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.

( 4 m + 5 n ) ^ { 2 } + ( 5 m + 4 n ) ^ { 2 }

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2.

B. I. A dealer bought 100 quintals of rice at Rs 700 per quintal. He sold 50 quintalsatRs1000guintal and the remaining at Rs 800 per quintal. Find his gain and gain per cent.

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Find the cost price:

1 quintal = Rs 700

100 quintal = 700 x 100 = Rs70,000

Find the selling price of 50 quintal:

1 quintal = Rs 1000

50 quintal = 50 x 1000 = Rs 50,000

Find the remaining amount of quintal:

Remaining amount = 100 - 50 = 50 quintal

Find the selling price of the remaining quintal:

1 quintal = Rs 800

50 quintal = 800 x 50 = Rs 40,000

Find the total selling price:

Total = 50,000 + 40,000 = Rs 90,000

Find the gain:

Gain = Selling Price - Cost Price

Gain = 90,000 - 70,000 = Rs 20,000

Gain percentage = gain / cost price x 100

Gain percentage = 20,000/70,000 x 100 = 28.57%

The gain is Rs 20,000 and it is 28.57%

thanks for this answer

3.

( 2187 ) ^ { \frac { 3 } { 7 } }

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(2187)³/⁷=(3⁷)³/⁷=3³=27

the ratio of the length of a vertical pole and it's shadow on the ground is 7:2 . find the length of the pole if the length of the shadow is 2.4.

4.

B, C and D are four points on aircle. AC and BD intersect at a point E suchthat BEC = 1300 and < ECD = 20°. FindZ BAC

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5.

1S:Value of (2187)7 is:

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thanks

6.

respectively. Prove that the height of the tower is ianß-tanss0. The angle of elevation of a cloudfrom a point 60m above a lake is 30- and theangle ofdepression of thereflection of the cloud in the lake is 60° Find the height of the cloud from the surfaće of the lake.ircle

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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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7.

Piz 10.38s In Fig 10.39.A. B, Cand D are four points on aircle. AC and BD intersect at a point E suchthat Z BEC 130 and ECD 20. FindВАС.orD)360Fig 10.39

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8.

8. निम्नलिखित संख्या श्रृंखला में प्रश्नचिह्न (?) के स्थान पर क्याआयेगा?2187 , 729,243 , 81,27,9, ?

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3 is the answer of this question

3is right answer ka answer hai

Given series 2187, 729, 243, 81, 27, 9,..... is geometric series with common ratio r= 729/2187 = 1/3and first term a = 2187

Its nth term = ar^[n-1]

Then 7th term = 2187 * (1/3)^[7-1]= 2187 * 1/(3)^6= 2187/729 = 3

Number in the place of ? will be 3.

3 is the right answer

3 is the answer for the question.

9.

BEFORE10 What power of 3 is 2187?

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Thecube rootof2187is 12.980246132767

2187/3=729729/3=243243/3=8181/3=2727/3=99/3=33/3=1

3×3×3×3×3×3×3=2187Hence3^7=2187

2187/3=729/3=243/3=81/3= 27/3=9/3=3; 3^7=2187

2187/3=729/3=243=81/3=27/3=9/3=3;3^7=2187

10.

iple Choice Questions (MCQs)sum of money is shared among Bobby, Sd Veenu in the ratio 1: 2:5. What percenmoney does Sania get?) 20%) 40%(b) 25%(d) 50%

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Let the share of Bobby be x the share of Saina be 2x the share of Veenu be 5x.

:. percentage of money that Sania gets={2x/(x+2x+5x)}×100={2x/8x}×100=0.25×100=25%

option (b) is correct.

11.

MuitipleChoiceQuestions(MCQs)i8. A sum of money is shared among Bobby, Sania and Veenu in the ratio 1 :2:5. What percentage ofmoney does Sania get?(a) 20%(b) 25%(c)40%(d)50%

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suppose shares of bobby sania and veenu is x 2x and 5xpercentage of sania=2x/8x*100=25%

12.

9. Simplify:) 32 +2/3 32

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13.

In a tennis tournament in which every pair has to play with every other pair, 10 players areplaying. Find the number of games played.

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Lets say we can do selection in way such that we need to select any 4 people out of 10 and out of these 4 we need to get max number of pairsthus no of ways of doing it =10C4×4C2= 1260

14.

9. Simplify:49 x z-3\77-30-5(Z 0)

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49 is 7^2hence7^2*z^-3/(7^-3*10*z^-5)=7^5*z^2/10

15.

Find the number of ways in which a mixed doubles tennis game can be arranged betweenplayers consisting of 6 men and 4 women.10

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thanks

16.

A body of mass 500g is thrown upwards with a velocity 20 m/s and reaches back tothe surface of a planet after 20 sec then the weight of the body on the planet is1.2N42.4N3.5 N4. 1 N

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4.Tine of ascent = Time of descentThus, time of ascent, t = 20/2 = 10 secLet the acceleration due to gravity on the planet is g'.then, by using v = u + at0 = 20 - (g' X 10) (as u = 20 m/s and t = 10s and direction of g' is opposite to that of u)g' = 2 m/s^2Thus, weight of the body = mg' = 0.5kg X 2 m/s^2 = 1 kgm/s^2 = 1N

17.

i6 A circular hall (big room) has a hemispherical roof. The greatest height is equal tothe inner diameter. Find the area of the floor, given that the capacity of the hall is48510m3.

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Let radius of the hall = rAs per question= Volume of cylindrical Hall + Volume of dome = πr²*r+ (4/3) πr³/2 = πr³ + 2πr³/3 =5πr³/3then we have 5πr³/3=48510 r³=9264.72 ⇒ r=21.0028 Area of floor= πr²=π*441.118=1385.81 Floor area is 1385 m²

18.

A circular hall (big room) has a hemispherical roof. The greatest height is equal to the inner diameter. Find the area of the floor, given that the capacity of the hall is 48510 m^3.

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19.

13. Consider the statement: Ratio of breadth and length of a hall is 2:5. Completefhefollowing table that shows some possible breadths and lengths of the hall40Breadth of the hall (in metres) 10ThLength of the hall (in metres) 25 50

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20.

13. Consider the statement: Ratio of breadth and length of a hall is 2:5. Complete thefollowing table that shows some possible breadths and lengths of the hall.Breadth of the hall (in metres) 10Length of the hall (in metres) 255040

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21.

oI lese26. y x+ 2 is any tangent to the parabola y8x. The pointP on this tangent is such that the other tangent from itwhich is perpendicular to it is

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22.

ircle1. A tangent to a circle is perpendicular to the radius through the point of contactOrd nernendicutar to it is a tangent to t

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23.

d. 2Sb. 15C. 354. If tangents AB and AC, inclined to each other at an angle of 120° are drawn to a circle withcentre of radius 6 cm, then find the length of each tangent.d. 4v3

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Let centre of circle be O.<BAC = 120°

consider ∆ABO and ∆ACO1) OA =OA --- common side2) OB = ON --- radii of same circle3) AB = AC --- tangents from same pointtherefore ∆ABO congruent to ∆ACOtherefore <ABO = <ACO = 60°

as tan 60° = √3therefore in ∆ABOBO/AB = 6/AB = √3AB = 6 / √3AC = 6 / √3

24.

58. Before 7 years, the ratio of ages of A and Bwas 3 : 4. After 9 years, ratio of their ages will be7: 8. The present age of B will be

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23yrs

25.

Fig. 10.4nght angies to the tangent (sce Fig 10.4). We shallnow prove this property of the tangent.Theorem 10.1 The tangent at any point of a circle is perpendicular to theradius through the point of contact.4. I

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Given :A circle C (0,r) and a tangentlat point A.

To prove :OA⊥l

Construction :Take a point B, other than A, on the tangentl. Join OB. Suppose OB meets the circle in C.

Proof:We know that, among all line segment joining the point O to a point onl, the perpendicular is shortest tol.

OA = OC (Radius of the same circle)

Now, OB = OC + BC.

∴ OB > OC

⇒ OB > OA

⇒ OA < OB

B is an arbitrary point on the tangentl. Thus, OA is shorter than any other line segment joining O to any point onl.

Here, OA ⊥l

26.

. Prove that the perpendicular at the point of contact to the tangent to athrough the centre.

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27.

10.1 : The tangent at any point of a circle is perpendicular toradius through the point of contact.

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28.

. Prove that a tangent to a circle is perpendicular tothe radius drawn from the point of contact.

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29.

Prove that atangent to a circle is perpendicular to the radius drawn from the pointof contact.

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13)

30.

दर 2 (o नका 500 + MQ_ 509 (q) (E i I)Q' ® € Sy e SO AR e Vbl e e

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31.

25.A boat, when sailing up the stream, takes 25minutes to cover a distance of 2 km and takes 20minutes to return. The speed of the stream is(A) 1.2 km/h(B) 1.1 km/h(C) 0.8 km/h(D) 0.8 km/h

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Let the speed of stream be uLet speed of boat in still water be v

Time taken to cover 2 km distance upstream =2/v - u = 25/60 = 5/125v - 5u = 24........ (1)

Time take to cover 2 km distance downstream =2/v + u = 20/60 = 1/3v + u = 6............. (2)

Multiply eq(2) by 55v + 5u = 30....... (3)

Add eq(1) and eq(3)10v = 54v = 5.4 km/hr

Put value of v in eq(2)v + u = 6u = 6 - 5.4u = .6 km/hr

Therefore, speed of stream = .6 km/hr

32.

Let d and b be any two vectors Than show that la. Bis lajb

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question is not clear enough..

33.

37. Four equal circles, each of radius 5 cm,touch each other, as shown in the figure.Find the area included between them.A*[Take x 3.14]B°C.

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34.

2. Renuka is 12 years old. Her brother Sanjay is 3 years older and her mother is 40 yearsold. Find the ratio between0 Renuka's age and Sanjay's age(i) Sanjay's and his mother's age

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Renuka=12so Sanjay=12+3=15Mother=40i) Renuka/Sanjay=12/15=4/5ii) Sanjay/mother=15/40=3/8

35.

\begin{array} { l } { 3 x - y = 3 } \\ { 9 x - 3 y = 9 } \end{array}

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36.

rre a, y bis the solution of the pair of equations x-y-2 and x + yvalues of a and b4, find the

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Given : x = a and y = b is solution of x - y = 2 and x + y = 4.

We have

x - y = 2 ....(1)x + y = 4 ....(2)

Eliminating y by (1) and (2)

2x = 6

x = 3

y = 4 - 3 = 1

So, x = a = 3 and y = b = 1

37.

mother is 25 years old and her son's find son's age if after 8 years ratio of son's is to mother age will be 4_9

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Let son's age is xafter 8 years, x+8/25+8=4/9x+8/33=4/99(x+8)=132x+8=132/9x+8=14.66x=6.66

let sons age be x so mother's age will be x+25

after 8 yrs sons age = x+8mother's age = x+25+8 = x+33

as per given condition x+8/x+33 = 4/9by cross multiply 4(x+33)=9(x+8)4x+132 = 9x+72subtracting 4x on both sides ( always try to take variables first this makes calculation easy)4x+132-4x = 9x+72-4x132=5x+725x+72=132 ( i am just interchanging the places)subtracting 72 on both sides5x+72-72=132-725x=60dividing by 5 on both sides5x/5 = 60/5x=12sons age 12mothers age 12+25 =37

38.

PC is a tangent to the circle at C. AOB is the diameterwhich extended meets the tangent at 'P. Find CBA,6e tangent at Find Zは0

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39.

2 y + \frac { 5 } { 2 } = \frac { 37 } { 2 } \quad ( b ) 5 t + 28 = 10 \quad ( c ) \frac { a } { 5 } + 3 = 2

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thank u very mych

thank u very much

thnx

40.

BTangent AC = 16Tangent DC = 4Tangent EF = 7Find the Perimeter of Triangle ACE

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given, AC(AB+BC)=16DC=4EF =7now, we know tangent drwan from point are equal. then, EF=ED. ........(I)

DC=BC. ......(ii) AB=AF. .......(iii) so, Perimeter of triangle =ED+DC+BC+AB+AF+FE=(ED+DC)+(BC+AB)+(AF+FE)=2DC+AC+2EF=2*4+16+2*7=8+16+14=28

28 is the correct answer of the given question

41.

Q.30. If A=0/LPlumn rule for mSolution : By the row-by-column rule for.1100AB=(r+23+370.x + 1 v + 2-AB =[ 0.8 + 0y +1:ButHence by the definition of equality of matx + 2 y + 3= = 60x + 1y+2: = 30x + Oy + 12 = 1.Hence == 1. y = 1. x = 1.1 -2 311 37B= -1 02.31. If 4-|-4 255(24)(1.1+(-2)(-1)+3.2.Solution : AB =

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1(-10)-2(5-12)+3(2+8)=-10-2(7)+3(10)=-10-14+30=30-24=6

42.

.Ahall36mlongand24mbroadallowing80 m for doors and windows, the cost of paperingthe walls at Rs 8.40 per m2 is Rs 9408. Find the height of the hall

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43.

, A hall 36 m long and 24 m broad allowing 80 m tor doors and windows me cost ofindows, the cost of paperingthe walls at Rs 8.40 per m2 is Rs 9408. Find the height of the hal

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44.

Find the values of a and b for which ax3 -11x2 + 11x + bis exactlydivisible by x24x .

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45.

29. Find the values of a and b for which ax3 11x2 +11x + bis exactlyifdivisible by x2-4x 5

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46.

13. Find the values of a and b so that the polynomial -10xx+bisexactly divisible by (x -1) as well as (x -2)

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47.

WHO S BIS NUMBER

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0.8 is bigger than 0.7 as comparing digit after decimal 8 is bigger than 7.

48.

Vbl BIS e blgh bl LS=o

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49.

0.)la ligure, a triangle ABC is drawn to circumscribe a circle of radius atriangle ABC is drawn to circumscribe a circle of radius 3 cm, such that the segment:sD and DC are respectively of lengths 6 cin and 9 cn. If the area of .ABC is 54 en, then findthe lengths of sides AB and ACA,C.~ 6 cm

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50.

If a.-bV3 = , then the value of a and bis2+13

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