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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. |
The internal and external diameters of a hollow hemispherical shell are6 cm and 10 cm respectively. It is melted and recast into a solid cone ofbase diameter 14 cm. Find the height of the cone so formed. [CBSE 2005C |
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| 2. |
5. In a hospital, used water is collected in a cylindrical tank of diameter2 m and height 5 m. After recycling, this water is used to irrigate apark of hospital whose length is 25 m and breadth is 20 m. If the tank isfilled completely then what will be the height of standing water usedfor irrigating the park? Write your views on recycling of water.(CBSE 2017] |
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| 3. |
Sum of n terms of three different arithmetic progressions are S, S2. S,. If first term ofall three A.Ps is 1 and their common differences are 1, 2 and 3 respectively, then provethat S, +S 22 |
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| 4. |
If S,s and S are the sum of first n, 2n and 3n terms of a geometric series resthen prove that Sl (S,-S) = (S2-Sly, |
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Answer» 1 2 |
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| 5. |
EXAMPLE 6IfcosB=ー,find the otherfive trigonometric ratios.3SQLI TTION TAlo |
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Answer» Clear picture please? |
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| 6. |
who is first prime minister of America |
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Answer» Peyton Randolph was the first PM of america. |
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| 7. |
10-[3*{4-(-4)}/{3-(5-3)}] |
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Answer» 10-[(3x8)/(3-2)]= 10-(24/1)= 10-24 = - 14 is the answer |
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| 8. |
0.3. Find the sum ofall the 11 terms of an AP whose middle most term is 30 |
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| 9. |
Convert the following ratios to percentages. -(2) 3:4(b) 2:3 |
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| 10. |
Q.3. Find the sum ofall the 11 terms of an AP whose middle most term is 30tne |
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| 11. |
Find the middle term of the AP 6,13,20,.....216 |
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Answer» thanks |
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| 12. |
Q. 14) IfS, S, and S, are respectively the sum ofn. 2n and 3n terms of a G.P, then prove that13 and s, are respectively the sum of n, 2n and 3n terms of a G.P.,that\mathrm{S}_{1}\left(\mathrm{S}_{3}-\mathrm{S}_{2}\right)=\left(\mathrm{S}_{2}-\mathrm{S}_{1}\right)^{2} |
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Answer» 1 2 |
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| 13. |
Ifthe sum ofn, 2n, 3n terms of an arithmetic progression are sı, s25 respectivelythen prove that s, 3 (s,-s,).1 700 oto in the |
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| 14. |
HOTS Prove that the sum of later half of 2n terms ofan AP is equal to one-third of the sum of the first 3nterms. |
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| 15. |
1.A park, in the shape of a quadrilateral ABCD, has 2 C = 90°, AB = 9 m, BC = 12CD = 5 mand AD = 8 m. How much area does it occupy?DAL |
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Answer» Given: ∠C = 90˚, AB = 9m, BC = 12 m, CD = 5m and AD = 8m.To Find: Area of quadrilateral ABCD.Concept Used:If sides of a triangle are a, b, and c, then area of a triangle is given by: Where s = semiperimeter of the triangle Area of a right-angled triangle Diagram: Explanation:Area of park = Area of ΔBCD + Area of ΔABDΔBCD is a right-angled triangle. Therefore,Area of ΔBCD = 1/2 × 12 × 5 m2 = 30 m2InΔ ABD, we have2s = 9 + 8 + 13 = 30 ⇒ s = 15 ∴ = 6√35 m2Area of park = (30 + 6√35) cm2Hence, the area of the park is (30 + 6√35) cm2. answer ask from school teacher 65.4cm2 is the most correct answer 65.4cm2 is the right answer 96 is a answer of this question 65.4 is the correct answer 65.4cm2 is the most correct answer 65.4 is the correct answer 65 is the best ansewr 65.4 is the best answer 56 meter square units 56 meter square units (30+√35)cm2 is the correct answer 65.4 is the correct answer (30+√35)cm.^2 is correct answer hiiiiiiiiiii friend nice question area of park is (30+6√35)cm2 65.4 cm2 is this is answer Hence, the area of the park is (30+6√35)cm2 pata nahin kya hai iska answer bhai 65.4 is the correct answer 65.4cm2 is the answer Let side be 'a'volume of a cube=a*3a*3 =4913a= cube root of 4913=17cm please like me do as best me i work very hard thanks |
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| 16. |
.Let the sum of n, 2n, 3n terms of an A.P. be S, S and S, respectively, show that |
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| 17. |
-4 3 310. If A 1 0 1 ,show that adj A A. |
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| 18. |
ae20. Show that(0 the points (0,-2), (3, 1), (0, 4), (-3, 1) are theyertices of a square |
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| 19. |
s Write the common difference of an A.P whoseterm is a,3 |
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| 20. |
12. The angles of a quadrilateral are in the ratios 3:5:7:9. Find the angles of aquadrilateral |
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Answer» 45 75105135 are the angles |
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| 21. |
2. How many numbers he betnbeet0.3. Find the sum of all the 11 terms of an AP whose middle most term is 30.is 225 and the su |
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| 22. |
Sum of n terms of three different arithmetic progressions are S,. S S, If first temmall three A.Ps is 1 and their common differences are 1. 2 and 3 respectively, then provethat S, +S2S2are S. S, S,. If first term of |
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Answer» s1= [2a +(n-1)d]n/2 =[2a +n-1)n/2 s2=[2a+(n-1)2]n/2 =[2a+2n-2]n/2 =(2an +2n^2-2n)/2 s3=[2a+(n-1)3]n/2 =(2a+3n-3)n/2 s3+s1=[2an+3n^2-3n +2an+n^2-n]/2 =(4an+4n^2-4n)/2 =2an+2n2 -2=2s2 |
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| 23. |
ARITHMETIC PROGRESSIONS17. Find the 20th term from the last term of the AP:3,8, 13,. . . 253.m of the 6ih a |
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Answer» a = 3. Common difference = 8-3 = 5. 20th term = a + (20-1)d.= 3+19(5)= 88Please hit the like button if this helped you |
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| 24. |
4. The spherical balloon with radius 21 E Is Ill5. A solid has hemi-spherical base with diameter 8.5 cm and it is surmounted by a cylinder vheight 8 cm and diameter of cylinder is 2 cm. Find the volume of this solid. (3.14) |
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| 25. |
4· The product of three numbers in G.P is 125 and the sum of their products taken inpairs is 87/2. Find themf their sguares is 189, Find the |
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| 26. |
6. The internal and external diameters of a hollow hemispherical shell are6 cm and 10 cm respectively. It is melted and recast into a solid cone ofbase diameter 14 cm. Find the height of the cone so formed. (CBSE 2005c] |
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Answer» sorry bhai main ne cube use magic kiya |
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| 27. |
Value of tan-60° is-(A)(BA1-(C)(D) |
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Answer» Answer:B)3Explanation:tan 60°=√3tan²60°=(√3)²=3 |
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| 28. |
l3) sin 90(4) cos 90°2.If tant-cot 370 , then the value of θ is |
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Answer» tan = cot (37°) tan = tan ( 90 - 53°) tan = tan (53°) So = 53° |
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| 29. |
24. The internal and external diameters of ahollow spherical shell are 6 cm and 10 cmrespectively. It is melted and recast intoasolid cone of base diameter 14 cm. Find theheight of the cone so formedCRSE D 05C |
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| 30. |
<m\z 0 एप्प 22 L3 Bl L 05०० +0ए5 [2 |
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Answer» tan θ =√3/2which gives p= √3k, b= 2khence, h= √(3k²+4k²) = √7kso, sinθ = p/h = √3/√7 and cosθ= b/h = 2/√7 so, sinθ + cos θ = (2+√3)/√7 |
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| 31. |
0 1show that ABBA.0 -1 |
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| 32. |
44. If S,, S2 and S3 are the sum of n, 2n and3n terms of an Arithmetic Progression(A.P.) then which one of the following istrue:(I) S3 S2 +S (2) S3 3 (S2-S1)(3) S3 2 (S2-S) (4) S3 4 (S, -S,) |
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Answer» Option- B Let ‘a’ be the first term of the AP and ‘d’ be the common differenceS1= (n/2)[2a + (n – 1)d] --- (1)S2= (2n/2)[2a + (2n – 1)d] = n[2a + (n – 1)d] --- (2)S3= (3n/2)[2a + (3n – 1)d] --- (3) Consider the RHS: 3(S2– S1)Substitute the values of S2and S1and simplify to get the LHS |
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| 33. |
24. If SI, S2 and S3 be the sum of n, 2n and 3n terms respectively of an AP, show that83 3(S2 - s). |
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Answer» S₁=Sₙ=n/2 (2a+ (n-1) d) s₂= 2n/2 {2a+ (2n-1) d} s₃=3n/2 {2a+ (3n-1)d} solving RHS 3{s₂-s₁) 3 [2n/2 {2a+ (2n-1)d} - n/2 {2a+ (n-1)d }] 3n/2 [2{2a+(2n-1)}]-[2a+(n-1)d] 3n/2 [4a+2(2n-1)d-2a-(n-1)d] 3n/2 [4a+ 4nd- 2d- 2a- nd+ d] 3n/2 [2 a+ 3nd-d] 3n/2 [2a+ (3n-1) d]=s₃ Please like the solution |
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| 34. |
I) If s, S2 and S3 are respectively the sum of2n and 3n terms of a G.P. then prove that(S3-S)(S2-S1)2 |
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Answer» wrong answer |
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| 35. |
124. If S, S2,Sn are the sums of infinite G.P.s whose first terms are 1, 2,3 ....n andsu12 3whose common ratios are 1/2, 1/3, ....../(n+1) then the value of S,+S2+S3n isc) in |
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| 36. |
endentlyThe sum of n, 2n, 3n terms of an A.P. are S, S2, S3 respectively. Prove that:Il thore chords which are parallel t8. |
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| 37. |
If S1, S2 and S3 are the sum of n terms of three arithmetic progressions, the first term of eachbeing unity and the respective common difference being 1, 2, 3; prove that S, +S 2S |
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Answer» Like if you find it useful |
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| 38. |
In a hospital, used water is collected in a cylindrical tank of diameter 2 mand height 5 m. After recycling, thiswater is used to irrigate a park of hospital whose length is 25 mand breadth is 20 m. Iftank is filled completelythen what will be the height of standing water used for irrigating the park ? |
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| 39. |
2. 3 B 3-13L3 1 =l o 2 हैं तो 28-98 ज्ञात कौजिए। |
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| 40. |
1 The height of a cone is 24 cm and the diameter of its base is 14 cm.Find the slant height, volume, area of curved surface and the totalsurface area of the cone. |
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| 41. |
?1. Using the primsquares.G) 400 |
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Answer» Prime factorisation of 400 400=2*2*2*2*5*5 Prime factorisation of root of 400 √400= 2*2*5= 20 Hence, the square root of 400 is 20. |
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| 42. |
04, A man on the deck of a ship 14m above the water level observes that the angleof elevation of the top of a cliff is 60째 and the angle of depression of the base ofthe cliff is 30째. Calculate the distance of a cliff from the ship and the height of thecliff. Take V3-1.732 |
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| 43. |
L3 AT (e B |
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Answer» (3x + 1)(2x + 3) = 36x^2 + 9x + 2x +3 = 36x^2 + 11x = 0x(6x + 11) = 0x = 0, - 11/6 |
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| 44. |
doch well with diameter 7 m is dug and the earth roma placform 22 m by 14m. Find the height of the platom |
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| 45. |
1) rational and equal 2) rational and not equal3) irrational4) imaginaryIf '1' is one of the roots of ax² + 3x +5=then the second root isIf'3' is root of x² + kor - 24 = 0 then it isroot of |
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Answer» 5.is.irrationally is |
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| 46. |
236 00 लरन८ ८5 अविस्ट निज ट-5न्द्ाड दिकद «नरक: ठप P-S— |
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Answer» 135 is the answer to that question |
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| 47. |
24. The internal and external diameters of ahollow spherical shell are 6 cm and 10 cmrespectively. It is melted and recast into asolid cone of base diameter 14 cm. Find theheight of the cone so formed.CBSE D 05C] |
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| 48. |
dle Areas ot Solids7856. The internal and external diameters of a hollow hemispherical shell are6 cm and 10 cm respectively. It is melted and recast into a solid cone ofbase diameter 14 cm. Find the height of the cone so formed. ICBSE 200sc |
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| 49. |
. 34/564If a and b are rational numbers anda:b is equal2-3'toV3:1EXPLANATION |
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| 50. |
2s. The length of the diagonal of a square is 20 cm. Its area is(b) 200 cm2(d) 100 2 cm2(a) 400 cm2(c) 300 cm? |
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