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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. |
30. AD is an altitude of an equilateral triangle ABC. On AD as base, another equilateral triangleADE is constructed. Prove thatArea (AADE): Area (AABC)3:4 |
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| 2. |
the coads, each of width 5 m, run at right angles through the centre of aranaan at the rate ofcross rrectangularTwo crossfwo mar park of length 70 m and breadth 45 m and parallel to its sides. Find200 per m2.area of the roads. Also find the cost of constructing the roads at the rate ofthe105 per m2. |
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Answer» Thanks |
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| 3. |
20) Arhombus shaped sheet with perimeter 40cm and one diagonal 12cm,ispainted on both sides at the rate of5 per m2. Find the cost of painting. |
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| 4. |
What will be the cost of fitting glass in four windows each of length 2,.5 m andbreadth 1.5 m at the rate of 150 per m2?30. |
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Answer» Area of a window = l*b = 2.5*.15 = 3.75 m² For four such windows area = 4*3.75 = 15 m² Cost = 15*150 = 2250 rupees |
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| 5. |
5. A cylindrical pillar is I m in diameter and 4.2 m in height. Find the cost of white washing thesurface of the pillar at the rate of? 15 per m2 |
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| 6. |
९1581apylr22ho8 2८21.Lo 5४ ARe (R 4SS |
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Answer» 4 square =165 square =256 square =36 |
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| 7. |
75A cube and a cuboid have the samevolume. The dimensions of the cuboid arein ratio of 1:2:4. If the differencebetween the cost of polishing the cuboidand cube at the rate of 5 per m2 is 80,then their volumes are - |
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Answer» answer of your this question is 30 answer of your question is 64 |
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| 8. |
12. Four cubes of edges 5 cm each are placed sideby side and stuck together. If the outer surfacealone is painted at 300 per m2, find the cost ofpainting |
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| 9. |
Four cubes of edge 5 cm each are placed side by side and stuck together as shown. If the outside surface alone is painted at 300 per m2, find the cost of painting. |
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Answer» wrong |
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| 10. |
7. The 16th term of an AP is 1 more than twice its 8th term. If the 12h termterm of an AP is 1 more than twice its 8th term. If the 12th termof the AP is 47, then find its nth term. |
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Answer» Solution:-Given : a₁₂ = 47 or a + 11d = 47a₁₆ = a + 15d and a₈ = a +7dNow, according to the question2(a + 7d) + 1 = a + 15d2a + 14d + 1 = a + 15d2a - a = 15d - 14d - 1a = d -1 .................(1)Substituting the value of 'a' in a + 11d = 47, we getd - 1 + 11d = 4712d = 47 + 112d = 48d = 4Substituting the value of 'd' in a + 11d = 47, we geta + 11*4 = 47a = 47 - 44a = 3Nownth term = a + (n - 1)d= 3 + (n - 1)4= 3 + 4n - 4nth term = 4n - 1 |
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| 11. |
If sum of first 20 term of AP is one third of next 20 term of AP and first term is 1. Find its sum 30 term of AP |
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| 12. |
L2, lha the AP.of an AP is equal to 6 times its 2nd term. If its 5th term is 22, find the AP25the 9th term(2,7,12,. |
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Answer» Let the first term be "a" and common difference "d" Ninth term = a + (9 - 1)d = a + 8dSecond term = a + (2 - 1)d = a + d A/Q,a + 8d = 6(a + d)a + 8d = 6a + 6d- 5a + 2d = 0 Fifth term = a + (5 - 1)d = a + 4d = 22 - 5a + 2d = 0a + 4d = 22 Solving the equations ,- 11a = - 22a = 2 Now, 2 + 4d = 224d = 20d = 5 First term = 2Second term = a + d = 2 + 5 = 7Third term = a + 2d = 2 + 10 = 12Fourth term = a + 3d = 2 + 15 = 17Fifth term = a + 4d = 2 + 20 = 22 The required AP = 2 , 7 , 12 , 17 , 22 Like my answer if you find it useful! |
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| 13. |
the sum of first n term of an AP is210, and sum of (n-1) term of the APis 1 71 and its first term is 3 findthe AP |
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| 14. |
Test -APORquell The 17th term of an Ap exceeds its 10th term by 7 find the common difference,quele if oth term of Ap in 4 and 9th term of Ap is t. Then find (pqgth of Ap.Then find sum of (99) term of A.P.Couet 3 which term of Ap 3, 15, 22 ......will be 132 more than its sath term.for what value of n, are the nth terms of two A.P. 63, 65. 67,... and 3, 10, 17. . . equal?COUNY A manufacturer of TV sets produced 6oo sets in the third year and 700 sets inthe seventh year. Assuming that the production increases uniformely by a fixed no.every year. is production in 1st year(in total production in first 7 year.Qeret: 5 which term of the sequence 20, 1912, 1842 , 177, is the first Aregative term?or if the sum of interme of Ap is aut in and its mith term in 164. find the value of m. |
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Answer» 1) 17th term= 7+10th termlet 1st term a, difference= da+(n-1)d= 7+a+(n-1)da+16d= 7+a+9d16d-9d= 77d= 7d= 7/7=1 |
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| 15. |
Find the 10th term of an AP 2,7,12 … |
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| 16. |
and (,-3).9. A point Pis at a distance of v10 from the point (4, 3). Find the co-ordinates of point Pif its ordinate is twice of its abscissa. |
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Answer» Let the point P is (x, y)Then, y = 2x Given Distance between points= sqrt(10) Thus,sqrt(10) = sqrt((4-x)^2 + (3 - y)^2))Squaring both sides10 = (4-x)^2 + (3 - 2x)^210 = 16 + x^2 - 8x + 9 + 4x^2 - 12x5x^2 - 20x + 15 = 05x^2 - 15x - 5x +15 =05x(x - 3) - 5(x - 3) = 0(5x - 5)(x - 3) = 0x = 1, 3 Coordinates are (1, 2) and (3, 6) |
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| 17. |
The 4th term of an AP is 0 .prove that the 25th term of the AP is 3times its 11th term |
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| 18. |
Example 28 Find the distance between the point P(6, 5, 9) and the plane determinedby the points A (3,-1,2), B (5, 2, 4) and C(-1,-1,6).the point P(6, 5, 9) and the plane determined |
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| 19. |
Find the 10th term of the AP: 63,58,53,48, |
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| 20. |
9. If point P lies on the join of points A(-2, -2) and B(2, -4) such that AP AB. Find tcoordinates of P. |
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| 21. |
Hind the distance between the point P(6, 5, 9) and the plane determinedA (3, - 1,2), B (S, 2, 4) and C-1,-1,6)y the pointsints A (3, -1, 2), B (5, 2, 4) and C(-1, - 1,6) |
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| 22. |
EXERCISE 18arts:R Take a point O on your notebook and draw circles of radil 4 cm. 5.3 cm and 6.2 em, eachhaving the same centre Oy a cirele with centre C and radius 4.5 em. Mark points P. 9. R such that P lies tn thelo nud R lies in the exterior of the circle |
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| 23. |
In an equilateral triangle ABC, D is a point on the side BC such thatBD-BC. Prove that 9AD 7AB2 |
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| 24. |
an equilateral Triangle ABC, D is a point on side BC such thatBDBC. prove that 9AD7AB |
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| 25. |
tshanequilateral triangle ABC, D is a point on side BC such that BD-9AD 7AB |
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| 26. |
15. In an equilateral triangle ABC, D is a point on side BC such that BD- 3 BC. Prove that9AD-7AB |
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| 27. |
puinits (x y), 11, 2) and (7, 0) are collinear19. In an equilateral triangle ABC, D is a point on side BC such that, BD BC. Prowe that,9AD 7AB |
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Answer» Like if you find it useful |
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| 28. |
a) DUnd Ciof A and B(c) 39 yearsThe average weight ol A. B and50 kg. If average weight of Aanis 48 kg and the average of Bandis 43 kg. then find the weight(b) 43 kg |
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Answer» Step-by-step explanation: (a+b+c)/3=50 a+b+c=150-----(1) (a+b)/2=40 a+b=80-------(2) (b+c)/2=43 b+c=86------(3) add(2) and (3) a+b+c+b=80+86=166 150+b=166 b=166-150=16 Kg the weight of b = 16 kg according to question(a+b+c)/3=50a+b+c=50×3a+b+c=150 ______(1)(a+b)/2=40a+b=40×2a+b=80______(2)(b+c)/2=43b+c=43×2b+c=86add (2) and (3)a+b+c+d= 80+86 =166putting the value of a+ b+c150+b = 166b= 166-150b= 16 kg (a+b+c)/3=50y=a+b+c=150.....(1)(a+b)/2=40a+b=80......(2)(b+c)=86.........(3)adding new(2)and(3)a+b+c+b=80+86=166150+b=166b=166-150=16kg A+B+c/3=50kgA+B+C=150kgA+B=80kgc=150-80c=70kg 16 kg is the right answer 16 kg is the correct answer |
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| 29. |
There are 35 students in a class. Numberof girls in the class is 5 more than the boys.The average weight of girls is 2 kg morethan the boys. The average weight of girlsis 2 kg more than the boy's average. Totalweight of girls is 190 kg more than that ofboys. Calculate the average weight of the |
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| 30. |
48. The average weight of 19 students is 15 kg.By the admission of a new student the averageweight is reduced to 14.8 kg. The weight ofthe new student is: |
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Answer» answer is 40 kg weight of new student |
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| 31. |
\cos 57 ^ { \circ } = \sin \box^\circ\ |
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Answer» We knowcos ( 90 - A) = sin(A)So, cos(57°) = cos ( 90-33) = sin(33°)So,cos(57°) = sin(33°) |
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| 32. |
The average weight of A, B, C is 45 kg. If the average weight of A and B be 40 kg and that of B andC be 43 kg, find the weight of B. 3ik |
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| 33. |
The average weight of 16 boys in aclass is 50.25 kg and that of theremaining 8 boys is 45.15 Kg. Findthe average weight of all the boys in |
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Answer» divided by 20 or 24 |
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| 34. |
\cos 57^{\circ}=\sin |
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| 35. |
4,8,12.......are in APfind 10th term |
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Answer» formula tn= a + (n-1)da= 4 , d=8-4=4t10= 4+(10-1)4t10= 4+36t10= 40 |
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| 36. |
29. A conical vessel of radius 6 cm and height 8 cm is completely filled with water. Asphere is lowered into the water and its size is such that it touches the sides it isjust immersed. What fraction of water overflows? |
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Answer» Radius (R) of conical vessel = 6 cm Height (H) of conical vessel = 8 cm volume of conical vessel (Vc) = 1/3πr^2h= 1/3π × 36 × 8= 96πLet the radius of the sphere be r cm. In right ΔPO'R, by Pythagoras theorem: L = √(64 + 36) L = 10 cm Hence sin = O'P / PR = 6/10 = 3/5 In right triangle MRO Sin = OM /OR = r / OR 3/5 = r / (8 - r) ⇒ 24 – 3r = 5r ⇒ 8r = 24 ⇒ r = 3 cm ∴ Volume of sphere (Vs) Now, Volume of the water = Volume of cone (Vc) = 96 π cm3 Clearly, Volume of the water that flows out of cone is same as the volume of the sphere i.e. Vs. ∴ Fraction of the water that flows out Vs/Vc = 36π / 96π = 3/8Vs : Vc = 3 : 8 |
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| 37. |
Nandini's house is i km from her school. She walked some distance andtook a bus for km to reach the school. How far did she wallf the same size nartly filled with bo |
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| 38. |
the diameter of base of a cylindrical drum is 35 cm and its height is 24 cm It is full of kerosene how many times is of size 25 cm into 22 cm into 35 cm can be filled with kerosene from the drum |
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| 39. |
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19n term |
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Answer» Let a and d respectively be the first term and common difference of the AP. Given a9= 0 So, a + (9-1)d = 0 a+8d=0 a= -8d Now, 29th term = a+28d =-8d+28d = 20d = 2 x 10d = 2(-8d + 18d) =2(a+18d) = 2 x 19th term Thus, the 29th term of the AP is twice the 19th term. please like the solution 👍 ✔️ |
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| 40. |
If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term |
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| 41. |
s, If the 9th term of an AP is 0, prove that its 29th term is double the 19th term. |
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| 42. |
g" Ifthe 9th term of an A.P. is zero then show that the 29th term is twice the 19th term. |
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Answer» Please like the solution 👍 ✔️ Let a and d respectively be the first term and common difference of the AP. Given a9= 0 So, a + (9-1)d = 0 a+8d=0 a= -8d Now, 29th term = a+28d =-8d+28d = 20d = 2 x 10d = 2(-8d + 18d) =2(a+18d) = 2 x 19th term Thus, the 29th term of the AP is twice the 19th term. |
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| 43. |
25-The 9th term of an AP is equal to 6 times its 2nd term. If its 5th term is 2 |
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Answer» Let the first term be "a" and common difference "d" Ninth term = a + (9 - 1)d = a + 8dSecond term = a + (2 - 1)d = a + d A/Q,a + 8d = 6(a + d)a + 8d = 6a + 6d- 5a + 2d = 0 Fifth term = a + (5 - 1)d = a + 4d = 22 - 5a + 2d = 0a + 4d = 22 Solving the equations ,- 11a = - 22a = 2 Now, 2 + 4d = 224d = 20d = 5 First term = 2Second term = a + d = 2 + 5 = 7Third term = a + 2d = 2 + 10 = 12Fourth term = a + 3d = 2 + 15 = 17Fifth term = a + 4d = 2 + 20 = 22 The required AP = 2 , 7 , 12 , 17 , 22 Like my answer if you find it useful! |
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| 44. |
If 3rd term of a G.P. is 324 and 7th term is 64then find 10th term |
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| 45. |
The 4th term of a G.P. is square of its second term, and the first term is - 3. Determine its 7thterm.) |
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| 46. |
4If 3rd term of a G.P. is 324 and 7th term is 64,then find 10th term |
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| 47. |
4If 3rd term of a G.P. is 324 and 7th term is 64,then find 10th term. |
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| 48. |
and5 |
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Answer» rational number is √4 = 2 = 2/1 irrational number is √3 |
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| 49. |
fa number. If'ist is a multiple of 3 write it in the red circle.ultiple of 5 write it in the blue circle.5is not ther ofI make 32e of 4,ansed circ57 It is aSome numbers are multiples of both 3 and 5.Sowe can say that they are common toboth3 and5.Thinkt If you write the multiples common to3 and 5 in the purple part, then will they still bein both the red and the blue circles?Which is the smallest among these commonmultiples?Repeat the game using the numbers 2 and7.# Write the common multiples of 2 and 791 |
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Answer» thank you |
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| 50. |
3. Flflu ilFind the solution of the equation 2 + 3 = 3:36-хуху-= 5 |
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