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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. |
20. In △ABC, <B = 90° and BD丄AC. Prove that <ABD = ZACBSX |
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| 2. |
Evaluate the following limits:\lim _{x \rightarrow \pi} \frac{\sin x}{x-\pi} |
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| 3. |
In DAB CqZA:B:C 22:35find LA LB and LC. |
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Answer» A =36, B =54, C =90 is correct answer 90 is the correct answer bhai question thik se likh ke bhejo let angle a=2xb=3x&c=5xput them:-2x+3x+5x=180'10x=180'x=180'/10x=18' then multiply the value with 2 ,3 and 5 |
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| 4. |
कर.मो आकृति 122 आकृति 12.503कृति 1254 मे ZACB = 40° g ZOAB 39 कीजिए । |
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| 5. |
12. In the figure, prove that La+Lb+ Lc 360°. |
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| 6. |
35. In een circle. Ob centre and ZRDC 42", the ZACB isto245 |
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| 7. |
12. In the figure, prove that LaLb+ Lc 360. |
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| 8. |
2 LA = 3 LB = 6 LCfindIn a triangle AABCthe angles. |
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Answer» angle A is equal to 90° " B " " " 60°. " C. ". " " 30° |
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| 9. |
Example in a right triangle ABC, right-angled at Bif tan A= 1 , then verify that2 sin A cos A 1. |
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| 10. |
8. To construct a triangle similar to AABC in which BC 45 cm, 4B-453and C-60, using a scale factor of 7, BC will be divided in the ratio(a) 3: 4(b) 4:7(c) 3:10(d) 3:7CBSE 2012 |
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| 11. |
gent to a circle of radius 4 cm from a point on the concentric circle ofand measure its length. Also verify the measurement by actual calculation., Construct6 cm |
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| 12. |
Expand each of the expressions in Exercises 1 to51.(1-2x)"2. |
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| 13. |
ent to a circle of radius 4 cm from a point on the concentric circle ofedius 6 cm and measure its length. Also verify the measurement by actual calculation |
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| 14. |
Expand each of the expressions in Exercises 1 to 5.1. (1 2x)2. |
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| 15. |
in Exercises 1 to 23V1+43x5. 1+2x |
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Answer» 2) |
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| 16. |
Expand each of the expressions in Exercises 1 to 51. (1-2x)52. |
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Answer» What is the answer of next qustiom |
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| 17. |
Evaluate the following limits in Exercises 1 to 22.1, limx +33, limar |
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Answer» 1. lim x + 3 = 6x--> 3 2. lim (x - 22/7) = pi - 22/7x--> pi 3. lim pi × r² = pir --> 1 |
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| 18. |
Construct a tangent to a circle of radius 4 cm from a point on theconcentric circle of radius 6 cm and measure its length. Also, verify themeasurement by actual calculation. |
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| 19. |
25.InatriangleABCrightangledatC,iftaaAshowthatsin-A.edsis-COSAsin B 1 |
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| 20. |
. Construct a triangle ABC in which BC-8cm, LB 45° and AB-AC-3.5 cm. |
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| 21. |
in triangle ABC, right-angled at B, AB 5cm and zACB 30 thenfind the length of the side BC. |
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| 22. |
5. In the given figure, LB = 65° and LC = 45° in △ABC and DAE 11 BC.+D-If <DAB = x。and <BAC = yo, find the values of x and y.65°45 |
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| 23. |
BL and CM are medians of a triangle ABCright angled at A. Prove that4(BL24 CMP) = 5BC2.CBSE 2012] |
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| 24. |
heigit UIThe area ofa rhombus is 42 m. If its perimeter is 24 m, find its altitude. |
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| 25. |
8. To construct a triangle similar to AABC in which BC 4.5 cm, LB 45and C60, using a scale factor of , BC will be divided in the ratioCBSE 2012)(a) 3:4(b) 4:7(c) 3:10(d) 3:7 |
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Answer» thanx |
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| 26. |
in the given figure , LB =65° and CC =45° in A ABC and DAE II BC. IF CD AB = xe and CEAC = y, findthe values of x and y. |
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| 27. |
11. A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side6 cm. What is the area of the left over aluminum sheet? (Take π-314) |
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| 28. |
6 (a) The median of the distribution 3, 11, 15, 17, q,q +2,27, 31,40, 42, is 23. Find q(b) A solid cylinder has a height 8 cm and the base with radius 6 cm. Two hemispheres of radius 2 cmand 3 cm are scooped from one of the bases. Calculate the voleme of the material remaining in thecylinder13] |
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| 29. |
A cone is 8.4 cm height and the radius of its base is 2.1 em. It is melted and recast intoa sphere, then find radius of the sphere.A) 2 cm2.B) 8 cmC) 2.1 cmD) 3 cm |
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| 30. |
ek Yha_ d\‘ugl\oh: oF o BhemS 00cm _ond Wl om (T फेर ककिडि- |
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Answer» Area = 0.5*product of diagonals= 0.5*16.5*14.2= 7.1*16.5= 117.15 cm² Please hit the like button if this helped you out |
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| 31. |
43. Bl and CMare medians of a triangle ABC right angled at A.Prove that 4(BL2+CMF) 5 BC2 |
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Answer» Given : ABC right angle triangle at A where BL and CM are the medians To prove : 4(BL^2 + CM^2)=5BC^2 Proof :Since BL is the median AL=CL=1/2 AC .............(1) Similarly CM is the median AM = MB = 1/2 AB .......) In triangle ABC BC^2 = AB^2 + AC^2 In triangle BAL BL^2 =AB^2 +AL^2 BL^2 =AB^2 +(AC/2)^2 On further little solving steps 4BL^2 =4AB^2 +AC^2 Then in triangle MAC CM^2 =AM^2 +AC^2 Doing same process here We get 4CM^2 =AB^2 +4AC^2 |
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| 32. |
Solve the inequalities in Exercises 1 to 6.1. 2 S 3x - 455 |
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Answer» the answer is2≤x≤3hope it is helpful |
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| 33. |
One circle has a radius of 98 cm and a second concentric circle has a radius of 1 m 260mHow much longer is the circumference of the second circle than that of the first? |
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| 34. |
1. The cost prlee ul a miA car which cost Rs 2,20,000 had to be sold at a loss of 35% since it failed in the safety test whatwas the S.P ? [ Ans : Rs 1,43,000!t 1 50, loss Ifthe cos |
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| 35. |
10.5: There is one and only one circle passing through three givennoi-collinear points. |
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| 36. |
Example 13: BL and CM are medians of ariangle ABC right angled at A. Prove that4 (BL2+ CM) 5 BC2 |
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| 37. |
5. The area of a rhombus is 96 sq. m. If its perimeter is 32 m, find its altitude.hown in the figure. Find its altitude |
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Answer» Perimeter of the rhombus = 32 m (Given)As we know that all the sides of a rhombus are equal. So,Each side of rhombus = Perimeter/4= 32/4Each side of the given rhombus= 8 mAs we know that the area of a rhombus is the product of its altitude and base.So, according to the question.Area = Altitude× Base96 = A× 88A = 96A = 96/8Altitude = 12m |
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| 38. |
. Find the area of a triangle whose base and altitude are 5 cm and 4 cm |
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| 39. |
24. Find the sum of the first 15 terms of the list whose nth term is given by a, 6 n25, Prove that the anole bat |
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| 40. |
5. Areas of two similar triangles are in the ratio25:36. If the altitude of the first triangle is 1.5 cm,find the altitude of the second triangle. |
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| 41. |
34 E4b) Prove that the sum of the exterior aAABC is 360°(21 +22+3360°). |
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Answer» Consider ΔABC in which ∠A = 1, ∠B = 2 and ∠C = 3Let the exterior angles of A, B and C be ∠a, ∠b and ∠c respectively.Recall that sum of angles in a triangle is 180°That is ∠1 + ∠2 + ∠3 = 180°From the figure, we have∠1 + ∠a = 180° [Linear pair]∠2 + ∠b = 180° [Linear pair]∠3 + ∠c = 180° [Linear pair]Add the above three equations, we get∠1 + ∠a + ∠2 + ∠b + ∠3 + ∠c = 180° + 180° + 180°⇒ (∠1 + ∠2 + ∠3) + ∠a + ∠b + ∠c = 540°⇒ 180°+ ∠a + ∠b + ∠c = 540°⇒∠a + ∠b + ∠c = 540° – 180° = 360°Thus sum of exterior angles of a triangle is 360°. |
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| 42. |
Example 13 : BL and CM are medians of atriangle ABC right angled at A. Prove that4 (BL' + CMP) = 5 BC2. |
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Answer» Since BL is the median AL=CL=1/2 AC .............(1) Similarly CM is the median AM = MB = 1/2 AB ........... (2) In triangle ABC BC^2 = AB^2 + AC^2 In triangle BAL BL^2 =AB^2 +AL^2 BL^2 =AB^2 +(AC/2)^2 On further little solving steps 4BL^2 =4AB^2 +AC^2 Then in triangle MAC CM^2 =AM^2 +AC^2 Doing same process here We get 4CM^2 =AB^2 +4AC^2 BC^2==AB^2+AC^2 4CM^2=AB^2+4AC^2adding the above equation4(BL^2+CM^2)=5BC^2 |
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| 43. |
6. In the given figure, a triangle ABC is drawnto circumscribe a circle of radius 2 cm suchthat the segments BD and DC into whichBC is divided by the point of contact D, areof lengths 4 cm and 3 cm respectively. If thearea of AABC 21 cm2 then find the lengths ofCBSE 2011]0sides AB and AC. |
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Answer» no |
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| 44. |
21. Construct a AABC in which LB 45,from the vertex A to base BC is 4.5 cm.C 60 and the perpendicular |
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Answer» Thanks |
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| 45. |
Example 13: BL and CM are medians of atriangle ABC right angled at A. Prove that4 (BL' + CMP) = 5 BC. |
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Answer» Since BL is the median AL=CL=1/2 AC .............(1) Similarly CM is the median AM = MB = 1/2 AB ........... (2) In triangle ABC BC^2 = AB^2 + AC^2 In triangle BAL BL^2 =AB^2 +AL^2 BL^2 =AB^2 +(AC/2)^2 On further little solving steps 4BL^2 =4AB^2 +AC^2 Then in triangle MAC CM^2 =AM^2 +AC^2 Doing same process here We get 4CM^2 =AB^2 +4AC^2 |
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| 46. |
is a median of A ABC. Prove that (AB + BC+CA)> 2AM(AC +MC) > AM (in ACM)Now, add the two inequalitiesHint. (AB+ BM)> AM (In A ABM) |
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| 47. |
The parallel sides of a trapezium are at a distance of 5 cm and in the ratio of 2:5. If thelength of longer side is 15 cm, find the area of the trapezium. |
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Answer» Are(trapezium) = sum of parallel sides ×distance between them /2longer side length = 15means 5x= 15 x=15/5 x=3then other side is 2x= 2×3=6distance = 5so,area= (15+6)(5)/2 =(21×5)/2 =105/2 =52.5cm^2 |
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| 48. |
0=7-A6—X€o=c-A¢-x (O = |
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| 49. |
é=¢8 (L2N zP jp el 2 1 A6 LBy |
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| 50. |
quaniuty Ul HIIK sold by him.(3 A room is 7 m 80 cm long and 5 m 20 cm broad. By how much is the room longer thbreadth? |
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Answer» Length of room = 780cmBreadth of room = 520cm Length/Breadth = 780/520 = 3/2 Length = 3/2 Breadth Room is 1.5 times longer than breadth |
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