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. |
n \sin A+\sin B-\sin C=-4 \cos \frac{A}{2} \cos \frac{B}{2} \sin \frac{C}{2} |
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Answer» A+B+C = piB+C = pi-A sin(B+C) = sin(pi-A)sin(B)cos(C)+cos(B)sin(C) = sin(pi)cos(A)-cos(pi)sin(A)sin(B)cos(C)+cos(B)sin(C) = sin(A)sin(B)cos(C) - sin(A) = -cos(B)sin(C)(sin(B)cos(C) - sin(A))^2 = (-cos(B)sin(C))^2sin^2(B)cos^2(C) + sin^2(A) - 2sin(A)sin(B)cos(C) = cos^2(B)sin^2(C)-2sin(A)sin(B)cos(C) = cos^2(B)sin^2(C) - sin^2(B)cos^2(C) - sin^2(A) |
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| 2. |
489. How many ribbons of -m can be cut froma ribbon of length 5 m? |
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Answer» 11/10; 10+1/2=11/2; 11/10-2/11=-8/11 11/10; 10+ 1/2=11/2 ; 11/10-2/11= -8/11 11/10; 10+1/2=11/2;11/10-2=-8/11 |
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| 3. |
1. राम ने एक साइकिल बिक्रीकर सहित ₹ 3300 में खरीदी। यदि बिक्री करकी दर 10% हो, तो साइकिल का वास्तविक मूल्य क्या है? |
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Answer» बिक्रीकर सहित 3300 बिक्री 10% वास्तविक मलय = 3300/1.1 = 3000 If you find this answer helpful then like it. |
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| 4. |
The area of a triangle is 48 cm. Its base is 12 cm. Find the length of its correspaltitude. |
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Answer» area of triangle = 1/2× base× altitude(48×2)/12 = altitude8 cm = altitude thanks |
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| 5. |
Sum of first 55 terms in an A.P, is 3300, find its 28i term. |
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Answer» S55 = 3300 [Given that]Now Sn = n/2[2a + (n – 1)d] ∴S55 = 55/2[2a + (55 – 1) d] ∴3300 = 55/2[2a + 54d] ∴3300 = 55/2 × 2[a + 27d] ∴3300 = 55 [a + 27d] ∴3300/55= a + 27d ∴a + 27d= 60 ......(i) Now, tn = a + (n – 1) d ∴t28 = a + (28 – 1) d ∴t28 = a + 27d Putting the value of a+ 27d ∴t28 = 60[From (i)] ∴Twenty eighth term of A.P. is 60. |
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| 6. |
sty dsuud)e de> 2(. 7 â-4 2 + X 8 |
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Answer» Degree of this polynomial is 8As the highest power of x is called a degree of a polynomial |
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| 7. |
दे... लक जि किक भी RO T TSty दाद दद्ध ' रदद्ध उस B P |
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Answer» Sol:1 / (√4 + √5)= [1 / (√4 + √5)] x [(√4 - √5)/(√4 - √5)]= (√4 - √5) / (√4)2 - (√5)2= (√4 - √5) / 4 - 5= (√4 - √5) / (-1)= (√5 - √4) (1 / √5 + √6) = [1 / (√5 + √6)] x [(√5 - √6)/(√5 - √6)]= (√5 - √6) / (√5)2 - (√6)2= (√5 - √6) / 5 - 6= (√5 - √6) / (-1)= (√6 - √5) Similarly,(1 / √6 + √7) = (√7 - √6)(1 / √7 + √8) = (√8 - √7)(1 / √8 + √9) = (√9 - √8) (1 / √4 + √5) + (1 / √5 + √6) + (1 / √6 + √7) + (1 / √7 + √8) + (1 / √8 + √9)= (√5 - √4) + (√6 - √5) + (√7 - √6) + (√8 - √7) + (√9 - √8)= 3 - 2= 1 |
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| 8. |
2८0 एक समचतुर्भज है और PO R sty g 5it AB, BC,CD 3R DA के मध्य बिन्दु है। उुकि 08 एक आयत है। ं |
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| 9. |
13 Find the degree and radian measure ofexterior and interior angle of a regulari) Pentagon ii) Hexagoniii) Septagon iv) Octagon |
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Answer» ( iv) octagon option D is correct answer option .iv. octagon is the right answer option (4) octagon is the right answer the correct answer is D |
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| 10. |
b. Can the exterior angle of a reguiar PolyBoli e B7. The angles of a pentagon are in the ratio of 1:3:5:4:5. Find the angles of the penta8. The average of 3 aneles of a quadrilateral which are in the ratio of 2:5:4 is 770 r |
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Answer» suppose angles are x,3x,5x,4x,5xso x+3x+5x+4x+5x=54018x=540so x=30so angles are 30,90,150,120,150 |
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| 11. |
2. Explain photo electric effect. |
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Answer» The photoelectric effect refers to theemission, or ejection, of electrons from the surface of, generally, a metalin response to incident light.Einstein proposed that the incident light consisted of individual quanta, called photons, that interacted with the electrons in the metal like discrete particles, rather than as continuous waves. For a given frequency, or 'color,' of the incident radiation, each photon carried the energy E = hf, where h is Planck's constant and f is the frequency. Increasing the intensity of the light corresponded, in Einstein's model, to increasing the number of incident photons per unit time (flux), while the energy of each photon remained the same (as long as the frequency of the radiation was held constant). Clearly, in Einstein's model, increasing the intensity of the incident radiation would cause greater numbers of electrons to be ejected, but each electron would carry the same average energy because each incident photon carried the same energy. [This assumes that the dominant process consists of individual photons being absorbed by and resulting in the ejection of a single electron.] Likewise, in Einstein's model, increasing the frequency f, rather than the intensity, of the incident radiation would increase the average energy of the emitted electrons |
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| 12. |
For any positive interger'n' prove that ni n is divisible |
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Answer» Thanks |
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| 13. |
3 A piece of wire of length 48.8 cm is bent in the form of an octagon. Find the side of the octagon |
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Answer» Octagon has 8 sides. So, each side has 48.8/8 = 6.1 cm |
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| 14. |
eetBieA piece of wire of length 48.8 cm is bent in the form of an octagon. Find the side of the octagon. |
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| 15. |
In AABC, if CosA 2 sn then prove that the triangle is anisosceles triangle.Sin BSin C |
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| 16. |
re are 102teachersin a school of 3300 students. Find the ratio of the numberTheof teachers to the number of students |
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| 17. |
find the value of a my end 2in the given fog of sty 2200 |
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Answer» As we knowx+y+z+130= 360100+z+130= 360z= 360-230z= 130 |
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| 18. |
I. If s(x)and g(x) 2x-3, then findthe functions fog and gof and specify theirdomains. |
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Answer» fog(x) = √(2x-3)gof(x) = 2√x-3 |
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| 19. |
Find i) gof and ii) fog wherei) f(x)-x-2, g (x) =x2 + 3x+2<x-2i)f(x) =x"g(x) =r+2 |
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| 20. |
Find the distance of the point (-3,4) from the x-axis. Give proper solution. |
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Answer» When we are asked to calculate the distance between a point and any of the axes, we calculate the perpendicular distance between them. Therefore, the point (-3,4) is 3 units away from the y-axis and 4 units from the x-axis. This is because in case of either axes the co-ordinate of the other axis is zero. Therefore the distance between the point P(-3,4) and x-axis is 4 units. Please hit like if you find my solution helpful |
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| 21. |
Write the number names for the following numerals.(d) 4,40,404(a) 53,701(e) 9,00,009(b) 91,001(1) 6,08,316(c) 8,08,808 |
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Answer» 1. five thousand seven hundred one |
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| 22. |
Prove that (सिद्ध करें कि) ।हैं।2 COSCOS-COS+COS-30| |
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| 23. |
2In the table below, write the number of sides the poyon hasNamesQuadrilateralOctagonPentagonumber ofsades |
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Answer» quadrilateral have 4 sides. octagon have 7 sides. pentagon have 5 sides. heptagon has 8 sides. hexagon have 6 sides. Q-4O-8P-5Hep-7hex-6 |
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| 24. |
Prove ihat Sn ni cosec24cosp2 |
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Answer» =(sinA+cosecA)²+(cosA+secA)² =sin²A+cosec²A+2sinAcosecA+cos²A+sec²A+2cosAsecA =sin²A+cos²A+cosec²A+sec²A+2sinA×1/sinA+2cosA×1/cosA =1+cosec²A+sec²A+2+2 =5+(1+cot²A)+(1+tan²A) =7+tan²A+cot²A Identities used:1+tan²A=sec²A 1+cot²A=cosec²A sin²A+cos²A=1 cosecA=1/sinA secA=1/cosA |
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| 25. |
Find the median mal Rs.7. The ages (in years) of 10 teachers in a school are34, 37, 53, 46, 52, 43, 31, 36, 40, 50.Find the median age. |
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| 26. |
Q.2 In a specific year the distribution of ages (in years) of primary teachers are given:Age (in years)15 2020 2525 -3030-3535- 4040 4545 50Number of Teachers1030505030i. What is the lower limit of third class interval.ii. What are the limits of fifth class interval.iii. What is the class mark of class 45-50. |
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| 27. |
Find fog if f(x) = 8x3 and g(x) = xã |
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| 28. |
3F&CD=21, 2GC730041, 0hommetocore (fog) onto (son Browne |
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Answer» (fog)oh=(fog)x^2=(f(3x^2+1)=3x^2+1-1=3x^2; fo(goh)=( fog)x^2=f(3( x^2)^2+1=f(3x^4+1)=3x^4+1-1=3x^4 |
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| 29. |
4.Discuss the requisites of successful enterprise |
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Answer» Requisites Of Business Success Following are the major components (requisites) required for successful business operation: 1. Establishment Of Clear-cut Objectives Clearly defined objective helps to provide guidelines for future business activities. Long-term and short-term objectives should be established in order to achieve goals. 2. Proper Planning And Clear Policy Proper planning helps the businessman to decide what to do and how to do different business activities. Correct and clear policy helps to perform work with minimum risk and maximum profit. 3. Sound Organization And Effective Management This is another essential requisite for business success. Proper organizational structure and quality management helps in planning, coordinating, motivating, directing and decision making. It helps proper utilization of resources and to achieve organizational goals. 4. Dynamic Leadership Dynamic leadership is another key factor for business success. Leader or manager with vision, courage, foresightedness, and motivating skills is needed to operate business successfully. 5. Pleasant Personality Manager should be physically and mentally sound to handle business activities smoothly. Manager or businessman with good communication skills, intelligence, experience, and good commanding is needed for business success. 6. Adequate Capital/ Proper Financial Planning A proper financial planning is needed to arrange adequate long-term and short-term capital to operate business. Suitable source of capital should be identified to run business smoothly. 7. Proper Location And Layout Proper location and layout helps to reduce production and operation cost and increase efficiency of the business. Suitable location and proper layout helps to maximize profit. 8. Employees Morale Encouraged and motivated employees play very important role in business. Success or failure of business depends on the morale of employees. Therefore, staffs should be motivated, encouraged, and properly trained to achieve organizational goals and objectives. |
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| 30. |
. You lay on that same rock at night so that you can keep warm bya. Conductionb. Radiationc. Convectiond. Gravity |
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Answer» With the help of convection we can get heatthanksplease like the solution 👍 ✔️ |
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| 31. |
60°Fig. (iv)(iv) In figure (iv), /||m, find the value ofx. |
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| 32. |
θ1.tind01+cos。羔If sin θ + sir)"thenthe valueeos-oIfA 45 and B 30s then find the value o sin A cos B -cos A sin B.. |
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Answer» hit like if you find it useful |
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| 33. |
(13) Cox - 7² - 16=0wasic |
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Answer» x= 11 is the correct answer of the given question X=11is correct answer |
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| 34. |
The value ofsin 20° sin 40° sin 60° sin 80° is |
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Answer» sin20. sin 40. sin60. sin80 => sin60[sin20.sin40.sin80] =>√3/2[sin20.sin(60-20).sin(60+20)] =>√3/2[sin 3(20)/4] =>√3/2[sin 60/4] =>√3/2[√3/2*4] =>√3/2*√3/8 =3/16 |
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| 35. |
(iii) 3(iv)IV)_ |
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Answer» the blue line is -2/5 , the red line is 1/5 , the yellow line is 8/3 , and the green line is 3(2/7) or 23/7. |
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| 36. |
US(a) In the given figure, the arcs are drawn withcentres P, Q and R of radius 14 cm. Find the area4of the shaded region. |
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| 37. |
us, the pair (a,r) is not equal to the pair2 (5 133find the values of x and y.1. If +1, yill be the same |
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| 38. |
EDUCACene,excelleeos 40%,cos20°sin 20 |
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Answer» calculate without using trigonometric table 2*cos40 - cos20 = cos40 + (cos40 - cos20) = cos40 - 2*sin((40+20)/2)*sin((40-20)/2) = cos40 - 2*sin30*sin10 = sin(90-40) - sin10 = sin50 - sin10 = 2*sin((50-10)/2)*cos((50+10)/2)=2*sin20*√3/2=√3*sin20√3*sin20 / sin20 =√3 |
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| 39. |
6nl biau dg.ind its volume3. If the curved surface area of a cylinder is 1760cm 2 and radius is 14cm Find its height and volune4. Find the curved surface area and the total surface area of a cene, whose radius in |
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| 40. |
COL15. निम्नलिखित सर्वसमिकाओं को सिद्ध करें:(i) (1-cos 9) (1 + cos e) (1+ cot-0)=1 |
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Answer» so(1-cos^2 theta)(1-cot^2 theta)sin^2 theta* cosec^2 theta= 1 |
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| 41. |
न N12. निम्नलिखित में कौन &0 45" के बराब्रर है? b(A) cos 45° . (B) sin 60° लि cos 60° (D) tan 45° |
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Answer» cos 60 is th right answer sin 45° = 1/√2 cos 45° = 1/√2 A) sahi hai |
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| 42. |
1.If A(32)= | , then |3A equals :1 -1)यदि A-(-३) है, तो 13A का मान है :(A)-45(B)45(C)15| (D)-15 |
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Answer» Given,A = |3 2| |1 -1| |3A| = |3(-3 - 2)| = |3*-5| = 15 (C) is correct option |
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| 43. |
(a) 30(b) 45(c) 60 |
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| 44. |
(52 â 4y?) (5X2 â 4y?) |
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Answer» (5x²-4y²)²=25x^4+16y^4-40x²y² (a-b)²=a²-2ab+b² |
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| 45. |
62. Sinh'3=- |
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Answer» sin (h^-1)x=log(X+√x^2+1)hence X=3hencesin h^-1 (3)=log (3+√10) |
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| 46. |
\sinh \left(\frac{x}{2}\right) |
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| 47. |
I () n(A) 75, n(B)-45, (AUB)-90[H.S. '04] 1 |
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Answer» It is a rong |
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| 48. |
25 cm: 1 m and40: 160 (b) |
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| 49. |
60 cm as percent of 1 m 25 cm |
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| 50. |
2. The distance between the points P(7.5) and gl.5 |
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Answer» Distance between P and Q=√((x2-x1)²+(y2-y1))²=√((2-7)²+(5-5)²)=√(-5)²+0=5 units |
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