Explore topic-wise InterviewSolutions in Current Affairs.

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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x-2=0-2+2=0

x-2=02-2=0

so,-2 and2 is factor of x+2

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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k=8.5 is the correct answer of the given question

7.

Write 2 equivalent ratios of 6:4

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3:2 and 12:8 here6:4 divided by 2 and multiplied by2 we get3:2and 12:8

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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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]

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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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

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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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

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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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

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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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

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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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

20.

x ^ { 3 } - 2 x ^ { 2 } - 9 \text { and } 5 x ^ { 3 } + 2 x + 9

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tx

21.

Add the polynomials $x^{3}-2 x^{2}-9$ and $5 x^{3}+2 x+9$

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x³ - 2x² -9 + 5x³ + 2x + 9(x³ + 5x³) + ( -2x²) +2x -9 + 96x³ -2x² + 2x

22.

Write any three rational numbers between 8.2 and 8.3

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Three rational number between 8.2 and 8.3 are 8.21, 8.22, 8.23.

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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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

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,-つ(

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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,∞)

28.

[4 '(8ाप। ज००पू,3) "0001 €

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1252163435127291000

5³ = 1256³ = 2167³ = 3438³ = 5129³ = 72910³ = 1000

29.

The decimal expansion ofrational number49will terminate after how many places ofdecimal ?4040

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30.

equivalent fractions

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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

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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9^m/3-²=9⁴3^²m /3-²=3^(2×4)since base are equal2m+2=82m=8-22m=6m=6/2m=3

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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9.9^3 = 9.9 x 9.9 x 9.998.01 x 9.9970.299

35.

Write three rational numbers betweenand+

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2*4/3*4 and 3*3/4*3=8/12 and 9/12=8.1/12,8.2/12,8.3/12

36.

5+2%62/1

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thanks frnd.

37.

10 20 30 )13. Write three rational numbers betweenand

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1/2 and 1/3hence3/6 and 2/6hence three rational numbers will be2.1/6,2.2/6,2.3/6

38.

DO Find a ratio that isequivalent to 7:20

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can you answer my other questuons

questions*

39.

6=Qx 900001 to & QOI - 08X ogto orPageDateCassmate

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we can't divide it by 0. Your question is wrong

40.

Page:Datel心

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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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3 is the correct answer

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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adjoint is (2 -3 -4 2)

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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second number correct answer

46.

1)The decimal expansion of 15/1600 will terminate after how many places of decimal?

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15/1600=0.0093756 decimal places

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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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

49.

MATHEMATICS4. Express in kg) 200 g5. Write the following decimal20.03

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1000grams = 1kg1 gm= 1/1000200gm= 200/1000= 2/10= 1/5kg

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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