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. |
mm(mn ) + n(m-n)chhava nrol |
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| 2. |
39.If x = sec - tano and y=cosec+ cote thenxy+1 isufc x = seco-tan y=cosec+ coto |
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Answer» 2 2 is the right✔ answer |
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| 3. |
8. Show that the points A(1,2), B(1, 6), c+23,4) are vertices of an equilateraltriangle. |
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9. Prove that the points (a, a), (-a, - a) and (-v3a, /3a) are the vertices of an equilateraltriangle |
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Answer» this question not match very bad |
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7. An open rectangular cistern when measured from outside is 1.35 mlong, 1.08 m broad and 90 cm deep. It is made up of iron, which is 2.5 cmthick. Find the capacity of the cistern and the volume of the iron used. |
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20. Find the locus of a point whiich moves in such a way that,0) isthe sum of its distances from the points (a, 0, 0) and (a, Oconstant. |
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| 7. |
iameter 2 cm.24. Water is flowing through a cylindrical pipe of intinto a cylindrical tank of base radius 40 cm, at the rate of 0.4 m persecond. Determine the rise in level of water in the tank in half an hour.ICBS 2013 |
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| 8. |
If I Ăs the midpoint ofthe lin esegment iningthepoints(2,0)andĺ˛,thenshowthattheline 5x + 3y +2 0 passes through the point (1, 3p). |
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Answer» let ( x1 , y1 ) = A( 2 , 0 ) ,( x2 , y2 ) = B ( 0 , 2/9 ) ; mid point of joining of A and B = ( x1+ x2 /2 , y1 + y2 /2 )( 1 , p/ 3 )= ( 0 + 2 /2 , 0 + 2/9 / 2 )= ( 1 , 1/9 )p/3 = 1/9 [∵ If ( a , b ) = ( c , d ) then a = c and b = d ] p = 1/3 --- ( 1 ) according to the problem given , put ( -1 , 3p ) in the equation 5x + 3y + 2 =05 ( -1 ) + 3× ( 3p ) + 2 = 0-5 + 3× 3 ( 1/3 ) + 2 =0 [ from ( 1 ) ]-5 + 3 + 2 =00 = 0 [ true ]Therefore ,5x + 3y + 2 =0 line passes through thepoint ( -1 , 3p ) . |
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| 9. |
Given that the circumference of a storage tank is 6.6 m, what is the measure ofthe radius of the tank? |
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Answer» Circumference = 2πr=> 2 × (22/7) × r = 6.6=> r = (6.6 × 7)/2 × 22 r = 1.05 cm |
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| 10. |
2Find the equation of a line passing through the point (3,- 4) andi) Parallel ii) Perpendicular to the line 5x - 2y + 3 = 0 |
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| 11. |
. Find the equation of the circle which hasits centre at the point (3,4) and touchesthe line 5x + 12y 110. |
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Answer» wrong 169 should no come and instead of 381 it is 9 |
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| 12. |
Q1. A conical tank is 3 m deep and its circular top has radius 1.75 m. Find thecapacity of the tank. |
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Answer» Given:-h=3mr=1.75m the volume of cone =1/3pi×r×r×h=1/3×22/7×1.75×1.75×3=385/40×1000/1000=9.62kl |
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| 13. |
Do+ 2+ usoProne that. (sino + 2+ Cecaso ). se o cos 0.2sin 0-14 |
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Answer» Let theta = x Then,(sinx + 1 + cosx)(sinx - 1 + cosx).secx.cosecx = (sinx + cosx + 1)(sinx + cosx - 1).secx.cosecx = [(sinx + cosx)^2 - 1].secx.cosecx = (sin^2 x + cos^2 x + 2sinx.cosx - 1).secx.cosecx = (1 - 1 + 2sinx.cosx).secx.cosecx = 2sinx.cosx.1/cosx.1/sinx = 2 |
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| 14. |
1. If m and n are zeros of the polynomial ax2 -5x + c, find the values of am +n 10 mn. |
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Answer» If you find this solution helpful, Please like it. |
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| 15. |
1. If m and n are zeros of the polynomial ax2 - 5x + c, find the values of a and c ifm+n=10 = mn. |
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Answer» m and n are zeroesm+n=5/amn=c/agivenm+n=10=mn5/a=10a=1/2c/1/2=10c=5 |
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| 16. |
5. If α and β are the zeros ofthe quadratic polynomial f(x)-kx44x+ 4 such that α=24then find the value of ksatisfying th |
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Answer» Given : f(x) = kx² + 4x + 4 and α and β are zero of f(x) so, α + β = -4/k and αβ = 4/k (α +β)² = α² + β² + 2αβ (-4/k)² = 24 + 2 × (4/k) 16/k² = 24 + 8/k 2/k² = 3 + 1/k 2/k² = (3k + 1)/k 2/k = ( 3k + 1) 2 = 3k² + k 3k² + k - 2 = 0 3k² + 3k - 2k - 2 = 0 3k ( k + 1) -2 ( k + 1) = 0 (3k - 2) ( k + 1) = 0 so, k = 2/9 and -1 |
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| 17. |
89 JulyAsin o has 0 20 find the valuesin ( -uuso-sin 40 caso |
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Answer» Given, sinθ-cosθ = 0 sinθ = cosθsinθ/cosθ = 1tanθ = 1 But, tan45 = 1 So,tanθ=tan45θ = 45° sin45 = 1/√2, cos45 = 1/√2 Therefore, sin⁴θ+cos⁴θ = (1/√2)⁴+(1/√2)⁴= 1/4+1/4 = 2/4 = 1/2 = 0.5 |
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| 18. |
Calculate area (APQR) from figure6 cm08 cm26 em |
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Q3If the product ofthe zeros of the polyriomial (ax2-6x-6) is 4,findthe value of a. |
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Answer» Given : ax² - 6x - 6 Product of zeros -6/a = 4 a = -6/4 = -3/2 |
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| 20. |
11. The cost of painting the total outside surface1of a closed cylindrical oil tank at 50 paiseper square decimetre is 198. The height ofthe tank is 6 times the radius of the base ofthe tank. Find the volume of the tank correctto two decimal places. |
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| 21. |
A cylindrical tank has a radius of 154 cm. Ifilled with water till a height of 3 metres. If somemore water to a height of 4.5 meters is pouredinto it, what will be the increase in the voluof the water? |
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Answer» Radius of cylindrical tank = 154cm = 1.54mheight of water =3mif height is 4.5 m then let the volume be vvolume of cylinder v = 22/7 *r *r*(H-h) =22/7*1.54*1.54*(4.5-3) =22/7*2.3716*1.5 =22*0.3388*1.5=11.1804 m^3please like the solution 👍 ✔️ |
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| 22. |
In a water tank whose radius is 3.5 m there is 76.93 cubic metres of water.What is the height of the water in the tank? (Take = 3.14) |
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| 23. |
1. Find the volu of Cos |
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| 24. |
-5 ind). ८ ५४७0 ।ततत ८ | oo 000l s il.._.M‘“-B%v”_ |
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Answer» Volume of cuboid = LBH = 57×4×3 = 684cm² |
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| 25. |
(c) The coordinates of the two points A (o, 4) and (3,7) respectively Find the equation of line AB andthe coordinates of the point where the line AB intersects x axis. (3) |
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Answer» Please like the solution |
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| 26. |
DetermineC if the line 5x-4y = Cintersects the x-axis at the point (2, 0).What are the coordinates of the pointof intersection with the y-axis? 3 |
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Answer» Y cordianate= 10/4x cordianate= 10/5 |
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| 27. |
ilomnce (3oLli | v ) o |
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Answer» (a/b)^[ x-1] = (b/a)^[x-3] (a/b)^[ x-1] = (a/b)^[-(x-3)] x - 1 = - x + 32x = 4x = 4/2x = 2 Value of x = 2 |
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16. If (r + iy)u+ iv, then show thatil V-y) |
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| 29. |
if the product of zeros of the polynomial ax2-6x-6 is 4 find the value of a |
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Answer» For polynomial ax^2 - 6x - 6 product of zeroes is 0 Then,Product of zeroes = - 6/a Hence,-6/a = 4a = - 6/4 = - 3/2 a=a, b=-6, c=-6Product of roots=4c/a=4-6/a=4a=-3/2 |
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| 30. |
35Caso |
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Answer» Let the larger angle be= asmall angles be = b, c 1. a= b+ca+b+c=180°acc to eq 1 2(c+b) = 180°c+b = 90° c+b = athereforeone angle is 90° i.e a.Hence proved. |
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| 31. |
(4) Provetherndfiusofthe ineircle ofan equilateral triangle is half the radiusof its circumcircle |
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| 32. |
I f а + b + С -0.lal-3 , lol5 . Ic-7, then the angle between a & b is : |
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| 33. |
at b caso |
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Answer» You give a wrong question Hii o know that these question Hii app konsse class may hoo |
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| 34. |
sino + caso = ?Theone who solve, will beaccepted asbest |
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Answer» sinx^4 + cosx^4=1; ( sinx^2 + cosx^2)( sinx^2+cosx^2)= (1)(1)=1 1answer is the best |
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| 35. |
If the product ofthe zeros of the polynomial (ax2-6x -6) is 4, findthe value of a.th |
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Answer» For equation (ax^2 - 6x - 6)Product of zeros is 4 We know for equation ax^2 + bx + c = 0Product of zeroes = c/a Then,-6/a = 4a = - 6/4 = - 3/2 |
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| 36. |
ic() Find the breadth and perimeter of a rectangle of area 962 cm2 and length 26 em. |
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| 37. |
How many Iitres of intik Claenspie& A hemispherical tank is made up of an iron sheet I cm thick. If the innerthen find the volume of the iron used to make the tankradius is2. |
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| 38. |
Example 6. A hemispherical tank is made upof an iron sheet I cm thick. If the inner radius is 1 m,then find the volume of the iron used to make the tank |
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Answer» the volume of the iron used to make tank is 44/21 m |
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| 39. |
What fraction of the volume of the earth is the volu IOU5. How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?6. A hemispherical tank is made up of an iron sheet I em thick.haptcefaceIf the inner radius is |
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Answer» The hemispherical bowl can hold milk is equal to the volume of the hemispherical bowl. Given diameter of the hemispherical bowl = 10.5cm radius of the hemispherical bowl (r) = 10.5/2 = 5.25 cm volume = (2/3)*Π*(5.25)3 = (2*3.14*5.25*5.25*5.25)/3 (Π = 3.14) = 2*3.14*5.25*5.25*1.75 = 302.91 cm3 = 303 cm3 Now 1000 cm3= 1 litre So 303 cm3= 303/1000 = 0.303litre |
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| 40. |
36ćžGhana MATHEMATICS FOR CLASS XIf A and B are (-2, 2) and (2,-4) respectively, find the coordinates of P sudhthat APAB and P lies on the line segment AB.x.14.3INCERT Textbook |
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Answer» thanks bhai |
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| 41. |
ME APPI-storeyed building are 30° and 45°, respectively. Find the heigh represppositMATHEMNfrom the angles of depression of the top and the bottom of an 8 m tall buildin slufrom the top of a multi-stof the multi-storeyed building and the distance between the two bunlaingsSolution : In Fig 9.9 Pd |
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| 42. |
Summthe sSuc aě´ the whose part |
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| 43. |
Example 3 In Fig 6.11, OP. OQ. OR and OS arefour rays. Prove that Z POQ+ Z QOR + Z SOR +POS = 360°. |
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| 44. |
In each of the following, give also the justification of the construction:で1. Draw a circle ofradíus 6cm. From a point 10cm away fromits centre, construct the pairof tangents to the circle and measure their lengths. |
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Answer» Thanks for the answer |
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| 45. |
s2 into fonur parts which are the fourterms ofan AP sudh that theis 210ide 32 intouct of the first and the fourth terms is to the product of the secondprand the third terms as 7: 15CBSE 2014] |
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| 46. |
Sino + Sino althan prove thatcoste LC050 L |
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| 47. |
e as o trz sino = zsinoProove that, sino-ro caso 20050 |
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| 48. |
Ifboth the zeros of the quadratic polynomial ax2 + bx + c are equal andopposite in sign, then find the value of b4. |
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Answer» Let p and -p are two zeroes of the quadratic polynomialFormula : sum of the zeroes = -b/ap-p=-b/a0=-b/aHence,b=0Answer: b=0 |
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| 49. |
I) VILIf a = x cose + y sino, b = x sino - y cose then x + y = |
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Answer» a×b=x²cos²A-y²sin²Aa×b=x²cos²A-y²(1-cos²A)ab-y²=cos²A(x²+y²)(ab-y²)/cos²A=(x²+y²) a²+b² is the correct answer of the given question |
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| 50. |
6 The diameter and height of a cylindrical tank is 1.75 m and 3.2 m respectivelyHow much is the capacity of tank in litre ? (22 )f ic em radius is ?.1 cm. Find its distance from |
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Answer» eight person can sit in a car how many cars will be needed for vansh 168 person person |
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