(m-n)d = 0⇒ a(m-n) + {(m-n)(m+n) -(m-n)} d = 0⇒a(m-n) +(m-n)(m+n -1) d = 0⇒ (m-n){a+ (m+n-1)d} = 0⇒a + (m+n -1)d = 0/(m-n)⇒a + (m+n -1)d = 0 |
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| 9. |
people in the group.28. If the mth term of an AP isand nth term isthen show that its (onn)th term is 1. |
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Answer» Given that, mth term=1/n and nth term=1/m.then ,let a and d be the first term and the common difference of the A.P.so a+(m-1)d=1/n...........(1) and a+(n-1)d=1/m...........(2).subtracting equation (1) by (2) we get,md-d-nd+d=1/n-1/m=>d(m-n)=m-n/mn=>d=1/mn. again if we put this value in equation (1) or (2) we get, a=1/mn.then, let A be the mnth term of the APa+(mn-1)d=1/mn+1+(-1/mn)=1 hence proved. hit like if you find it useful |
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| 10. |
A rectangular dissel tanker is 200 cm long, 200 cmwide and 4 cm deep. How much litres of dissel can ithold ?10 |
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| 11. |
If the nth term of a progression is (4n-10) show that it is an AP. Find its(i) first term, (ii) common difference, and (iii) 16th term. |
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| 12. |
4. Are the following statements true!() 39 kg : 36 kg 26 men : 24 men(i) 45 km : 60 km 12 hours : 15 hours(iii) 40 people : 200 people 1000 : 75000(iv) 7.5 litres : 15 litres 15 children : 30 childrenz21ine if the following ratios form a proportio |
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Answer» 39/36=13/12 26/24=13/1245/60=3/4 12/15=4/540/200=1/5 1000/5000=1/57.5/15=1/2 15/30=1/2 |
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| 13. |
10 A businessman buys 200 litres of vegetable oil at the rate of60 per litre. He spends? 2000 onandpackaging and 6000 on transport. He then sells 1-litre packets for 120. Does he make a profit?What is the profit or loss percentage? |
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| 14. |
(x+1)/2 + (y-1)/3 = 8 ; (x-1)/3 + (y+1)/2 = 9 |
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| 15. |
4 A car in a journey requires 6.38 litres of petrol per hour. How many litres ofpetrol will be required for a journey of 7.25 hours? |
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Answer» Total = 6.38*7.25 = 46.225 litres |
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| 16. |
5. Acertain freezing process requires that room temperature be lowered from 40째C at the rate of 5째C every hour Whattemperature 10 hours after the process begins ? |
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Answer» Every hour temperature decrease by 5°c Then in 10 hours temperature will decrease by 10*5 = 50°c Therefore,After 10 hours temperature will be = (40 - 50) = - 10°c |
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| 17. |
cooling machine requires that room temperature to be lowered from 50째C at the rate of 5째Cery hour. What will be the room temperature after 6 hours, after process begins? |
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Answer» Initial Temperature = 40° CRate of change in temperature = 5°C/hourTime = 10 hours So, in 10 hours the temperature would be decreased by 10*5 = 50°C. So, Final Temperature = 40 - 50 =- 10°C |
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| 18. |
\operatorname { lim } _ { x \rightarrow 64 } \frac { x ^ { 1 / 2 } - 8 } { x ^ { 1 / 3 } - 4 } |
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| 19. |
Ifmissing frequency (f1 , f2):frequency5the mean of the following frequency distribution is 65.6, find thewhere fi 50.10-30 30-50 50-70 70-90 90-110 110-130f1 208f2220ht 1d cm is in the form |
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Answer» 10-30. 5. 20. 10030-50. 8. 40. 32050-70. f1. 60. 60f170-90. 20. 80. 1600 90-110. f2. 100. 100f2110-130. 2. 120 240________________________________submission of Fi=35+f1+f2------------(1) submission of fixi=2260+60f1+100f2mean=65.6fixi/fi= 65.62260+60f1+100f2/50 = 65.660f1+100f2=1020divide by 203f1+5f2=51-----------------(2)solving (1) and (2) by eliminationmultiply by 3 in (1)3f1+3f2 =453f1+5f2 =51-2f2=-6f2=3put in (1) f2=3f1=12 |
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| 20. |
A wire of 1m length and 4mm radius is clampedat upper end. The lower end is twisted by anangle of 30°. The angle of shear is9. |
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Answer» The answer is 0.12 degrees. |
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| 21. |
The lower window of a house is at a height of 2 m above the ground and its upper windowis 4 m vertically above the lower window. At certain instant the angles of elevation of aballoon from these windows are 60 and 30° respectively. Find the height of the balloonfrom the ground.30. |
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| 22. |
1312 |
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Answer» (25)^(-2) × (16) ^ (-3/2)5^(-4) × ( 4²)^(-3/2)4^(-3) × 5^(-4)1/625×64=1/ 40,000 |
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| 23. |
Solity12:002) 3253) 13of4) (-2) 13-5) 2.4 x 3.8 x 1.26) (0.05)7) 0.42 + 1.4(0.38)(0.4)9) 131210) 20.799 |
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| 24. |
In the adjoining figure, state whether ( CAB andZ ABD) is a pair of adjacent angles. If not, why ?9. |
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Answer» These are not adjacent angles. Adjacent angles must have a common vertex and a common side. These are alternate angles. |
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| 25. |
6. Is the number (5+ 4)(5-14) rational or irrational?z If x2 = 18, then is x a rational or an irrational number?!8) State whether -1 + 12 lies in the negative or positive side |
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Answer» irrational because x=√18 so it will be irrational |
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| 26. |
If A-(1, 2, 3), B (4, 5, 6, i ni(3, 6)) is a function from A to B2ether f'is one-one or not. IAll Indla 201Find whether the function :Z, defined bLOx)-x+5 vre Z is one-one or not.SHORT ANSWER Type Questions2 Marks/State whether the function f:R R, defined hf(x)デ3-4x is onto or not.L AR- R be defined by f(x) x+1nen, find pre-images of 17and achecktheinjectivityoffhefunction f : R → RATS)given by f(x)-INCERT"(, 3), (3, 5), (4, 7)) a tuncuon: if g isdescribed by g(x)-a.x +B. Then, what valueshould be assigned to α and β? [NCERT ExemplarShow that the function :RVyR, given byη is n ither one-one nor onto. |
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Answer» Injective function is the function , which has different values for every domain and for that f'(x) should be either +ve or -ve here f(x) = x³. => f'(x) = 3x² which is always +ve , so the function is injective. |
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| 27. |
2.Make the greatest and the smallest 8-digit numbers using the digits 2, 0, 4, 9,5,8,7 andRepetition is allowed. |
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Answer» 98754210 is the greatest and10245789 is the smallest smallest 01245789 largest 98754210 |
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| 28. |
Revision of Numerals0. Write the greatest and the smallest three-digit numbers that can be made by usingthe digits:(2) 27,9(6) 4,50(c) 6,2,1 |
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Answer» right answer c 6,2,1. |
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| 29. |
\left| \begin{array} { l l } { x } & { 2 } \\ { 5 } & { 2 } \end{array} \right| = 0 |
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Answer» determinant 2x -10 = 02x = 10x = 5 |
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| 30. |
\left. \begin array l l \text (A) & 0 \\ \text (C) & - 1 \end array \right. |
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| 31. |
3. Form the greatest and smallest 6-digit number using the digit 1, 5, 3, 4, 0 and 8 each-onlyonce. |
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Answer» Greatest-854310Smallest-103458 Greatest =854310Smallest =103458 smallest =103458greatest=854310 |
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| 32. |
9.101 Wilmu ya 15 2,652. Find the sum.5. During every financial year, the value of amachine depreciates by 12%. Find the originalcost of a machine which depreciates by2,640 during the second financial year of itspurchase. |
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Answer» Let say X is the original cost of machine.It depreciates 12% every year, so after completion of 1 year machine cost isX - 0.12X ( 12% of X) = 0.88X and after completion of second year machine cost is0.88X - 0.1056X (12 % of 0.88X) = .7744X .7744X = 2640X = 2640/.7744 = 3409 Rs |
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| 33. |
Q80. Aperson is to go up a tree 60ft in height. In every second, he climbs 5ft but slipsdown 4ft. After how many seconds, will he be able to reach the top of the tree? |
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Answer» Let the total time taken to climb 60 ft be x.Given :-in every second, he climbs 5 feet but slips down 4 feet. ∴5x-4x=60=>x=60 ∴Time taken to climb 60 ft is 60 seconds. |
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| 34. |
1916. If in a mushroom,20is water, what fraction of it is solid matter? |
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Answer» To find this subtract from.totalhence1-19/20=20-19/20=1/20 |
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| 35. |
8. Two trains ofhe same length but with different speeds pass a static pole in 5 seconds and 6 secondsrespectively. In what time will they cross each other when they are moving in the same directio(3) 1 min(4) 60 min(5) of theseis and q seconds |
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Answer» Length of the train = l meter. Speed of the two trains are l/5 and l/6. Total distance = 2l. In same direction Relative speed is (l/5 - l/6). = l/5 - l/6 = l/30. Required Time = Distance/Speed. = 2l/(l/30) = 60 seconds. Shortcut method: Formula = 2(Product of time taken)/Difference of time taken. = 2(6 * 5)/(6 - 5) = 2 * 30 = 60 seconds. |
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| 36. |
Δ ABC ~ Δ PQR, A(A ABC)-80, A(Δ PQR)-245. Complete theactivity to find ABA(A ABC) 80PQ245ABaAB4POPO |
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Answer» please like my answer if you find it useful |
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| 37. |
8. A train runs at 45 km/h. How far does it go in 6 seconds? |
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| 38. |
B-5Find the largest number that divides 245 and 1029 leaving a remainder of 5 in each |
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Answer» First subtract 5 in each case then do hcf H.C.F is the ans. 245-5=2401029-5=1024HCF of 240 and 1024 == 240)1024(4 960 -------------- 64)240(4 240 ------------- ××× -------------- |
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| 39. |
Answver ue Tength of a diagonal of square is 2 (6+245)om Then find its length of side of square |
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| 40. |
1.Find the value of:(a) of 32 kg |
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Answer» 32 kg = 32000g=3/4 x 32000g= 3 x 8000g= 24000g = 24 kg 24 kg is a write answer |
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| 41. |
WUE 10Find the largest number which divides 245 and 1037, leavingremainder 5 in each case.er divides 1245 - 5 = 240 and |
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Answer» the required number is 24 of this sum |
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| 42. |
O = \left( \begin array l \varepsilon \\ x \end array \right) \left( \begin array l l 0 & \varepsilon - \\ z & 1 \end array \right) ( \varepsilon , \tau ) |
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| 43. |
\begin{array} { l } { \text { Which of these is the odd one out? } } \\ { \begin{array} { l l } { \text { (A) } 2012 } & { \text { (B) } 2010 } \\ { \text { (C) } 2008 \quad \text { (D) } 2004 } \end{array} } \end{array} |
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Answer» option (B) is odd one out, because, starting from 2004, at an interval of 4 , we obtained 2004,2008,2012 |
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| 44. |
\left. \begin{array} { l } { 2 / 14 } \\ { 5 / 20 } \end{array} \right. \quad \left. \begin{array} { l } { 3 / 12 } \\ { 7 / 28 } \end{array} \right. |
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Answer» a) 2/14 , kyoki baki sab ka anupat 1/4 |
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| 45. |
3.14x18-19U3312. A chord of a circle of radius 6 cm subtends an angle of60° at the centre. Find the area of the corresponding (i) minorsegment and (ii) major segment (take n 3.14 and 3--1.73 |
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Answer» Like if you find it useful |
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| 46. |
3. Attempt the following:13 marks]. Find the volume of a sphere whose surface area is314cm2. (Take n3.14)Ans. |
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Answer» Surface area=4πr^2314 cm^2 = 4πr^225 cm^2 = r^2r = 5cmVolume = 4/3 π r^3 = 4/3 (3.14)(5)^3 =523.33 cm^3 |
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| 47. |
\begin{array} { l } { \text { following in metres } } \\ { \text { (b) } 8.49 \mathrm { dcm } } \end{array} |
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Answer» dcm= m/0.10000 so 8.49 dcm is equal to 0.849m |
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| 48. |
iv) singlesA cricketer hit 120 runs in 150 balls during a test match . 20% of the runs came ines,30% in 4's, 25% in 2's and the rest in 1's. How many runs did he score in(ii) 4's(iii) 2's(iv) singleshat % of his shots wor |
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| 49. |
PQRS is kite in which <OQR = 15° and <ORS = 40°. Find :.<PSQ |
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| 50. |
(e) 2 of the weight of a boy is 32 kg. What is his weight? |
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