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. |
05% +sin’A » cos’A - sin'AProve the following:cosA + sinA cosA - sinA |
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| 2. |
Evaluatesin2 63°+ sin2 27°0)cos 17 +cos 73 |
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| 3. |
Prove that CosA - SinA +1/cosA +SinA - 1=cosecA +cotA |
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| 4. |
3. Evaluate:sin2 63°+ sin2 27°cos2 17 cos 73° |
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Answer» =sin^2(90-27)+sin^227/cos^2(90-73)+cos^273=cos^227+sin^227/sin^273+cos^273now cos^2A+sin^2A=1hence1/1=1 |
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| 5. |
91 cosecA = 4/3 A + B = 90 secB = |
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Answer» as A+B =90 secB =sec(90-A) = cosecA = 4/3 {because sec(90-x) =cosec(x)} |
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| 6. |
25. Simplify:A.22.*Y240B.1>1250c.xyD. _*?y? |
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Answer» b is a right answer ok B is the correct answer option B is correct answer. B.-x^2y^2÷50 is the correct answer |
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| 7. |
26, prove that: (tanA+cosecB)-(cotB-secA)-2tanAcotB(cosecA+ secB)27. The angle of elevation of the top of a vertical tower from a point on the gr60 degree, from another point 10m vertically above the first, its angle of elevat30 degree. find the height of the tower/ |
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Answer» LHS= (tanA + cosecB)^2 - (cotB-secA)^2= (tan^2A + 2tanAcosecB + cosec^2B) - (cot^2B - 2cotBsecA + sec^2A)= tan^2A + cosec^2B + 2tanAcosecB - cot^2B - sec^2A + 2cotBsecA Substituting (tan^2A = sec^2A - 1) and (cosec^2B = 1 + cot^2B) in the above step:(sec^2A - 1) + (1 + cot^2B) + 2tanAcosecB - cot^2B - sec^2A + 2cotBsecA= 2tanAcosecB + 2cotBsecA= 2(tanAcosecB + cotBsecA) RHS= 2tanAcotB(cosecA + secB)= 2tanAcotB((1 / sinA) + (1 / cosB))= 2(tanA / sinA)cotB + 2tanA(cot B / cosB)= 2(sinA / (cosAsinB))cotB + 2tanA(cosB / (sinBcosB))= 2(1 / cosA)cotB + 2 tanA(1 / sinB)= 2secAcotB + 2tanAcosecB= 2(secAcotB + tanAcosecB) LHS = RHS |
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| 8. |
oet66Show that pe+y34 |
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| 9. |
2)pute the followin |
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| 10. |
6. Show that: |
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Answer» Sorry I don't know answer |
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| 11. |
No.1) Ify=f(x)=r-1, then f(y) is--tNo.2) Limit of lx -2| at x2 isNo.3) If f(x) x* andf (1) 5, then K isNo.4) Gradient of the curve y logg, at the point where it meets the x-axis isNo.5)Iff(x) =e*xandf'(x) = 0,thenxisNo.6)Theminimumpoint of thefunctionf(x)=x2-10x + 36,is5 |
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| 12. |
8. If 2x:-3y6", show that-+-+--0 |
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Answer» LET 2^x=3^y=(1/6)^z=k Therefore, K^(1/x)=2 K^(1/y)=3 K^(1/z)=(1/6),Multiply these 3 equations to get: K^[(1/x)+(1/y)+(1/z)]=1 Hence we can conclude that either k=1 ( which is totally false) or power is equal to “0”. The correct answer is :[(1/x)+(1/y)+(1/z)]=0 Like my answer if you find it useful! |
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| 13. |
allletters in the followin23o |
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Answer» Photo sahi bhej de samajh me Nahi aaraha hai |
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| 14. |
7. Prove that /coseca +1 + lcosecA+1 = 2cosecA-1cosecA +1cosecA-1 |
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| 15. |
(cotA+cosecA-1)/(cotA+cosecA+1)=(1+cosA)/sinA |
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| 16. |
In A.C supply number of cycles per second is called-a. Frequencyb. Voltagec. Currentd. Resistance |
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Answer» Number of cycles per second is Frequency |
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| 17. |
The edge of cubical box whose volume is 64 cm is |
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Answer» Given:- the volume of the cubical box is 64 cm³ Let the edge of the cubical box be a cm =>a³=64=>a=4 ∴Edge of the cubical box= 4 cm |
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| 18. |
The edge of cubical box whose volume is 64 cm is(A) 4(B) 8(C) 1 |
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Answer» volume=(side)^364 cm^3=(side)^3(4cm)^3=(side)^3side=4cm hit like if you find it useful |
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| 19. |
4. The edge of cubical box whose volume is 64 cm is(A) 4(C) 16(D) 32 |
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Answer» Volume of cubical box = (Side)³ 64 = (Side)³ Side = ∛64 = 4 cm(A) 4 cm *Unit given in the question is wrong* |
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| 20. |
|LEVEL-1-]EXAMPLE IPreme thit the function f R → R defined as f (x)-2-3 is invertible. Also, find f |
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| 21. |
. The edge of cubical box whose volume is 64 cm2 is(A) 4(B) 8(C) 16(D) 32 |
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Answer» Volume=side³Volume=64cm³64=side³side=4cm Option A is correct |
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| 22. |
Show that the function,f: R → R,Lined as f(x) = x2, is neither one-one nor onto |
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| 23. |
8. If a function f: R-R is given by f(x +y)f (x)+ f (y) forall x, y e R andf(1) = a. Find1l |
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Answer» tnxs |
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| 24. |
KAMPLE 6Show that the function f : RR:f(x) = x is one-one and onto. |
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| 25. |
Expand the followiner (2x + 3y + 42)2g: |
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Answer» (2x+3y+4z)(2x+3y+4z) = 2x*2x+3y*3y+4z*4z+2(2x)(3y)+2(3y)(4z)+2(4z)(2x) = 4x*x+9y*y+16z*z+12xy+24yz+16xz |
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| 26. |
28.An open metal bucket is in the shape of a frustum of a cone, mounted ona hollow cylindrical base made of the same metallic sheet (see figure). Thediameters of the two circular ends of the bucket are 45 cm and 25 cm, the totalvertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Findhe area of the metallic sheet used to make thc bucket, where we do not take intoaccount the handle of the bucket. Also, find the volume of water that the bucketcan hold. |
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Answer» answer not open |
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| 27. |
An open metallic bucket is in the shape of afrustum of a cone mounted on hollowcylindrical base made of metallic sheet. Ifthe diameters of the two circular ends of thebucket are 45 cm and 25 cm, the totalvertical height of the bucket is 30 cm andthat of the cylindrical portion is 6 cm, findthe area of the metallic sheet used to makethe bucket. Also, find the volume of water itcan hold. [Take π 23A22.5 cm6 cm12.5 cm |
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| 28. |
RTANT RULE A rational number is expressible as a termtinating decimalwhen prime factors of q are 2 and 5 only1 3 7 13 |
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Answer» let x=p/qbe the given rational number. If the prime factorization of q is of the form 2^nx5^m, where n, m are non-negative integers. Thenxhas a decimal expansion which terminates. |
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| 29. |
256Example 14: An open metal bucket is in theshape of a frustum of a cone, mounted on ahollow cylindrical base made of the same me-tallic sheet (see Fig. 13.23). The diameters ofthe two circular ends of the bucket are 45 cmand 25 cm, the total vertical height of the bucketis 40 cm and that of the cylindrical base is6 cm. Find the area of the metallic sheet usedto make the bucket, where we do not take intoaccount the handle of the bucket. Also, findthe volume of water the bucket can hold.Fig. 13.4Take |
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| 30. |
Q.3 (A) Explain the statements with reasons. (Any 2)Marks 6)1. Bakhar is an important type of historical documents. |
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Answer» Ans :- ◾️Bakhar is an important type of historical document written in Marathi language. ◾️It is the earliest Marathi genre of the medieval period. ◾️There were almost 200 bakhars written between the seventeenth and the nineteenth century. ◾️The most important of them was about Shivaji. ◾️Bakhars are considered as assets that describe the Marathi history and the criticism in that period. ◾️They were written in Marathi prose and enhanced the patriotism of the people. ◾️Earlier, Persian words were used to but later it was written in Sanskrit. ◾️Some common bakhars are Sabhasad bakhar, Mahikavatichi bakhar, Kalmi bakhar, Chitnis bakhar, Peshwayanchi bakhar and Bhausahebayanchi bakhar. PLEASE LIKE THE ANSWER
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| 31. |
10. A hollow cylindrical pipe is made of copper. The volume of the metal used inthepipeis718cubiccm. Its external radius is 9 cm and length is 14 cm. Find the thickness of the pipe. |
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| 32. |
A hollow cylindrical pipe is made of copper. The volume of the metal used in the pipe is 718 cubiccm. Its external radius is 9 cm and length is 14 cm. Find the thickness of the pipe10. |
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| 33. |
X+5×2=15 |
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Answer» x+ 5×2=15x+ 10=15x=15-10x=5 |
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| 34. |
simplify 1/6+(-2/5)-(-2/15) |
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| 35. |
Art-6. IfLt f(x) exists finitely, then prove that it is unique. |
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| 36. |
Ly sE‘:}‘ o S उन कि.e |
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Answer» please like my answer if you find it useful |
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| 37. |
5 persons can save 15 litres of water if they take bath using a bucket insteadofshower. Then 25 persons can save how many litres of water? |
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Answer» 5 person can save 15 litres of waterthen one person can save = 15/5= 3 litrenow 25 persons can save = 25*3= 75 litres of waterPlease like the solution 👍 ✔️ |
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| 38. |
(Ul LyA e DRन कि८2०. 0७817 00062 / 00९ 0 1.हि... it %S |
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| 39. |
iJ—_—(lc—osfi)(l— ८०89)(1+cos 0) (1-cosB) |
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Answer» √( 1-cos theeta)^2/√1-cos^2 theeta= √((1-cos theeta/sin theeta)^2= 1-cos theeta/ sin theta cosectheta - cot thetathanksplease like the solution 👍 ✔️👍 |
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| 40. |
0.Solve the following: |
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| 41. |
15,Solve for |
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Answer» x²-(√3+1)x+√3=0 x²-x-√3x+√3=0 x(x-1)-√3(x-1)=0 (x-1)(x-√3)=0 x=1,√3 |
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| 42. |
x^2- x-1 = 0 Solve for x . |
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| 43. |
5. 5 persons can save 15 litres of water ifthey take bath using a bucket insteadof shower. Then 25 persons can save how many litres of water? |
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Answer» If 5 people can save 15 litres of waterThen 25 people can saveas 5*5==15*5litres25people===75litres |
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| 44. |
Anju is making two stacks one with Cubes of sides 4 cm and the other with cubes of sides 9 cm to make the heights of the stacks equal What should be the least possible height of each |
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| 45. |
2+4+6+8= |
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| 46. |
SECTION-AQL For any integer a and 3, there exists unique integer q and r such that a = 3q + r Find the possible value of tPage 1 |
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Answer» Given equation :a = bq+r As per Euclid division lemma r should be larger or equal to zero and smaller to bThus, 0<=r<b. For b=3a=3q+r.0<=r<3r=0,1,2 Therefore possible values of r are 0,1,2. |
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| 47. |
6. If the distance between the points (4, k) and(1, 0) is 5. Then what can be the possible valueof k? |
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| 48. |
25. Solve for x and y:5215 |
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Answer» any another method |
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| 49. |
1431cylindrical tank full of water is emptied by a pipe at the rate of 25 litres perlow much time will it take to empty half the tank, if the diameter of its basentire liquidh 5 m. Find2 A cylindricalis3 m and its height is 3.5 m? [Use π-22/71 |
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| 50. |
¢ 33 + है हकsGx+y 4 B 57 + - z)s«का सान ज्ञात कीजिए जबकि (o _ जि है e Tfigfi =YP(x ० ) Py _ g2 —3%F KP a3 2 gt ly X |
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Answer» यदि एक्स माइनस वन p(x)का गुणनखंड हैput x= 1p(1)= 1+1+k= 0k= -2 2)k-3+k= 02k= 3k= 3/2 |
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