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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16. The floor of a room is square in shape. If the side of the floor is Sm, find the area of the floor |
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Answer» area= side × side = 5m × 5m = 25 m^2 hit like if you find it useful |
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| 2. |
una wants to cover floor of a room whichis 3 m wide and 4 m long by square tileseach square tile is of side 20 cm, find thenumber of tiles required to cover the floorof the room.1013. Ar. If |
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Answer» Area of floor Af = length*breadth = 4x3 = 12 m^2 = 120000 cm^2 Area of each tile At = side*side = 20*20 = 400 cm^2 Let no. of tiles required to cover floor = n Then, n*At = Afn = 120000/400 = 300 300 tiles required to cover floor |
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| 3. |
18. A room floor is 192 sq m in area. If itslength is 16 m. Then, its perimeter is1001 |
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Answer» Given:Area of floor=192sq mlength=16mNowArea=l×b192=16×bb=192/16b=12m Now perimeter=2(l+b)=2(16+12)=2(28)=56m the. correct answer is 56m..... |
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| 4. |
the area of the floor of a room is 67.5 sq.m . it's volume is 270 m cube.find the height of the room |
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Answer» area = length x breadth=67.5 sq.m volume=270m cube volume of a cuboid=lxbxh 67.5xh=270 h=270/67.5 =4m |
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| 5. |
18. The volume of a room is 378 m3 and the area of its floor is 84 m2. Find the height ofthe room |
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Answer» thanks |
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| 6. |
whichis greate(1/2)power -1/2or(1/3)power1/3 |
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Answer» 1/2is athe greatest power among them 1/2 is a the greatest power among them 1/3 power 1/3 is the greater |
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| 7. |
225raised to power 1/2 |
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Answer» 225^1/2 = √225 = 15 |
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| 8. |
The volume of a room is 120 m^2 and the area of its floor is 30 m2. Find the height of the room |
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| 9. |
A room is 4 m long and 3 m 25 cm wide. How many square metres of caneeded to cover the floor of the room? |
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Answer» Length of the room = 4 m Width of the room is 3 m 25 cm = 3.25 m To carpet the room, we need to find the area of the floor. So, Area of the room = length × breadth = 4 × 3.25 = 13 sq. m length of floor = 4mbreadth= 3m 25cm =3.25marea of floor=4*3.25 =13 square metres13 square metres of carpet is required to cover the floor |
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| 10. |
Exercise 51press the following in exponential notations.81b) 125e) 343d) 216 |
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Answer» A) 3 power 4 B) 5 cubeC) 6 cube D) 7 cube |
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| 11. |
arc definition with one example |
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Answer» An Arc is a curved line that is a part of a circle. |
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| 12. |
chord definition with one example |
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| 13. |
tangent definition with one example |
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Answer» thestraight linethat "just touches" the curve at that point is called the tangent. |
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secant definition with one example |
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Answer» Secant is a straight line that intersects a curve at two or more points. |
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| 15. |
65. A vessel fuil of water is in the form can inverted cone of height 8 cm and theradius of its top, which is open is 5 cm. i100 spherical lead balls are dropped intethe vessel. One-fourth of the water flowsout of the vessel. Find the radius ot thespherical ball.[CESE 201E |
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Answer» We know that Volume of cone = πr²h/3 =π*5²*8/3 =200/3π Now volume of liquid displaced=volume of balls dropped 1/4(200/3)π=100*4/3πr³ 50=100*4r³ 50/4=100r³ 50/400=r³ 1/8=r³ r=1/2=0.5cm |
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| 16. |
Show that 41 divides 2^20 - 1 |
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| 17. |
The ratio in which the point (8, 7) divides the line segment joiningthe points 33and33the points (28,and僴,20 203 3 is k1. The value of k is |
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| 18. |
11. 3/125%343 का मान है : |
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| 19. |
If-=-=-=1 , then prove that--+-+--1+a 1+b 1+c(b)b+c c+a a+ b |
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Answer» please complete the question |
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| 20. |
\sqrt [ 3 ] { \frac { - 125 } { 343 } } X \sqrt [ 3 ] { - 64 } |
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| 21. |
(49/343)power 1/3 |
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Answer» 49/343=49×1/49×3=1/3 |
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| 22. |
125*((-343)*f(-8)) |
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Answer» cube root will be 70 (-8)*(-343)*(125) 3√(-8)*(-343)*(125)3√(-2*-2*-2)*(-7*-7*-7)*(5*5*5)-2*-7*5=70 |
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| 23. |
If (343)^2/x =49. Find x |
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Answer» (7)^(6/x) =7²So x=6/2=3 |
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| 24. |
Q.3. Two solid spheres made of the same metal havemasses of 5920 g and 740 g respectively. Determinethe radiĂşs of the larger sphere, if the diameter of theINCERT Exemplar]smaller sphere is 5 cm. |
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Answer» Given :- Weight of the heavier sphere = 5920 g weight of the lighter sphere = 740 g Diameter of lighter sphere = 5 cm or radius = 2.5 cm Let the volume of the heavier sphere be 'V1' and the volume of the lighter sphere be 'V2'. Radius of the heavier sphere be 'r1' because the diameter of the lighter sphere is given so the radius is 2.5 cm. Weight of an object = density× volume of that object So, (Weight of the heavier sphere/weight of the lighter sphere) = (Density× V1/density× V2) As both the spheres are made up of same metal, therefore, the ratio of their weights will be equal to the ratio oftheir volumes. (weight of the heavier sphere/weight of the lighter sphere) = (V1/V2) ⇒ (5920/740) = (4/3πr₁³)/(4/3πr³) ⇒ (5920/740) = (4/3×22/7×r₁³)/(4/3× 22/7× 2.5× 2.5× 2.5) ⇒ 8 = r₁³× 1/2.5× 1/2.5× 1/2.5 ⇒ 8 = r₁³× 1/15.625 ⇒ r₁³ = 8× 15.625 ⇒ r₁³ = 125 ⇒r₁ = 5 cm So, the radius of the heavier sphereis 5 cm. |
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| 25. |
Two solid spheres made of the same metal havemasses of 5920 g and 740 g respectively. Determinethe radius of the larger sphere, if the diameter of the smaller sphere is 5 cm. |
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Answer» Given :- Weight of the heavier sphere = 5920 g and weight of the lighter sphere = 740 g, and diameter of lighter sphere = 5 cm or radius = 2.5 cmLet the volume of the heavier sphere be 'V1' and the volume of the lighter sphere be 'V2'. Radius of the heavier sphere be 'r1' because the diameter of the lighter sphere is given so the radius is 2.5 cm.Weight of an object = density× volume of that objectSo,(Weight of the heavier sphere/weight of the lighter sphere) = (Density× V1/density× V2)As both the spheres are made up of same metal, therefore, the ratio of their weights will be equal to the ratio oftheir volumes.(weight of the heavier sphere/weight of the lighter sphere) = (V1/V2)⇒ (5920/740) = (4/3πr₁³)/(4/3πr³)⇒ (5920/740) = (4/3×22/7×r₁³)/(4/3× 22/7× 2.5× 2.5× 2.5)⇒ 8 = r₁³× 1/2.5× 1/2.5× 1/2.5⇒ 8 = r₁³× 1/15.625⇒ r₁³ = 8× 15.625⇒ r₁³ = 125⇒r₁ = 5 cmSo, the radius of the heavier sphereis 5 cm.Answer. |
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| 26. |
A spherical solid material of radius 18 cm is melted and recast into three small solid spherical spheres of different sizes. If the radii of two spheres are 2cm and 12 cm, find the radius of the third sphere |
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Answer» Big sphere: r = 18cm Vol = 4/3πr³ = 4/3*22/7*18*18*18 = 24438.8cm³ Other 3 spheres: r₁ = 2cm Vol = 4/3πr³ = 33.52cm³ r₂ = 12cm Vol = 4/3πr₃ = 7241.1cm³ Vol of 3rd sphere = Vol of big sphere - vol of both small spheres 4/3πr₃³ = 24438.8 - (33.52+7241.6) 4/3πr³ = 17163 r³ = 4095.7 r = ∛4095.7 r = 34.4cm Like my answer if you find it useful! |
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| 27. |
The milkman divides 20.41 L of milk into 13 cans. How muchmilk is there in each can? |
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Answer» Milk in each can =20.41L/13 = 1.57L Ans: Each can will have 1.57L =1570 mL. |
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| 28. |
A spherical solid material of radius 18 cm is melted and recast intespherical spheres of different sizes. If the radi of two spheres are 2em and 12 cm. findthe radius of the third sphere. |
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Answer» Volume of sphere = (4/3)Πr³ (4/3) Π (18)³ =(4/3) Π (2)³ +(4/3) Π (12)³ +(4/3) Π r³ (4/3) Π (18)³ =(4/3) Π [(2)³ +(12)³ +r³ ] (18)³ =[(2)³ +(12)³ +r³ ] 5832 = 8 + 1728 +r³ 5832 = 1736 +r³ 5832 - 1736 =r³ 4096 =r³ r =∛16x16x16 r = 16 cm Radius of third sphere = 16 cm |
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| 29. |
1. If 3-27, then 3n-2 ÄŻs |
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| 30. |
4. If t, 3n- 2, then s, |
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| 31. |
4. If t, 3n-2, then s, -S,.. |
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Answer» it's not correct |
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| 32. |
3. Prove that:c +ca+a1 |
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| 33. |
Show that, 13 divides 3n+2 + 42n+1 |
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| 34. |
In an AP the sum of first n terms is 3n^2/2+13n/2 Find the 25th term. |
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Answer» N term sum = 3n²/2 + 13n/2as we know that nth term = (Sum of nth term ) -( sum of (n-1)th term) so 25th term = (sum of 25terms) - ( sum of 24 terms) =(3×(25)²/2 +(13×25)/2) - ( 3×(24)²/2 + (13×24)/2) = 1100 - 1020 =80 |
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| 35. |
5+8+11+....+(3n-1)= 1/2 n (3n+1) |
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| 36. |
Xoy A +5n+7—Bbm—n—3and 3m -3—3n+2 |
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| 37. |
B(2,8) into four equal parts. Sind ti rea of a thombus ifits vertices are (3, 0), (4, 5), -1, 4) and (-2,-1) taken innder (Hint: Area of a thombus (prodtict of its diagonals)]of a r |
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Answer» Sol:Coordinates of the opposite vertices of the rhombus are (3, 0) and (-1, 4); (4, 5) and (-2, -1). Length of the diagonals:Length of first diagonal joining the vertices (3, 0) and (-1, 4) = √[(-1-3)2+ (4 - 0)2] = √[16 + 16] = √32 = 4√2Length of first diagonal joining the vertices (4, 5) and (-2, -1) = √[(-2-4)2+ (-1 - 5)2] = √[36 + 36] = √72 = 6√2Area of the rhombus = 1/2 x product of the diagonals= 1/2 x 4√2 x 6√2= 24 sq units. |
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| 38. |
1 a bcEvaluate Δ 1 b ca1 c ab |
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Answer» thanks sir.... it was helpful |
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| 39. |
If a, b and c are three vectors, such that a + b + c=0, la|=1,Ibl=2,lcl=2,then ab +bc+ca isa) -9/2b) 7c)1d) of these |
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| 40. |
Prove that:1 a b+ c1 ca+ b |
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| 41. |
. Give reasons for the following statements:2, 3, 5, 7,9, 11) (v: is a prime number, 12)(1, 64, 125) #1x :x is a perfect square and perfect cube, x(0125)(ii) |
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Answer» 1)The given statement is true as the set contains a composite number that is 92)The given statement is true because 125 is a perfect cube but not a perfect square. |
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| 42. |
10. The base of a parallelogram is twice its height. If its area is 512 cm', find the baseand the height |
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Answer» thanks you |
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| 43. |
10. The base of a parallelogram is twice its height. If its area is 512 cm, find the baseand the height |
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St. XI10. Can two mumbers have 12 as their HCF and 512 as their LCM? Justify your answer.vaceeditins 90P Digital |
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Answer» LCM×HCF= product of no12×512=product of no6144= product of no hcf= product of no/LCM = 6144/512=12LCM= product of no/HCF = 6144/12=512 |
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| 45. |
10. Can two numbers have 12 as their HCF and 512 as their LCM? Justify your answer. |
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Answer» no they can't have 512 as least common multiple |
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| 46. |
1.1 a b + c| be + a _1 c a + b(a)abc(c)0(bab+bc+ca(d) इनमें से कोई नहीं |
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Answer» 1[b( a+b)+a(1(a+b)-c+ |
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| 47. |
bc b+c 1ca c+a 1-(a-b) (b-c)(c-a)ab a + b 1nat |
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| 48. |
Take Ď, unless stated o1. A metallic sphere of radius 4.2 cm is melted and recast into the shaand recast into the shape of a cylinderleftradius 6 cm. Find the height of the cylinder.om and 10 cm, respectively, are melted to form a sin |
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| 49. |
21 a a1 a bciii 1 b bb ca1 c ab2 |
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| 50. |
Which of the following are the cubes of even numbers?(i) 729(i) 216(iii) 512 |
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