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. |
2. If a transversal intersects two parallel lines, prove that the bisectors of two pairs of internal anglesenclose a rectangle. |
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| 2. |
54, ABDC is a flower bed. If, OB = 21 m and14 m, find the area of the bed.ODTake Ď =14 m21 m |
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| 3. |
(2) If a transversal intersects two parallel lines, then write the sum of the interiorangles on the same side of the transversal. |
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| 4. |
which is the tem af the st negative tearm od |
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Answer» For term to be -ve , equate tn with 0 => 0 = a +(n-1)d=> 21+(n-1)(-3) = 0=> (n-1) = -21/-3=> n-1 = 7=> n = 7+1 = 8 so, 8th term will be 0 and after that 9th term will be first negetive term |
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| 5. |
ULPUU.1. Which was the largest dominant party at the time of Independence? |
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Answer» the party at the time of independence was national congress party consists of more than 300 member under mahatma Ghandi and pandit Jawaharlal Nehru |
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| 6. |
Identify the greaternumber in each of the following pairs.(ii) 53 or 35(i) 2 or8(i) 23 or 32 |
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Answer» what is this |
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| 7. |
If the point P[2,2] is equidistant from the points A (-2, k) and B (-2k, 3) find K. Also find thlength ofAP.Q.И |
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| 8. |
The base BC of an equilateral triangle ABC hes on y-axis. The coordinates of point Care (O:3)Thethe base. Find the cooridnates of the points A and B. also find thecoordinates of another point D such that BACD Is a rhombus. |
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| 9. |
Ex.5: Show that the lines givenby(2+k)x + (1+h)y 5 +7k pass through a fixedpoint for different values of k. Also, find the co-ordinates of the fixed point. |
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Answer» tks |
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| 10. |
MATEMAn102D s eguidistnt fom PiS, -) and Ros, 6, find the values of x. Also find thedtant frorn the pointdistances QR and PK |
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| 11. |
APetrol tank is 10 m long and 4 m wide. Itcan contain 20000 I of petrol. What is thedepth of the tank?1 m 1000 |
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Answer» Petrol tank dimensionsLength = 10m, Width = 4m, Depth =? Volume of tank = 120000 l = 120000/1000 m^3 Volume of tank = length*width*depth120 = 10*4*depthDepth = 12/4 = 3 m |
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| 12. |
p. The amount of petrol in a tank is twice of that in another tank. If we draw out 25 litres from the firstand add it to the other, the amount of petrol in both the tanks will be the same. Find the amount ofpetrol in each tank now |
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Answer» Let amount of petrol in another tank = n Then amount of petrol in first tank = 2n As per given condition2n - 25 = n + 252n - n = 50n = 50 Therefore,Amount of petrol in first tank = 2n = 100 litresAmount of petrol in another tank = n = 50 litres |
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| 13. |
If iz3 + z2-z + i = 0, then show that \ z|-1. |
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| 14. |
62. If z, and z2 are two complex numbers suchthat Izil=lzl, then(b) z and z2 are conjugates of each other(c) either zÄą = z2 or z,-22(d) of these |
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Answer» b)they are conjugates |
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| 15. |
For any two complex numbers z, and z2, prove thatRe (, z) = Reg Re z2-1mzi İmz2. |
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Answer» let z1 = x+iy and z2 = u + iv Rez1*Rez2 - Imz1*Imz2 = xu-vy now z1z2 = (x+iy)(u+iv) = xu + ixv + iuy + i²vy = (xu-vy) + i(xv-uy) so, Re(z1z2) = (xu-vy) => L.H.S = R.H.S |
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| 16. |
OD ST Sve21. In the adjoining figure Z1 = Z2, Z3 = 24. Show that PT.QR = PRST.004 |
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| 17. |
[y2+yz +z2/(x-y)(x-z)]+[z2 + zx + x2/(y-z)(y-x)]+[x2 + xy+y2/(z-x)(Z-y)] |
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Answer» thank you so much |
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| 18. |
(x2-y2)3 + (y2-z2 3 + (z2-x2)3 = ?2 232 2353.(3) (x -y) (y+ z) (z+x) (4) x-yz |
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Answer» Like my answer if you find it useful! tnq |
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| 19. |
TERMINATIONTENTIONRMINATE(b) DESTINATION(d) DOMINATE |
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Answer» (b) DESTINATION Explanation:Given word does not contain the letter S. Therefore, a word containing S cannot be formed. |
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| 20. |
16. A car has a petrol tank 40 cm long, 28 cm wide and 25 cm deep. If the full consumptionof the car averages 13.5 km per litre, how far can the car travel with a full tank dfpetrol? |
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Answer» Volume of tank = 40*28*25= 28000cm³= 28dm³= 28 LDistance the car can travel = 13.5*28= 378 kms Please hit the like button if this helped you |
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| 21. |
5. Milk is sold atper litre. Find the costres of milk. |
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Answer» rs 151/4 -1 litre cost of 32/5 litre - 151/4/32/5- 755/128 rupees RS 151/4 - litre cost of 32/5 litre- 151/4/32/5-755/128 rupees |
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| 22. |
find the erea of a square plot of sides 14 cm |
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| 23. |
2. Find the missing side in each of the given triangles.b)20 m4 cm12 m |
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Answer» other side is 16 cm ,20+12+16= 50 other side is 16 vm ,20+12+16=50 16m is the right answer |
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| 24. |
IS+5+7-1252 |
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Answer» 5+6+7-12÷65+6+7-218-216 5+6+7-12÷6=18-2=16 16is the right answer |
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| 25. |
Q. 4. Define poly phase circuit and phase angledifference in poly phase circuit.Answer |
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Answer» Polyphase System is a combination of two or more than two voltages having same magnitude and frequency but displaced from each other by an equal electrical angle. As poly means, many (more than one) and phase means windings or circuits. Each of them has a single alternating voltage of the same magnitude and frequency. |
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| 26. |
if the radius of a sphere is 2r then what is it's volume |
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Answer» volume of sphere =4/3πr^3=4/3π(2r) ^3=4/3π8r^3=>32/3πr^3 32/3 π r^ 3 is the correct answer of the given question |
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| 27. |
The largest sphere (with maximum volume) is carved out of a cube of sides 14 cm. Find the volume ofthe sphere |
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Answer» Like my answer if you find it useful! |
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| 28. |
A cylinder of maximum volume is cut from a wooden cuboid of length 30 cm andcross-section a square of side 14 cm. Find the volume of the cylinder and the volumeof the wood wasted. |
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| 29. |
A ——x+2 T xX+4 X1 152, 4 |
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| 30. |
Prove that the height of a cylinder of maximum volume, inscribed insphere of radius 'a' is 2a/V3. |
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Answer» Let r be the radius and h the height of the inscribed cylinder ABCD.let V be its volume.then , V = πr²h------( 2 )clearly, AC = 2R.ALSO, AC² = AB² + BC² => (2R)² = (2r)² + h²=> r² = 1/4(4R² - h²)--------( 2 ) using----( 1 ) & -----( 2 )V = πh/4(4R² - h²)=> dV/dh = (πR² - 3/4πh²) and d²V/dh² = -3/2πh. for Maxima or minima, we have (dV/dh) = 0 now, dV/dh = 0=> πR² - 3/4πh² = 0h = 2R/√3. therefore,[d²V/dh²](at h = 2R/√3) = -3/2π * 2R/√3= -πR√3 < 0. So, V is maximum when h = 2R/√3.hence, the height of the cylinder of maximum volume is 2R/√3.Largest volume of the cylinder = π×1/4[4R² - 4R²/3] × 2R/√3 = 4πR³/3√3. |
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lustrative Examples):2+1x-x+1T, 2000;2dxxx +1321 |
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| 32. |
xx+2/6=x+2/4 |
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| 33. |
What fraction of these shapes are(a) trianglesb) circles(c) rectangles |
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Answer» 1. 3/9 or 1/3 2. 2/9 3. 4/9 Kaisha circles ka hua ha |
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| 34. |
The radius of a sphere is 2r, then its volume will be(A) 13 (B) 41tr3 (C) nr3 (D) { nr3 |
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Answer» option d is the correct answer of the given question |
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| 35. |
Prove that the height of a cylinder of maximum volume, inscribed inRadius 'a' is 2a/3. |
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Answer» Let r be the radius and h the height of the inscribed cylinder ABCD.let V be its volume.then , V = πr²h------( 2 )clearly, AC = 2R.ALSO, AC² = AB² + BC² => (2R)² = (2r)² + h²=> r² = 1/4(4R² - h²)--------( 2 ) using----( 1 ) & -----( 2 )V = πh/4(4R² - h²)=> dV/dh = (πR² - 3/4πh²) and d²V/dh² = -3/2πh. for Maxima or minima, we have (dV/dh) = 0 now, dV/dh = 0=> πR² - 3/4πh² = 0h = 2R/√3. therefore,[d²V/dh²](at h = 2R/√3) = -3/2π * 2R/√3= -πR√3 < 0. So, V is maximum when h = 2R/√3.hence, the height of the cylinder of maximum volume is 2R/√3.Largest volume of the cylinder = π×1/4[4R² - 4R²/3] × 2R/√3 = 4πR³/3√3. |
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| 36. |
0) A 16N UA = | ,find Aâ˘Â°. |
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| 37. |
рдкреЗ woudy S StaMJa:mQ Srn % a o[/mucoro}\'c esl/ua},cm |
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Answer» the standard form of a quadratic equation is ax2+bx+c=0 |
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| 38. |
344 /12 lowest form |
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Answer» 344/12 Cancel using 2 172/6 Cancel using 266/3 Cancel using 322 |
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| 39. |
236. Afiter how many decimal places will the decimal expausion of 344terminate? |
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Answer» 23/200 can be terminated as0.115so three places after decimal |
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| 40. |
060" cos 30° + sin 30° |
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Answer» From which book have you taken this question? Please tell us so that we can provide you faster answer. |
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| 41. |
त्रि थी 0 5: and d =060 न पर० लण्ड D) |
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Answer» please give his formula |
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| 42. |
6. दी गई आकृति में, यदि |||m है, तब 2 का मान ज्ञात कीजिए।PL060°B++m |
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Answer» Dil Le Koi rokna tha kya hoga hoga Gaya pardesiMera sochna tha 120 hogaord 60 ho jaayega corresponding angle se cro 120 linear angle sum 180 Iska Ans hai 120° kyon ki angle 60 is vertically opposite and then it is alternate interior angle and finally 180-60=120 120° as angle on straight line is 180° and here angle ORD= 60° corresponding anle so angle x= 180-60=120° using AIA angle and corresponding angle answer is120 This is opposite angle and answer 60 |
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| 43. |
atx R—Xx अन्दडa-x a+x a—-xa—x a—x atx |
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| 44. |
यदि = 4 हो, तो xx-x--x) का मान ज्ञात क(A) 2816 (B) 3328 (C) 2516 (D) २००० |
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| 45. |
(xx) x-a + x-b-x-c , xa, b, c |
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| 46. |
X 2 X x Xx =% y " y |
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Answer» 4*2=8x*X=x^2y*y*y=y^38x^2y^3 |
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| 47. |
. कक का |—8x+2y=-22 |
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| 48. |
At what point, the slope of the curve y=x^{3}+3 x^{2}+9 x-27 is maximum. Also find maximum slope. |
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| 49. |
)40 cm (1) 60 cmFind the one having maximum(Nagaland B 2018rectangles, each of which has perimeterP.B. 2010one having maximum area. Also find that area |
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Answer» if length of rectangle is l and breadth b area is maximum when l=b so given perimeter( 1 ) 2(l+b)=40 so as l = b l = 10So maximum area is L2=100 cm^2( 2 ) 2(l+b) = 60so as l = bl = 15maximum area is L^2 = 225 cm^2 (b)is correct answer Higher the perimeter higher will be the area so,PERIMETER: 2(l+b) = 60 l+b= 30 l =15b = 15 AREA: l×b= 15×15 = 225cm²:.AREA IS 225cm² |
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| 50. |
uestion 17.Show that the height of the cylinder of maximum volume2Rthat can be inseribed in a sphere of radius R isAlso, find themaximum volume. |
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Answer» ty |
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