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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. |
EIS 1115 usual speeuT48. The difference of squares of two numbers is 88. If the larger number is 5 less than twice thesmaller number then find the numbers. |
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Answer» Let the smallest number be x and largest number be y y²-x²=88....(1)y=2x-5...(2) from(1)(2x-5)²-x²=884x²+25-20x=883x²-20x-63=0(x-9)(3x+7)=0x=9From (2)y=2x-5=2(9)-5=18-5=13 |
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| 2. |
Write the formula of Euclids Division Lemma |
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Answer» According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist unique integersqandrwhich satisfies the conditiona = bq + rwhere 0≤ r ≤ b. |
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| 3. |
11. The ratio of the speeds of a car, a train and a bus is5:9:4. The average speed of the car, the bus andthe train is 72 km/hr. What is the average speed ofthe car and the train together? (Bank P.O., 2010) |
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Answer» Let speed of car = 5xLet speed of train = 9xLet speed of bus = 4x Average speed of car, train and bus = (5x + 9x + 4x)/3= 18x/3 = 6x Then,6x = 72x = 72/6 = 12 Hence,Speed of car = 5*12 = 60 km/hrSpeed of train = 9*12 = 108 km/hrSpeed of bus = 4*12 = 48 km/hr Therefore,Average speed of car and train= (60 + 108)/2= 168/2= 84 km/hr |
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| 4. |
y Name the quantity from below which determinesthe loudness of a sound wave:a) Wavelength (b) Frequency, and (c) Amplitude. |
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Answer» option c amplitude is the answer. The amplitude of asound wave determinesitsloudnessorvolume. A larger amplitude means a loudersound, and a smaller amplitude means a softersound. |
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| 5. |
Find\int \frac{\sin ^{2} x-\cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x |
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| 6. |
\frac{(1+\sin 2 x)+\cos 2 x}{(1+\sin 2 x)-\cos 2 x} |
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| 7. |
\sin ^{2} 6 x-\sin ^{2} 4 x=\sin 2 x \sin 10 x |
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| 8. |
Differentiate(log x* w.r.t.x |
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| 9. |
Differentiate log(1 +x2) with respect to tanx. |
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| 10. |
3 writeote the t and swallat noerence |
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Answer» Greatest number formed by digits 5,3,4,0= 5430 Smallest number formed by digits 5,3,4, 0= 3045 Difference of greatest number and smallest number = 5430 - 3045 = 2385 |
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| 11. |
The ratio of two numbers is 3 8 and theirerence ise smaller number iS |
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Answer» let the two numbers be x & ythe 1st equation is :- x/y=3/82nd equation is :- x-y = 115or , x = 3y/8Now putting the value of x in 2nd equation , we get3y/8 - y = 115on solving we get y = -184putting the value of y in 1st eqn we get x = -69so the greater number is -69 . |
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| 12. |
3. Write three division of integers such that the fractional form of each will be79 |
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Answer» We can do this by getting the multiple of the fraction. 1.) When the multiple is 3-7/9 × 3/3 = -21 / 27 2.) When the multiple is 2-7/9 × (2/2) = -14/18 3.) When the multiple is 4-7/9 × (4/4) = -28/36 Like my answer if you find it useful! thanks |
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| 13. |
Simplification of 2.75 -1.25 +4.75 -3.80 infractional form is :(4) 20.(B) 200 |
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Answer» Option A 2.45 |
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| 14. |
What points on tme aks aThe distance between (6, 2) and (0, x) is 10. Find the value of x.- |
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| 15. |
Drew a pie chart to depict the above data.The data on mode of transport used bystadents to come to school are givenbelow -Mode of transport No. of studentsBusCycleTrainCar12018024080100Drew a pie-chart to depict the given data. |
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Answer» Thanks for your answers |
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| 16. |
s Tme segment joining Af1, 2) and B6. 7),and coordinates of a point P on the 3Find theline s2such that AP AB.CBSE March 2015] |
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Answer» Tu bta bta bhi de ab |
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| 17. |
\int_{0}^{\pi / 4} \log \sin 2 \theta d \theta=-\frac{x}{4} \log |
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| 18. |
\int _ { 0 } ^ { 2 } ( 2 { log } \sin x - { log } \sin 2 x ) d x |
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| 19. |
3. यदि y= logSV1-sin x1+ sin xहै तो सिद्ध कीजिए किdy-= secxdr |
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Answer» -sec2 is the right answer |
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| 20. |
(iii) Differentiate log(sin(9x)) |
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Answer» let Y = log(sin(9x)) dY/dx = (1/sin9x)•cos9x•9 = 9cot9x |
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| 21. |
Solve the differential equation:dy(x + y)--|dr |
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| 22. |
D16.7. In the given AABC, D, E and F are pointson AB, BC and AC respectively such that ADEF is aparallelogram, then prove that CF _ ADFA™ BD[CBSE SP 2011] |
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Answer» Given - ADEF is a parallelogram. To prove- CF/FA = AD/BD Proof-In triangle ABC, FE // AD ........(given) therefore,FE // AB ALSO, CF/FA = CE/EB .................(BY B.P.T) .........(i) now, DE // CF.........(given) therefore, DE // AC also,BE/EC = BD/AD.................(BY B.P.T) or,CE/EB = AD/BD.........(ii) comparing eq..(i) n (ii),,we get: CF/FA = AD/BD hence proved |
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| 23. |
Find dy if y = log(sin x)dli |
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| 24. |
\int _ { 0 } ^ { \frac { \pi } { 4 } } \frac { \sin x \cos x } { \cos ^ { 4 } x + \sin ^ { - 4 } x } d x |
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Answer» 1st part 2nd part 3rd |
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| 25. |
UVUVUDUWhen the repeating decimal 0.363636.... is written in simplest fractional form, find thesump +. |
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Answer» If p/q=0.363636=3636/10000So,p+q=10000+3636=13636 |
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| 26. |
Convert the following repeating decimal numbers into fractions.().23 (ii) 7.67 (iii) .237 (iv) .897 |
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Answer» 1) .23=23.23/100.000; 2) 7.6767=767.6767/100 |
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| 27. |
Laloo lent Baloo 32,500 to purchase.acar at 12.5% per annum. If the interest iscompounded semi-annually find the interestpaid by Baloo after 1 ½ years. |
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Answer» Principal = Rs 32500Rate of interest per annum = 12.5 %Rate of interest per half year = 12.5/2 = 6.25 %Time = 3/2 yearAmount at compound interest = P[1 + r/100]n= 32500[1 + 6.25/100]^2*3/2= 32500[1.0625]³= 32500 x 1.1995= 38,983.75 Compound interest = 38,983.75 - 32500= Rs 6,483.75Interest paid by laloo after 3/2 year = Rs 6,483.75 |
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| 28. |
wd and18. Talan est part of abiy toll of chart paper for making a greeting card andstrip of paper. He used anotherfor making a chart How much paper was |
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| 29. |
area of the chart paper used to make the curved surface of arical kaleidoscope of length 25 cm and radius 3.5 cm. |
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| 30. |
10y, A train 270 m long is running at 80 kmh. How-tme wawiato-platform 130 m long? |
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Answer» Speed of the train = 80 km/hr = 80 x 1000/3600 80 x 5/18 = 200/9 m/secDistance = length of the trian + length of the platform = 130 m + 270 m = 400 m Time = Distance / Speed= 400x9 / 200= 2 x 9= 18 sec. |
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| 31. |
\int _ { 0 } ^ { \frac { \pi } { 4 } } \frac { \operatorname { sin } x \operatorname { cos } x } { \operatorname { cos } ^ { 4 } x + \operatorname { sin } ^ { 4 } x } d x |
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| 32. |
A train 270 m long is running at 80 km/hr. How much time will it take to crossa bridge 130 m long ?6.3 |
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Answer» Speed of the train = 80 km/hr = 80 x 1000/3600 80 x 5/18 = 200/9 m/secDistance = length of the trian + length of the platform = 130 m + 270 m = 400 m Time = Distance / Speed= 400x9 / 200= 2 x 9= 18 sec |
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| 33. |
\int_{0}^{\frac{\pi}{4}} \frac{\sin x \cos x}{\cos ^{4} x+\sin ^{4} x} d x |
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| 34. |
s m long and 3.5 m widest is the depth of the pit?uptis dug to a certain depth.If the volume of carth taken out of it is 14 m'volune of |
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Answer» I can't understand |
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| 35. |
(cos y) then finddydrIf(cos x) |
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| 36. |
Evaluate: sin^2 31°- cos^2 59° |
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Answer» Thanks |
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| 37. |
In how many years a sum of 6400, compoundedquarterly at the rate of 5% pa. will amount to 6561? |
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| 38. |
-dis well-dats SCIIS.What can the maximum number of digits be in the repeating block of digits in thedecimal expansion of 17 ? Perform the division to check your answer. |
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| 39. |
5) Sixty per cent of 120 workers in a factoryare women. Find the number of womenand men. |
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| 40. |
ound interest on? i2800 for 1 year at 7-% per annum.3. Find the amount and the compcompounded semi-annually |
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| 41. |
mpounded nar-yealy.Find the amount and the compound interest on 12800 for 1 year at 72% per annumcompounded semi-annually. |
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| 42. |
Solve.Calculate the interest on ? 2,500 for 1 year at the rate of 10 р.с.р.ld he the interest for one year |
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Answer» SI = P*R*T/100Given P = 2500, R = 10%, T= 1 Then,SI = 2500*10*1/100 = 25*10 = 250 Interest on amount 2500 = Rs 250 |
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| 43. |
0. A train 270 m long is running at 80 km/hr. How much time will it take to cross aplatform 130 m long? |
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Answer» = Total distance traveled by the train = 270+130 = 400 m. = Speed = 80 km/h = 80 * 5/18 = 22.22 m/s. = Speed = distance / time = Time = 400 / 22.22 = 18 seconds. |
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| 44. |
10. A train 270 m long is running at 80 km/hr. How much time will it take to cross aplatform 130 m long? |
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Answer» Speed of the train = 80 km/hr = 80 x 1000/3600 80 x 5/18 = 200/9 m/sec Distance = length of the trian + length of the platform = 130 m + 270 m = 400 mTime = Distance / Speed= 400x9 / 200= 2 x 9= 18 sec |
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| 45. |
Example 3 : Savitri had to make a model of a cylindrical kaleidoscope for her scienceproject. She wanted to use chart paper to make the curved surface of the kaleidoscope(see Fig 13.10). What would be the area of chart paper required by her, if she wanted |
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Answer» Radius of the base of the cylindrical kaleidoscope (r) = 3.5 cm. Height (length) of kaleidoscope (h) = 25 cm. Area of chart paper required = curved surface area of the kaleidoscope = 2πrh =2×22/7×3.5× 25 cm2 = 550 cm^2 |
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| 46. |
dr(4 cos x +3sin x) |
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| 47. |
e* secx (1+ tan x) dr |
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| 48. |
Q.6(COS 6 x + cos 2 x dr |
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| 49. |
In how many years will Rs 20,000 amount to RS 23,000 at 5% pa. simple interest? |
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Answer» Principal = Rs 20000Amount = Rs 23000Rate = 5%Let time be T yrs.S.I. = Amount - PrincipalS.I. = 23000 - 20000 = 3000A to QS.I. = P x R x T/1003000 = 20000x 5 x T / 100T = (3000 x 100) / (20000 x 5)T= 300000/100000T = 3yrs. |
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| 50. |
Example 31 Evaluatesin' x dr |
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Answer» 1-cos2x= 2sin^2x∫1-cos2x/2dx= sin^2x[1/4(x+sin2x)] |
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