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.

The length of an arc and radius of acircle is 12 cm and 7 cm respectively. Find thearea of the minor sector of circle.

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2.

ainao 17, PQRS and ABRS are parallelogramsn Fig. 9.1and X is any point on side BR. Show that(i)ar(PQRS) = ar (ABRS)PAQ B(ii)ar(AXS)=-ar (PQRS)Fig. 9.17

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3.

A Jay bought a TV for 15000 and sold it for 14100. Find the loss percent

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4.

The number of stamps in the collections of Jay, Sourav and Mayank are in the ratio 34:5. If Saurav has collection of 108 stamps, find the number of stamps that Jay andMayank each has.h tokg of the ratio 2 5 so that it may hecame equal to

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Let no. Of stamps Jay has = 3xSaurav has = 4xMayank has = 5xGiven 4x = 108 x = 27

Stamps Jay has = 3*27 = 81Stamps Mayank has = 5*27 = 135

5.

Qr Find the decimal exporusion of ea0 Paint Pus on -wiy and is at a distance of snuts foom y-axs to left. Write the coQ4 In lhe gives' fig AB แ CD anj 2 is transversa, ihen calculate thr vulne of tordises of point PA 3x+3Calculate the edse of the cube: fits vohume s 13316 Fund the moke of the mumbers:14. 14. 15. 2726 27.27 2221Section-B12x6-12QI Find the valw of K. -2is afoctor ofp(x)-x2 + Kx + 2Kge ar-15) and (5) are compliemerntary angles find the angesIn the fos below, ABCD is a soqucre and P is the mid-poum of AD. BP and CP are jomedthor ZPCBLPREo10 In the iven R LABC 69 and ZAC31"find ERDC.IA Acone in & 4cm high and the rodius of its bae is .t om itmehed and recas intphere. Find the radus of sphere.

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wat u want plzz snd perticular

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6.

Find the value of a for which (x+1) is a factor of (axs +x -2x + 4a-9)

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if X+1 is a factorthenx=-1 will satisfy the equation a(-1)^3+(-1)^2-2(-1)+4a-9=0-a+1+2+5a-9=04a+3-9=04a-6=0a=3/2

7.

The area of a minor sector of a circle is3.85 cm and the measure of its central angle is36º. Find the radius of the circle.

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8.

he area of a minor sector of a circle is3.85 cm2 and the measure of its centralangle is 36. Find the radius of the circle.

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9.

1. If radius of a circle is 10 cm and of minorsectoris100sq.cm.,thenfindtheareaof major sector. (1-3·14)ove 2. In figure, A-D-C: and B-E-C,5I(DE) II I(AB), if l(AD) 5, I(DC)- 3, /(BC) 6.4, the I(BE)?3XE 6.4-x

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1. Radius of circle=10 cmarea of the circle=πr² = 22/7 x 100 = 314.28 cm²now area of minor sector= 100 cm²therefore, area of major sector= (314.28 - 100) cm² = 214.28 cm²

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10.

1. The perimeter of a sector of a circle with central angle 90° is 25 cm. Find the areaof the minor segment of the circle.

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11.

Prove that each angle of an equilateral triangle is 60

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12.

नाo 3 2eree, o 2रण A Mho»\r»d( ”LL‘?-"--H‘-1 कौर... Aoy=Bz | fied हद. कि

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13.

Reducing Equations to Simpler6x +1x-3le 16: Solve+ 1 =

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(6x + 1)/3 + 1 = (x - 3)/6

(6x +1 + 3)6 = 3(x - 3)

2(6x + 4) = (x - 3)

12x + 8 = x - 3

12x - x = - 8 - 3

11x = - 11

x = - 11/11 = - 1

6x+1÷3 +1=x-3÷66x+4÷3=x-3÷66(6x+4)=3(x-3)36x+24=3x-936x-3x=-9-2433x=-33x=-1..ans

14.

find the measure of each exterior angle of a equilateral triangle

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15.

7. Find the measure of each angle of an equilateral triangle.

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Each angle of equilateral triangle is equal let them be a.As sum of angles in triangle is 180° So,a+a+a = 1803a = 180a = 180/3 = 60°

So each angle of equilateral triangle is 60°

in equalateral tringle sides are equal then sum of tringle is equal to 180 so let the angle of tringle be x then 3x =180 so x=60

16.

2. Prove that each angle of an equilateral triangle is 60

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17.

hand in 5 minutes.centre. Find the aaA A chord of a circle of radius 10 cm subtends a right angle at the12(ii) major sector. (Use π=3Ssends an angle of 60° at the centre. Find(ii) major sector. (Use T-3.14)the corresponding : (i) minor segment

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18.

, find the value of016. If이이

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p/q= (6/5)²×1=36/25(p/q)-²=(6/5) -⁴

19.

गा (016 -- (668 (0620 A_(अ+.मि. 8 ह . .:

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(cotA -cosA)/(cotA + cosA)

((cosA/sinA)-cosA)/((cosA/sinA)-cosA) cotA=cosA/sinA

taking cosA common from numretor nd denominatr nd cancelling it we get

((1/sinA)-1)/((1/sinA)+1) since 1/sinA=cosecA

therfore

(cosecA-1)/(cosecA+1)

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(cotA-cosA) /(cotA+cosA)

20.

B 8. PORS and ABRS are parallelgmm nd Xsany point on the side BR. Show that0) artPORS)-a ABRS)(ii) artanxs-jar( PORS)

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21.

6) The sum of four consecutive integers is 178.What are the integers? (Is there a quick solutionto this problem?)14

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Four consecutive integers are following :-43444546

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22.

.PQRS and ABRS are parallelograms and Xisany point on the side BR. Show that(i) ar(PQRS)-ar(ABRSY)(ii) ar(AAXS) 2ar(PQR)S- ar

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Proof:

(i)Here, Parallelograms PQRS andABRS lie on the same base SR and between the same parallel lines SR and PB.

∴ ar(PQRS) = ar(ABRS) — (i)

(ii) In ΔAXS and parallelogram ABRS are lying on the same base AS and betweenthe same parallel lines AS and BR.

∴ ar(ΔAXS)= 1/2 ar(ABRS) — (ii)

From eq (i) and (ii),

ar(ΔAXS) = 1/2 ar(PQRS)

23.

s In Fig IH17, PORS and ABRS are parallelogramsand N is any point on side BR. Show that(Oar(PORS)-ar(ABRS)()ar(AXS)-ar (PORS)Fig. 11.17

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Given:

PQRS & ABRS both are parallelograms and Xis any point on BR.

To show:

(i) ar (PQRS) = ar (ABRS)

(ii) ar (AXS) = ar (PQRS)

Proof:

(i)Here, Parallelograms PQRS andABRS lie on the same base SR and between the same parallel lines SR and PB.

∴ ar(PQRS) = ar(ABRS) — (i)

(ii) In ΔAXS and parallelogram ABRS are lying on the same base AS and betweenthe same parallel lines AS and BR.

∴ ar(ΔAXS)= 1/2 ar(ABRS) — (ii)

From eq (i) and (ii),

ar(ΔAXS) = 1/2 ar(PQRS)

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24.

Fig. 9.16Eig. 9.17, PORS andABRS are parallelogramsand X is any point on side BR. Show that()ar(lPQRS)-ar (ABRS)Q B(ii) ar (ANS)--ar (PORS)

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Parallelograms on the same base and betweenthe same parallels are equal in area.

If a parallelogram and a triangle are onthe same base and between the same parallels then area of the triangle is halfthe area of the parallelogram.

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Given:

PQRS & ABRS both are parallelograms and Xis any point on BR.

To show:

(i) ar (PQRS) = ar (ABRS)

(ii) ar (AXS) = ar (PQRS)

Proof:

(i)Here, Parallelograms PQRS andABRS lie on the same base SR and between the same parallel lines SR and PB.

∴ ar(PQRS) = ar(ABRS) — (i)

(ii) In ΔAXS and parallelogram ABRS are lying on the same base AS and betweenthe same parallel lines AS and BR.

∴ ar(ΔAXS)= 1/2 ar(ABRS) — (ii)

From eq (i) and (ii),

ar(ΔAXS) = 1/2 ar(PQRS)

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25.

In Fig. 9.17, PQRS and ABRS are parallelogramsand X is any point on side BR. Show that(i) ar (PQRS) ar (ABRS)(ii) ar (AX S)--ar (PQRS)2

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26.

7, PORS and ABRS are parallelogramsIn Fig. 9.1and X is any point on side BR. Show that4G) ar (PORS) ar (ABRS)(ii) ar (AX S) ar (PORS)

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27.

s in Fig 9.17. PORS and ABRS are parallelogramsAand X is any point on side BR. Show that(i) ar (PRS) = ar (ABRS)(ii) ar (Axs-2 ar (PQRS)Fig. 9.17

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28.

I. Market value of a share is 200. If the brokerage rate is 0.3% then findthe purchase value of the share.

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29.

Tea3le matrithe| 13 a skerI value ofSymmetric finda and be

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30.

22for begino and alkaen te fied to+ b +C =0 and at+ C416 inI value of ab + dctca

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31.

The side of an equilateral triangle is ½ cm. The perimeter of thetriangle isA) 1B) 2C) 3/2 ofthese

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perimeter of equilateral triangle=3×side =3×0.5 =1.5cm Ans.

the answer is option Dplease like

32.

se Fig. 7.34). Shotw uABCisaright angled triangle in whicland AB-AC. Find 4 B and 2 CLC-Show that the angles of an equilateral triangleare 60° each.22180

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We know that the sum of angle of triangle is 180°

if angle A is 90°

then,,180-90= 90.

AB=AC

Therefore,, angle B =angle C= 45°

33.

The measure of each angle cequilateral triangle is

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34.

I. A piece of string is 30 cm long. What will be the length of each side if the stringis used to form:(a) a square?(b) an equilateral triangle?(c) a regular hexagon?

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1. A square has 4 sides. Length of each side = 30/4 = 7.5 cm. 2. An equilateral triangle has 3 equal sides. Length of each side = 30/3 = 10cm. 3. A hexagon has 6 sides. Length of each side = 30/6 = 5cm

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35.

Show that the points A(a, c), B(-a,-a) and C(_aV3, aV3)form an equilateral triangle.

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36.

Q15 Define constellation. Draw one such constellaiu016 Write a short note on global warming and its consequencest he taken while taking

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Ans :- Global warming is the average temperature of earth has increase since 1950 until now the temperature continuing increasing. Global warming can also refer to climate change that caused an increase in temperature . However Global warming are causes By natural events and human that are believed to be contribute to increase in average temperature.

The effects of global warming are the environmental and social changes caused (directly or indirectly) by human emissions of greenhouse gases.

37.

2ree consecutive integers add up to 51. Find these integers.

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Let the three consecutive integers be x,x+1,x+2. x+(x+1)+(x+2) = 51 3x+3=51 3x=48 x=16. So the numbers are 16,17,18.

38.

number2. When fourconsecutive integers are added, the sum is 46. Find the integers

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X+x+1+x+2+x+3=464x+6=464x=40x=10the integers areX=10x+1=10+1=11x+2=12x+3=13

thaxx

39.

5. Construct a Δ4BC in which ABAC,5.2 cm and LA-| 10°. Draw ADBC also.D 450

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40.

ained is. Find use lauo2consecutive integers add up to 51. Find these integers.es of 8 is 888. Find the mu

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Three consecutive integers are x,x+1,x+2. x+x+1+x+2=51 3x=48 x=16 So the integers are 16,17,18.

41.

12. ABCD is a trapezium in which AB II CD andADBC (see Fig. 8.23). Show that(iii) Δ ABC Δ BAD(iv) diagonal AC-diagonal BD1)Fig. 8.23Hint: Extend AB and draw a line through Cparallel to DA intersecting AB produced at E.]

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42.

we have to find five rational numbers that lies between the number-4/5 and -2/3

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43.

How many rational number between two numbers?(a) 1 (b)2. (c) 3 (d) of these

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d) of these, as between two numbers there are infinite rational numbers

44.

he triangle ABC, where A is (2, 6), B is(-3, 5) and C is (4, 7), is reflected in they-axis to triangle A'B'C, Triangle A'B'C' isthen reflected in the origin to triangleAB"C"(i) Write down the co-ordinates of A", B"and C"

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When reflected about y axis the sign of x coordinate changes soNow A'(-2,6) B'(3,5) C'(-4,5)After reflection in the origin the sign of both coordinates change.Now A''(2,-6) B''(-3,-5) C''(4,-5).

45.

5. If a, b and c are the sides of a right angled triangle 'c' is hypotenuse, thenprove that the radius r' of the circle which touches the sides of the triangleisa t b-c

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Let the circle touches the sidesAB,BC andCA oftriangle ABCat D, E and F

Since lengths of tangents drawn from an external point are equal We have

AD=AF, BD=BE and CE=CF

Similarly EB=BD=r

Then we have c=AF+FC

⇒ c=AD+CE

⇒ c= (AB-DB)(CB-EB)

⇒c = a-r +b-r

⇒ 2r=a+b-c

r =( a+b-c)/2

46.

If (a, b), (b, c) and (c, a) are the vertices of a triangle and the centroid of triangle is origin, then a + b + c =

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Coordiante of the centroid of the triangle is:x=(x₁+x₂+x₃)/3 , y=(y₁+y₂+y₃)/3∴, According to the given question,(a+b+c)/3=0or, a+b+c=0 -----------------(1)

Now, (a+b+c)³=a³+3a²b+3ab²+b³+3a²c+6abc+3b²c+3ac²+3bc²+c³or, (a+b+c)³=a³+b³+c³+3a²(b+c)+3b²(c+a)+3c²(a+b)+6abcor, a³+b³+c³=(a+b+c)³-3a²(-a)-3b²(-b)-3c²(-c)-6abc [Using (1)]or, a³+b³+c³=3a³+3b³+3c³-6abcor, a³+b³+c³-3a³-3b³-3c³=-6abcor, -2a³-2b³-2c³=-6abcor, a³+b³+c³=3abc Ans.

47.

In the given figure, name the(a) vertices of the triangle.(b) sides of the triangle.(c) angles of the triangle.

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vertices : L , M, Nsides : LM, MN, NL angles : <L , <M, <N

48.

4. Draw LABC-60° such that AB = 6.5 cm and BC = 45 cm. Through C, draw a lineparallel to BA and through A, draw a line parallel to BC intersecting each other at D.Measure AD and CD.

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49.

a, b and c are the sides of a right triangle, where c is the hypotenuse. A circle, of radius r, touches thea+b-csides of the triangle. Prove thatr=\frac{a+b-c}{2}

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Let the circle touches the sidesAB,BC andCA oftriangle ABCat D, E and F

Since lengths of tangents drawn from an external point are equal We have

AD=AF, BD=BE and CE=CF

Similarly EB=BD=r

Then we have c=AF+FC

⇒ c=AD+CE

⇒ c= (AB-DB)(CB-EB)

⇒c = a-r +b-r

⇒ 2r=a+b-c

r =( a+b-c)/2

50.

ORThe first term. common difterence and last term of an AP are 12. 6 and 252 respectivel, Findthe sum of all terms of this APd 252 respectively. Find

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