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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. |
In the adjacent figure, the bisectors of Z A and Bmeet in a point P. If < C = 100° and < D 60° , findthe measure of ZAPB.60°100 |
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| 2. |
(Use n 3.14)me of a right circular cone of height 9 cm is 48base.Tcm', find the diameter of is |
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| 3. |
ExERCList five rational numbers between:(i)-1 and 0(i)-~ and-I |
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| 4. |
List five rational numbers between:(i)-1 and 0(ii)-2 and-1 |
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| 5. |
1.List five rational numbers between:(G) -1 and 0 i) -2 and -1 |
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| 6. |
1.List five rational numbers between:G)-1 and 0 (ii) 2 and -1 |
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| 7. |
The perimeter of a triangle is 8 + 13a + 7aand two of its sides are 2a2 + 3a + 2 and 3a²-4a-1, then the third side of the triangle is |
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Answer» Let X , Y, Z are three sides of triangle & P be the perimeter of triangle where X=2a^2+3a+2Y=3a^2-4a-1 Z=?P=7a^2+13a+8Now P= X+Y+Z7a^2+13a+8=2a^2+3a+2+3a^2-4a-1 +Z7a^2+13a+8=5a^2-a+1+1Z=7a^2-5a^2+13a+a+8-1Z=2a^2+14a+7Hence , the third side of triangle =2a^2+14a+7. |
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| 8. |
(3) За-20If S is themcentre, O is the orthocentre of AABC, then SA+SB SC equa |
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| 9. |
Aia te vabue K |
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| 10. |
Arithmetc1. The sum of HCF and LCM of two numbers is 435. LCM is 28 times the HCF.If one of the numbers is 60, find the other number |
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Answer» (HCF + LCM) = 435LCM = 28 HCF=> HCF + 28 HCF = 435 29 HCF = 435 HCF = 15LCM = 28 × 15 = 440HCF × LCM = product of numberssecond number = (440 × 15)/60 = 110 |
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| 11. |
3. In the given figure, O is the centre of thecircle and arc ABC subtends an angle of130° at the centre. If AB is extended toP, find ZPBC. |
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| 12. |
3. In the given figure, O is the centre of thecircle and arc ABC subtends an angle of1300 at the centre. If AB is extended toP, find ZPBC |
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| 13. |
3. In the given figure, O is the centre of thecircle and arc ABC subtends an angle of130° at the centre. If AB is extended toP, find ZPBC.0 |
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| 14. |
02EXERCISE 7.4Show that in a right angled triangle, thehypotenuse is the longest side.In Fig. 7.48, sides AB and AC of Î ABC areextended to points P and Q respectively. Also,ZPBC< 40CB. Show that AC>AB |
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Answer» 1 |
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| 15. |
Circumference of the edge of hemispherical bowl is132 cm. Find the capacity of the bowl. [Use n-22/7 |
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Answer» circumference=132 cm2πr = 132 cm2 × 22/7× r = 13244/7 x r = 132r= 132 x 7/44r = 21 volume of hemisphere = 2/3 πr³=2/3 x 22/7 x 21x21x21=44x 441=19404 cm³ (ans) |
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| 16. |
24,lমস- avis, find a and b.ম |
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| 17. |
5. In the given figure, O is the centre of thecircle. If ZPBC 25 and ZAPB 110 findthe value of 4ADB.Al-110 |
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| 18. |
List five rational numbers between(i)(iy-2 and-l42and-1 and 01l(iv2. Write four more ti |
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| 19. |
Find a quadratic polynomial each with the given numbers as the sum and product ofizeroes respectively2.(0 -14(ii) 0, 51l(iv) 1,1(vi) 4,1 |
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| 20. |
\begin{array}{l}{p=-2, q=-1} \\ {p^{2}+q^{2}-r^{2}}\end{array} |
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| 21. |
if S is the circumcentre ,O is the orthocentre of triangle ABC , then SA +SB +SC equals |
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| 22. |
6. If S is the circumcentre, O is the orthocentre of AABC, then SA+ SB+SC equa |
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Answer» Part 1 Part 2 thanks |
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| 23. |
find the perimeter of a buangle whereI side aia 3a +260 + 2a + 3b ts andYa-sb-60 |
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Answer» Ans of this question = 9a - 4c. 3A + 2b + c; + 2a+ 3b + c, - 4a-5b- 6c=5a+5b+2c+4a-5b-6c=9a-4c |
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| 24. |
Two numbers are such that the ratio between themis 3:5. If each is increased by 10, the ratio betweenthe new numbers so formed is 5:7. Find the originalnumbers. |
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| 25. |
Two numbers are such that the ratio between themis 3: 5. If each is increased by 10, the ratio betweenthe new numbers so formed is 5:7. Find the originalnumbers. |
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| 26. |
wird,28 Two numbers are such that the ratio between themis 3:5. If each is increased by 10, the ratio betweenthe new numbers so formed is 5:7. Find the originalnumbers. |
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| 27. |
A balloon, which always remains spherical, has a variable diameter (2x +1). Find the rate of changeof its volume with respect to |
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Answer» Step 1:Diameter of the sphere =32(2x+1)Therefore radius r=34(2x+1)Volume of the sphere v=43πr3Substituting for r we get,v=43π[34(2x+1)]3Step 2:Differentiating w.r.t x on both sides,dvdx=43x×(34)3×3(2x+1)2(2)=278π(2x+1)2 |
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| 28. |
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm andassumed that space of the cube remains unfilled. Then, find the numbers of marbles that theitis8cube can accommodate. |
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| 29. |
INDEFINITE INTC04x1 |
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Answer» I=∫(1+cos4x)/(cotx-tanx) dx I= ∫(1+ cos4x)sinx cosx/(cos²x-sin²x) dx = ∫(1+ 2cos²2x-1)sin2x/2cos2x dx I= ∫cos2x sin2xdx = 1/2∫ sin4xdx = 1/8 [-cos4x] +c |
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| 30. |
Z Ih the figure, AB is parallel to CD, find .140150° |
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| 31. |
1. Show that the four triangles as shown in the adjoining figureformed by diagonals and sides of rhombus are congruent.IHIV1l |
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| 32. |
3 Ih the given figure, O is the centre of thedirdle and arc ABC subtends an angle of130P at the centre. If AB is extended toP End ZPBC |
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| 33. |
etuey. Prove that QRIADt ih the given figure, the side BC of a triangle ABC is bisected at D:O is amy point in AD S0 and COgrodaced meet AC and AB in E and F respectively and AD is procduced bo X so that Dis the mid-poin oox. Prove that AO : AX AF : AB and show that FEIBCFg.4.26 |
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| 34. |
l. In which of the following situations, does the list of numbers involved make an arithmeticprogression, and why?1) The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for eachadditional km. |
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Answer» (i) It is an A.P.The rate for first kilometer is 15 and after that for each additional kilometer the rate increases at a constant rate. The common difference is 8.15, 23, 31,..... |
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| 35. |
\sec 50 ^ { \circ } \sin 40 ^ { \circ } + \cos 40 ^ { \circ } \csc 50 ^ { \circ } |
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| 36. |
B)Attemptany -efthe toltowing sb qtuestions.L. Amissing helicopter is reported to have crashed somewhere in the rectangularregion shown in the given figure. What is the probability that it crashed insidethe lake shown in the figure?Lake45 k2km |
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| 37. |
6. Simplify each of the following:wa |
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Answer» 6/25×6/25×6/25×5/3×5/3×5/3×5/2×5/2×5/2=1 |
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| 38. |
\frac{\sin 50^{\circ}-\sin 40^{\circ}}{\cos 50^{\circ}-\cos 40^{\circ}}= ______(a) - 2(b) 2(c) -1(d) 1 |
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| 39. |
n to give a sum ofde |
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Answer» A.p= 9,17,25a=9d=17-9=8Sum of n terms=n÷2[2a+(n-1)d 636=n÷2[2(9)+(n-1)8]636=n÷2[18+8n-8]636=n÷2[10+8n]1272=10n+8n^28n^2+10n-1272=02[4n^2+5n-636]=04n^2+5n-636=04n^2+53n-48n-636=0n(4n+53)-12(4n+53)=0(n-12)(4n+53)=0n-12=0n=12 12 terms must be given to sum of 636 |
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| 40. |
\operatorname { sin } ( 40 ^ { \circ } + \theta ) \operatorname { cos } ( 10 ^ { \circ } + \theta ) - \operatorname { cos } ( 40 ^ { \circ } + \theta ) \operatorname { sin } ( 10 ^ { \circ } + \theta ) = \frac { 1 } { 2 } |
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Answer» Here,= Sin (40 + A) Cos (10 + A) - cos (40 + A) Sin (10 + A)As, sin A cos B - cos A sin B = sin (A - B)so,= sin (40 + A - 10 - A)= sin 30= 1/2 = RHSHence, proved. here, for convenience we used theta as A |
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| 41. |
25. A ballon which always remains spherical is being inflated by pumpingin gas at the rate of 900 cm/sec. find the rate at which the radius of theballoon is increasing when the radius of the ballon is 15 cm. |
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| 42. |
Seven times a two digit number is equal to four times the number obtained byversing the order of its digits. If the difference of the digits is 3, determine thenumber |
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| 43. |
A two digit number is seven times the sum of its digits and is also equal to 12 less than three times the product of its digits. Find the number. |
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Answer» i had a doubt that why we take sum of digit x+y not 10x + y beacuse we are talking about digit'slike consider a number 43 , sum of digit is 7 but number can be written as 4×10 + 3 |
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| 44. |
Seven times a two-digit number is equal to four timesthe number obtained by reversing the order of itsdigits. If the difference between their digits is 3, findthe number19. |
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| 45. |
o. In how many years will1800 amount to2178 at 10% per annum when compoundedannually? |
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Answer» thank u |
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| 46. |
The compound interc st ()n Rs 1800 at 10% per annum, for a certain period of timeis Rs 37s. Find the timc in years. |
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| 47. |
19- The sum of digit of a two digit number is 12. If the new number formed by reversing the digits is greaterthan the original number by 18· find the original number. |
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Answer» send me the image isme kuch aa ni raha |
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| 48. |
The length of a room is double its breadth. Its height is 5 m. The area of its four walls (including doorsand windows) is 210 sq. m. Find its volume |
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| 49. |
Ans. 17901ExareadfSxamplelu) The length of a hall is 10 m and breadth of a hall is twice its height. IFaAwalls (including doors) is 144 m2, find the volume of the hall. |
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| 50. |
3.ThelengthofacoldO TS OFDE Square metre.storage is double its breadth. Its height is 3m. thearea of its four walls(216 m3)(including doors) is 108m2. Find its volume1 4 |
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Answer» let the breadth of the storage be b metrestherefore the length of the storage l=2b metresheight of the storage =3 metres now the area of the four wall = 2(l+b)h we already know that area= 108 m2 (given)2(l+b)h =1082(2b+b)3=1082 x 3b x 3=10818b=108b=6m now l=2b=2x6=12ml=12m now volume of the storage is l x b x h= 12m x 6m x 3m= 216m^3 |
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