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. |
44,x=41, y = |
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| 2. |
Show that the eigenvalues of a triangularmatrix are the entries on its main diagonal. |
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| 3. |
Very-Short-Answer Questions1. IfA is a 2x2 matrix such that IA|关0 and i Al-5, write the value of 14Al. |
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Answer» det(αA) = α^n det(A) |4A| = 4^(2) |A| = 16 * 5 = 80 |
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| 4. |
IfA-B 21and X is a 2x2 matrix such thatAX=1,then find X. |
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| 5. |
If a matrix has 24 elements, what are the possible order itcan have? What, if it has 13 elements? |
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Answer» We know that, if a matrix is of order m x n, it has mn elements, where m and n are natural numbers.We have, m x n = 28⇒ (m, n)= {(1, 28), (2, 14), (4, 7), (7, 4), (14, 2), (28, 1 )}So, the possible orders are I x 28, 2 x 14, 4 x 7, 7 x 4, 14 x 2, 28 x 1.Also, if it has 13 elements,then m x n = 13⇒ (m, n)= ((1, 13), (13, l)}Hence, the possible orders are 1 x 13, 13 x 1. |
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| 6. |
Find the distance of the point (2, 3) from the line 2x-3y + 9 = 0 measured along a linemaking an angle of 45° with the x-axis. |
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Answer» Slope of 2x - 3y + 9 = 0 is 2/3Slope of x - y + 1 = 0 is 1Angle between the two lines= arctan (1 -2/3) / (1 + 2/3)= arctan (1/4)= 14°Perpendicular distance from (2, 3) to the line 2x - 3y + 9 = 0 isp = l 2*2 - 3*3 + 9 l / √(2^2 + 3^2) = 4 / √(13)distance of (2,3) from 2x - 3y + 9 = 0 along x - y + 1 = 0 isp sin 14°= [4/√(13)] sin14°= 0.268. |
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| 7. |
3.Annetulicshight Som. Find hew muny cones are cbauiedet ofta us 115 mis me tedand then reca tutto s mill cores each ofranusămut |
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Answer» Solution:-Volume of sphere = 4/3πr³= 4/3*22/7*10.5*10.5*10.5Volume of metallic sphere = 4851 cm³Now,Volume of one cone = 1/3πr²h= 1/3*22/7*3.5*3.5*3Volume of one cone = 38.5 cm³Total number of cones = Volume of metallic sphere/volume of one cone= 4851/38.5= 126 conesTotal number of cones can be formed is 126 |
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| 8. |
28. If a cos, θ + 3a sin-θ co s θm+n +m-n)am and a sin' θ + 3a sinθ cos2 θ-n, prove that2/3 |
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| 9. |
(i)sin? A + co. Ay= cos2 A + sin' A |
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Answer» sin^2 A-sin^4A= cos^2A-cos ^4Asin^2A(1-sin^2A) = cos^2A(1-cos^2A) cos^2A= cos^2A |
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| 10. |
402 4.6? te 2:50 and ab the tes :47 find at a tilte |
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Answer» ab+bc+ca=47hence2*(ab+bc+ca)=2*47=94hence(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)hence(a+b+c)^2=50+94=144hencea+b+c=12 |
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| 11. |
WELR2, 3, 4,7. Find three different irrational numbers between the rational numbers(NCERT |
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| 12. |
T of 2% + 20+1=1280; Then find thevalue of som |
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| 13. |
A cylinder and a cone have equal bases.The height of the cylinder is 3 cm and thearea of its base is 100 cm2.The cone is placedupon the cylinder. Volume of the solidfigure so formed is 500 cm. Find the totalheight of the figure. |
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| 14. |
S काहै: 9 [जिSN <T R Lo-X |
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| 15. |
ह०६८, 500 + oL],800oLT (WIS +o£9 SLo |
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Answer» sin^2 63 + sin^2 27/cos^2 17 + cos^2 73 (using cos (90 - x) = sinx sin(90 - x) = cosx sin^2 x + cos^2 x = 1) = sin^2 63 + cos^2 (90 - 27)/ sin^2 (90 - 17) + cos^2 73 = sin^2 63 + cos^2 63/ sin^2 73 + cos^2 73 = 1 |
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| 16. |
Construct a 2x2 matrix Awhose elements in the ith row and in column are given by ayTf |
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| 17. |
\begin{array} { l } { \text { Transform } \left[ \begin{array} { c c c } { 1 } & { - 1 } & { 2 } \\ { 2 } & { 1 } & { 3 } \\ { 3 } & { 2 } & { 4 } \end{array} \right] } \\ { \text { triangular matrix } } & { \text { by suitable row } } \\ { \text { transformations. } } \end{array} |
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Answer» your answer your answer |
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| 18. |
[P.S.E.B.[PS.Е.В6. Find the sum of first 15 multiples of 9. |
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Answer» multiples of 9 are 9 18 27.......a=9d=9n=15 S=n/2 (2a+(n-1)d)S=15/2 (2*9+(15-1)*9)S=7.5(18+14*9)S=7.5(18+126)S=7.5*144S=1080 |
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| 19. |
. 18. A cone is 8.4 em high and the radius of its base is 2.1 cm. It is mlteand recast into a sphere. Find the surface area of the sphere. |
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| 20. |
लिन TRe oo angl of o quadbidad cw dn A sabio1:2:3 and e Peunkh ongl 868 Find ऊन oAl dhe anele - |
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| 21. |
7. How many lead balls, each of radiun 1 cm, can be made from a sphereof radius 8 em? |
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| 22. |
2) Write multiples of 9 greater than 72 but less than 99 |
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Answer» 81 and 90 is your answer 81 and 90 is the most correct answer 9×9 =81 and 9×10=90 are the correct answers 90 is answer and 81is also 90 is the right answer correct answer is 90 of the following question vice chief minister of bihar vice chief minister of bihar 81 and 90 81 and 90 is the correct answer of the given question. 81 and 90 is the right answer 81 and 90 is the right answer |
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| 23. |
is-lust-one-dia it-on-the-right-which is without bair |
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| 24. |
- ---(1) മ--(ഗവ്യം , '4 ( 161 4ം 2 144 199 fift?6 (2) 8(3) ) (4) 12. |
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Answer» 64²×16²/8³×4⁴÷4/38²×4²/1³×1⁴÷4/38²×4²÷4/364×16÷4/364×16×3/4768 option (1) 6 is the right answer according to your question 64²×16²/8³×4⁴÷4/364×16/8×4²÷4/364×16/8×16÷4/38×1÷4/38÷4/38×3/42×36so i)6 option is the answer |
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| 25. |
PAGE Noalue st Cost coos Cos2 |
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Answer» note that cos90° = 0 Cos 1× cos 2× cos 3× ......× cos179= cos 1× cos 2× cos 3× .....× cos 90× .....× cos 179=cos 1× cos 2× cos 3× .....× 0 × .....× cos 179=0×cos 1× cos 2× cos 3× .......× cos 179=0 |
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| 26. |
1. Find the multiples of 9 and 12 and then find theirLCM. |
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Answer» the multiples of 9 and 12 is 36,72 because 36 and 72 divides both 9 and 12. |
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| 27. |
-12+-√144+144/6 |
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| 28. |
23. A solid sphere of radius 10.5 cm is meltedand recast into smailer solid cone, each ofradius 3.5 em and height 3 cm. Find the 30. The dirnumber of cones so formed100 cm |
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Answer» Volume of sphere = 4/3πr³= 4/3*22/7*10.5*10.5*10.5Volume of metallic sphere = 4851 cm³Now,Volume of one cone = 1/3πr²h= 1/3*22/7*3.5*3.5*3Volume of one cone = 38.5 cm³Total number of cones = Volume of metallic sphere/volume of one cone= 4851/38.5= 126 conesTotal number of cones that can be formed is 126 |
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| 29. |
5, गुणनखंड ज्ञात कीजिए:) xX*-2x*—x+2 :(i) x°+13x2+3 2:४१ 20 |
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Answer» i) x*x*x - 2x*x - x + 2 = x*x(x-2)-1(x-2) = (x*x-1)(x-2) = (x+1)(x-1)(x-2) ii) x*x*x+13x*x+12x+20 = x*x*x+x*x+12x*x+12x+20x+20 = x*x(x+1)+12x(x+1)+20(x+1) = (x*x+12x+20)(x+1) = (x+1)(x+2)(x+10) If you find this answer helpful then like it. |
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| 30. |
3.Divide 5x3-13x2 + 21-14 by (3-2x + x*) and verify the division algorithm. |
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Answer» Given f(x) = 5x^3 - 13x^2 + 21x - 14. Given g(x) = 3 - 2x + x^2. We need to divide f(x) by g(x). 5x - 3 ---------------------------------= > x^2 - 2x + 3) 5x^3 - 13x^2 + 21x - 14 5x^3 - 10x^2 + 15x --------------------------------- -3x^2 + 6x - 14 - 3x^2 + 6x - 9 ----------------------------------- -5. Here, Dividend = 5x^3 - 13x^2 + 21x - 14 Divisor = 3 - 2x + x^2 Quotient = 5x - 3 Remainder = -5 Division Algorithm: Dividend = Divisor * Quotient + Remainder = (3 - 2x + x^2) * (5x - 3) + (-5) = 15x - 9 - 10x^2 + 6x + 5x^3 - 3x^2 - 5 = 5x^3 - 13x^2 + 21x - 14. LHS = RHS |
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| 31. |
L2= 7+ Vuo Find The value of 5x + L |
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Answer» Given: x = 7 + √40 = 5 + 2 + 2√10 = (√5 + √2)² √x = √5 + √2 1/√x = 1/(√5 + √2) = (√5 - √2)/((√5 + √2)(√5 - √2) = (√5 - √2)/(5 - 2) = (√5 - √2)/3 √x + 1/√x = √5 + √2 + (√5 - √2)/3 = (2/3)(2√5 + √2) |
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| 32. |
A Box containt no dfscs uohiuh ave numbered1-90 ,in onedisc% drau) random hom box.fndnumbuç˝Apuleenombea |
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| 33. |
Examplé 10. If circles are drawn taking twosides of a triangle as diameters, prove that the pointof imersection of these circles lies on the third side. |
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| 34. |
2aa hom buy39asioo2.OneFind tRe oths dia gon al28cmduagor |
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Answer» Like if you find it useful |
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| 35. |
Multiples9. Find the HCF of(i) 9 and 12 |
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| 36. |
ORmetallie sphere af radius 15 em is melted and a wire of diameter 1 em is drawnhom t. Find the length of the wire |
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| 37. |
Ulayuldu . 19. If A is a row matrix as well as a column matrix, then order of A is |
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Answer» When the number of columns of the 1st matrix must equal the number of rows of the 2nd matrix. In other words, To multiply an m×n matrix by an n×p matrix, the n's must be the same, and the result is an m×p matrix. |
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| 38. |
420 1442ayrft 6.12 |
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Answer» This is a graphical representation of the data, pie chart |
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| 39. |
(४) (२८ + b ) | Je ++d \} =+ac + Jad + Jbe +N —\2 B |
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| 40. |
jeverite the Property vay = yes by taking se |
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Answer» Directive property of multiplication is the property I think |
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| 41. |
29. What must be subtracted from the polynomial f(x) x4+2x-13x-122x 13x2-12x + 21 so that theresulting polynomial is exactly divisible by x2 -4x+3?30. What must he daod |
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| 42. |
2= 7+ Vuofind the value of Je to |
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Answer» this question is wrong |
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| 43. |
From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the areaof the remaining sheet. (Take π = 3.14)swers5.las tohle cover of diameter LS m |
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| 44. |
1. Some questions and their alternative answers are give. Seleti. Out of the following which is the Pythagorean triplet?swers are givei. Serett I1m(R (3, 4,5)(C)(2, 2, 2) |
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Answer» a, b, c are Pythagorean triplet then a² + b² = c² So, 3² + 4² = 5² B) is correct option R your sister gave you six five rupee notes to buy something in the market .how much money did you get from your sister? answer is third 2 2 2 |
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| 45. |
Find the first two terms of the sequence Sn=n^2(n +1). |
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| 46. |
a-b=7,ab=9 find {asq+ bsq |
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Answer» a-b = 7ab = 9we have(a-b)² = a² + b² - 2ab7² + 28 = a² + b²a² + b² = 49 + 28 = 77 |
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| 47. |
13. If the sum of three numbers is 10 and the sum of their squares is 38, find the sum of the products of thenumbers taking two at a time. |
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Answer» let a,b,c be the three numbers. According to question,a+b+c=10a²+b³+c³=160 |
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| 48. |
10 - рдк 8+ (420 |
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Answer» 10-{8+(4÷2)}=10-{8+2}=10-10=0. |
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| 49. |
The angle of elevation onI lake is 200 de angle offind the height of200 m above lencland Hom a bointdepression of is reflection is 60dend. |
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| 50. |
Wewman -What wwwbee comes inside the codewceA) 5 B)6, 98, )?(10214SEO DELO OLA) 508, B) 518, C)418, D) 420Section: 1/1SetValue: 6.9cm. Row 1 Column 17Word17214here to search |
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Answer» 23) Sum of each row is 3 times the middle number.4+3+2=9=3*35+3+5+1+1=15=3*56+1+2+8+3+3+1=24=3*87+2+8+4+3=24=3*8So,9+x+3=3xx=6(B)6 is the correct answer. 24) Each number is multiplied with increasing multiples of 2.7+2^0=88+2^1=1010+2^2=14..........262+2^8=518(B)518 is the correct answer. |
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