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.
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14) A cylindrical can, whose base is horizontal andsufficient water soof radius 3-5 cm, containsthat when a sphere is placed in the can, thewater just covers the sphere. Given that thesphere just fits into the can, calculat(i) the total surface area of the can in contactwith water when the sphere is in it;(ii) the depth of water in the can before thesphere was put into the can. |
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Answer» In the cylinderof radius R, the sphere just fits. So its radius is R. Volume of of cylinder up to the height 2R in the cylinder =πR² * 2R = 2π R³Volume of sphere = 4πR³/3 Volume of water in the gap between cylinder and sphere = 2πR³-4πR³/3 = 2πR³ /3 2) Depth of water in the can before sphere is put inside it = volume of water/area of cross section of can = (2π R³ / 3 )/π R² = 2 R/3 = 2 * 3.5 /3 = 7/3 cm 1) Surface area surface area of can in contact with water = flat surface + curved surface =πR² + 2π R * 2 R = 5π R² = 5 * 22/7 * 3.5² cm² = 110 /7 * (7/2)² cm² = 385 / 2 cm² |
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| 2. |
107.+limn->00II 1+-(r=1(B) |
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Answer» D) is right correct answer |
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fly 137269owing numbers, replace by the smallest number to make it divisible by 3:( 90135111. In each of the following numbers, replace by the smal(in 8-711H) 27.4tu) 5346ivil 6-1054fiv) 62-35iv) 234.17mhar to make it divisible by 9:w |
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Answer» thanks sir (i) 2724Here, 2 + 7 + * + 4 = 13 + * should be a multiple of 3.To be divisible by 3, the least value of * should be 2, i.e., 13 + 2 = 15, which is a multiple of 3.∴ * = 2 (ii) 53046Here,5 + 3 + * + 4 + 6 = 18 + * should be a multiple of 3.As 18 is divisible by 3, the least value of * should be 0, i.e., 18 + 0 = 18.∴ * = 0 (iii) 81711Here, 8+ * + 7 + 1 + 1 = 17 + * should be a multiple of 3.To be divisible by 3, the least value of * should be 1, i.e., 17 + 1 = 18 , which is a multiple of 3.∴ * = 1 (iv) 62235Here, 6 + 2 + * + 3 + 5 = 16 + * should be a multiple of 3.To be divisible by 3, the least value of * should be 2, i.e., 16 + 2 = 18, which is a multiple of 3.∴ * = 2(v) 234117Here, 2+ 3 +4 + * + 1 + 7 = 17 + * should be a multiple of 3.To be divisible by 3, the least value of * should be 1, i.e., 17 + 1 = 18, which is a multiple of 3.∴ * =1 (vi) 621054Here, 6 + * +1 + 0 + 5 + 4 = 16 + * should be a multiple of 3.To be divisible by 3, the least value of * should be 2, i.e., 16 + 2 = 18, which is a multiple of 3.∴ * =2 |
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| 4. |
3. Find the equation of the parabola itf(i) the focus is at (-6, -6) and the vertex is at (-2, 2).(ii) the focus is at (0, 3) and the vertex is at (0, 0).(ii) the focus is at (0,-3) and the vertex is at (-1,-3).(iv) the focus is at (a, 0) and the vertex is at (a', 0)(v) the focus is at (0,0) and vertex is at the intersection of the lines x +y[BTE 2006]1 andx-y 3.(vi) the focus is at (0, 2) and the vertex is at (0, 4). |
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| 5. |
8Find the equation of the parabola whose focus is (0,0) and vertex (0,2).(UP 2004,0Given that focus S (0, 0) and vertex A (0,2) |
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Answer» this is wrong nice answer.................. |
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| 6. |
Find the 15th term of the series |
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| 7. |
(i) ‘ Find the 15th term of the sequence, 12, 18,482. |
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| 8. |
whai is the volume of cylinder ifradusr) is equ: to its height |
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Answer» Volume of cylinder=πr^2hr=hV=πr^2×rV=πr^3 |
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| 9. |
)Find the 15th term of the sequence, V2,V8.18.32, |
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| 10. |
find the 15th and nth of the AP 16,11,6,1,-4,-9,----- |
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Answer» 15th termt15 =-54nth termtn=20-5n |
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| 11. |
Find the 15th term of the A.P. 3, 8, 13, 18, |
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| 12. |
7 The perimeter of a trapezium is 52 cm. If its noaltitude is 8 cm, find the area of the trapezium.outer dlagonal.n-parallel sides are 10 cm each and its |
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| 13. |
MPLE 3Give an example of two sets A and B such that P(A) υ P(B)P(AU B). |
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| 14. |
3. The perimeter of a trapezium is 52 cmand its non-parallel sides are each equalto 10 cm. If its altitude is 8 cm, what is itsarea? |
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Answer» perimeter of trapezium=sum of parallel sides + sum of non parallel sides52=10+10+sum of parallel sidessum of parallel sides=32cmarea=sum of parallel sides×altitude ×1/2a=32×8/2=128 |
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26. A rectangle is 10 cm long and 8 cm wide. When each side of the rectangle is increasedby r cm, its perimeter is doubled. Find the equation in x and hence find the area ofthe new rectangle. |
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Answer» initial perimeter is 10+8=18now after increasing x perimeter doubledso 10+x+8+x=36so 2x=18so x=9so area of new rectangle 19*17=323 cm^2 |
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| 16. |
12 kg 450 g = |
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Answer» 1 kg = 1000 gSo, 1 g = 1/1000 g = 0.001 gSo, 450 g = 450/1000 g = 0.45 g So,12 kg 450 g = 12.45 kg |
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| 17. |
Without actual division, prove thatr +2r -3.+2r- 2x+2x -3 is exactly divisibie Exa |
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| 18. |
The differential equation of all circles at fixed centre (α, β) isdyx-αdydx(4) of these |
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| 19. |
Solve the following equ1.x-2=7 |
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Answer» x-2=7x=7+2x=9 Thats right the answer of your question is x=7-2=5 x=5 |
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| 20. |
Solve each of the following equ1. x2+30 |
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| 21. |
e the following simultaneous equ3a 5b 26; a 5b 22 |
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| 22. |
Solve the following equR.402,+18 = 12(e) 52+8=-2 |
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Answer» 2x=12-182x=-6x=-6÷2x=-3 2x + 18 = 12 2x = -6 x = (-6)/2 x = -3 |
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| 23. |
8: Anil was admitted to a hospital on 15th May, 2011 anddischarged on 15th June, 2011. How long did he remainin the hospital? |
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Answer» Admitted on 15th May 2011 and discharged on 15th June 2011 so number of days = 17 days of May + 15 days of June = 32 days |
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| 24. |
1 inch equal to how many cm |
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Answer» 1 inch= 2,54 centimetres please like my answer if you find it useful |
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| 25. |
A piece of rectangular cardboard sheet measuring40 inch x 25 inch is made into an open chocolate boxby cutting out squares of side 'p' from each corner.Which of the following expressions is equivalent tothe volume of the box?A. 4p^3-120p^2 + 950pB. 4^p +130p^2 + 1000pC. 4^p- 130p^2 + 1000pD. of these |
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| 26. |
mple4: Find the square root of 6400. |
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Answer» 6400 = 80²So,√6400 = 80 |
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| 27. |
dymple 4. Ifx - a sin3 e, y a cos3 e, then finddx |
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| 28. |
mple 2 Write the standard form ofa) 3 hundreds + 5 ones+6 tenths +4 hundredths |
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| 29. |
21. ABCD is a square. E, F, G, H are the mipoints of AB, BC, CD and Drespectively. What fraction |
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Answer» please post a complete question for proper answer |
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| 30. |
7. Find the area of a rectangle whose sides are 2a and 3a. |
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Answer» Area = 2a*3a = 6a² units |
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| 31. |
find the length of the diagonal of a rectangle whose sides are 12cm and 5cm |
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| 32. |
A tangent to a circle intersects it inpoint (s). |
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Answer» A tangent to a circle intersecting it in one point |
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| 33. |
2 x + k y = 10 \text { intersects } y \text { -axis at } ( 0,2 ) |
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Answer» put x=0 and y = 2 in 2x +ky = 102×0+k×2 = 10k = 5 Thnk u |
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| 34. |
(i)A tangent to a circle intersects it inpoint (s). |
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Answer» intersect it in one point |
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| 35. |
PQRS is a square. PRand SQ intersects at O. State the measure of LPOQ |
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Answer» All the angle made at O is equal. Sum of all the angles=360°total no of angles made=4Hence each angle=360/4=90° |
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| 36. |
--ind the perimeter and area of a rectangle whose sides are 30 mand 20Arrange the following |
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Answer» L=30mW=25mP=2(l+w)==2(30+25)2(55)=110m A=w×l=25×30=750m^2 perimeter=2(l+b)=2×(30+25)=2×55=110 Given Length = 30m breadth =25mperimeter of rectangle = 2 (length + breadth)= 2 (30+25)=2× 55=110 marea of the rectangle = length × breadth = 30 × 25=750 m^2 |
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| 37. |
Fll in the blanks:A tangent to a circle intersects it in____point (s). |
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Answer» i) A tangent to a circle intersect it in a one point. |
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| 38. |
How much GST at 28 % will Kumar pay on MRP45,000 of an article? |
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| 39. |
Find the length of the diagonal of a rectangle whose sides are 12 cm and 5 qm. |
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| 40. |
parallelogram.Find the length of the diagonal of a rectangle whose sides are 12 cm and 5 cm. |
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| 41. |
A rectanglewhose sides 4 cm and 3 cm is inscribed in a circle. Find the area enclosedbetween the circle and the rectangle. |
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Answer» The sides of rectangle are 4 cm and 3 cm, hence the diagonal is (3^2 + 4^2)^1/2 = (9 + 16)^1/2 = 25^1/2 = 5This will become the diameter of the circle hence area of circle = 22/7 x 2.5 x 2.5 = 3.14 x 6.25 = 19.625Area of rectangle = 4 x 3 = 12 sq cmHence area enclosed between circle and rectangle = 19.625 - 12 = 7.625 sq cm |
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| 42. |
Find tuwoointegSaua |
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| 43. |
[Nov. 2009) |
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Answer» sin inverse y=cos inverse x +C |
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| 44. |
The cost of an apple is 2xThe cost of a guava isyThe total cost of 5 applesand 12 guavas is 156If the number of fruitsis interchanged the totalcost increases by 28Equation 1Equation 2 |
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| 45. |
(2) A transversal intersects two parallel lines. If the measure of one of the angles is40°, then find the measure of its corresponding angle. |
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Answer» it will be 40° only because it will be same as it corresponding angle |
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| 46. |
The diagonals of Convex PQRS intersects each other at right angle then prove thatPQ^2 + RS^2=PS2 +QR^2 on" (March'15)), |
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| 47. |
The angle at which the curve ythe y-axis isintersects |
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| 48. |
1. For his birthday, Ajay gave 20450 ml of milk to the children in anAshramshala and 28/ 800 ml to thechildren in an orphanage. How muchmilk did Ajay donate? |
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Answer» For this add both the amountshence20l 450ml+28l 800ml=48l +(450+800)ml=48l+1250mlas 1250ml=1litre 250mlhence49litre 250ml |
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| 49. |
rol costs 270.ses 18 m of laceteses il she need to make 16 such dresses?to make 2 dresses (of the same size and design),. How450 ml of4.50 ml ofice-cream to make milkshake for 15 people. How muchKumar uske need to make milkshake for 8 people (each person has the samel she need to make |
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Answer» Lace needed for 2 dresses = 18mLace needed for 1 dress = 18/2= 9mLace needed for 16 dresses = 9*16 = 144m Please hit the like button if this helped you |
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| 50. |
3. वह व्यंजक ज्ञात करें जिसे 7ab2c2 से गुणा करने प14dbc' + 35a bsc _494b6c4 प्राप्त होता है।Type II.| दीर्घ उत्तरीय प्रश्न |
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