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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. |
RPN लगा 3 W O O का रत लत न हक L1. . बदि बहुपद (८* + 9) + 135 + 6० का एक मूल दूसरे व्युत्क्रम हैं, तो « काAL1 मान ज्ञातपक रा T i o |
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Answer» If one of the zero is reciprocal of the other,let one zero beαother zero will be 1/α Product of roots = c/a⇒α× 1/α = 6a/(a²+9)⇒ 1 = 6a/(a²+9)⇒ a² + 9 = 6a⇒ a² - 6a + 9 = 0⇒ a² - 3a - 3a + 9= 0⇒ a(a-3) -3(a-3) = 0⇒ (a-3)(a-3) = 0⇒ (a-3)²= 0⇒ a = 3 Value of a is 3 |
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| 2. |
| (1) 4 ()5 3) 6 3 ;किसी संख्या का पाँचवाँ भाग उसके नौवें भाग से 12 अधिक है, तो® संख्या कौन-सी है1) 135 (2) 145 ) 155 1651 W e e 8 हरि गे |
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Answer» supposeवह नंबर एक्स हैx/5= x/9+12x/5-x/9= 124x/45= 124x= 45*12x= 45*3= 135 |
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| 3. |
From a point on the ground, the angles of elevation of the bottom and the top of atransmission tower fixed at the top of a 20 m high building are 45° and 60° respectivelyFind the height of the tower. |
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| 4. |
From a point on the ground the angle of elevation of bottom and the top of a transmission tower fixed at a top of a 20 m high building are 45 degree and 60 degree respectively, find the height of tower? |
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| 5. |
Example 16: Monica has a piece of canvas whose area is 551 m2. She uses i thave a conical tent made, with a base radius of 7 m. Assuming that all themargins and the wastage incurred while cutting, amounts to approximately I m2,fiadthe volume of the tent that can be made with it. |
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| 6. |
9.A heap of wheat is in the form of a coni whose diameter is 10.5 m and height is 3 m.Find its volume. The heap is to be covered by canvas to protect it from rain. Find thearea of the canvas required. |
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| 7. |
\begin{array}{l}{5 q=50} \\ {12 x=-108} \\ {x-8=16}\end{array} |
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Answer» d) 5q = 50divide by 5 on both sidesq = 50/5 = 10 h) 12x = -108divide by 12 on both sidesx = -108/12 x = -9 d) x - 8 = 16add 8 on both sidesx - 8 + 8 = 16 + 8x = 24 thanks |
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| 8. |
( x - 1 ) ^ { 2 } - 108 ( x - 1 ) - 330 = 0 . \text { Find the value of } x |
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| 9. |
Q15. The volume of a rectangular block of stone is 10368 dm2. Its dimensions are in the ratio of 3:2:1. If itsentire surface is polished at 2 paisa per dm2, then find the cost incurred to polish. |
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Answer» The dimensions are 3x : 2x : x The volume is { 6x }^{ 3 }=10368 So, x is { 6x }^{ 3 }=10368 therefore x= 12 So, the dimensions are 36cm, 24cm and 12 cm respectively. The surface area is 2(36×24+ 24×12+ 12×36)=3168 cm^2 Total cost is 3168 ×0.02=Rs. 63.36 |
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| 10. |
)A solid is made up of a cylinder with hemispherical ends. If the whole lengthof solid is 104 cm and the radius of each hemispherical end is 7 cm, find thecost of polishing its surface at a rate of Rs. 10 per dm2 |
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| 11. |
4. A design on the wall of room consists of 1000 tiles of the shape of parallelogram. Ifaltitude and base of each tile is 10 cm and 4 cm respectively, find the cost of polishingthe design at the rate of 9.50 per dm2. |
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| 12. |
e14.Theouterdimensionsofaclosedwoodenboxare16cmby12cmby8cm.Thicknessofthewoodis1 cm. Find the total cost of the wood required to make box, if 1 cm3 of wood costs? 2.50. |
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| 13. |
A design on the wall of room consists of 1000 tiles of the shape of parallelogram. Ifaltitude and base of each tile is 10 cm and 4 cm respectively, find the cost of polishingthe design at the rate of 9.50 per dm2. |
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| 14. |
24. Monica has a piece of Canvas whose area is 551 m2. She uses it to have a conical tent made,with a base radius of 7m. Assuming that all the stitching margins and wastage incurred whilecutting, amounts to approximately 1 m2. Find the volume of the tent that can be made with it. |
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| 15. |
If sin-k-cos-1x =Ď , find x. |
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Answer» Wehave,sin-1x-cos-1x=π/6⇒sin-1x+cos-1x-2cos-1x=π/6⇒π2-2cos-1x=π/6⇒2cos-1x=π2-π/6⇒2cos-1x=3π-π/6⇒2cos-1x=2π/6⇒cos-1x=π/6⇒x=cosπ)6= Under root3/2Please like the solution 👍 ✔️ |
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| 16. |
in AABC and AXYZ. if k A andare acute angles such that cos A-cos X thenshow that △杉ㄥㄨˊ |
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| 17. |
The equation k cos x-3 sin xbelongs to the intervalk+ 1 is solvable only ifk(c) (-00, 4](d) of these |
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Answer» K(cos x) - 3(sin x) = k + 1k(cos x) - (k + 1) = 3(sin x)[k(cos x) - (k + 1)]^2 = [3(sin x)]^2k^2cos^2x - 2k(k + 1)(cos x) + (k + 1)^2 = 9sin^2xk^2cos^2x - (2k^2 + 2k)(cos x) + (k + 1)^2 = 9(1 - cos^2x)(k^2 + 9)cos^2x - (2k^2 + 2k)(cos x) + (k^2 + 2k - 8) = 0 Here we have a quadratic equation in terms of (cos x).This equation is only solvable when the determinant b² - 4ac greater than or equal to 0, otherwise the solution will be complex. b² - 4ac greater than or equal to 0[-(2k^2 + 2k)]^2 - 4(k^2 + 9)(k^2 + 2k - 8) greater than or equal to 0(4k^4 + 8k^3 + 4k^2) - (4k^4 + 8k^3 + 4k^2 + 72k - 288) greater than or equal to 0-72k + 288 greater than or equal to 072k less than or equal to 288k less than or equal to 4 i.e. -infinity<k<4 = k belongs to (-infinity, 4] |
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| 18. |
at x = 0,CONTINUITY1. Find the value of k when 1(x) is continuous1 - Cos 4xwhere 1(x)= x |
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| 19. |
For what value of K, the following function is continuous at x = 01-cos 4x, x# |
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Answer» thnks.. |
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| 20. |
ny cm 01 wood are there in lt?7. The outer dimensions of a closed wooden box are 10 cm by 8 cm by,7 cmI cm. Find the total cost of wood required to make the box if 1 cm of wood costs 2.00 |
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Answer» Please like the solution 👍 ✔️ |
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| 21. |
3.Find the height of a cylinder whose radius is 7 cm and total surface area is 968 cm2 |
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Answer» thanks |
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| 22. |
\frac{d y}{d x} \text { if } x=a(k-\sin t), 4=a(1+\cos t) |
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| 23. |
(i) Find the height of a cylinder whose radius is 7cm and the total surface area is 968 cm2 |
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Answer» TSA of cylinder=2pie r (r+h)TSA=968 2*22/7*7(7+h)=9682*22(7+h)=968 (7+h)=968/447+h=22h=22-7=15 cm HEIGHT OF CYLINDER=15CM |
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| 24. |
Find the height of the cylinder whose radiusis 7 cm and the total surface are is 1100 cm2 |
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| 25. |
Find the height of the cylinder whose radius is 7 cm and the total surface area is 968cm square |
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| 26. |
Find the mean of the following data :| निम्नलिखित आँकड़ों का माध्य ज्ञात कीजिए :ClassesFrequency(बारबारता)| (वर्ग)।10-2020-3030-4040-5050-6060-70 |
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| 27. |
if 60 = 24 × m + n, find the value of m and n |
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Answer» Given,60 = 24*m + n For given equation there are two possible solution If m = 160 = 24*1 + nn = 60 - 24 = 36 If m = 260 = 24*2 + n60 = 48 + nn = 60 - 48 = 12 |
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| 28. |
who's formula in this question Find the area of canvas required for a conical tent of height 24m. and base radius 7m. |
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| 29. |
ORA building is in the form of a cylinder of radius 7m and height 6m, scone of same radius and of slant heighturmounted by a14m. Calculate the outer surface area of theuilding. |
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Answer» We have r= 7m and h=6mSurface area of building wall= 2πr.h=7*6*22/7= 132 m²As the vertical angle is 60 degree we have slant height= dia l= 2r= 14lateral surface area of cone= πrl=22*7*14/7=308 m²Total surface area = 132+308= 440m²Painting rate is Rs 30/m²Total cost of painting= 440*30= Rs13200 like if you find it useful |
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| 30. |
Divide 104 pencils among three children in the ratio1/2 1/3 1/4 |
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Answer» let X be the common multiplehence1/2x,1/3x,1/4x104=1/2x+1/3x+1/4x104=6/12x+4/12x+3/12x=13x/12hence104*12/13=xX=96hence1/2x=96/2=481/3x=96/3=321/4x=96/4=24 |
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| 31. |
7. Simplify the following.(1) 72X34(111) 5° x10(ii) 3²x24 |
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Answer» it's a correct answer so nice could book club book for Greg Hill good (7×7) × (3×3×3×3)49×81=3969 good question nicely |
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| 32. |
28. If three points (q , yı ), (x2, Уг), (x3Ws) lie on the3 11 2 |
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| 33. |
IfA = {x:x is a factor of 24}, then find n(A). |
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Answer» A = {2, 2, 2, 3} Thenn(A) = 4 24 = 2×2×2×3A = { 2,2,2,3 }So, n(A) = 4 Ans. |
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| 34. |
TRY THESE(a) Match the following figures with their respective areas in the box7 cm7 cm14 cmc m14 cm |
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| 35. |
Find the volume and the total surface area of a right cylinder whose radius is!7m and height is 10 m. |
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| 36. |
010 1५%. 0टो = XThl + 6T~ |
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| 37. |
7 m24. An empty cylindrical container of radiusand height 10 m is covered by a conical cap ofradius 10.5 m and height 9 m. Calculate thevolume of the air trapped inside.9 m10 m10.5 m7m |
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Answer» Volume of cone = 1/3*22/7*10.5*10.5*9 = 1039.5now the upper cone is similar to the bigger cone.So, by using similarity,height of upper cone/height of bigger cone = radius of upper cone/radius of bigger cone i.e.h/9 = 7/10.5 Thus,h = 6now,height of cylinder inside the cone is 3area of this cylinder = 22/7*7*7*3 = 462capacity of air inside the solid is 1039.5 - 462 = 577.5 |
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| 38. |
(a)A milk tank is in the form of cylinder whose radius is 1.5m andlength is 7m. Find the quantity of milk in litres that can be storedin the tank?(2.5) |
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| 39. |
clygmomiat010. 4shos |
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| 40. |
S i12 0५ 9८ 9द्ु रा मत in an APamnd व्यू बचत पका | |मै 225 Heow L\’I\J 'fl'LQ UMt 5# एल 24 fenm 9 | |
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Answer» Like if you find it useful |
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| 41. |
(Ö) Solve the quadratic equation x^2 -15x+54 =0 byfactorization method. |
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| 42. |
16. The cost of a pen is 16010d that of a pencil is 4-. Which costs more and by how much? |
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| 43. |
(ii) Prove that Harmonic mean of the roots of equation ax + bx+c=0a0, is independent of a.11.1+113. Find14. Find |
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Answer» For a simpleharmonicoscillator, an object's cycle ofmotioncan be described by theequationx ( t ) = A cos ( 2 π f t ) x(t) = A\cos(2\pi f t) x(t)=Acos(2πft)x, left parenthesis, t, right parenthesis, equals, A, cosine, left parenthesis, 2, pi, f, t, right parenthesis, where the amplitude is independent of the ... |
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| 44. |
If A (2, 3, 5), find Awo and фИА andcompare |
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Answer» Au∅=(2,3,5)= ∅∪AAs phi means empty set |
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| 45. |
3. There are n A.M's between 7 and 85 such that (n 3)th mean : nth mean is as 11 : 24find n. |
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| 46. |
EXERcIs1.Find the area of each of the following pcm7 cm |
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Answer» Given, Base = 4 cm Height = 7 cmArea of parallelogram= base *height= 4*7 = 28 cm^2 Ans. Area is 28 cm^2 |
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| 47. |
EXERCIS3.3x244 |
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Answer» 3/4 × 24(3 × 24)/ 43 × 618 3/4x24(3×24)/43×6=18 3/4×24=3/1×6=3×6=18 iska write answers 18hoga 3/4×244×6=246×3 =18 3/4×24(3×24)/472/418answer =18 3/4×24(3×24) /4= 3×6= 18 18 is the answer.......... 3/4×24(3×24)/4=3×6=18. |
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| 48. |
EXERCISomplete the table of 3.Multiplying by 31 three is 3 |
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Answer» 1 three is = 1×3 = 3 = three |
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| 49. |
11IULUICUCCIOCULUI2) Lines X, Y and MN intersect at O. If ZPOY=90° and a : b = 2:3, find c. |
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Answer» Given,∠POY = 90° & a : b = 2 : 3 A/Q ∠POY+∠POX =180° [By linear pair axiom] ∠POY+ a + b = 180°⇒90° + a + b = 180°⇒a + b = 90° Let a = 2x & b= 3x2x + 3x = 90°⇒5x = 90°⇒x = 18° ∴ a = 2×18° = 36° b = 3×18° = 54° Now, OX is a ray on the line MON. ∠XOM + ∠XON=180°b + c = 180° (by Linear Pair axiom)⇒54° + c = 180°⇒c = 126° The value of c =126° 126° is the right ans of this question the correct answer is 126° of the following right answer is 126° of the following question the correct answer is 126° the value of c is 126 v zgdh uvyduudhfch udjcuj jvyvjd p is 126 i think that so please like me the value of c = 126° let a=2xlet b=3x 2x+3x+90=180(by linear pair)5x=180-905x=90x=90÷5x=18on line MN there is c and bb=3×18=54b+c=18054+c=180c=180-54c=126 126 is the right answer of following questions c=126° a x + b x is equal to 90 if you take two asex then 5 x is equal to 90 then b equal to 54 then b + C is equal to 180 after that C is equal to 126 c= 85 answer to the same wright a/b=2/3i.e. a=2x = 2×18° =36°and b=3x = 3×18°= 54°so to find c for straight line MON b + c = 180°54 + c = 180° c = 180° - 54°c = 126° ans. the value of c is 126 the value of c is = 126 degree.please like as best Answer of the above question is 126° the value of c is 126 degree .please like as best for the points a+90°=ca=2so,90°+2=92°c=90° A:B=2:3 let us imagine that 2x=a A.T.PanglePOX+anglePOY=180A+B=180-902X+3X=905X=90X=18 DEGREE 126 is a measure of angle c my answer is126' and it's correct a=36°,b=54°c=180-54=126° leta+b=90 a=2x b=3x2x+3x=905x=90x=90/5x=18^2*=2×18=36=a3*=3×18=54=bb+c=180^54+c=180c=180-54c=126^ Given,∠POY=90°∠POY=90°anda:b=2:3a:b=2:3.  Let, common ratio ofaandbbex. a=2x,b=3xa=2x,b=3x By property of Linear pair of Angles, ∠XOM+∠POM+∠POY=180°3x+2x+90°=180°5x=90°x=18°∠XOM+∠POM+∠POY=180°3x+2x+90°=180°5x=90°x=18° Now, a=2x=2×18=36°a=2x=2×18=36° By Vertically Opposite Angles, ∠XON=∠MOY=a+90°=36°+90°=126°∠XON=∠MOY=a+90°=36°+90°=126° Thus,c=126°c=126°. therefore angle at c is 126degree what are your responsibility option a is correct hi I'm arundfhiijgfffghjijjyhhuuuuiiiiiuyyytyyuuuu XY and MN are linesanglePOY=90°a:b=2:3from the figure a+b=90°sum of the terms of the ratio a:b=2+3=5therefore b=3/5×90=54°from the figure b+c=180°(linear pair of angles)54+c=180°c=180°-54=126° C=126° is the correct answer C is 120 degree as it a is 36 degree and b is 54 degree a:b=2:3angle poy=90degrees=2x+3x+90=180=5x=90x=18=2x=2(18) =36=3x=3(18) =54angle poy=90 degreespoy+54=180angle poy=180-54 =126a=36b=54c=126 now angle c is 126 bcoz 180 -54.i.e angle b=126° 144 is right answer.. |
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| 50. |
2. if A (2, 3, 5), find Awo and OLIA andcompareeoolutions of the folloi- |
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Answer» Au∅=(2,3,5)= ∅∪AAs phi means empty set |
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