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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.
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(99 9): 995] |
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ue of40-(A) ред(C) 165(B) 13(D) |
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| 3. |
T/V) B+ <z(fimz—_vmopv[vi ue) -y uisपा! +प्य्त (71 |
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Answer» LHS:sin A.tan(A/2) + 2cosA(using cos 2A = 1-tan^2 A/1+tan^2 Asin 2A = 2tan A/1+tan^2 A) =(2tan A/2)/(1+tan^2 A/2). tan A/2 + 2(1-tan^2 A/2)/(1+tan^2 A/2) = (2tan^2 A/2 + 2 - 2tan^2 A/2)/(1 + tan^2 A/2) = 2/(1 + tan^2 A/2) = RHS Hence proved |
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| 4. |
Volume ofa wooden cube is 729 cubic centimetres. Ais carved out from it.square pyramid of maximumm4.a) What is the volume of the pyramid?b) What is the height of the pyramid?s e11 ch uestion carries3 |
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Answer» Volume of cube is 729 cubic centimeters. Cube root of 729 is 9, so cube is 9 x 9 x 9 cm. Maximum pyramid would have a 9x9cm base with a height of 9cm. Volume of pyramid is length * width * height / 3 = 9 * 9 * 9 / 3 = 729 / 3 = 243 cm^3. |
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The sum of 3 consecutivintegess lo mose than twicethe smallest of the ntegefind the intege0s |
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| 6. |
3. A square pyramid hascedgesesfacesvertices and |
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Answer» It has 5 faces, 5 vertices, and 8 edges. |
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| 7. |
जाग xpx,ue | |
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Answer» ∫ tan²x dx= ∫ sec²x - 1 dx= tanx - x + constant |
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| 8. |
0 3 triangles?NO(ii) a square and four triangles? PhyranenIt possible to have a polyhedron with any given number of faces?a pyramid).3. Which are prisms among the fo |
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Answer» Yes, it can bepossibleonly if thenumber of facesis four or more than four. Sol: Since, a prism is apolyhedronhaving two of itsfacescongruent and parallel, where as otherfacesare parallelogram. |
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| 9. |
हे ue) + Y 095 =v Em + |
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Answer» Like if you find it useful |
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| 10. |
88enue |
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Answer» thanks |
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| 11. |
.................. =g 995 3b - =g ue) yo |
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Answer» tanθ=3/5tan²θ+1=sec²θsec²θ=9/25 +1sec²θ=34/25secθ=√(34)/5 |
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| 12. |
45. MODELING WITH MATHEMATICS Flying fish usetheir pectoral fins like airplane wings to glide throughthe aira. Write an equation of the form y a(x- h)+with vertex (33, 5) that models the flight path,assuming the fish leaves the water at (0, 0). |
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| 13. |
B 2ol ue<yA\ G\ |
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Answer» 2x+3y=163x+3y=16.................-x+0=0x=0 2(0)+3y=163y=16y=16/3y=5.33 |
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| 14. |
touw mauny mose uwi't cubes sheulel be acldab make Utuis into 4x4 x4 cube? |
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Answer» you can add 7 more cubes to make total of 8 cubes , with each side.. 8 × 8×8 your question is incomplete then. |
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् 1 3००) s = (¥ 1-809) UE) (31) |
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| 16. |
hell avelesc.. 16 (x- 3) 87 17x or x (7 48) 39.Ex. 15. Distance between two stations A and B is 778 km. A train covers the journeyfrom A to B at 84 km per hour and returns back to A with a uniform speed of 56 kmper hour. Find the average speed of the train during the whole journey2x 84 x 56(hr |
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| 17. |
The diagonals of a rhombus are & omand 6 om. Find its area and perimeter. |
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Answer» A=pq/2=8*6/2=24cm^2side is √p^2+q^2/2=√8^2+6^2/2=10/2=5cmhenceperimeter will be 4a=4*5=20cm |
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| 18. |
If the sum of first m term of A.p is n and the sum of first n term of A.Pism.Find sum of (m + n) term.V |
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Answer» arghy grt bheji 356×568_67&++#*(9×;|3%589830 n + m is the right answer n+m is the correct answer |
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| 19. |
ABC is a triangle right angled at A. AB 6cm and AC 8cm. A circle with centre O isinscribed inside the triangle. Find the radius of the inscribed circle. |
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Answer» This is a right angled triangle with sides 6 and 8 .Third side will be 10(Pythagorean triplets) .The circle is inscribed in the triangle . So all the three sides are at tangent to the circle .A line drawn from center of the circle will be perpendicular to the sides of the triangle Area of triangle :6*8=48The larger triangle can be broken into three smaller triangles with base =8,height=r ,base=10,height=r ,base 6 height=r .Sum of areas of these three triangle :8r+10r+6r=24r .24r=48 ,hence r=2 . |
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| 20. |
4.Draw two nets for a hexagonal prism. |
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| 21. |
in fiel3),a circle is inscribed in an equilateral triangle ABC of side 12cm Find the rad us ofinscribed circle and the area of the shaded and region. (Use π-3.14) |
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| 22. |
Identify the nets which can be used to make cubes(cut out copies of the nets and try it1. |
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| 23. |
In the given figure, a circle is inscribed in anequilateral triangle ABC of side 12 cm. Find theradius of inscribed circle and the area of theshaded region. [Use V3 1.73 and π 3.141ICBSE 2014] |
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Answer» thanks |
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| 24. |
Verify Euler's formula for these solids |
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Answer» tq hanumant |
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| 25. |
6.Verify Euler's formula for these solids.LTО To |
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Answer» face =7vertices=10edegs=15 By euler's formula F+V=E+27+10=15+217=17 Euler's formula verified |
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| 26. |
6. Verify Euler's formula for these solids. |
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Answer» In 1st figureFaces =6Edges=12Vertices =8Verification :F + V= E + 2=>6 + 8 =12 + 2=>14 = 14. verified In 2nd figureFaces = 9Edges = 16Vertices=9Verification :F + V = E + 2=>9+9=16+2=>18 = 18. verified the answer is 18 is correct |
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14. Verify Euler's formula for a cuboid. |
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Answer» Euler's formula = F+V-E= 2F= facesV= verticesE = edges cuboid Prism= 6+8-12= 2pentagonal= 7+10-15= 2square= 5+5-8= 2pyramid= 6+6-10=2 |
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3. Verify Euler's formula Bin the followingpolyhedron. |
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| 29. |
ExerciseUsing Heron's formula, find the area of a triangle whose sides are |
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Answer» S= (a+b+c)/2= (1.8+8+8.2)/2= 18/2= 9 area of formula√9(9-1.8)(9-8)(9-8.2)√(9*7.2*1*0.8 = 7.2m^2please like the solution 👍 ✔️ |
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| 30. |
In Fig. 6, ABC is a right-angled triangle with AB 6 cm and AC 8 cm. Acircle with centre O is inscribed inside the triangle. Calculate the value of r,the radius of the inscribed circle. |
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Answer» In Given Triangle ABCAC2+ AB2= BC2BC2=(6*6)+(8*8)=100 Area of Triangle ABC= 8*6/2 =24 Cm2Semiperemetre of ABC= (8+6+10)/2 =12cm Radius of circle= Area Of Triangle /Semiperimeter of triangle = 24/12 = 2 cm Hence Radius of circle is 2 cmLike if you find it useful |
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| 31. |
(b) ABC is a right-angled triangle with AB6cm and BC 8m. A circle withcentre O has been inscribed inside thetriangle. Calculate the value of x, theradius of the inscribed circle. 46 om |
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| 32. |
A top is shaped like a cone surmounted by a hemisphere. The entire top is 5cm in height and the daimeter of hemisphere is 7 cm. Find the total surfacearea of the top |
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Answer» Given, the height of entire top = 5 cm and the diameter of top = 7 cm ∴ radius of hemisphere = 7/2 = 3.5 cm As both the hemisphere and cone are on the same base, therefore, radius of hemisphere = radius of cone = 3.5 cm Now the height of cone h = height of top – radius of hemisphere= (5 – 3.5) cm = 1.5 cm In order to calculate the total area of top, we have to find out the sum of curved surface area of both the cone and the hemisphere. ∴ Total Area = C.S.A of cone + C.S.A. of Hemisphere = πrl + 2πr^2 = πr(l + 2r) l = sqrt(r^2 + h^2) l = sqrt(3.5*3.5 + 1.5*1.5)l = sqrt(15.5)l = 3.93 Total Area = 22/7*3.5(3.93 + 7)= 11(10.93)= 120.93 cm^2
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| 33. |
3. Is your Maths book shaped like a cube? Why?What do you think of an alphabet block? Canyou name three other objects that are shapedlike a cube? |
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Answer» Mostly books are shaped like cuboids in order to make them easily handle. Dice is also shaped like cube. |
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| 34. |
Draw two nets for a triangular pyramid |
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| 35. |
A car jack is shaped like rhombus. The sides of car jack are 17 cm long When thehorizontal distance between the vertices is 30 cm, the vertical distance between theother two vertices is30 cm |
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| 36. |
2. सीधे गुणा किए बिना निम्नलिखित गुणनफलों के मान ज्ञात कीजिए: 103x107 (i) 95x96 (iii) 104%96 |
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Answer» 1. (100+3)(100+7)100²+(3+7)100 +3*710000+1000+2111021 |
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| 37. |
Draw two nets for a triangular pyramid. |
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| 38. |
/ de 96 am il५02४ 5 Qfi&m 16 दा है.oy sIS |
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Answer» note : since cost of tile is not clear in image so.......I am putting formula for calculating here total cost = cost of each tile * 1125 |
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| 39. |
A playing top is made up of steel the top isshaped like a cone surmounted by ahemisphere. The total height of top is 5 cm andthe diameter of the top is 3.5 cm. Find thevolume of the top. |
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| 40. |
didesequaly among 3 children. Furach chudostot h_ motdons?"St、Find the cost of one metre of cloth.3 |
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Answer» To find the cost of 1m cloth, = 75 1/3 ÷ 1 1/2 = 226/3 ÷ 3/2 = 226/3 * 2/3 = 452/9 = 50 2/9 Like my answer if you find it useful! Please send the statement also This question statement answer tell please not that |
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| 41. |
breadth 6 m,te Tergtsa7 per sqcm6.Find the cost of painting a square board of side 44 cm at the rate off squares on a square gameboard of side 8 cm, if the |
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Answer» Area = 44×44 = 1936 sq cm 1 sq cm is of 7 1936 sq cm is of 1936×7 = 13552 If you find this answer helpful then like it. |
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| 42. |
verify euler formulabon rectangular base pyramid |
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| 43. |
27 s a square prism same as a cube ? Explain, also verify Euler formula for cube.lOSO72006 S76 06. |
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Answer» No, it is diffrent.in square prism,no. of faces is 6 as 2 square faces and 4 rectangular faces.but, cube have 6 equal faces |
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| 44. |
verify euler formula on rectangle base pyramid |
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| 45. |
using Euler formula find the number of edges in a polyhedron if the number of faces is 20 and the number of vertices is 12 |
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| 46. |
1)) Verify that y = log x is a solution of reply conVerify that y = log x is a solution of x+=0.dyX |
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Answer» Yes correct answer |
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| 47. |
Divide the polynomial 2.3-2x22x2-x + 1 by x + 1 and verify remainder by using remainderby x +1 and verify remainder by using remaindertheorem. |
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| 48. |
what is the shape of a brick. Write the number of faces, edges and vertices |
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Answer» Shape of a brick is cuboid. It has 6 faces, 8 edges and 12 vertices |
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| 49. |
A horse is tied to a peg at one corner of a squareshaped grass field of side 15 m by means of a 5 mlong rope (see Fig. 12.11). Find(1) the area of that part of the field in which thehorse can graze(ii) the increase in the grazing area if the rope were10 m long instead of 5 m. (Use π-3, 14) |
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| 50. |
8. A horse is tied to a peg at one corner of a squareshaped grass field of side 15 m by means of a 5 mlong rope (see Fig. 5.11). Find0 the area of that part of the field in which thehorse can graze.(i) the increase in the grazing area if the rope wereFig. 5.1110 m long instead of5 m. (Use π = 3.14) |
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Answer» thank you |
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