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. |
Determinate which of the following polynomials, (x+ 1) is a factor of(i) x4 +x3 + x2 + x + |
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| 2. |
2. The radii of the circular ends of a solid frustum of a cone are 33 cm and27 cm, and its slant height is 10 cm. Find its capacity and total surface[CBSE 2005]area. Take π = 22, |
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| 3. |
Check-2 and 2 are zero of polynomials x + 2. |
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Answer» x-2=0-2+2=0 x-2=02-2=0 so,-2 and2 is factor of x+2 |
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| 4. |
The sum of the digits of a 2-digit number is11. The number obtained by adding 4 to thisnumber is 41 less than the reversed number.Find the original number. |
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| 5. |
The sum of the digits of a 2-digit number is 11. The number obtained by adding 4 to this number is 41 less than the reversed number. Find the original number. |
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| 6. |
For what value of k. - 4 is a zeroes of the polynomials x? - -(2k + 3)? |
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Answer» k=8.5 is the correct answer of the given question |
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| 7. |
Write 2 equivalent ratios of 6:4 |
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Answer» 3:2 and 12:8 here6:4 divided by 2 and multiplied by2 we get3:2and 12:8 |
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| 8. |
(pq+1)2히If the pth term ofan AP isand the q1h term is-, show that sum of first py terms。(pq+1) |
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| 9. |
Q.19) If the pth term of an AP be and qth term by -, thenprove that the sum of the first pq terms must be (pg+ 1)2 |
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Answer» Given pth term = 1/q That is ap= a + (p - 1)d = 1/qaq + (pq - q)d = 1 --- (1) Similarly, we getap + (pq - p)d = 1 --- (2) From (1) and (2), we getaq + (pq - q)d =ap + (pq - p)daq - ap = d[pq - p - pq + q]a(q - p) = d(q - p) Therefore, a = dEquation (1) becomes,dq + pqd - dq = 1 d = 1/pq Hence a = 1/pq Consider, Spq= (pq/2)[2a + (pq - 1)d] = (pq/2)[2(1/pq) + (pq - 1)(1/pq)] = (1/2)[2 + pq - 1] = (1/2)[pq + 1] |
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| 10. |
. In an A.P., if pth term isand qh term is, prove that the sum of first pqterms is-(pq +1), where p # q. |
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| 11. |
n terms lie between 7 and 49 in an AP. Ifratio of the fourth term anterm is 5: 4, then find the value ofn.d the (n-1)2 |
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| 12. |
8.If 6 times the 6th term of an A.P is equal to 11 times its 11th term, then find its 17'th term.OR |
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Answer» 6×6th term = 11×11th term 6(a+5d) = 11(a+10d) 6a+30d = 11a+110d -5a = 80d so a=-16d 17th term = a + 16d = -16d + 16d = 0 |
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| 13. |
34. IfA.[.], find x and y such that A2.xly. HeCBSE 2005] |
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| 14. |
ABC is a triangle in which AB AC and D is any point in BC. Prove thatAB2-AD2 BD. CDCBSE 2005 |
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Answer» AB^2=AE^2+BE^2------(1)AD^2=AE^2+DE^2------(2)(1)-(2)AB^2-AD^2=AE^2+BE^2-AE^2-DE^2=(BD+DE)^2-DE^2=BD^2+2BD(BE-BD)=2BD.BE-BD^2=BD(2BE-BD)=BD(BC-BD)AB^2-AD^2=BD.CD |
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| 15. |
2. The radii of the circular ends of a solid frustum of a cone are 33 cm andcm, and its slant height is 10 cm. Find its capacity and total surfaceCBSE 2005]area. Take π = 237. |
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| 16. |
write any three rational numbers |
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Answer» 2/3 , 7/9, 3/5 is the correct answer of the given question 3/6, 1/4, 9/5 can be rational numbers 2/3,4/9 ,3/8 is the correct answer 3/2,4/10, 9/100 are some rational numbers rational numbers are numbers that can be expressed in p/q form where p and q are integers and q is not equal to 0.examples of rational no. are ÷2/3,1/9,7/2 Three rational numbers are-2/3,3/6,4/8 22/72/33/2are some rational no. 1234,1423,1523 ,1534 1/3,1/9,9/1 ect. are rational number 1352345324543,5467325680 ,34624645624 |
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| 17. |
Find the quotient and remainder, when the difference of the(i) number 27 and the reversed number is divided by 9 |
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| 18. |
EXERCISE 1.11. (a) Write any three rational numbers(b) Explain rational number is in your own words |
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Answer» 1a) 1, 3/5, 4 b) A number which can be written in form of p/q where p and q are integers and q is not 0 is called rational number write any three rational number s |
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| 19. |
The sum of the digits of a 2-digit number is 7. If 27 is added to the number,interchanged. Find the original number. |
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Answer» Let the units place be xthen the tens digit be 7 - xnumber formed by these digits = 10 x t's digit+u's digit=> 10(7-x)+x70 x -10 x +x70 x -9xwhen the digits are interchanged than,t's digit= xu's digit = 7-xthe new no. formed = 10x + 7-x= 9 x +7given that the no. exceeds by 27new no. - given no.9x +7 - (70-9x)=279 x + 7 - 70 + 9x =2718x -63= 2718 x = 63+2718 x= 90x = 90/18=5the no. = 70- 9x=> 70-45=> 25 ansverify : 2+5 = 7 thanks |
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| 20. |
x ^ { 3 } - 2 x ^ { 2 } - 9 \text { and } 5 x ^ { 3 } + 2 x + 9 |
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Answer» tx |
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| 21. |
Add the polynomials $x^{3}-2 x^{2}-9$ and $5 x^{3}+2 x+9$ |
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Answer» x³ - 2x² -9 + 5x³ + 2x + 9(x³ + 5x³) + ( -2x²) +2x -9 + 96x³ -2x² + 2x |
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| 22. |
Write any three rational numbers between 8.2 and 8.3 |
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Answer» Three rational number between 8.2 and 8.3 are 8.21, 8.22, 8.23. |
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| 23. |
Find the adjoint of \left[ \begin{array}{rr}{-3} & {4} \\ {2} & {7}\end{array}\right] |
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| 24. |
8. Write three different irrational numbers between the rational numbersand |
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| 25. |
1. (a) Write any three rational numbers(b) Explain rational number in your own words. |
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Answer» a) 10/5 , 20/2 , 2.17 a. rational number are 2/5 , 8/7 ,9/5 etc ..b.rationla numbers are those number which are represent in the form of p/q where q is not = to 0. b) The rational is known as the number which is in the form p/q and q is not equal to 0 three rational. no. are 1,2,3and the no's. which are in the form of p/q where q is not equal to 0are called rational numbers |
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| 26. |
\left. \begin{array} { l } { L ^ { - 1 } [ \frac { 2 s - 5 } { s ^ { 2 } + 4 } ] } \\ { L ^ { - 1 } [ \frac { s + 2 } { ( s - 1 ) ( s + 3 ) } ] } \end{array} \right. |
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| 27. |
Eind-therRHangathe-function,-ă¤( |
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Answer» since √x²-1 cannot be -ve and 0 , so so, when X→∞ or -∞ , the f(x) will become (1/∞)≈0 when X=1,-1 it will become 1/0 ≈ ∞ so, range will be (0,∞) |
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| 28. |
[4 '(8ाप। ज००पू,3) "0001 € |
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Answer» 1252163435127291000 5³ = 1256³ = 2167³ = 3438³ = 5129³ = 72910³ = 1000 |
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| 29. |
The decimal expansion ofrational number49will terminate after how many places ofdecimal ?4040 |
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| 30. |
equivalent fractions |
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Answer» An equivalent fractions can be defined as fractions with different numerators and denominators that represent the same value or proportion of the whole. Here’s an example of equivalent fractions1/2 = 2/4 = 4/8 |
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| 31. |
Find after how many places of decimal the decimal form of the number27will terminate.2.54.32 |
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| 32. |
Find adjoint of each of the matrices in Exercisel and 2Q1.3 4 |
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| 33. |
9^m/3^(-2)=9^4 |
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Answer» 9^m/3-²=9⁴3^²m /3-²=3^(2×4)since base are equal2m+2=82m=8-22m=6m=6/2m=3 |
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| 34. |
(ii) (9.9)3(iii) (598/(ii) (3x + 8ヅ-(3x-8yy(iv) (7k-5が-(1k+ 5が(1) 983(i) (x+が-(x-7)323/(2 3TE-y=4awTxy = 21. Tx3-V4T TA可ταす fan食1乀// |
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Answer» 9.9^3 = 9.9 x 9.9 x 9.998.01 x 9.9970.299 |
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| 35. |
Write three rational numbers betweenand+ |
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Answer» 2*4/3*4 and 3*3/4*3=8/12 and 9/12=8.1/12,8.2/12,8.3/12 |
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| 36. |
5+2%62/1 |
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Answer» thanks frnd. |
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| 37. |
10 20 30 )13. Write three rational numbers betweenand |
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Answer» 1/2 and 1/3hence3/6 and 2/6hence three rational numbers will be2.1/6,2.2/6,2.3/6 |
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| 38. |
DO Find a ratio that isequivalent to 7:20 |
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Answer» can you answer my other questuons questions* |
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| 39. |
6=Qx 900001 to & QOI - 08X ogto orPageDateCassmate |
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Answer» we can't divide it by 0. Your question is wrong |
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| 40. |
Page:Datelĺż |
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| 41. |
3 + 5+7+n5+ 8+11++ 10 terms1. If- 7, then the value ofn is |
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| 42. |
PAGE NO.:,4++=०है ।Cta(4-15काab(b+c (८+१)ताल की हि |
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Answer» 3 is the correct answer |
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| 43. |
+7+-+ n-=- 7, then the value ofthen t1. If5+ 8+11+. + 10 termsn is |
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| 44. |
Find adjoint of the matrix\left( \begin{array}{ll}{2} & {3} \\ {4} & {2}\end{array}\right) |
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Answer» adjoint is (2 -3 -4 2) |
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| 45. |
3. (2EXERCISE 5B1. Express cach of the following numbers in standard form:(i) 538(ii) 6428000 (ili) 82934000000(v) 23000000(iv) 94000000004.2 Frescobl .... |
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Answer» second number correct answer |
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| 46. |
1)The decimal expansion of 15/1600 will terminate after how many places of decimal? |
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Answer» 15/1600=0.0093756 decimal places |
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| 47. |
2 3Find the adjoint of matrix A =\left[ \begin{array}{cc}{2} & {-3} \\ {4} & {1}\end{array}\right] |
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| 48. |
1/15, 1/12, 1/10,....., to 11 terms |
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Answer» The given AP is 1/15, 1/12, 1/10........ 11 terms a = 1/15, d = 1/12 - 1/15 = (5 - 4)/60= 1/60 We know, sum of n terms Sn = n/2[2a + (n-1)d] Then, sum of 11 terms of given APS11 = 11/2[2*1/15 + 10*1/60] = 11/2[2/15 + 10/60] = 11/2[(8 + 10)/60] = 11/2(18/60) = 33/20 |
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| 49. |
MATHEMATICS4. Express in kg) 200 g5. Write the following decimal20.03 |
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Answer» 1000grams = 1kg1 gm= 1/1000200gm= 200/1000= 2/10= 1/5kg |
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| 50. |
If one of the dllgangles? Give examples of at least HeIn the figure given below, I Il BC. Prove that a + b+c 180°2 |
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