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. |
solve the equation using systematic Method 3 (x+2)-2 (x-1)=75 (x-1)+2 (x+3)+6=0 |
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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 |
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| 2. |
7) State Huygen's principle |
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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 |
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| 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. |
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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 |
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| 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? |
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Answer» teeno rule se bataiye |
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| 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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Answer» y - 8 = 4y = 4+8y = 12 |
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| 7. |
Chalienge !12 using a suitable identity, find the value of2+ |
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Answer» My dear friend, thank you very much |
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| 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 |
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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 |
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| 11. |
hcTadlivand, the length o/ an are is Ron.Find the arta the Sector. |
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Answer» Area of the sector = 1/2 x ( length of the corresponding arc) x radius = (1/2) x 12 x 6 = 36 cm² |
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| 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 |
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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 |
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| 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 |
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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 |
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| 16. |
Find the area of a sector whose arc length is30 π cm and the angle ofthe sector is 4002. |
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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 |
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| 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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Answer» 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 |
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| 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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Answer» 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. |
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| 21. |
6. If A laysuch that ay (i j then find trace of A. |
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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. |
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| 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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Answer» thanks |
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| 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 |
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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 |
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| 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? |
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Answer» Increased by 30%hence250*30/100=75 rupees increasehence250+75=325rupees in one dayIn 6 days=6*325=1950 rupees |
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| 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 |
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Answer» Question you have submitted is incomplete. Please post a complete question. Could u please provide the figure? |
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| 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. |
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Answer» Please post a clear image with proper lighting. We cannot provide a solution without a clear image of question. ok |
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| 35. |
(2) Solve the following simultaneous eq(i) 2x+y 5; 3x-y 5 |
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Answer» x=2 y=1 |
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| 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 |
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Answer» x=1. aayga bhai a right answar hai bhai 4x + 6 = 104x = 10 - 64x = 4x = 4/4x = 1 |
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| 38. |
3. Solve the following simultaneous eq(1) 3x - 4y = 10 ; 4x + 3y = 5 |
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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. |
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| 39. |
Find the value of x from the adjoining figure.メc3x + 19"/4x + 21°56x-5 4x 20°8Fig. Q.9Fig. Q.10 |
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Answer» thanka |
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| 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 |
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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 |
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| 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 |
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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 |
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| 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 |
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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. |
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| 43. |
The radius of the base of the cone is 7 cms and its height is 12 cms. Calculatethe volume. |
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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% |
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| 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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Answer» (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. |
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| 48. |
1. Find the sides of a rectangle whose area is 240 cms. and the perimeter is 200 cms.[ Ans. : 60 cms., 40 cms.] |
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Answer» Here there is a mistake in the given area. the area should be 2400 cm^2 |
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| 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. |
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| 50. |
Two sevens are |
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Answer» Two sevens are fourteen. |
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