Explore topic-wise InterviewSolutions in Current Affairs.

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1.

solve the equation using systematic Method 3 (x+2)-2 (x-1)=75 (x-1)+2 (x+3)+6=0

Answer»

3x+6-2x+1=7x+7=7x=7-7x=1

sorry. its x=0

1) 3x + 6 - 2x +1 =7 (3-2)x + 7 = 7 x = 7-7 x = 0

2) 5(x-1) +2(x+3) +6 = 0 5x - 5 +2x + 6 +6 = 0 (5+2)x +1 +6 =0 7x = - 7 x = - 1

2.

7) State Huygen's principle

Answer»

Huygens principle states that each point of a wavefront is the source of secondary wavelets (small waves) which spread in all directions with the speed of the wave. The new wavefront is formed by drawing a line tangent to all the wavelets

Thanks

3.

OAB is a sector of the circle havingcentre at 0 and radius 12 cm. Ifm ZAOB = 45", find the differencebetween the area of sector OAB andsector AOB.

Answer»

Area of Sector is = (Theta/360) ✖ pi ✖ r^2 = (45/360)*(22/7)*12*12 = 88 sq. cm.

Area of circle = pi ✖ r^2 = (22/7) 12 ✖ 12 = 3168/7 sq.cm

area of Sector AOB = (3168/7) - 88 = 2552/7 sq cm..

difference between area of Sector AOB and area of Sector OAB = (2552/7) - 88 = 1936/7 sq.cm (ANS)

if you like the answer, Mark it as best bro..

if u like the answer,mark it as best

o is center of the circle then :-45°=[45×π÷180]=π/4r=12 then 1/2×12×12×π/418πsq cm

4.

Differentiate (r2 - 5x + 8) (r + 7x+ 9) in three ways mentioned below:() by using product rule(ii) by expanding the product to obtain a single polynomial.(ii) by logarithmic differentiation.Do they all give the same answer?

Answer»

teeno rule se bataiye

5.

Find the exact value of sin 22.5° using the half-angleidentity for sine.

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6.

quations by systematic method(b) y -8-4

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y - 8 = 4y = 4+8y = 12

7.

Chalienge !12 using a suitable identity, find the value of2+

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My dear friend, thank you very much

8.

10÷(5×2)=(10+5)×(10+2)

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9.

SecH + ‘LOYLS L o |BN, ~ ron bt‘0561 IRE| —Sing

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10.

बहुपदों के शून्यक ज्ञात कीजिए:() x* +6x° +11x+6et —2x% - Tx* +8x+12(४) x*=3x*-9x-5

Answer»

x*x*x*x - 2x*x*x - 7x*x + 8x + 12 = x*x*x*x - 2x*x*x - 7x*x + 14x - 6x + 12 = x*x*x(x-2)-7x(x-2)-6(x-2) = (x-2)(x*x*x-7x-6) = (x-2)(x*x*x+x*x-x*x-x-6x-6) = (x-2)(x+1)(x*x-x-6) = (x-2)(x+2)(x-3)(x+2)

zeroes are -2,2,3

11.

hcTadlivand, the length o/ an are is Ron.Find the arta the Sector.

Answer»

Area of the sector = 1/2 x ( length of the corresponding arc) x radius

= (1/2) x 12 x 6

= 36 cm²

12.

DAVINDRATHREEOIMatch the following:() Area of sector(i) Length of an arc of a sectorof a circle with radiuscircumference of a circle(ii) radius of a circleτα29/360)(iv) Area ofof a circle2tr0/360

Answer»

Area of sector -> (pi)r(square)(theta)/360Length of an arc of a sector of a circle with radius -> picircumference of a circle/radius of a circle -> 2(pi)r(theta)/360area of 1/4 of a circle -> (pi)r(square)/4

13.

same tume.ables is 1. Hence it is a linear equation.x (2) Solve the following simultaneouquations.3x -4y - 15 0y tx+2 0

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14.

9 Find the value using identity (93)10. Subtract 4x 2x from 3x-4x

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15.

16(3x-5)-10(4x-8)4=80

Answer»

x=10\7 is the right answer

48x-80-40x+80×4=8048x-40x=80+80-80×48x=80×48x=320x=320÷8x=40

( 48x -80) -10(16x-32) =8048x-80 -160x+320=80-112x +320-160=0-112x+160x= 160÷112x= 1.42

16.

Find the area of a sector whose arc length is30 π cm and the angle ofthe sector is 4002.

Answer»

wrong

Sorry for the error in the previous answer. This one is the correct solution.

calculations is wrong i think so

coz, ans is 6361.72 sq.cm

17.

(A) 34the first three terms in the expansions (1+ ax) in ascending powers of x are 1+ 12x+ 64x* , find a

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18.

4. In a circle of radius 21 cm, an arc subtends an angle of 60 at the centre. Find the length of the arc.

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19.

17, 5x-lay-Tx-(3x-2y) + 4z-3(x + 3y-2z))

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5x - (4y- (7x-3z+2y +4z - 3x - 9y + 6z))= 5x - (4y-(4x - 7y + 5z))= 5x - (4y-4x+7y-5z)= 5x - 4y + 4x - 7y + 5z= 9x - 11y + 5z

20.

4In fig O is the centre of acircle, chord PQ chord RSIf LPOR 70°and (arc RS)-80°, find1) m(arc PR) 2) m(arc QS)3) m(arc QSR)

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1). Chord PQ = RS so m(arc PQ) = m( arc RS) = 80 degree.2). m (arc QS) = 360- 80-80-70 = 130.3). m (arc QSR) = 130 + 80 = 210.

21.

6. If A laysuch that ay (i j then find trace of A.

Answer»

The trace of a matrix is sum of its diagonal element for that i = j

so the first element will be aij = (i+j)² = (2i)² = 4 the second element of trace is = (2+2)² = 16the third element of trace will be (3+3)² = 36

so, the trace = sum of all even no. squares => 2n(n+1)(2n+1)/3.

22.

rove that the angle subtended by an are of a circle at the centre is double the angle subtended/by it at,any point on the remaining part of the circle

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thanks

23.

Prove that the angle subtended by an arc of a circle at the centreis double the angle subtended by it at any point on the remainingpart of the circle.

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24.

e alun umum sheet? (Take π 3.14)15. The shape of a garden is rectangular in the middle and semi-circular at the ends as shown in the figure.Find the area and the perimeter of this garden.8.4 m21 m

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25.

8.Prove that the angle subtended by an arc of a circle at thecentreis double the angle subtended by it at any point on the remainingpart of the circle.

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26.

9. Find the arc length of RS.17 m

Answer»

diameter=17mradius=17/2=8.5mcircumference=2πr=3.14×2×8.5then arc, RS =circumference/2=3.14×8.5m

26.69 is the correct answer of the given question

27.

7 Im a circle of radius 21 cm, an arc subtends an angle of 60 at the centre.Find : (i) the length of the arc ?2D)(ii) area of sector formed by the arc 2

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28.

15. Kosgei earns sh 250 a day. If his dailywages was increased by 30%, howmuch did he earn in 6 days?

Answer»

Increased by 30%hence250*30/100=75 rupees increasehence250+75=325rupees in one dayIn 6 days=6*325=1950 rupees

29.

mon solution. So,E 3.3s by the substitutior() s-r 33

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30.

26. Prove that the angle subtended by an are of a circle at the centre is double the angle subtendedby it at any point on the remaining part of the circle

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31.

26. Prove that the angle subtended by an are of a circle at the centre is double the angle subtendedby it at any point on the remaining part of the circle.

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32.

26. Prove that the angle subtended by an arc of a circle at the centre is double the angle subtendedby it at any point on the remaining part of the circle.

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33.

n fig 3.38 A QRS is aniangle. Prove that,1) arc RS arc QS2) m(arc QRS) 240

Answer»

Question you have submitted is incomplete. Please post a complete question.

Could u please provide the figure?

34.

us of a cylinder is doubled and height is halved, then what effect would it have on the volumeof the cylinder?A rectangular sh6.

Answer»

Please post a clear image with proper lighting. We cannot provide a solution without a clear image of question.

ok

35.

(2) Solve the following simultaneous eq(i) 2x+y 5; 3x-y 5

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x=2 y=1

36.

the capacity of closed cylinder of vessel of height 1meter is 15.4 liter.how many square meter of metel sheet would be needed to make it

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37.

4x + 6 = 10

Answer»

x=1. aayga bhai a right answar hai bhai

4x + 6 = 104x = 10 - 64x = 4x = 4/4x = 1

38.

3. Solve the following simultaneous eq(1) 3x - 4y = 10 ; 4x + 3y = 5

Answer»

3x - 4y = 10, 4x +3y =5; 4(3x-4y=10); 3(4x+3y =5); 12x - 16y = 40; 12x + 9y = 15; 12x +9y = 15/25y = 30; y = 30/25=6/5; 3x -4(6/5)=10; 3x = 10+ 24/5 = 50+24/5=75/5; x = 75 /5×3=25/5=5

-10/7 is correct answer.

39.

Find the value of x from the adjoining figure.メc3x + 19"/4x + 21°56x-5 4x 20°8Fig. Q.9Fig. Q.10

Answer»

thanka

40.

metallic sphere of radius 4.2 cms. is melted and recast into the shape of a cylinderof radius 6 cms. Height of the resultant cylinder would be: Ile110 cms/1103.84 cms/ 3.84rt. 30 cms/30 ft. 2.74 cms/ 2.74

Answer»

If a solid is recasted in any other solid the volume remains the same.so,vol.of sphere=vol. of cylinder•4/3πr cube= 2πr square ×h 4/3×22/7×42/10×42/10×42/10 = 2×22/7×6×6×hh= 98.784/36H=2.744 cm

41.

● Determine n if 2nc2" nc2-12:1Find a if the 1 7th and 18th terms of the following expansion are equal: (2+ a)SIn an 4.P the first term is 2 and the sum of the first five terms is one fourth of t50

Answer»

(2+a)^50=(a+2)^5017th term=18th term50C17*a^17*2^33=50C18*a^18*2^32so a=50C17*2/50C18a=(50!/33!*17! *2)/(50!/32!*18!)so a=2*32!*18*17!/(33*32!*17!)so a=2*18/33=36/33=12/11

42.

OAB is a sector of the circle with centre O andradius 12 cms. If m angleAOB 60°, find the differencebetween the areas ofsectors AOB and ΔΟΑΒ

Answer»

Area of Sector is Theta/360*pi*r^2 = 60/360*22/7*12*12 = 75.4 sq. cm.

Area of equilateral triangle.

Since the triangle is an equilateral triangle, then height is sqrt (12*12-6*6) = sqrt(144-36) = sqrt(108) = 10.39

Therefore area = 1/2 * 10.3923 * 12 = 10.39 * 6 = 62.35 sq. cm

Thus, the difference between areas of sector and triangle is = 75.4 - 62.35 = 13.05 sq. cm.

43.

The radius of the base of the cone is 7 cms and its height is 12 cms. Calculatethe volume.

Answer»

volume of cone= πr^2h /3=22/7 ×(7)^2×(12) /3= 3.14×49×12/3=1848/3= 616cm^3

vol of cone is 1/3πr^2×h=1/3×22/7×7×7×12=1/3×22×7×12=1848/3=616cm^3 is correct answer 100%

44.

Find the 7th term in expansion of104x2vx

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45.

find the 7th term in the expansion of (4x/5+5/2x)8

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46.

10Find the 7th term in the expansion of 3x

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47.

(a) 6037 Two circles of radius 4oms and 3cms touch each other. Distance between theircentre will be(a) 7 Cms (b) 7 Cms or 1 Cm () 1 Cm(d) 4 Cms

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(b) 7cm or 1cmIf two circles touch internally then the distance between their centres is equal to the difference of their radii.4 - 3 = 1cmIf two circles touch externally then the distance between their centres is equal to the sum of their radii.4 + 3 = 7cmTherefore either 7cm or 1cm.

48.

1. Find the sides of a rectangle whose area is 240 cms. and the perimeter is 200 cms.[ Ans. : 60 cms., 40 cms.]

Answer»

Here there is a mistake in the given area. the area should be 2400 cm^2

49.

Find the difference between the place values of(a) two fours in 60,474.(b) two sevens in 17,479.(c) two eights in 8,90,853.

Answer»
50.

Two sevens are

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Two sevens are fourteen.