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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. |
EXERCISE 8.2Apark, in the shape ofa quadrilateral ABCD. has2 C-90°, AB=9 m, BC-12CD-5 m and AD 8 m. How much area does it occupy?1. |
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| 2. |
1I'm is a natural number, then find the average of n, (ii 1 )(n+2), (n+3), (n+4) and (ni5).ăľ |
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Answer» Average = [ n + n + 1 + n + 2 + n + 3 + n + 4 + n + 5 ] / 6= (6n + 15) /6 = n + 2.5 PLEASE HIT THE LIKE BUTTON |
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| 3. |
1. Prove : n+4 is a composite number for n>1. |
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Answer» you worked on this for any length of time without success, you'll kick yourself now: n4+4 can be factored. Here it is: n^4+4n^4+4n^2+4-4n^2( n^4+4n^2+4) -4n^2((n^2+2)+2n)((n^2+2)-2n) And since n>1 you can show that both factors are larger than one. You're done. A similar problem was suggested to me, to prove that n^4-20n^2+4 is not prime. This one had me stumped for a while because I was trying this: n^4- 20n^2+4n^4+4n^2+4-24n^2( n^4+4n^2+4) -24n^2((n2+2)+sqrt(24)(n))((n2+2)-sqrt(24(n)) But those factors, while real, are not integers. So it doesn't help in the effort to show compositude. Sorry, I can't help making up new words. Here's the real answer: n4- 20n2+4n4-4n2+4-16n2( n4-4n2+4) -16n2((n2-2)+4n)((n2-2)-4n) Here, the first factor is greater than one if n>0 -- that's the point where the n2and n terms overpower the constant. The second factor is greater than one if n>4, where the n2term overpowers the n term. So the polynomial is composite for all n>4. It's composite for n=0, 1, 2, 3, and 4, too, because its values are 4, -15, -60, -95, and -60. |
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| 4. |
1, A park, in the shape of a quadrilateral ABCD, has C 90, AB-9 m,-5 m and AD -8m. How much area does it occupy? |
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Answer» 1 2 3 |
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| 5. |
1. A park, in the shape of a quadrilateral ABCD, has L C 90, AB-9 m, BC 12m,cD-SmandAD-Sm. How much arca does t occupy? |
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Answer» Solutions are uploaded in order! Why |
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| 6. |
4. In the given figure, two sides AB and BC and the median AD of ÎABC areequal respectively to the two sides PQ and QR and the median PM of theother triangle PQR.INCERTProve that[CBSE 2011] |
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Answer» Solution: Given: AD is the median of ∆ABC & PM is the median of ∆PQR. AB = PQ, BC = QR & AD = PM To Show: (i) ΔABD ≅ ΔPQM(ii) ΔABC ≅ ΔPQR Proof: Since AD & PM is the median of ∆ABC (i)1/2 BC = BD & 1/2QR = QM (AD and PM are median) Now, BC = QR. (given) ⇒ 1/2 BC = 1/2QR (Divide both sides by 2) ⇒ BD = QM In ΔABD and ΔPQM, AD = PM (Given) AB = PQ (Given) BD = QM (Proved above) Therefore, ΔABD ≅ ΔPQM (by SSS congruence rule) ∠B = ∠Q (CPCT) (ii)In ΔABC & ΔPQR, AB = PQ (Given) ∠B = ∠Q(proved above in part i)BC = QR (Given) Therefore, ΔABC ≅ ΔPQR ( by SAS congruence rule) |
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| 7. |
9, If 16% of a number is 72, find the number |
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| 8. |
of a tow14. The angle of elevation of a tower from a point on the same level as the foot of30°. On advancing 150 metres towards the foot of the tower, the angle of elevation of thetower becomes 60°. Show that the height of the tower is 129.9 metres (Use 3 -1.732)ICBSE 2006 |
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| 9. |
Section-CShow that exactly one of the number n,n+ 2 or n +4 is divisible by 3. |
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Answer» We applied Euclid Division algorithm on n and 3.a = bq +r on putting a = n and b = 3n = 3q +r , 0<r<3i.e n = 3q -------- (1),n = 3q +1 --------- (2), n = 3q +2 -----------(3)n = 3q is divisible by 3or n +2 = 3q +1+2 = 3q +3 also divisible by 3or n +4 = 3q + 2 +4 = 3q + 6 is also divisible by 3Hence n, n+2 , n+4 are divisible by 3. |
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| 10. |
13. In the given figures, two sides AB, BC andthe median AD of AABC arecorrespondingly equal to the sides PQ, QRand the median PM of APQR.Prove that AABCAPQR.C Q |
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Answer» 1 2 |
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| 11. |
13. In figure, if D is the centre of circleand angle ADC 150°, find angle ABC |
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| 12. |
9. In the given figure, O is the centre of acircle and LBOD 150°. Find the valuesof χ and y |
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| 13. |
49^x=7^3 |
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| 14. |
SECTION BSolve the following : (3 marks eachl12espeed of a faster car and a slower car is 20 km/hr. I theur more than the faster car to travel a distance of 400 km,find speed of both the cars.Iole thr anelr of elevation of an advertising |
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Answer» speed of slower car = 80speed of faster car= 80+20= 100 |
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| 15. |
A park, in the shape of a quadrilateral ABCD, hasCD 5 m and AD 8 m. How much area does it occupy?1.C = 90°, AB-9 m, BC-12m, |
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| 16. |
Water is flowing at the rate of 2.52 km/hr through a cylindrical pipeinto a cylindrical tank, the radius of whose base is 40 cm. If theincrease in the level of water in the tank, in half an hour is 3.15 m,find the internal diameter of the pipe.CBSE 2015) |
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| 17. |
Water is flowing at a speed of 15Km/hr through a pipe of diameter 14cm in to a cuboidal pond which is 50long and 44m wide. In what time will the level of water in pond rise by 21 cm? |
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| 18. |
A park, in the shape ofa quadrilateral ABCD, has < C-900, AB-9 m, BC = 12m,CD1.5 m and AD = 8 m. How much area does it occupy? |
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| 19. |
he angleL A park, in the shape of a quadrilateral ABCD, has C . AB-9m, BC 12mINCERTC-5 m and AD-8m. How much area does it occupy?m and ather sides are 25 cm and 26 |
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| 20. |
standing waltr27. A farmer connects a pipe of internal diameter 25 cm from a canal into acylindrical tank in his field, which is 12 m in diameter and 2.5 m deepIf water flows through the pipe at the rate of 3.6 km/hr, in how muchtime will the tank be filled? Also, find the cost of water if the canaldepartment charges at the rate of 0.07 per mCBSE 2009c] |
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| 21. |
)135 2that anyaldosititeod wyger is ofthe fprm6q +1, or 6g+ 3, or60+5,whereqis some integer. |
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Answer» Let a be any positive integer and b = 6. Then, by Euclids algorithm, a = 6q + rfor some integer q ≥ 0, and r = 0, 1, 2, 3, 4, 5 because 0 ≤ r Therefore, a = 6q or 6q + 1 or 6q + 2 or 6q + 3 or 6q + 4 or 6q + 5 Also, 6q + 1 = 2 × 3q + 1 = 2k1+ 1, where k1is a positive integer 6q + 3 = (6q + 2) + 1 = 2 (3q + 1) + 1 = 2k2+ 1, where k2is an integer 6q + 5 = (6q + 4) + 1 = 2 (3q + 2) + 1 = 2k3+ 1, where k3is an integer Clearly, 6q + 1, 6q + 3, 6q + 5 are of the form 2k + 1, where k is an integer. Therefore, 6q + 1, 6q + 3, 6q + 5 are not exactly divisible by 2. Hence, these expressions of numbers are odd numbers. And therefore, any odd integer can be expressed in the form 6q + 1, or 6q + 3, or 6q + 5. |
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| 22. |
(6)135 and 225(11) 190 aldgr fifefom lororky3 whre jasome integer.nh hehind an army band of 32 members in |
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| 23. |
ald irdtioialnHHlalloalnumber4.)two zeros of the polynomial3x20x2 6x + 36 are 2 and- /2, find the other zerosof the polynomial. |
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| 24. |
and AC and median AlDCA PORAB4Rre amedian FPQR. Shoad PR respectively proportional to sides PQ Bow median PM of another triangle |
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Answer» thanks |
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| 25. |
- 4 - 5AMPLE 29 : Add the rational numbers912" |
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Answer» identity -107 -6 705 - 4 - 6 1989 - 11 12 12 - -4/9 -5/12+11/28= ________________________________ 9,12,28/3=3, 4, 28/2=3, 2, 14/2 3, 1, 7=3×2×2×3=9×4=36 "_______________________________ -16 -15+22/36=-31+22/36=-9/36=-1/9 -16/36"-15/36+22/36= -16-15+22/36=-31+22/36=-9/36=1/-4 -4/9-5/12+11/28; -16-15+22/36= - 31+22/36= -9/36= =1/-4 This question answer is -1/4 correct answer is 1/-4, -9/36 |
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| 26. |
The length of a rectangular field is twice its breadth. If the perimeter of the field is 150 metres, fitits length and breadth. |
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| 27. |
if length is 15 and area is 150 find the breadth |
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Answer» area = length × breadth 150 = 15 × breadth so breadth = 150/15 = 10 . |
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| 28. |
८ 05७2 ५०0] ४1६ , 912: 2-10 260 , 1सं० T 222 |
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Answer» पृथ्वीराज रासो'' एक ऐसा महाकाव्य है जिसे साहित्य का सर्वाधिक प्राचीन महाकाव्य माना जाता हैं | अब तक कई प्रतिया प्रकाश में आई हैं | इसकी कई प्रतियाँ उदयपुर राज्य के पुस्तकालय में सुरक्षित रखा गया हैं | इसकी सभी उपलब्धियाँ प्रतियाँ संवत 1750 बाद लिपिबद्ध की गई है | प्रारम्भ में ''रासो'' को एक प्रमाणिक ग्रन्थ समझा गया था | फ्रांस के विद्वान् ''गार्सा द तासी'' ने भी इसे प्रामाणिक माना था | बंगाल की ''रॉयल एशियाटिक सोसाइटी'' ने तो इसका प्रकाशन भी शुरू कर दिया था , किन्तु इसी बिच सन 1875 ई० में ''प्रो० बूलर'' को कश्मीर में ''जयानक'' द्वारा रचित ''पृथ्वीराज विजय'' नामक संस्कृत काव्य उपलब्ध हुआ | |
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| 29. |
Find the value of the middle most term of the AP: -11,-7,-3,......49. |
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| 30. |
12110 \times \frac { 21 } { 66 } |
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Answer» 110*21/66 = 21/60 = 7/20 thank you Didi shukriya |
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| 31. |
plot the following points on a graph paper(a) L(0, 5)(b) M(-2, 4)(c) P(4,-3)into lio on thfe ts-cogy(d) Q-3,0) |
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| 32. |
¢ lbb कि पार ते (४ 'डि 912 [2 पतिbbb ke Bk । है 9222८ Bkl 1 [१६100 e |
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Answer» LCM× HCF = product of two number216 × HCF = 7776HCF = 7776/216=36 |
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| 33. |
(a) The smallest counting number is |
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Answer» I think 1 is the smallest counting number 1 is the smallest counting number the smallest counting number is 1 0 is the correct answer 0 is the correct answer 1is the smallest counting number my answer is 1 is smallest counting number 0 is the smallest counting no. I think 1 is the smallest counting or 0 i think 1 is the smallest counting number 1 is the smallest counting number. 1 isthe smallest countingno (a) The smallest counting number is 1 l think 1 is smallest one or 0 1 is the correct answer i think - infinite is smallest counting number One is the smallest counting number 1 is the smallest counting number 0/ 1 is the smallest counting number 1 is the smallest counting numbers l think 1 is the smllest one is smallest number of counting number i think 1 is smallest counting number (a) The smallest counting number is 1 1 is the smallest contig numbar the smallest counting number is 1. The smallest counting number =1 one is the smallest counting number correct answer is zero 1 is the smallest counting number 0.1 is a smallest counting number 0.01 is a smallest counting number smallest counting number is 1 counting numbers are numbers that are used to count physical things. So 1 is the smallest counting number 1 is smallest counting number The smallest counting number is ...1.. is the right answer according to me it is 1 i think 0 is the smallest counting number zero is the smallest counting number 1 is the smallest counting number I think so 1 is the smallest counting nom 1 is the smallest counting number I think 1 is the smallest counting nummber 1 is the smallest counting number 1 is the smallest counting number I thing so (1) one is the smallest counting number The smallest counting number is one (1) . 1 is smallest counting number 1 is the smallest counting no as u asked the smallest counting number is 1 1st is the correct answer The smallest counting number is (1= one) one is the smallest counting number..................... 1 is the smallest counting number the smallest counting no. is 1 1 is the smallest counting number . 1 is the smallest counting number 1 is the smallest counting number. the smallest counting number is zero the smallest counting no. is 0 The smallest counting number is 1 0 and 1 is smallest number 1 is the smallest counting number cause we 1 is smallest number The smallest counting number Is....... 1 1 is the correct correct answer do you understand I say 1 is the correct answer Natural numbers are also called as counting numbers so,the smallest counting number is 1 (1) is the smallest counting number I think the smallest number is 1 1 is the smallest counting number 0 is the smallest counting number |
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| 34. |
2. ABCD is a parallelogram. AE is perpendiolon DC and CF is perpendicular on AlD.If AB-10 cm, AE-8 cm and CF-12mFind AD |
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| 35. |
Hoes many spheres 12 cm in diameter can be made from a metalliccyinder of diameter 8 cm and height 90 cm? |
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| 36. |
Write the numbers countingby tens |
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Answer» 10,20,30,40,50,60,70,80,90 the number are, 10,20,30,40,50,60,70,80,90 |
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| 37. |
Number Used for counting 1,2,3,4 are known as Natural Number. |
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Answer» yes they are natural number sss. they. are ya... they r natural no. yes the numbers are natural yes the numbers are natural |
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| 38. |
are UDmany spcm in diameter can be made from a metallicHow many spheres 1210. Hinder of diameter 8 cm and height 90 cm? |
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| 39. |
25. A hollow sphere of internaland external diameters 4 and 8 cm respectively is melted intoa cone of base diameter 8 cm. ind the height of the cone |
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| 40. |
12. A well of diameter 150 cm has a stone parapet around it. lí the length of the outer edge of the paragis 660 cm, then find the width of the parapet. |
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| 41. |
Find the cost of carpeting a room 13 m by 9 m with a carpet of wdth 75 cm at the rate dt 105 per metre. |
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| 42. |
Constructs a triangle ABL in whihFind the cost of carpeting a room 13m by 9f with a carpet of width 75cm at the rate of105 per metre. |
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| 43. |
।।।।।१५।एक थैले में 50 पैसे और 25 पैसे के कुल 94 सिक्के हैं। यदि थैले में कुल 29.75 रुपयेहैं, तब बताइए कि थैले में 25 पैसे और 50 पैसे के सिक्कों की संख्या कितनी है? |
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| 44. |
11 73. Value of 50 + 25 is equal to- |
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| 45. |
makes in 10 minutes when the car is travelling at a speed of 66 kt yel lio21. A hollow sphere of external and internal diameters 8 cm and 4 cm respectively is melted into acone of base diameter 8 cm. Find the height of the cone.400 TV neture tubes tested in a tube company is |
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| 46. |
ET/IX/2018(ii)The cost of painting the whole surface area of a cube at the rate of 13paise per cm2 is 343.98. The volume of the cube is:(1) 8.0 cm3(3) 10.648 cm3O.(2) 9.261 cm(4) 13.824 cm38.0聑衬ofto10.648 ofto(2)(4)9.26 1日可,,to(1)(3)13.824o |
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Answer» It takes Rs.13/100 to paint 1cm² Total cost was Rs.343.98 Total area of the cube is 343.98/0.13=2646cm² TSA of cube = 6s² 6s²= 2646 s² = 2646/6 s²= 441 s = √441 = 21cm Volume of cube is s³ s³ = 21³ = 9261cm³. The option given is wrong, this answer is correct. Like my answer if you find it useful! |
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| 47. |
कि. नीचे दिए गए त्रिक पाइथांगोरीयं त्रिक हैं अशुवा नहीं ?हा! e10, 15, 25) v 11 |
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Answer» As5^2+12^2= 13^2अतः यह एक पाइथागोरस प्रमेय को सिद्ध करता है please like the solution 👍 ✔️ |
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| 48. |
a. 154b. 88С. 132A well diameter 140 cm has a 7 cm wide parapet around it. Find thearea of the parapet.h2093134 d. 3234 |
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| 49. |
area is onedauch aeol rod which is 25 em long and of 20 em in diameter is melted to form adiameter. Find the length of the new rod. |
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Answer» volume of rod =πr^2hvolume of 1st rod = π(20/2)^2 ×25 = π×2500 Radius = 20, height = 25 cmvolume of 2nd rod = π(19/2)^2×h = π×9.5^2× h Radius = 19, h not known π×2500= π×9.5^2×hh = 2500/(9.5^2) = 27.70 cm thanks |
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| 50. |
17) A squareerimeter. The length of the side of theaare is 8 cm. If the width of the rectangleis 6 cm, find the length of the rectangle andhence find its area. |
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