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. |
उदाहरण 24. सिद्ध कीजिए : lim...N1+x-01-x=1हल : बायाँ पक्ष |
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Answer» This matter will take you through all the steps and then the next few steps are done for your family and your business with our business plan that you can provide your business with our |
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| 2. |
\sin 35^{\circ} \sec 55^{\circ}+\frac{4 \sec 32^{\circ}}{\csc 58^{\circ}} |
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| 3. |
(01 + x) (t+x)(j) |
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Answer» (x + 4) ( x + 10) x² + 10x + 4x + 40 x² + 14x + 40 |
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| 4. |
(01 +x) ( x) ( |
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| 5. |
2ITA12.3.Bxx is a root of5x+6 01. then findCA 13(ii) Are they equal sets?(iv) Are they equivalent sets? |
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Answer» aUb is set -2,-3,2,3. A intersection B is an empty set. there are not equal set . there are equivalent set because both set a and B as 2 no of sets sets are equal A-(2,3) B-(2,3) roots are 2,3 of QE |
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| 6. |
19. The distance of the point P(2, 3) from the x-axis is:(2) 2 (6)3 (01 (d) 5 |
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Answer» The answer is 2 as the first number is always given on /-axis The ans for P(2,3) is 2 the distance from x-axis of the point p (2,3) by the formula distance from x-axis=the value of yd distance from x-axis =value of y=3 |
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| 7. |
Assume Ď, unless sind the surface area of a sphere of radius(i) 5.6c(i)10.5 cm |
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Answer» i)4 pi r² = 4 × 3.14 × (10.5)² = 1,384.74 cm² ii) 4 pi r² = 4 × 3.14 × (5.6)² = 393.8816 cm² |
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| 8. |
01.Find the domain and range of following(1) f(x) = (x2 â 3x+2. |
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Answer» x^2-3x+2=0(x-1)(x-2)=0range is [1,2]domain is (-infinity,1]U[2, infinity) |
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| 9. |
4. Evaluate: \left(\sin ^{2} 30^{\circ}+4 \cot ^{2} 45^{\circ}-\sec ^{2} 60^{\circ}\right)\left(\csc ^{2} 45^{\circ}+\sec ^{2} 30^{\circ}\right) |
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| 10. |
1,000 bananas weigh 141.7 kg. How muchdoes each banana weigh? (Assume allthe bananas are of equal weight). |
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| 11. |
4 a(5 a-6 b)-12 a^{2}(5 a-6 b) |
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| 12. |
4. Which is greater:دا |OFOrolu |
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Answer» 3/5 of 5/8 is greater (3/5 of 5/8) > (2/7 of 3/4 ) . |
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| 13. |
-=then x is equal to84(b) 3ooltolu |
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Answer» x-3/8=1/4x=1/4+3/8x=5/8option d is a correct answer X=1/4+3/8X=5/8 answer x-3/8=1/4x=1/4+3/8x=5/8option d is correct answer. correct answer is 5/8 x=5/8 is the right answer x - 3/8 = 1/4; x =1/4 +3/8 = 2+3/8=5/8 x=5/8 is the right answer x =5/8 is the right answer ×-3/8=1/4×=1/4=3/8×=5/8😨😨😈😈😠😠😠😤 X=1/4+3/8X=5/8 answer x-3/8=1/4x=1/4+3/8x=5/8option d is correct answer 5/8 is the right answer |
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| 14. |
OLUThere are 3 red and 5 black balls in a bag. One ballis drawn from the bag. The probability of beingred is |
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| 15. |
( a + 4 ) ^ { 2 } - 5 a b - 20 b - 6 b ^ { 2 } |
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Answer» question nhi ayga paper mai a^2+16+8a-5ab-20b-6b^2 |
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| 16. |
C = 8:10, C:0=6:5, thenif A: B= 4:6, BA:B:C:D = ? |
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Answer» A: B:C:D=16:24:30:25 |
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| 17. |
An aeroplane at an altitude of 1200 meters finds that two ships are saliling towards itin the same direction. The angle of depression of the ships as observed from theplane are 60° and 30° respectively. Find the distance between the two ships.aero |
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Answer» The height of the aeroplane can be AB and C and D be the position of 2 ships. Let ∠ ABC = 60° and ∠ADB = 30° Let BC = xm, CD = y m in triangle ABC, tan 60° = AB/BC √3 = 1200/x x = 1200/√3 = √3/√3 = 400√3 m In triangle ABD tan 30° = AB/BD = 1/√3 = 1200/ x + y y = 1200/√3 - 400√3 = 800√3 The final answer for this question is 800√3 |
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| 18. |
Question 14. If each clement of a second order determinant is aero orwhat is the probability that the values of the determinant is pusitvethat the individual entries of the determinant are chosesAssumeadependendly, each vahue being assumed with pribabilitseach value being assumed with pobability |
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| 19. |
ŠSimplification of the following gives |
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Answer» 170.5 9/2 is correct answer |
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| 20. |
er or the figure obtained. (Take Ď = 3.14)e area swept by the 3.5 cm long minute hand of a clock in 2 hoursFin, A circular park of 20 m diameter ho |
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Answer» Area swept in 2 hrs= 2*pi*r*r r = 3.5 cmArea swept = 2*22/7*3.5*3.5 = 44*.5*3.5 = 22*3.5 = 77 cm^2 thanks friend |
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| 21. |
7. Simplification of the following gives |
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Answer» 9/2 this is 100persent right answer 15 1/2 - [12/5 * 5/8 + (7 ÷ 1 3/4)] * 2 = 31/2 - [3/2 + (7 ÷ 7/4)]*2 = 31/2 - [3/2 + (7 * 4/7)]*2 = 31/2 - [3/2 + 4]*2 = 31/2 - [(3 + 8)/2]*2 = 31/2 - 11 = (31 - 22)/2 = 9/2 = 4 1/2 |
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| 22. |
41. Simplification of the following gives |
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Answer» 9/2 is correct answer. 9/2 is correct answer |
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| 23. |
In the given below figure, in ΔΑΙ3C, D and E are the midpoint of the sides BC and ACrespectively. Find the length of DE. Prove that DE ABB (2. -2)C(4.-2) |
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Answer» Like my answer if you find it useful! |
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| 24. |
\frac \sin ^ 2 65 ^ \circ %2B \sin ^ 2 25 ^ \circ \sec ^ 2 30 ^ \circ - \cot ^ 2 60 ^ \circ %2B 2 \sin 36 ^ \circ \sin 42 ^ \circ Sec 48 ^ \circ \sec 54 ^ \circ |
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| 25. |
41. Simplification of the following gives :O 01x2 |
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Answer» 31/2-[12/5*5/8+(7÷7/4)]*231/2-[3/2+4]*231/2-11/2*231/2-1131-22/29/2 is carcat answer 9/2 |
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| 26. |
2. Semplification of the following gives :oluNININ19(D) |
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Answer» 31/2 -[3/2 +(7 ÷ 7/4)]×231/2 -[3/2 + 4]×231/2 -[11]=9/2 |
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| 27. |
= 2500 + 200 - 12 |
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Answer» 2500 + 200 -12 = 2700 - 12 = 2688 thanks 2500+200-12 2700-12 2688 |
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| 28. |
The points A(-3,6), B(0,7) and C( -points of the sides DE, EF andFD of a triangle DEF. Show that the quadrilateral ABCD is a parallellogram.7.(1,9) are the mid |
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Answer» A (-3,6) is the midpoint of DE , B(0,7) is the midpoint of EF and C(1,9) is the midpoint of FD. Let D = (x1, y1) , E = (x2 , y2) and F = (x3 , y3) so, A is the midpoint of DE so, (-3, 6) = {(x1 + x2)/2, (y1 + y2)/2} x1 + x2 = -6y1 + y2 = 12 Similarly, B is the midpoint of EF so, x2 + x3 = 0y2 + y3 = 14 and C is the midpoint of FD so, x3 + x1 = 2 y1 + y3 = 18 now, solving equations, x1 = (x1 + x2 + x3) - (x2 + x3) =-2 + 0 = -2 x2 = (x1 + x2 + x3) - (x1 + x3) = -2 -2 = -4 x3 = (x1 + x2 + x3) - (x1 + x2)= -2 - 6 = -8 Similarly, y1 = (y1 + y2 + y3)- (y2 + y3)= 22 - 14 = 8 y2 = (y1 + y2 + y3) - (y1 + y3) = 22 - 18 = 4 y3 = (y1 + y2 + y3) - (y1 + y2) = 22 - 12 = 10 hence, D(-2,8) , E(-4, 4) and F(-8, 10) now, we have to show that ABCD is a parallelogram. we know, diagonals of parallelogram intersect at midpoint. e.g., midpoint of diagonal AC = midpoint of diagonal BD. midpoint of AC = {(-3+1)/2, (6+9)/2} = (-1,15/2)midpoint of BD = {(0-2)/2, (7+8)/2} = (-1,15/2) hence, it is clear that, ABCD is a parallelogram. |
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| 29. |
- 嚲 25002500 |
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Answer» 4500+3000+2500+2500 = 4500+3000+5000= 12500. sum of 4500+3000+2500+2500=12500 005754 this is right answer |
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| 30. |
oints on sides AB and AC respectively of AABC such thatDBC)ar (EBC). Prove that DE I BC |
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| 31. |
19106 Lk 1 del1B 2 1Bk Lelky I—V 1 ¥ 1 O I s_g 1O Lkdb} 21० ॥+५%। 4०११९] अफ B3 स् थे 0 व "2 009§ 266 |
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Answer» माना R को एक्स भाग मिलाsoQ will get x/4P will get3x/20nowx+3x/20+x/4= 80x+12x+20x/4= 5600112x= 5600*4x= 200P will get = 3*200/20= = 30 |
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| 32. |
25 The angle of elevation of anaeroplane from a point on the ground isAfter lying for 15 sconds, the elevation changes to 30s If the aeroing at a height of 2500 metres, find the speed of the aeroplaneacroplanes |
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| 33. |
. el le e S At gt ot .i — दि B3 F o]नेe e |
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Answer» Sin73° = cos17=and cos 37° = sin 53°so we know that sin^2+cos^2= 1then sin^2(73)+cos^2(73)/cos^2(37+sin^2 (37}1/1= 1 Answer sinjskwkakskkskskwkskwkwkw sjjwjsjsjwjwkwkwo |
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| 34. |
Express the following in the form of atib, a, beRíー、CT- State the values, of a and b.i(4+3i)i) (1+2)(-2+) ii) (I+ǐ)(1-i).1 iii) (1-i) |
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Answer» thank you very much |
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| 35. |
5. 1b30-/2002. |
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Answer» 3/4(7x-1) - (2x - (1-x)/2) = x + 3/221x/4 - 3/4 - 2x + 1/2 - x/2 = x + 3/221x/4 - 3x - x/2 = 3/2 + 3/4 - 1/2(21x - 12x - 2x)/4 = (6 + 3 - 2)/47x = 7x = 7/7 = 1 Value of x = 1 |
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| 36. |
a huge park, people are concentrated at threepoints (see Fig. 7.52):A: where there are different slides and swingsfor children,near which a man-made lake is situated,which is near to a large parking and exit..C:re should an icecream parlour be set up soWhethat maximum number of persons can approachFig. 7.52it?(Hint : The parlour should be equidistant from A, B and C) |
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| 37. |
InisjueBUE % e e b IS ksl HB“Ble B2 1(€1°6 Lidbslie Lualb)Bl 12 o0€ 1boR (कफ कल2o bhb & 13 09 ol Bhiese यु [डिडिि 1०5o e 12 pRY e ksl 2 3o{162 f 1B bl kb 2 Bats |Wess b bl Wbl wh Wz फूo RS |
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| 38. |
itbl 18 12 € = ला g’i 1Bw \ &lodbikh 9 loadine |
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Answer» 1/x + 5/y = 2........(1)3/x + 10/y = 3......(2) Multiply eq(1) by 33/x + 15/y = 6...... (3) Subtract eq(2) from eq(3)15/y - 10/y = 6 - 35/y = 3y = 5/3 Put value of y in eq(1)1/x + 5/(5/3) = 21/x = 2 - 31/x = - 1x = - 1 |
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| 39. |
002. Find the value of tan 42-sec 4222 |
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Answer» tan^2x - sec^2x = 1 As we know the above formula, x = 42 1/2 Like my answer if you find it useful! |
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| 40. |
Simplification of the following gives(A)21B |
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| 41. |
2500*12 |
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| 42. |
6765201/2500 |
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Answer» the answer is 2706.0804 |
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| 43. |
Which angle is included between the sides DE and EF of ADEF |
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| 44. |
if a+b=5 ab=6 then 1/a+1b? |
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Answer» Given- (a+b)= 5 and ab=6 (1/a +1/b)= (a+b)/ab = 5/6 (1/a+1/b)=(a+b)/ab=5/6 (1/a+1/b)=(a+b)ab=5/6 Given-(a+b)=5 and ab=6 (1/a+1/b)= 5(a+b)/ab=6 =5/6 given (a+b)=5 and ab=6. (1/a+1/b)=(a+b)/ab. =5/6 given,a+b=5 and ab=6 1/a + 1/b= a+b/ab =5/6 1/5 Given that , a+b =5ab=6 then (1/a+1/b) = a+b/ab = 5/6 ORLet , a=3 and b=2 then put these value in these equation then answer is 5/6 1/a+1b = 1/(a) + 1(b)... (one and one cancelled)= a+b =5 if a+b=5 also ab =6then 1/a + 1/b =a+b/ab=5/6=8.33 given (a+b)=5and ab=6(1/a+1/b)=(a+b)ab=5/6 your answer is this -5/6 (1/a+1/b)=(b+a)/ab5/6 a+b=5,ab=61/a +1/ba+b/ab=5/6 5/6 is the solution to the above question Given ( a + b ) = 5 and ab = 6 ( 1 / a + 1 / b ) = ( a + b ) / ab = 5 / 6 if, a=3, b=2a+b=53+2=5 (as,a=3 & b=2)ab= 63*2=6 (as, a=3 & b=2)so, 1/a+1b1/3+1*2=2*1/3 i dont know it is difficult If a+b=5 an=6then 1\a+1b1\2+1×31\2+31+3\24\2=2that is your ansI hope it will help you to prove :1/a+1/b=b+a/ab=a+b/ab=5/6 1/a+1/b=(a+b)/ab = 5/6 (1/a+1/b)=(a+b)/ab=5/6 (1/a+1/b)=5 (a+b)/ab=6=5/6 (1/a+1/b)=(a+b)ab=5/6 a+b=5a=5-bab=6b=6/anow1/5-b+6/aa/11-b 1/a+1/b(a+b)/aba+b=5;ab=6so, 5/6 a+b=5 and ab=6 By observation value of a and b are 3 and 2So nxt 1/a and 1/b=?1/3+1/2 =2+3/6this implies that the value is 5/6 if a+b =5 ab=6 then 1/a+1b? given that,a+b=5andab=6 now, (1/a+1/b)=(a+b)/ab=5/6 1/a+1b=1/2+1/3=5/6(a=2 and=3 given (a+b)=5 and ab=6(1/a+1/b)=a+b)/ab= =5/6 (1/a+1/b) =(a+b)/ab =5/6 |
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| 45. |
Water lilies double in area every 24 hours. In spring one water lily on a lake. In sixtydays the lake is completely covered with lilies. How many days did it take to cover halfof the lake? |
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Answer» 1 2 4 8 161 2^1 2^2 2^3 2^(n-1)a a2^1 a 2^2 ....geometric sequence witha = 1r = 2n = number of days 2^59 = area 2^x = 2^59/2x = n-1 = 58 so 59 dayswhich we could have said right offbecause if you cover the whole lake in 60 days then the day before you must have half the lake covered. |
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| 46. |
rea of rhombus is 63 sq. m. If its perimeter is 28 m, find itsare 12 cm and 8 cm. The lee a |
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Answer» It is givenPerimeter =28m4*side=28mSIDE=28/4SIDE=7 CMANOW According to the question AREA=BASE*ALTITUDE 63m^2=7*ALTITUDE ALTITUDE=63/7m |
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| 47. |
28. In AABC and ADEF, if mZA=mZD,mZB=mZE, AB=3 cm, BC =5 cm andDE=6 cm, then what is EF in cm ?(A) 4 (B6(C) 8 (D) 10 |
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| 48. |
27If the angle of elevation of a cloud from a point 60 meters above a lake is 30° and the angle ofdepression of its reflection in the lake is 600. Find the height of the cloud from the surface ofthe lake. |
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Answer» Let AO=HCD=OB=60mA'B=AB=(60+H)m In triangke AOD,tan30'=AO/OD=H/OD H=OD/√3OD=√3 H Now, in triangle A'OD,tan60'=OA'/OD=(OB+BA')/OD√3=(60+60+H)/√3 H =(120+H)/√3 H=>120+H=3H 2H=120 H=60m Thus, height of the cloud above the lake = AB+A'B =(60+60) = 120m |
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| 49. |
showthat all, -1) 1B (-2,2), ((42) andD (7,5) are vodies of a rectangle |
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| 50. |
44. The angle of elevation of a stationary cloud from a point 2500 m above a lake is 30and the angle of depression of its reflection in the lake is 45'. What is the height of thecloud above the lake level? |
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Answer» what is your question Self respect self confidence self-reliance how can you show to others that you have these qualities give some examples I can't read questions |
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