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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. |
a ( \operatorname { cos } B + \operatorname { cos } C ) = 2 ( b + c ) \operatorname { sin } ^ { 2 } \frac { A } { 2 } |
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| 2. |
\left. \begin{array} { l } { \operatorname { cos } A + \operatorname { cos } B - \operatorname { cos } C } \\ { = 4 \cdot \operatorname { cos } ( \frac { A } { 2 } ) \cdot \operatorname { cos } ( \frac { B } { 2 } ) \cdot \operatorname { sin } ( \frac { C } { 2 } ) - 1 } \end{array} \right. |
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| 3. |
\operatorname { cos } A + \operatorname { cos } B + \operatorname { cos } C = 1 + 4 \operatorname { sin } \frac { A } { 2 } \operatorname { sin } \frac { B } { 2 } \operatorname { sin } \frac { C } { 2 } |
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Answer» LHS = ( cos A + cos B ) + cos C = { 2 · cos[ ( A+B) / 2 ] · cos [ ( A-B) / 2 ] } + cos C = { 2 · cos [ (π/2) - (C/2) ] · cos [ (A-B) / 2 ] } + cos C = { 2 · sin( C/2 ) · cos [ (A-B) / 2 ] } + { 1 - 2 · sin² ( C/2 ) } = 1 + 2 sin ( C/2 )· { cos [ (A -B) / 2 ] - sin ( C/2 ) } = 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - sin [ (π/2) - ( (A+B)/2 ) ] } = 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - cos [ (A+B)/ 2 ] } = 1 + 2 sin ( C/2 )· 2 sin ( A/2 )· sin( B/2 ) ... ... ... (2) = 1 + 4 sin(A/2) sin(B/2) sin(C/2) = RHS .. |
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| 4. |
sector10. AB is a chord of a circle with centre O and radius 4 cm. ABis of length 4 cm. Find the areaof the sector of the circle formed by chord AB. |
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| 5. |
\left. \begin{array} { l } { \operatorname { cos } 2 A + \operatorname { cos } 2 B + \operatorname { cos } 2 C } \\ { = - 1 - 4 \cdot \operatorname { cos } A \cdot \operatorname { cos } B \cdot \operatorname { cos } C } \end{array} \right. |
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| 6. |
\operatorname { cos } 2 A - \operatorname { cos } 2 B + \operatorname { cos } 2 C = 1 - 4 \operatorname { sin } A \operatorname { cos } B \operatorname { sin } C |
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Answer» cosC = cos(180−(A+B))........ = −cos(A+B)........ = −(cosA cosB − sinA sinB)........ = sinA sinB − cosA cosB LHS = 2(cos²A + cos²B + cos²C) -3....... =2 [cos²A + cos²B + (sinA sinB − cosA cosB)²] -3....... = 2[cos²A + cos²B + sin²A sin²B − 2 sinA sinB cosA cosB + cos²A cos²B] -3....... = 2 [cos²A + cos²B + (1−cos²A) (1−cos²B) − 2 sinA sinB cosA cosB + cos²A cos²B] -3....... = 2[cos²A + cos²B + 1 − cos²A − cos²B + cos²A cos²B − 2 sinA sinB cosA cosB + cos²A cos²B] -3....... = 2 − 4 sinA sinB cosA cosB + 4cos²A cos²B -3....... = -1 − 4 cosA cosB (sinA sinB − cosA cosB)....... = -1 − 4 cosA cosB cosC....... = RHS |
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| 7. |
\operatorname { sin } A + \operatorname { sin } B + \operatorname { sin } C = 4 \operatorname { cos } \frac { A } { 2 } \operatorname { cos } \frac { B } { 2 } \operatorname { cos } \frac { C } { 2 } |
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Answer» hii |
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| 8. |
Diameter of the base of a cone is 10.5 cm and its slant height is 10cm. Find its curvedsurface area.I.clant hoigbtis 21 m and diameter of its base |
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| 9. |
What is meant by the barter system |
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Answer» Barteris asystemof exchange by which goods or services are directly exchanged for other goods or services without using a medium of exchange, such as money. It is distinguishable from gift economies in that the reciprocal exchange is immediate and not delayed in time. please like the solution 👍 ✔️ |
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| 10. |
be covertu8. From a solid cylinder whose heightis 2.4 cm and diameter 1.4 cm, a conical cavity of thesame height and same diameter is hollowed out. Find the total surface area of theremaining solid to the nearest cm2 |
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| 11. |
Find the value of x if AOB is a straight line.42°30°3x |
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Answer» sum of angles on a st. line 180°30+42+18+2x-48+3x-12=1805x+90-60=1805x+30=1805x=180-305x=150x=30 |
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| 12. |
A=1,2, 3,5,6,7,8find A3 and Au3 |
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Answer» thanx |
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| 13. |
100 + [25 x 140 (20 5)] |
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Answer» please like my answer if you find it useful |
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| 14. |
f-1, find the value of a3-53 |
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| 15. |
(i) 24.65in)(6) 12.4065 (ii)() 164 2 +3(ii) 100 + 20 + 5 +10 100 |
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| 16. |
(72 + 8 >9) जल + 8 अब 9) |
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| 17. |
Find the first term if as - a3 4 |
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Answer» Herea5= a+4da3 = a+2d2d= 4d= 2third term= a+4fifth term= a+8 |
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| 18. |
a3 = 15 , S10 = 125 find d and a10 |
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| 19. |
If a-b=4 ab=21 find the value of a3-b3 |
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| 20. |
9+9-9+8+1-8 |
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Answer» correct answer is 10 please accept as best |
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| 21. |
10. The base radius of a right circular cone is 6 cm and its peheight is 8 cm. Find its(i) curved surface area (ii) total surface area(iii) volume (π=3.14) |
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| 22. |
In any triangle ABC, if a 18.b 24, c-30,1.cos A, cos B, cos C2.sin A, sin B, sin C |
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Answer» thus cosA=adj/hypo=24/30cosB=18/30and cosC=0as angle C is 90° |
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| 23. |
16mdeepwellwithdiameter3.5misdugupandtheearthfromitisspreadevenlytoform a platform 27.5 m by 7 m. Find the height of the platform. |
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Answer» thnx |
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| 24. |
Q.10 Find the curved surface area10cm and height is 49.cm.and total surface area of cylinder whose radius is |
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Answer» Given:Height,h=15cmRadius,r=7cm(i)Curvedsurfacearea,S1=2πrh=2×227×7×15=660cm2(ii)Totalsurfacearea,S2=2πr(r+h)=2×227×7×(7+15)=44×22=968cm2(iii)Volumeoftherightcircularcylinder,V=πr2h=227×72×15=2310cm3 (I) answer is 3080 cm^2 and (ii) answer is 3708.571428 |
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| 25. |
Find the total surface area of a solid cylinder whose diameter of the base and the height are 14 cm and10 cm, respectively |
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Answer» If you like the solution, Please give it a 👍 |
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| 26. |
Find the ratio in which the line x-3y-0 divides the line segmentjoining the points 2, - 5) and (6, 3). Find the coordinates of the point ofintersection. |
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Answer» x - 3y divides the line in 13/3 |
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| 27. |
Find the orthocenter of the triangle formed by the lines x+2y=0, 4x+3y-5=0 and 3x+y=0 |
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| 28. |
5×20+5= |
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Answer» 5×20+5=(5×20)+5=100+5=105 |
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| 29. |
A well of diameter 8 m has been dug out to a depth of 21m.The volume of earth dug out is.... |
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Answer» Volume=πr^2h=(22/7)*4*4*21=1056m^3 |
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| 30. |
(2)Find the value of x, if AOB is a straight line3x+5)(2x-25) |
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Answer» 2x-25+3x+5=1805x-25=1805x=205x=205/5x=41 |
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| 31. |
2x /3xStraight Line |
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Answer» from the property of linear pairs 2x+3x = 180°=> 5x = 180°=> x = 180/5 = 36° so, angles are 2x = 72° and 3x = 108° |
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| 32. |
(-100)/(-20)=5 |
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Answer» the right answer is 5 5 is the correct answer for you 5 is right answer of this question. please like my answer LHS=RHSis the right answer LHS=RHS CORRECT ANSWER 5 is the correct answer of the following question |
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| 33. |
If a -b 7 and a2 + b 85 then find a3 - b3. |
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Answer» a-b=7a²+b²=85 (a-b)²=a²+b²+2ab7²=85+2ab.2ab=49-85=-36 ab=-18 (a-b)³=a³-b³+3ab(a-b)7³=a³-b³+3(-18)(7)343+378=a³-b³=721 |
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| 34. |
32. In a corner of a rectangular field with dimensions 35 m × 22 m, a wellwith 14 m inside diameter is dug 8 m deep. The earth dug out is spreadevenly over the remaining part of the field. Find the rise in the level ofHOTSthe field. |
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| 35. |
6. Find the ratio in which the line 2x + 3y-5 =0 divides the line segment joining the points(8,-9) and (2, 1). Also find the co-ordinates of thepoint of division. [Board Term-2, 2012 Set (21)] |
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| 36. |
(d) 625 cm21. A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What ts thevolume of the earth dug out? |
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| 37. |
も2Find the equation of a st. line parallel to Y-axis and at a distance (i) 7 units to right(i) 3 units to the left. |
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| 38. |
Find the equation of a line parallel to the y-axis at a distance of6 units to its right (ii) 3 units to its left. |
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Answer» (i)x=6(ii)x=-3. |
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| 39. |
STRAIGHT LINES5 The Point P(2,7) is translated parallel to theline La-y= 4 by 213 units.丿f the new point0 lies in the third quadrant, then the equationof the line passing through Q andperpendicular to L is.+y 3-26 4) 2x+2y-1-6 |
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| 40. |
0. A triangle is formed by the straight linesx2y 3 0, 3x - 2y 7 0 andy +1 0. Find graphically:(i) the co-ordinates of the vertices of the triangle. |
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| 41. |
6.Which of the following pairs represent the same rational number?y STeandăŤ21 920an20(ii) andd-33-1220(iv) and2415(v)-and-(vi) andvii)--and |
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Answer» hi d i am hajira, any answers hi haji.Now only I see you |
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| 42. |
Find the ratio in which the line 2x + 3y 5 0divides the line segment joining the points(8, -9 ) and (2,1). Also find the coordinatesof the point of division. |
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| 43. |
9/20 |
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Answer» 45 is right answer bro |
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| 44. |
Visualise 3.465 on number line, using successive magniçŚ6: Find the value of k if (x-2) is a factor ofkx. 3x+ k.ification. |
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| 45. |
k Find the coordinates of the foot of the perpendicular from the origin on the straightline 3x +2y13 |
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Answer» mam /sir not understanding for me. please tell me easily. |
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| 46. |
x + 9 = - 20 |
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Answer» x = -20-9 x = -29 |
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| 47. |
-9) 205 |
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| 48. |
8.A bus stop is barricaded from the remaining part of the road, by using 50 hollowcones made of recycled cardboard. Each cone has a base diameter of 40 cm and height1 m. If the outer side of each of the cones is to be painted and the cost of painting isRs 12 per m2, what will be the cost of painting all these cones? (Use π= 3.14 and takeV1.04 1.02) |
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| 49. |
A well of diameter 14 m is dug 15 m deep. Thein the shape of a circular ring of width 7 mtot85 m deep. The earth taken out of it has been spread evenly all around itng of width 7 m to form an embankment. Find the height of the embankment(AP. 2017) |
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Answer» Please post a clear picture of the questions The height of the embankment is 60 m . |
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| 50. |
Mass1(vourite of15. A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all aroundit to a width of 7.5 m to form an embankment. Find the height of the embankment |
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