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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. |
Find four rational numbers between 4 and 5. |
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| 2. |
A circular mirror of radius 21 cm is surrounded by a circular frame ofwidth 3.5 cm. Find the cost of making the frame at R 15 per cm2. |
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| 3. |
2. The front compound wall of a house isdecorated by wooden spheres of diameter 21cm, placed on small supports as shown in Fig13.32. Eight such spheres are used for thispurpose, and are to be painted silver. Eachsupport is a cy linder of radius 1.5 cm and heightT7 cm and is to be painted black. Find the costof paint required if silver paint costs 25 paiseper cm2 and black paint costs 5 paise per cm2Fig. 13.32 |
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| 4. |
2. The front compound wall of a house isdecorated by wooden spheres of diameter 21cm, placed on smail supports as shown in Fig13.32. Eight such spheres are used for thispurpose, and are to be painted silver. Eachsupport is a cylinder of radius 1.5 cm and height7 cm and is to be painted black. Find the costof paint required if silver paint costs 25 paiseper cm2 and black paint costs 5 paise per cm2.Fig. 13.32 |
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| 5. |
divide 6.7÷1000 |
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Answer» 6.7/100067/100000.0067 |
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| 6. |
A man donates 10 aluminum buckets to an orphanage. A bucket made of aluminum isof height 20 cm and has its upper and lowest ends of radius 36 cm and 21 cmrespectively. Find the cost of preparing 10 buckets if the cost of aluminum sheet isR 42 per 100 cm2. Write your comments on the act of the man. |
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Answer» Surface area of bucket = π(r1 + r2)l + πr12 l = √[h2 + (r2 - r1)2] = √625 = 25 cm ∴ Surface area of 1 bucket = 22/7 × 1866 cm2 Surface area of 10 buckets = 22/7 × 18660 cm2 Cost of aluminium sheet = Rs. 24631.20 Like my answer if you find it useful! |
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| 7. |
mirror of length 20 cm and width 15 cm is toe framed with a 2 cm wide frame. Find the areaof the frame required. Also, find the cost offraming at the rate of15 per cm2. |
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Answer» Area of frame required=2(20*2+15*2) cm²=2(40+30) cm²=2*70 cm²=140 cm² Cost of framing 1 cm²=₹15Cost of framing 140 cm²=₹15×140=₹2100 |
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| 8. |
Divide 4a2 -b2+ 2a+b by (2a +b) |
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| 9. |
4. The 1st common multiple of 6 and 15 i30. The 2nd common15 is 60. Find the 3rd, 4th and 5th common multiples of 6 and 15 |
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| 10. |
If the nth term of an art2437then it2ndterm of an arithmetic progressiontermis(A)181B)15(c)0(D) 2 |
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Answer» an=24-3na2=24-3(2) =24-6 =18 |
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| 11. |
divisions.hese4389480 +12450 7Check your results by multipd) 90010e) 678 +6f) 247511 |
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Answer» correct answer |
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| 12. |
Sum of 4 consecutive terms of an A.P is 32. The ratio of product of 1st and last term andproduct of 2nd and 3rd term is 7:15. Find the terms. |
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Answer» Let the four consecutive numbers in AP be a-3d,a-d,a+d,a+3d. a-3d+a-d+a+d+a+3d=32 4a=32 a=8 1 (a-3d)(a=3d) /(a-d)(a+d)=7/15 15(a2-9d2) = 7(a2-d2) 15a2-135d2 =7a2-7d2 8a2-128d2= 0 d2= 4, ±2 Therefore d=4 or d=±2 1m So, when a=8 and d=2, the numbers are 2,6,10,14. When a=8,d=-2 the numbers are 14,10,6,2 |
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| 13. |
(Multipos 2 A in terms of tan ASin 2A IL.S.C. 1978)Express sin 2 A andcve that : () 2 tan A1+tan A |
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Answer» sin2A = 2tanA/ (1+tan^2 A) We will start from the right side and prove the left side. We know that tanA = sinA/cosA OR.......... ==> 2tanA / (1+tan^2 A) = 2(sinA/cosA) / [1+ (sinA/cosA)^2] = 2sinA/ cosA[ 1+ (sin^2A/cos^2 A)] = 2sinA/ cosA*[(cos^2 A + sin^2 A)/cos^2A] But we know that sin^2 A + cos^2 A = 1 ==> 2tanA/ (1+tan^2 A)= 2sinA/ (1/cosA) = 2sinA* You want the following to be proved: sin 2A = 2tan A/ (1 + (tan A)^2). We know that tan A = sin A/ cos A and (sin A)^2 + (cos A)^2 = 1. 2tan A/ (1 + (tan A)^2) => [2* sin A / cos A]/ [ 1 + (sin A)^2 / (cos A)^2] => [2* sin A / cos A]/ [ ((cos A)^2 + (sin A)^2) / (cos A)^2] => [2 sin A* (cos A)^2 / cos A]/ [ (cos A)^2 + (sin A)^2] => [2 sin A * cos A] / 1 => sin 2A Therefore sin 2A = 2tan A/ (1 + (tan A)^2). |
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| 14. |
cos l 50+51ncos 15°- sin 15value of SCos5+sin 15 |
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| 15. |
(iv) A train travels a distance of 480 km at a uniform speed. If the speed had beenless, then it would have taken 3 hours more to cover the same distance. We8 km/hneed to find the speed of the train. |
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| 16. |
(iv) A train travels a distance of 480 km at a uniform speed. If the speed had beenless, then it would have taken 3 hours more to cover the same distance. We8 km/hneed to find the speed of the train |
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Answer» thanks why you have not done 480/x -480/x-8 |
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| 17. |
ASSIGNMENT 5.41. Multiple Choice Questions (MCQ)Choose the correctopti(i) The product of (x + y), (x -y) and (r2 + y2) is(a) x2-y2(b) 4 +y4(c) x4 -y4 |
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Answer» (x+y)(x-y)(x²+y²)=(x²-y²)(x²+y²)=x⁴-y⁴Ans:c (x+y)(x-y) =(x²-y²) by formula (a+b)(a-b) =(a²-b²)so'(x²-y²)(x²+y²)by same formula (c) is ans. |
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| 18. |
sum of two number is 95.if one exceed the other by 15 find the number. |
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Answer» Let x be the bigger number and y be the smaller number x = y + 15 Also, Sum = 95x + y = 95y + 15 + y = 952y = 80y = 40x = 40 + 15 = 55The numbers are 55 and 40 |
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| 19. |
Multiply 3x®y4 by 5xºy |
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| 20. |
Y4-2 is divided by 2y-1 |
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Answer» (4y-2)/(2y-1)=2(2y-1)/(2y-1)=2 4 is the power of y..... |
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| 21. |
D, ë¤The GCD of x4 -y4 and x2y2 is |
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Answer» thank you |
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| 22. |
if x=3 and y=4, find the valuea) x³+y4 |
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| 23. |
4118 52y3 y2y4 + +x2 x30 |
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Answer» 3) x + y = 48........(1) x + 4 = 5/2 (y + 4) 2x + 8 = 5y + 20 2x - 5y = 12........(2)(1)×2;2x + 2y = 96.........(3)(3)-(2);7y = 84;y= 12then x = 36 6)3x + 2y = 6......(1) 2x + 3y = 6......(2)(1)×3;9x + 6y = 18........(3)2x + 6y = 12........(4)(3)-(4);7x = 6x = 6/7then y = 12/7 |
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| 24. |
find the remainder when p(y)=y4+y2+2y+3 is divided by y+2 by long division method |
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| 25. |
Which one of the following representsthe number 'eleven thousand elevenhundred eleven'?48. |
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Answer» eleven thousand eleven hundred eleven11,111 |
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| 26. |
10. The moon is about 384400 km from the earth and its path around the earth is nearly circular.Find the circumference of the path described by the moon in lunar month. |
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| 27. |
s) = 3 then find the value of Tan36.Find the value of cos2n "coste , cos8π·cosm15 ,'15'… 15 |
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| 28. |
Find the value ofcos15 +sin 15cos 15 -sin 15 |
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Answer» thank uuuu |
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| 29. |
Find the number whose 15% 15 2One number is six times the other. If their sum is 147, find the numbers |
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Answer» Let first number be x and other number (147 - x) Then,As per given condition (147 - x) = 6x7x = 147x = 147/7 = 21 Therefore,Numbers areFirst number x = 21 and other number (147 - x) =(147 - 21) = 126 |
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| 30. |
hitsradius05. A spherical snow ball is melting so that its volume is decreasing at the rate of 8 cc/sec. The rate at whicis decreasing when it is 2 cm is(b)(21)cm sec(c)(1)omrsecb) 2T(c) 1-1 cm/sec(d) π cm/sec(d) π cm/seca) 2 π cm/secin/sec |
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| 31. |
6. The edge of a cube is decreasing at the rate of0.6 cm/sec. The rate at which the surface area is decreasing whenthe edge of the cube is 12 cm, isa) 86.1 cm/sec(b)86.2 cm /secc) 86.3 cm/sec(d) 86.4 cm/sec |
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| 32. |
4. In ΔPQR, LQ = 90°, PQ =-3 cm and QR = 1 cm. Find the values of tan R,cosec R, sin Pand sec P |
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| 33. |
1.EvaluatewhenVIffind the value3-1 31if both a and b are rational numbers |
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Answer» nxdjisd😎😉😍😉😍😍😉😃😉😄😁😍😉😍😉😍😉😍😉😍😉😘😉😃😁😎😁😄😄😉😇😉😍😉😎😊😍😉😎😉🤗😉🍓🍏🍋🍏🍈🍈🍌 a=2+V3; a^2+1/a^2=(2+V3)^2+1/(2+V3)^2=(4+3+4V3)+1/(4+3+4V3)=(7+4V3)!+1/7+4V3=(7+4V3)^2/7+4V3=49+48+2.(7)(4V3)/7+4V3=07+ a= V3+V2/V3-V2=V3+V2/V3-V2 x V3-V2/ V3-V2=(3-2)/(V3-V2)^2=1/3+2-2V6=1/5-2V6___________€___(1), h=V3-V2/V3+V2 x V3-V2/V3-V2=(V3-V2)^1/3-2= ( 3+2-2V6/1)=5-2V6/1__€____(2), 1/5-2 V6/1 +5-2V6/1= 5-2V6-1/5-2V6-1=98-5=93 |
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| 34. |
me digit 6 in the fuel JUUSL.8. Find the difference between the place value and the face value of the digit 9 in thenumber 229301. |
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Answer» place value of 9=9000face value of 9=9 so difference between 9000 - 9 =8991 |
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| 35. |
14. How many times does the digit 9 occur between 1 and 100?(a) 11(b) 15(c) 18(d) 20 |
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| 36. |
If the polynomial 6x4 + 8x3- 5x2 + ax+ b is exactly divisible by the polynomial2x2-5, then find the value of a and b.iog on the line segment ioining the |
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| 37. |
10.af sín 2A = 2sin A8,オA=A) 0°B) 30°C) 45D) 60 |
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Answer» sin2A = 2sinAcosA cosA = 1 sin2A = 2sinA*(1) = 2sinA A = 0 |
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| 38. |
11. Prove that:- sin780'sin480°+cos120°sin 150°== |
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| 39. |
2÷5×13×3÷5×13-10 |
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| 40. |
7. Find three rational numbers betvw(i)-3/13 and 5/13(ii) 3.913 |
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Answer» -2/13,1/13,2/13,3/13,4/13 |
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| 41. |
13 13 13of peper is 5 5 cm long and 3cm wide. Find its perimeter |
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Answer» length=((3*5)+2)/3 =17/3 cmbreadth=((5*3)+1)/5=16/5cmPerimeter of rectangle=2×(length+breadth)perimeter=2×(17/3 +16/5)take LCM of 5 and 3 =15, multiply with 15perimeter=17.34cm |
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| 42. |
using the appropriate properties of operation of rational numbers evaluate the following 3/13*4/5-7/5-4/5*5/13 |
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Answer» 3/13 × 4/5 -7/5'-4/5×5/13=2/13'×4/5-7/5-4/13=8/65-7/5-4/13=2/13-7/5=7(13)-7(2)/65=91-14/65=77/65 99/65 is the correct answer |
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| 43. |
wU14. How many times does the digit 9 occur between 1 and 100?(c) 18(b) 15(a) 11(d) 20 |
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| 44. |
vor has e6eyudle nnd 8cm.high Pind th olum |
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| 45. |
eind the valu ofin the u |
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Answer» angle ABC = 180° - 106° = 74° angle ACB = 180° - 118° = 62° angle A + ABC + ACB = 180° angle A = 44° |
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| 46. |
19. Find the values of χ and y, when |
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| 47. |
Write the absolute valu3 |
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Answer» i) The absolute value of -3 is 3 The absolute value of - 3 is 3 |
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| 48. |
Find the value of the polynomial S3 tothe valuaf 30=3nomial Site+3 |
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| 49. |
19. Find the value of x. |
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| 50. |
19.Find the value of sin 150 |
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