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. |
A well with 10m inside diameter is dug 14m deep. Earth taken out of it is spread all around it tomake an embankment like a hollow cylinder of height 4m. What is the width of the embankment:(a) 5m2(b) 4m(c) 4.3m(d) 6m |
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Answer» Radius of well = 5 mdepth = 14 mvolume of earth taken out =πr² h =π×(5)²×14= 1100 m³now, it is spread to form embankment, which is in the form of hollow cylinder,inner radius, r= 5 mouter radius = 5 +5 = 10 mheight= hthen, 1100 =π×h(10²- 5²)⇒h = 350/75 = 14/3 = 4.67 m |
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| 2. |
26 A wall of length 10m has to be built across an open groundThe height of the wall is 4m and thickness of wall is 24cm. Ifthis wall is to be built up with bricks whose dimensions are24cmx10cmx8cm, how many brick would required? |
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| 3. |
3xf4r-5) + 3 and find its values for Gas Giaata+a+l)+5 and find its value for 0-.ptp-g).qtg-r) andr(r-p2r-1-y) and 2y C-y-x)31-4m+5 n) from 41C 10m-3+2За (a + b+c)--2b(a-b+ c)from 4c (-a+b |
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Answer» A={5,6} B={4,5,6} C={5,6,7} எனில் A×A={(B×B) வெட்டு (C×C)} என்பதை சரிபார்க்க? |
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| 4. |
5. How is adiabatic process diffĂŠreht6. Explain, why a cricketer moves his hand back while holding a catch?the relatign between linear speed and angular speed.wbich one has a great |
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Answer» While catching a fast moving cricket ball , a fielder in the ground gradually pulls his hand backwards with the moving ball, In doing so, the fielder increases the time during which the high velocity of the moving ball descrease to zero. Thus, the accleration of the ball is descreased and therefore the impact of catching the fast moving ball is also reduced. If the ball stopped suddenly then it's high velocity is descreases to zero in a very short interval of time. Thus, the rate of change of momentum of the ball will be large. Therefore, a large force would have to be applied for holding the catch that may hurt the palm of the fielder. Please hit the like button if this helped you. |
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| 5. |
Water in a cylindrical tank of diameter 4m and height 10mcylindrical pipe of diameter 10 cm at the rate of 2.5 Km/hr. Hoto empty the half of the tank? Assume that the tank is full of water to begin withis released throughaw much time will t take |
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Answer» Diameter of the cylindrical tank = 4 m radius of the cylindrical tank = 2 m height of the tank = 10 m Diameter of the cylindrical pipe = 10 cm radius of the cylindrical pipe = 10/2 = 5 cm = 5/100 m speed of water = 2.5 km/hr 1000 m = 1 km = 2.5 x 1000 = 2500 m/hr Volume of water discharged from the cylindrical pipe = (1/2) Volume of cylindrical tank Area of cross sectionxtimexspeed = (1/2)Πr² h Πr²xtimexspeed = (1/2)Πr² h (5/100)²xtimex2500 = (1/2)(2)² (10) (5/100)x(5/100)xtimex2500 = (1/2)x(2)x2x(10) Time =2x10x(100/5)x(100/5)x(1/2500) Time =80/25 = 3.2 hour 1 hour = 60 minute = 192 minute = 180 + 12 3 hour and 12 minute Therefore time taken to empty the half of the tank is 3 hour and 12 minute |
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| 6. |
What should be divided byto get -11 |
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Answer» 6/11÷x= 3/56/11× 1/x = 3/530/33= X10/11= x |
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| 7. |
what rational number should be subtracted from -3/4 to get -11/14 |
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Answer» Let the number be x.-3/4 - x = - 11/14That is x = 11/14 - 3/4 find Lcm and find ans :) |
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| 8. |
11. What11. What should be added to 7% to get 18 |
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Answer» the answer is 10 a whole number 2 by 5 |
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| 9. |
40x-18=36 |
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Answer» 40x - 18 = 3640x = 36 + 1840x = 54x = 54/40x = 27/20 ye hi mera answer hai |
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| 10. |
consecutive numbeĺin APJs 3Q and |
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Answer» Let the four consecutive numbers in AP be; (a - 3d), (a - d), (a + d) and (a + 3d) So, according to the question a - 3d + a - d + a + d + a + 3d = 32 4a = 32 a = 8 Now, (a - 3d)(a + 3d) / (a - d)(a + d) = 7/15 15(a² - 9d²) = 7(a² - d²) 15a² - 135d² = 7a² - 7d² 8a² = 128d² Putting the value of a = 8, we get d² = 4 d = ±2 So, the four consecutive numbers are 2, 6, 10, 14 or 14, 10, 6, 2 yes it is right |
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| 11. |
3(ii) (5p - 3q) |
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| 12. |
Prove that\frac{\sec 8 \alpha-1}{\sec 4 \alpha-1}=\frac{\tan 8 \alpha}{\tan 2 \alpha} |
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Answer» LHS(sec8θ-1)/(sec4θ-1)=(1/cos8θ-1)/(1/cos4θ-1)=[(1-cos8θ)/cos8θ]/[(1-cos4θ)/cos4θ]=(2sin²4θ/cos8θ)/(2sin²2θ/cos4θ) [∵, 1-cos2θ=2sin²θ]=2(2sin2θcos2θ)²/cos8θ×cos4θ/2sin²2θ=4cos²2θcos4θ/cos8θRHStan8θ/tan2θ=(sin8θ/cos8θ)/(sin2θ/cos2θ)=2sin4θcos4θ/cos8θ×cos2θ/sin2θ=2.2sin2θcos2θcos4θ/cos8θ×cos2θ/sin2θ=4cos²2θcos4θ/cos8θ∴, LHS=RHS(Proved) I took theta on the place of alpha don't worry about that |
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| 13. |
-$-16(2p -3q)* - 42p-39)ÂŁ |
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| 14. |
\frac { \sec 8 \theta - 1 } { \ sin 4\theta - 1 } = \frac { \tan 8 \theta } { \tan 20 } |
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Answer» (sec8θ-1)/(sec4θ-1)=(1/cos8θ-1)/(1/cos4θ-1)=[(1-cos8θ)/cos8θ]/[(1-cos4θ)/cos4θ]=(2sin²4θ/cos8θ)/(2sin²2θ/cos4θ) [∵, 1-cos2θ=2sin²θ]=2(2sin2θcos2θ)²/cos8θ×cos4θ/2sin²2θ=4cos²2θcos4θ/cos8θRHStan8θ/tan2θ=(sin8θ/cos8θ)/(sin2θ/cos2θ)=2sin4θcos4θ/cos8θ×cos2θ/sin2θ=2.2sin2θcos2θcos4θ/cos8θ×cos2θ/sin2θ=4cos²2θcos4θ/cos8θ∴, LHS=RHS(Proved) |
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| 15. |
So, the height ofand the distance between the two buildings is alsoEsample 7: From a pothe inint on a bridge across a river, the angles of depression ofy. If the bridgehetankson poste sdes of the river are 30 and 45p, respectively. If theis at a height of 3 m from the banks, find the width of the river. |
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| 16. |
) x+T+40x- 3) |
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Answer» hello game hacker how are you |
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| 17. |
gUimplify & state which of the following are irrational:40x/200 |
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| 18. |
11.What should be added toto get? |
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Answer» think so ,should be added XX+7/15=9/5X =9/5-7/15 =27-7/15 =20/15 =4/3 is answer |
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| 19. |
if the polynomial x4-6x3 + 16x2-25a + 10 is divided by (x2-2p + k) thereminder comes out to be a + a, find k and a. |
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Answer» 2k= 10 k = 5 a= -5 |
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| 20. |
8. By what number should-11be divided to get? |
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| 21. |
MATHEMATICS -VIlling 4. In Figure given below, HELP is a rectangleIts diagonals meet at O. Find 'y if OH -2y-9and OF-y+1 |
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Answer» since diagonals are equal in the rectangle , so their bisected parts are also equal => 2y-9 = y+1=> y = 1+9= 10 so, the value of y = 10. |
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| 22. |
uestion numbers 1 to 6 carry 1 mark each.ind the common difference of the A.P.nd the common |
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Answer» For AP1/2q, (1-2q)/2q, (1-4q)/2q,... Common difference= (1-2q)/2q - 1/2q= (1-2q - 1)/2q= - 2q/2q= - 1 Therefore for given AP common difference = - 1 |
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| 23. |
A bridge across a river makes an angle of 45°with the river bank. If the length of the bridgeacross the river is 200 metres, what is the breadthof the river? |
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| 24. |
A bridge across a river makes an angle of 45with the river bank. If the length of the bridgeacross the river is 200 metres, what is the breadthof the river? |
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Answer» Thanx |
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| 25. |
1 1-p 1-2pFind the common difference of the AP |
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Answer» Common difference of an AP= Difference of two consecutive terms i.e. second term-first term= ((1-p)/p)-1/p=(1-p-1)/p=-p/p=-1 |
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| 26. |
(1 + tan9) (1+ tan 36)(1 + tan 8) (1+tan 37)1) 12) 24) 43) 312n then the common diferer |
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Answer» tq |
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| 27. |
12. Find the common difference of the A.P.1 1-6q 1-12q3q 3q 3[CBSE 2013] |
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Answer» Comman ratio will be= ( next term- previous term)1-6q/3q-(1/3q)= -2Please like the solution 👍 ✔️ |
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| 28. |
A Bridge across a river makes an angle of45 with the river bank. If length of thebridge across the river is 150m, the widthof the river is.a. 107.05mb. 106.05mc. 100md. 102.05m |
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| 29. |
EXERCISEUsing appropriate properties f(i)--3x-+--5x6Write the additive inverse of everify that-(-x) = x for. |
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| 30. |
Find the multiplicative identity of the number which is obtained by dividing additiveinverse of 5 by 1.9. |
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| 31. |
16x2 + 40x + 25 |
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Answer» _40 +/- √40×40_ 4×16×25/2×16 We need to select one pair from the top list and one pair from the bottom list. It is usually smart to start with the pairs that have two numbers close in value. So let's try(5,5)with(4,4). (4x+5)(4x+5)=16x²+20x+20x+25 =16x²+40x+25 This one worked! Hence, the factored form is: (4x+5)(4x+5)=(4x+5)² Solving: (4x+5)²=0 4x+5=0 4x=−5 x=−5/4 so both are correct answer s |
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| 32. |
The rainwater from a roof 22 m x 2 m drain into a conical vese having diamter of hase2 m & and height 3.5 m. If the vessel is just full, then find the rainfall. |
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Answer» We know that volume of roof is equal to volume of Cylindrical tankl × b × h = π r^2 h22×2×h = π(1)^2 × 3.5h = 1/0.25mor h = 4m |
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| 33. |
hal kijiye 3×3×=55 |
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Answer» Ans : 3 ×3 × x = 55 : 9x = 55 : x = 55/9 : x =6.11 |
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| 34. |
1016x2-32 |
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| 35. |
ulalIniagrilindi shor hal |
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| 36. |
Answer the questions(1) When a number is divided by 8, it gives a remainder of 3. What vill be the temainder it the squareof that number is divided by 8? |
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Answer» thanks very much you are such a genius |
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| 37. |
8. By what number should 33 be divided to get 11,8 |
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Answer» -11/2÷ -33/8-11/2 × -8/334/3 |
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| 38. |
नोर दवाई याज़ा में कया HAL E9 |
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Answer» भारत में सबसे ज्यादा उपयोग की जाने वाली यात्रा रेल यात्रा है क्योंकि यह सस्ती है तथा सुखम् है रेल यात्रा में रेल यात्रा में रेल पटरी पर दौड़ती है क्योंकि लोहे से बनी होती है जबकि हवाई यात्रा में हवाई जहाज हवा में उड़ान भरता है रेल यात्री बहुत अधिक मात्रा में यात्रा कर सकते हैं जबकि हवाई यात्रा में ऐसा संभव नहीं है भारत में मध्यम वर्गीय परिवार ज्यादातर रेल यात्रा करते हैं रेल यात्रा सुगम तथा सरल होती है |
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| 39. |
8 divided by 4144 |
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Answer» 8/4144=0.00193 is the answer |
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| 40. |
Constšuct a Suase twhich hal a dliagonal measuoing |
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Answer» We know that diagonal of square =√2×sideSo;√2×side= 7 cm⇒Side=7√2=7√2×√2/√2=7/2√2=3.5×1.41= 4.935 cm≈5 cmSo, each side of square is 4.935 cm and each angle is of 90 degree.Now we construct a square of diagonal 7 cm and each side of 5 cmSTEP I : Draw a line segment PQ = 5 cm.STEP II: Take Q as a point and draw a line segment QR = 5 cm such that∠PQR=90°STEP III: Take R as a point and draw a line segment RS = 5 cm such that∠QRS=90°STEP III: Join SP. and PR. This forms a square PQRS having diagonal PR = 7 cm and each side of 5 cm. |
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| 41. |
Agc and AcrsmesY at atoove hal |
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| 42. |
(h) Find the sum of the additive inverse and multiplicative inverse of 9. |
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Answer» additive inverse of 9 is -9 multiplicative inverse of 9 is 1/9 |
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| 43. |
(iv) Additive inverse of an integer 8 is (-8) and additive inverse of (-8) is 8.Catebeth |
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Answer» Yes its rightadditive inverseof 8 is -8 as8-8= 0thanks |
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| 44. |
Find the multiplicative identity of the number which is obtained by dividing additiveinverse of - 5 by 1.9., its additive inverse. [HOTS |
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| 45. |
3. Find the additive Inversee Inverse of:(1) -83 |
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Answer» 83 is the additive inverse |
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| 46. |
16 x ^ { 5 } - 144 x ^ { 3 } |
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| 47. |
Find the sum of additive inverse and multiplicative inverse of 9 |
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Answer» additive inverse of 9 is -9 multiplicative inverse of 9 is 1/9 |
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| 48. |
2x + 3y = 44x -3y =9 |
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| 49. |
The sum of the additive inverse andmultiplicative inverse of is |
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Answer» additive inverse of 1/5 is -1/5so1/5 + (-1/5) = 0 its incorrect multiplicative inverse is 5/1 ya can you solve again |
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| 50. |
2X+3Y=44X-3Y=9 |
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Answer» 2x + 3y = 4 .....(1)4x - 3y = 9 .......(2) Eliminating y by adding (1) and (2)6x = 13x = 13/6 3y = 4 - 2x3y = 4 - 2 × 13/6 3y = 4 -13/33y = (12-13)/33y = -1/3y = -1/9 |
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