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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. |
32If tano + sino = m and tano - sine = n. Show that m? - nOR= 4 mn |
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Answer» tanA+sinA=msquaring both sidetan^2A+sin^2A+2sinAtanA=m^2 ----(1)tanA-sinA=nsquaring both sidestan^2A+sin^2A-2sinAtanA=n^2----(2)by substrate 1 -24sinAtanA= m^2 - n^2 |
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| 2. |
if tanA + sinA = m and tanA - sinA = n . Then prove that m × m + n × n = 4√ mn |
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Answer» Like if you find it useful |
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| 3. |
(126)ěA+B-C= 180°elit,al)tan).tan-(a) 0 (b) 1 (c) 2 (d) 32 |
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Answer» A+B+C = piso A/2 + B/2 + C/2 = pi/2 or A/2 + B/2 = (pi/2- C/2)take tan of both sides tan (A/2 + B/2) = tan (pi/2-C/2) = cot C/2 = 1/ tan C/2 or (tan A/2 + tan B/2)/(1- Tan A/2 tan B/2) = 1/tan C/2 or tan C/2 tan A/2 + tan C/2 tan B/2 = 1 - tan A/2 tan B/2or tan A/2 tan B/2 + tan B/2 tan C/2 + tan A/2 tan C/2 = 1proved |
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| 4. |
if tan θ +sin θ = m and tan 0-sin θ=n, showthat m12-n-4./mn .13.IAI 1997] |
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| 5. |
2 tan 30°1 + tan2 30 |
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| 6. |
Prove that1 + tan2 A (1-tanA 2= tan2A |
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| 7. |
Raghav offers to carry his mother'sShopping bed bage. She had bouane - 2 Theof plums t I kg of onions and II kg ofpotatoes. What å the total weight ofthe grocery Prem? |
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Answer» 2*1/2=2.51/4=0.25now total weight =2*1/2+1/4+1/4=2.5+0.25+0.25=2.5+0.5=3Hence total weight is 3kg |
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| 8. |
presentage.Rajesh's father is 3 times as old as Rajesh was two years ago. Today, the sumof their ages is 62. Find their ages.4.hor In 12 vears. her mother will be |
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| 9. |
2ăSintanA2.Cot A |
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Answer» Kindly replace Theta by A. wrong |
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| 10. |
Nikhil spent 5% of his monthly income on his children's education, invested 14% inshares, deposited 390 in a bank and used 40% for his daily expenses. He was left with abalance of Rs. 19,000. What was his income that month . |
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| 11. |
e ) .Prove that: sin A-2Sin"A = tanA2 cos’ A - cos A ] : |
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Answer» Like if you find it useful |
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| 12. |
In AABC if a, b, c are in A.P then TanA/2*TanC/2= |
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Answer» if a b and c are in AP tan(A/2) .tan(c/2) = 1/3 |
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| 13. |
Prove that(1 + tan2A(1- tanA 2OR |
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| 14. |
If tanA + sinA=m and tanA - sinA =n, show that (m^2 -n^2)=4root(mn) |
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| 15. |
d a pair of integers whose sum is - 2 |
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Answer» -3+1= -2 is the right answer -6 + 4,-5 + 3, -4 + 2 and many more can be there. -3 +1= -2 is the right answer -4+2=-2 is the right answer |
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| 16. |
Which one of the followinsum of 2 integers whose product(A) 12(C) 20is the minimumis 64?(B) 8(D) 16 |
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Answer» Xy = 64 the best choice for the answer is...8*8 = 64 8+8=16 |
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| 17. |
11, Rajesh sold his scooter to Rahim at 8% lossand Rahim, in turn, sold the same scooter toPrem at 5% gain. If Prem paid 14,490 forthe scooter; find:(i) the S.P. and the C.P. of the scooter forRahim.(ii) the S.P. and the C.P. of the scooter for. Rajesh. |
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| 18. |
If you can now move 2 Matches,Whats the biggest possiblenumber? |
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Answer» 999 is the biggest number possible. answer is In 5 digit number |
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| 19. |
Rajesh deposited 40,000 in his bank fora period of five years. What rate of interestwill give him an interest earning of 10,000 |
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Answer» thanks |
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| 20. |
20. Rajesh deposited40,000 in his bank foa period of five years. What rate of interestwill give him an interest earning of 10,000 |
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| 21. |
The value of2 tan 301+ tan2 30° |
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| 22. |
Prove that1 tan2 A (1 - tanA 2- tan2A |
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| 23. |
x+66-6=70 |
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Answer» x+66-6=70x=70-60 =10 |
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| 24. |
In a supermarket, 78.25 kg of rice and 92.7 kg ofwheat is sold on Monday. 125.5 kg of rice and128.5 kg of wheat is sold on Tuesday. Which itemis sold more in the two days-rice or wheat, andby how much? |
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Answer» rice=78.25kg+125.5kg=203.75kgwheat=92.7kg+128.5kg=221.2kgwheat is sold more by 221.2kg-203.75kg=17.45kg |
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| 25. |
NUMERICALWhich one of the following is themsum of 2 integers whose prodtuct isQ39 |
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Answer» Y = 64X + Y = minimum.SubstitutingX + 64/X = minimumTo find the minimum (or maximum), differentiate with respect to X and set the result to zero.ThereforeIf you want the sum to be a minimum then you must select X=8, Y=8 Like my answer if you find it useful! |
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| 26. |
100. What is the difference (in 3) in compound interestearned in 1 year on a sum of 10,000 at 40% perannum compounded quarterly and annually?101 |
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| 27. |
666.66+66.66+6.66+6+.66 |
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| 28. |
which6 66of following in biggest numberate |
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Answer» 0,is a number in funny but b |
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| 29. |
in a partnership business if the ratio of three persons is 3: 5: 8.If the profit of 1st person rs. 60 is less than 3rd person. what is the total profit? |
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Answer» Let the profit of first partner = 3xthe profit of second partner = 5xthe profit of third partner = 8x Given, 3x = 8x - 605x = 60x = 12 Total profit = 16x = 16*12 = Rs 192 tq so much |
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| 30. |
business started with cash ₹3000 , goods ₹20000 and loan from Rajesh ₹10000 |
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Answer» What is to be done with the question? |
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| 31. |
शसर्वसम्तिका Cosec?A = 1+Cot2A को'कीस्निए--CosA — S nA + 1 . — = Cosec A+ CotACosA + SinA —1स्नागू_ करके =a |
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| 32. |
Prove that1 cot2A 1-cotAOR |
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Answer» L.H.S1+tan^2A/1+cot^2A=(1+sin^2A/cos2A)/(1+cos^2A/sin^2A)=((cos^2A+sin^2A)/cos^2A)/(sin^2A+cos^2A)/sin^2A=(1/cos^2A)/(1/sin^2A)=1/cos^2A*sin^2A/1=sin^2A/cos^2A=tan^2A M.H.S(1-tanA/1-cotA)^2=(1+tan^2A-2tanA)/(1+cot^2-2cotA)=(sec^2A-2tanA)/(cosec^2A-2cosA/sinA)=(sec^2A-2*sinA/cos A)/(cosec^2A-2cosA/sinA)=(1/cos^2A-2sinA/cosA)/(1/sin^2A-2cosA/sinA)=[(1-2sinAcosA)/cos^2A]/[(1-2cosAsinA)sin^2A]=(1-2sinAcosA)/cos^2A*sin^2A/(1-2sinAcosA)=sin^2A/cos^2A=tan^2A R.H.S=tan^2A Hence L.H.S=M.H.S=R.H.S Please post a clear image with proper lighting. We cannot provide a solution without a clear image of question. |
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| 33. |
21 tan2 A I1 + cot2A1 -tan A-cot A |
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| 34. |
write the value of cot2A -1/sin2A |
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| 35. |
1 + cot2Ais equal to |
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Answer» 1 + cot²A---------------1 + tan²A 1 + 1/tan²A-----------------1 + tan² A ( 1 + tan²A)---------------------------tan²A ( 1 + tan²A) 1/tan²A cot²A |
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| 36. |
Simplify the following numerical expressions(i) (10 + 17) + 3 |
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Answer» According to bodmas10+17= 1717÷3= 17/3Is the answer (10 + 17) ÷ 3= 27 ÷ 3= 99 is answer of the given question. 17÷317/3 answer right (10+17)÷3= 27÷3= 9 10+17/3 Final result : 47 —— = 15.66667 3 Step by step solution : Step1: 17 Simplify —— 3 Equation at the end of step1: 17 10 + —— 3 Step2: Rewriting the whole as an Equivalent Fraction : 2.1Adding a fraction to a whole Rewrite the whole as a fraction using3as the denominator : 10 10 • 3 10 = —— = —————— 1 3 Equivalent fraction :The fraction thus generated looks different but has the same value as the whole Common denominator :The equivalent fraction and the other fraction involved in the calculation share the same denominator Adding fractions that have a common denominator : 2.2 Adding up the two equivalent fractionsAdd the two equivalent fractions which now have a common denominator Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible: 10 • 3 + 17 47 ——————————— = —— 3 3 Final result : 47 —— = 15.66667 3 Processing ends successfully (10+17)/3 Final result : 9 Step by step solution : Step1: 9 Simplify — 1 Final result : 9 Processing ends successfully 27/39 is correct answer 27/3=9 is the correct answer (10+17) ÷3=27 ÷3= 99 is answer 9 is correct answer for questions 10+17 = 2727÷3=9 9 is the answer 9 is the answer for this question according to the question = 10+17÷3 = 27÷3 = 9 answer |
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| 37. |
2. In a town, there are 2 public libraries. The number of books in onelibrary is 3,48,386 and the number of books in the other is 5,17,058What is the total number of books in both the libraries? How manymore books does the second library have than the first?A supermarket earned 1,56,48,000 in a year. If the expenses we |
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| 38. |
Best Friendsfind thesolutionthe Equation sind etcost. I sina costHirdle sirex Boste 1-2 sinxcoĹĄe :) |
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| 39. |
What comes next in the series?2, 3, 6, 10, 17, 28,? |
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| 40. |
ट झथ है मे. 60०व्लकाकर! o ‘f[ L; ypowricl T Jum%l, v L3 A_PL{_&" g pre ) o‘b _phore Zunw ue न |
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Answer» Like if you find it useful |
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| 41. |
Cos4A=1-8sin²A |
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Answer» Show that cos(4A)=8sin^4(A)-8sin^2(A)+1? |
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| 42. |
The denominator of a fraction exceeds its numerator by 3.If 3 is added to both numerator and denominator, thedifference between the new and the original fraction isFind the original fraction. |
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| 43. |
2.Which of t57he following is an irrational number?23(d) 1719a)ä¸ |
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Answer» b) √7 is irrational. Reason : √7 can't be written as p/q form |
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| 44. |
Which one of the following is an irrational nu3\begin{array}{lll}{\frac{\sqrt{16}}{25}} & {(B)} & {(C) \frac{3}{9}} & {(D) \sqrt{196}}\end{array} |
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| 45. |
7. Given that /2 is irrational, prove that (5+3/2) is an irrational number. |
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| 46. |
7, Given that 2 is irrational, prove that (5+3/2) is an irrational numberna ahnth of the altitude. |
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| 47. |
(1+1\tan2A) (1+1\cot2A)=1\Sin2A-Sin4A |
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| 48. |
4x / 2 root (4x^2-1) = 5/3 |
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| 49. |
1.दो सिक्के एक साथ 40 बार उछाले गये । यदि HH, HT, TH क्रमशः 9, 8, 12 बारआये हों तो ज्ञात कीजिये कि TT कितनी बार आया होगा ? |
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Answer» Firstly add the HH HT TH= 9+8+12=29 then subtract it from 40 and the answer be 11 |
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| 50. |
Solve the trigonometric equation Sina+Sin2a+Sin3a+Sin4a=0 |
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