Explore topic-wise InterviewSolutions in Current Affairs.

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.

A car covers 50km in 2 hr and 60km in 3hr. What is its average speed?

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average speed=(total distance)/(total time)=(50+60)/(2+3)=110/5=22km/h

2.

. If a man covers half of his journey at an averagespeed of 60km/h and the remaining at 40km/h,what is his average speed during the wholejourney?

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3.

ii.In the given figure, SV is the median and SW 1. TU. Prove that,SUP-ST* = 2TUX VWLV

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4.

of the plariet tupláfdel CalExample 2.1 Calculate the angle of(a) 1° (degree) (b) I' (minute of are or aremin)and (c) 1"(second of arc or are second) inradians. Use 360°-2n rad, 1°-60' andl' 60"

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360° = 2π rad 1° = 2π/360radso, 10° = 10× 2π/360 rad =π/18 rad

1' ( it means minute )60 minutes (60') = 1°1 minute = 1/60°but 1° =π/180 radso, 1/60° =π/60×180 =π/10800 rad

1'' = ? rad60'' = 1 minuteand 60' = 1° so, 3600'' = 1°so, 1'' =π/180×3600 =π/648000 rad

5.

111 Broup Di Luw did nuns, the number of legs are 14 more than twil trenumber of heads. The number of cows is:गायों व मुर्गियों के एक समूह में कुल पैरों की संख्या कुल सिरों की संख्या के दो गुने से 14ज्यादा है। ऐसे समूह में कुल गायों की संख्या होगी।(1) 5(2) 7(3) 10(4) 12

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6.

come part of a journey of 555 km was completed by a car with speed of 60 km/h thenthe speed is increased by 15 km/h and the journey is completed. If it takes 8 hours toreach. Find time taken and distance covered by 60km/h.father today the sum of their mar than lain

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Total time taken = 8 hrTotal distance covered = 555 kmInitial speed of car = 60 km/hr

Let time taken at speed 60 km/hr = tLet distance covered at speed 60 km/hr = d

As per given conditiond/75 + (555 - d)/60 = 8(4d + 5(555-d))/300 = 84d + 2775 - 5d = 24005d - 4d = 2775 - 2400d = 375 km

Now,60*t = 375t = 375/60 = 6.25 hrs

Therefore,At speed 60 km/hr time taken = 6.25 hrsAt speed 60 km/hr distance covered = 375 km

7.

12. Write a letter to the editor of a newspaper (within 100 words) about theproblems faced by commuters due to reckless driving of public vehicles.

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first you can write your name than address than date

8.

9. Write a letter to the Headmaster/Principal of your school (within 100 words) requestingfor organising an educational trip to a place of historical interest. You can suggest a few10names of such places mentioning the historical importance of those places.

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Tothe principalKendriya Vidyalaya DelhiSir,sir we want to visit a historical place as for example the Taj Mahal the Lal Kila and other historical places nearby us sofa please we are kindly requested you for gifted of a historical place for enjoyment and there anything this is the ways of all hole my class and we want we learn our culture and our immunity please sir we hope you will do that what we want thank you sir...your obedientlyclass 11th A Kendriya Vidyalaya delhi class captain dash Gaurav nagayach

9.

J anuA- axis25. A train covered a certain distance at a uniform speed. If the train would have been6km/h faster, it would have taken 4 hours less than the scheduled time. And, if thetrain were slower by 6km/h, it would have taken 6 hours more than the scheduled. Findthe length of the journey

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thanks

10.

Tn the given figure PQ and RS are two lines intersecting at point 'O'. If ROT = 90, find the value of x, y and z.

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thank friend

11.

284. A train travels a distance of 300 km at a constant speed. If the speed of the train is increased bykm an hour, the journey would have taken 2 hours less. Find the original speed of the trainE 11

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Let speed be 's ', time be 't ' and distance be 'd 't, t = d / s t = 300 / s,d = (s + 5)(t -2)=> d = (s+5)(300/s-2) {t=300/s}=> 300s = (s+5)s(300/s-2) [multiplyning both sides with s]we get = > 300s = (s+5)(300 - 2s)=> 300s = 300s - 2s2+1500 - 10s=>300s =300s-2s2+ 1500 - 10s=> 0 = -2s2+1500 - 10s=> 0 = 2s2+10s - 1500 [multiplying both sides -1 ]=> 0 = 2s2+60s - 50s - 1500=> 0 = 2s(s + 30) -50(s + 30)=> 0 = (2s - 50)(s + 30)=> s = 25, -30 Since, speed cannot be negative, we take speed 25Km/h.

12.

tanting point, which is 5m om tuns bock with idepitin tho buicket nuns bock de pickthe nort-pot at o nuns Jo dhe bucket do-once inono don palot s in tho.Jinnd book

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we have to find the ap

13.

Selve tho

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14.

thoarea241

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sides of rhombus are equallet side be athen perimeter 4a=80a=20mdiagonal,d=24mas diagonals of rhombus bisect each other at 90°by using pythagoras theorem we getother diagonal(l)as(l/2)^2 =20^2 -12^2l^2 /4=400-144l=32marea of rhombus=l×d /2=24×32/2a=12×32=384m^2

15.

tl:un tho

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16.

25+25/5+25=?

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55 is the right answer of the following

17.

fig., PQ | | RS, LQPR = 70°,ROT = 20°, find the value of x.70°20

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18.

points (ABC is a rght angled triangle whose 1 is righeon the sides ABl and BC respectiange l plits D and E are suatsthen prove that ABeCADf a eyelic quadrilateral are paralle, then prove that othder sides aequal and its diagonals are also equal to each other.S-09- Mathematics

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Let ABCD be quadrilateral with ab||cdJoin bcIn triangle abd and CBD,Angle abd=angle cdb(alternate angles) Anglecbd=angle adb(alternate angles) Bd=bd(common) Abd=~CBD by asa testAd=BC by cpctSince ad =bc ABCD is a isosceles trapeziumAngle d= angle c - - - - - - (1)Join ac. In triangle adc and bcdCd=cd(common) Angle d =angle c(from 1) Ad =bc(proved above) Triangle adc=~bcd by sas testAc=bd by cpcth. p..

19.

Pat Dy . Find the numbers.14. A fruit vendor buys some oranges at the rate of Rs 5 per orange. Halso buys an equal number of bananas at the rate of Rs. 2 perbanana. He sold the oranges at a profit of 20% and the bananas at aprofit of 15%. At the end of the day all the fruits are sold out. Histotal profit is Rs 390, find the number of oranges purchased

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20.

Findthevalueof,forwhichone rot of the quadratic equstin koe-14x-8-012

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21.

rot-,hind n and an

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a=2d=8Sn=90Sn=(n/2)[2a+(n-1)d]90*2=n[2*2+(n-1)8]180=n[4+8n-8]180=n[8n-4]180=4n[2n-1] 180/4=n[2n-1]45=n[2n-1]45=2n²-n2n²-n-45=02n²-10n+9n-45=02n(n-5)+9(n-5)=0(n-5)(2n+9)=0

n=5,-9/2

n must be positive integerSo, n=5

an=a+(n-1)dan=2+(n-1)8an=2+8n-8=8n-6

22.

whese diagoralfs [ 5cn-g

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23.

Prove that $\sqrt{3} \cos 23^{\circ}-\sin 23^{\circ}=2 \cos 53^{\circ}$

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24.

*Prove that 5-53 is an irrationalnumber

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5-V3 × 5+V3/5+V3=(5-V3)^2/5+V3=5+V3

25.

जाए ००० है + झा 6 2 cos 0, prove thatcos 6 —sin 8= J2 sin 8.i 21>

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26.

03.of coseco-sino =m andseco-coso =1, Prove that(min 53 min 3=1.

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Given cosec theta - sin theta = m, sec theta - cos theta = nGiven that cosec theta - sin theta = m→ !/sin theta - sin theta = m⇒(1-sin² theta)/sin theta = m→ cos² theta/sin theta = mand sec theta - cos theta = n⇒1/costheta - cos theta =n→ (1-cos² theta)/cos theta = nsin² theta/cos theta = nNow (m²n)²/³ + (mn²)²/³⇒(cos⁴ theta/sin² theta × sin² theta/cos theta)²/³ + (cos² theta/sin theta× sin⁴ theta/cos² theta)²/³⇒ (cos³ theta)²/³ + (sin³ theta)²/³⇒cos² theta + sin² theta= 1 Hence proved

27.

owhese samefind the area of the towangeCorresponding altitude ich 16 cm

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28.

(क)यदि /, 8, और 0 किसी 8»कोण हो, तो सिद्ध A ) ool4 रव 1 सिप्स जज b

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Hum jante hai

A + B + C = 180°

(B + C)/2 = 90 - A/2

So, tan(B+C)/2

= tan( 90° - A/2)

= cot (A/2)

29.

52 Construct an isosceles triangle whose base is 8 cm and altitude 4 cm und then unother trsingle whesesides are l 늑times the corresponding sides ofthe isosceles triangle

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30.

of a rational no blos and mefind Frational nobetween them.

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31.

26. The anglof a quadrilateral are in AP whose common differenceFind the angles.

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32.

in m2lindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of paintingA cythe curved surface of the pillar at the rate of12.50 per m2

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33.

The curved surface of a cylindrical pillar is264 m2 and its volume is 924 m3. The diameterof the pillar is

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34.

egitsucm. Find the total surface area of the cylinder.(a 3.14)cylindrical pillar is 1 m in diameter and 4.2 m in height. Find the cost of white washing the curvednmsurface of the pillar at the rate of 15 per m21584 m2

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Curved Surface Area = 2* (22/7) * r * h= 2*(22/7)*0.5*4.2= 13.2 sq mCost = Area*rate= 13.2 * 15= Rs. 198

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35.

6. The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3 Findthe diameter and height of the pillar

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36.

Acylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of paintinge curved surface of the pillar at the rate of 12.50 per m2.

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37.

. A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of paintingthe curved surface of the pillar at the rate of12.50 per m2

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38.

Evaluate tan 2tan5) 4

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39.

secO—tan() ———— = ]_2gsec 0 tan® +2tan?’ 0.‘secB+tan

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LHS:=(secA − tanA) / (secA + tanA)= (1/cosA − sinA/cosA) / (1/cosA + sinA/cosA)= (1 − sinA) / (1 + sinA)= {(1 − sinA)(1 − sinA)} / {(1 + sinA)(1 − sinA)}= (1 − 2sinA + sin²A) / (1 − sin²A)= (cos²A + sin²A − 2sinA + sin²A) / cos²A= (cos²A − 2sinA + 2sin²A) / cos²A= cos²A/cos²A − 2 (1/cosA)( sinA/cosA) + 2(sin²A/cos²A)= 1 − 2secAtanA + 2tan²A= RHS

40.

sec^4-tan^4= 1+2tan^2

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sec⁴x - tan⁴x (1+tan²x)² - tan⁴x1+tan⁴x+2tan²x -tan⁴x1+2tan²x

41.

Example-6853Prove that 2tan-11-tan--= tan-14

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42.

\tan \left(\frac{\pi}{4}+A\right)+\tan \left(\frac{\pi}{4}-A\right)=C) 2tan 2 AD) 2 cos ec2 AA) 2sec 2AB) 2sec 2 A

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43.

(L)(İ) Thodo maionfuncti on스2-1 g-,ofthey=Ca) -co, o(b)(-oo) (d)

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For function to be defined 1+x^2 should not be equal to zero

which is true for all the values of x

hence

option d is the correct answer..

44.

The product of three terms in G. P. IS 210 ndIf tho continued product of three numbers in G. P. is 216 and the sum of their

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let a/r , a , ar are in GP

A/C to question, (a/r ) × a × ar = 216a³ = 216a³ = (6)³ a = 6

again, sum of their products in pair = 156 (a/r ) × a + a × ar + ar × (a/r) = 156 a²/r + a²r + a² = 15636/r + 36r + 36 = 156 36( 1/r + r + 1) = 156 3(r² + r + 1) = 13r 3r² + 3r + 3 - 13r = 03r² -10r + 3 = 03r² - 9r - r + 3 = 0r = 3 and 1/3

so, numbers are 6/3, 6 , 6×3 => 2, 6, 18 numbers are 6×3 , 6 , 6/3 => 18, 6, 2

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45.

Which of the following pair of elements represents a mole ratio of 1:1?(a) 10 g of calcium and 12 g of magnesium(c) 12 g of carbon and 20 g of calcium(b) 12 g of magnesium and 6 g of carbon(a) 20 g of sodium and 20 g of calciurm7. Which of tho fallouri

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46.

2a×6b

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12ab is the product.

The answer is 12ab as 2a*6b=12ab

47.

PRACTICE LONE1. Solveective

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48.

Sth ininatingContinuing the above procedure and moving further towards left- 2 into 7 equal parts again. Thus, two points left to -1, we obtahere by A.2 areSELF PRACTICE1. Represent the following rational numbers onthe number line:eis(in)(iii) 17(iv) -(111)5Sol.

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3/5=0.6 kya ma na jo keya ha vo hi shi ha I am not sour but I am sure this answers

first make a line and write with start point 123 after 123 you write 0 after0 you write 12345

49.

Practice Time1) Do these divisions. CHa) 438 = 9b) 3480 = 12c) 450 = 72) Solve the given sums abelow. See what

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1:48.662:2903:64.28

50.

75 रुपये 25 पैसे > 75 = 0 e

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100 paise = 1 rupee. 25 paise = 0.25 rupees.75 rupees 25 paise = 75.25 rupees.

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