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.

Prove that the functionf(x)-x" is continuous at x = n, where n is a positiveinteger

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2.

UJU(a) 42. The factors of expression r? + (a + b)x + ab are-( h

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3.

( x + i y ) ^ { 3 } = u + i v , \text { then show that } \frac { u } { x } + \frac { v } { y } = 4 ( x ^ { 2 } - y ^ { 2 } )

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4.

( x + i y ) ^ { 3 } = u + i v \text { then show that } \frac { u } { x } + \frac { v } { y } = 4 \left( x ^ { 2 } - y ^ { 2 } \right)

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5.

Show dhat ane and onlu one uandis

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x is an integer. So,it is of the form 3k,3k+1 or 3k+2 where k is an integer.

If x=3k,then

x+1=3k+1,not divisible by 3

x+2=3k+2,not divisible by 3

If x=3k+1(not divisible by 3),then

x+1=3k+2,not divisible by 3

x+2=3k+3=3(k+1), divisible by 3

If x=3k+2(not divisible by 3),then

x+1=3k+3=3(k+1),divisible by 3

x+2=3k+4=3(k+1)+1,not divisible by 3

Hence by seeing all the above cases,we can safely say that:out of x,x+1 and x+2,only one is divisible by 3.

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6.

)What number is 748 more than 66 443

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We are looking for a new number which is 748 more than 66443.We will get the new number by adding 748 to 66443.We write it down as:66443+748=67191

66443 more then numbers

7.

In a two digit number, digit at the ten's place is twiceplace. If the number obtained by interchanging the digits is added to theoriginal number, the sum is 66. Find the number.

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I want equation in one variable😅

8.

मैदान का परिमाप 200 मीटर है। और इसकी चौड़ाई 40 मीटर है तो इर मैदान को 1.25 रं/मी* की दर से समतल कराने की लागत ₹ 900 हैं यदिसकी चौड़ाई कितनी है?SOy i) e s e

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9.

In a two digit number, digit at the ten's place is twice the digitplace. If the number obtained by interchanging the digits is addedoriginal number, the sum is 66. Find the number

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Let the tens digit be x and the units digit be y.

So the number=10x+y

A.q.=>x=2y(equation 1)

After interchanging the digits we get10y+x

Also,=>(10x+y)+(10y+x)=66

=>10x+y+10y+x=66

=>11y+11x=66

=>11(y+x)=66

=>y+x=66/11

=>y+x=6

From equation 1 x=2y

So, y+2y=6

=>3y=6

=>y=6/3

=>y=2

And x=2(2)=4

Hence the number is 42.

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10.

Question No. 89The difference between Compound Interest and Simple Interest on a certain sum for 2 years at 12.5% rate isRs.45. What is the sum?A)Rs.2880B)Rs.2440C)Rs.3000D)Rs.2000

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A. us right answer

A is the correct answer 1st si is 360 and second principal+ si then 405 difference is 45

B) is correct answer

option C ) is the correct answer

11.

(b) Find the greatest number that will divide 33, 44 and 66 exactly.

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By using prime factorisation 33 = 3*11 44= 2*2*1166= 2*3*11

so, in all these only 11 is common.. so the answer is 11.

12.

latOne of the digits of a two-digit number is five times the other. If we interchange the digits ofthis number and add the resulting number to the original number, we get 66. What is the originalnumber?

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Let the two digit number be (10a+b)According to the question(10a+b)+(10b+a)=66; 11a+11b=66;a+b=6;And also it is given that a=5b or b=5aIf a=5b then put in the above equation 6b=6; then b=1 then a=5...then the number is 51 and if a=1 then b=5 then the number is 15

13.

Define a real function. Find the domain andrange of the real functionf(x) 12-1 1

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In mathematics, a real-valued function is a function whose values are real numbers. In other words, it is a function that assigns a real number to each member of its domain. Many important function spaces are defined to consist of real-valued functions

Domain (1/2 to infinity) and range (0 to infinity)

14.

कै: + (4) + 3(100)(4)(100 न 4)0000 + 64 + 1248004864

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15.

DEEP RIVEBecause weblend!Hever- OILSUNFLOWERexclusively inCookedGive a Chip3. If in a class of 40 students, 70% studentsare girls then what is the number of boys inthe class.

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12 boys are there in the classthis is the correct answer for this question Thank you sir

this is the crispy snacks

deep river is a snacks.

12 boys are there in the class

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deep river is the snacks...

12 boys are there in class

Total students =40no. of girls= 70% of 40 =70/100*40 =28therefore number of boys= 40-28=12

12 is the correct answer for this question

16.

Fill in the blank with proper alternative. 0000.......think then act.1) Secondly 2) First 3) Don't 4) Neverविषय - इंग्रजीप्रज्ञाशोध परीक्षा मार्गदर्शक इ. 6 वी (303)

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first think then act is the right answer

17.

Find the median of the values: 25, 31, 27, 29, 32.25 28.25The weight in kg) of 15 students of a class are

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25+31+27+29+32+28+25=190/15=12.667

25+31+27+32+28+25=190/15=12.667

12.667 is the correct answer

12.667 is the. correct. answer

18.

UJU0) 29%23.0707. What per cent of(a) 60 is 600?(b) * 50 is * 250?(c) 8 hrs is 2 days?(d) 125 g is 2.5 kg

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(a) Let the per cent be a. 600 x a /100 = 60 600a = 60 x100 a = 60 x 100/600 a = 10 % similarly you can do every question. But, for their unit should be sameLike in (c) convert 8hrs to day by dividing by 24 and in

19.

ला 15९ 40.8. 210000/0000 -ढ 1 \

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3+√2/4√2*4√2/4√2=12√2+8/32=3/8√2+1/4

20.

26] Poces 4 cnd 6 awe 0k obart on o highwous.0ne ey stkIdrom A ond_angthe Bt dhe same Giwe वी ity e braelI Aoume okirecfiof 0 cM_m_fiM&' 2८१1 sheeds ,m 05कलम अदा मर | 400५ नी! (०७००0 ch दि मच 10 000. (छा areफल -भु# 4७ 100 0000 है

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Let, speed of faster car = x km/hSpeed ofslowercar = y km/h

Relative speed when both cartravelsinsame direction= x - yIf the cars travel in thesame directionat different speeds, they meet in 5 hoursSpeed = distance/ timeTotal distance= 100 kmSpeed, x – y = 100/5x – y = 20x = 20 + y................…(1)

Relative speed when both cartravelsin opposite direction = x + yIf they travel towards each other, they meet in 1 hour.Speed = distance/ timeTotal distance= 100 kmSpeed, x+ y = 100/1

Put the value of x from eq(1)We get, 20 + y + y = 1002y = 80y = 40

Put the value of y in eq(1)we get,x= 20 + 40x = 60

Hence speeds are 40 km/h and 60 km/h

21.

If five times the 5th term of an A.P. is equal to eight times its 8th term, then show thatits 13th term is zero

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22.

36. If five times the ffth term of an AP is equalto eight times its eighth term, show that[CBSE 2012]its 13th term is zero.

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Explanation : 5*5th term = 8*8th term 5(a + 4d) = 8(a + 7d) 5a + 20d = 8a + 56d 3a = -36d a = -12d a + 12d = 0 13th term = a + 12d = 0 13th term is 0.

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23.

(4) If five times the 5th term of an A.P. is equal to eight times its 8th term, then show thatits 13th term is zero.

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let first term be a and common difference be daccording to given question5 × a(5) = 8 × a(8)5(a + 4d) = = 8(a + 7d)5a + 20d = 8a + 56d3a + 36d = 0a + 12d = 0a = -12dso,a(13) = a + 12d = -12d + 12d = 0

24.

(1 + 0000 - 005600) (1 + рео8119 + 8600) > 2

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(1+cot A -cosec A)(1+ tan A + sec A)

Lhs

=(1 +cos A/sin A - 1/sin A)(1 + sin A/cos A +1/cos A)

=(sin A+cos A -1/sin A)(cos A +sin A+1/cos A)

=(sin A+cos A-1)(sin A+cos A+1)/sin Acos A

=[(sin A+cos A)^2-(1)^2]/sin Acos A

=[sin^2A+cos^2A +2sin Acos A- 1]/sin Acos A

=[1-1+2sin Acos A]/sin Acos A

=2sin Acos A/sin Acos A

=2 =Rhs

25.

if rs 2500 becomes rs 3000 in 5 years ,then what will be the rate of interest?

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Interest = 3000- 2500= 500.INTEREST = PRT/100=> R = (500*100)/(2500*5)=> R = 4 %

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26.

am - aAnTo foto ye, —t given)(given)am n = 1

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am=1/na+(m-1)d=1/n--------(1)

an=1/ma+(n-1)d=1/m---------(2)

(1)-(2)(m-n)d=1/n - 1/md=1/mn

put in eq(1)a+(m-1)/mn=1/na=1/n - (m-1)/mna=1/mn

amn=a+(mn-1)damn=1/mn+(mn-1)/mnamn=1

27.

Find the domain and the range of the real functionf defined byf(x) =\sqrt{(x-1)}

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Therangeof an even indexed radical starts at its startingpoint(1,0)(1,0)and extends toinfinity.

[0,∞)[0,∞)

{y|y≥0}

Domain:[1,∞),{x|x≥1}

28.

EXAMPLE 1 Find the mean deviation about the mean for the following data15, 17, 10, 13,7, 18, 9, 6, 14, 11

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29.

2 , then what is x equal to?80. If x+1+2+(A) 1013(B) 10(C) 1017(D) 10

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30.

Calculate the speed of sound in air at N.T.P.if thedensity of air at N.T.P. is 1.29 kg/m and y for air is1.4

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31.

I 4. A certain sum of money at compound interest becomes?7396 in two years andRs7,950.70 in three years. Find the rate of interest.

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32.

le 32. A manufacturer's catalogued price of a scooty is 45000, but he allows the retailer 30%discount. What does the retailer pay for the scooty?

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33.

If cos (40% xo ).ur sin-30°itherA) 2024.B) 40C) 60°

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34.

8. A sum of money doubles itself at compoundinterest in 15 years. In how many years it willbecome eight times ?

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If the sum doubles (x2) in 15 years.

Then it to become 2*2*2 = 8 times as large it should double three times.

so three 15 years time period are needed, which is 3*15 = 45 years.

So the answer is 45

35.

At what rate percent will a principal amount of Rs.1000becomes Rs.1102.50 in 2 years at compound interest?

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36.

IF8809 6 , 7111: 02172 0 ,6666-40000 4,33330THEN,2581 ?

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37.

III6666666666666I + 66666I + 6666| + 666| + 66"+ 6

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10100100010000100000100000010000000sab ke sab live wise answer hai isliye Ab Mujhe like karo, jawab mat khao a b c d e f g h s s i number likhe Hain

38.

\left. \begin array l = 1 %2B 6666 \\ = \quad 1 %2B 666 \end array \right.

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a. 10000b. 100000Yeh Hai Nabi Ka answer Ab Mujhe like karo please

39.

1 1 the mapping fand g are given byf ((1,2)(3,5),(4, 1) andg (2, 3).(5, 1).(1.3))then write fog

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40.

he sum of two numbers is 80 and the greater number exceeds twiceFind the numbers.

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Let smaller number be nThen greater number = 2n + 11

Given,n + 2n + 11 = 803n = 80 - 11 = 693n = 69n = 69/3 = 23

Smaller number = 23Greater number = 2*x + 11 = 2*23 + 11 = 46 +11 = 57

thankyou

41.

12 The difference between squares of two numbers is 120. The square of smallernumber is twice the greater number. Find the numbers

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plants whose stem we eat

plants whose stem we eat

Let the numbers be x and y where x>y so,

x^2 - y^2 = 120.....(1)

y^2 = 2 x.....(2)

Putting (2) in (1), we get

x^2 - 2x = 120

x^2 - 2x - 120 = 0

x^2 - 12x + 10x - 120 = 0

x(x -12) +10(x - 12) = 0

(x-12)(x+10) = 0

So x can be 12 or -10, but we are given that the square of smaller number is twice the larger number, therefore the square of any number cant be negative,

Thus x cant take value of -10

So x = 12, so y^2 = 2 (12)

y^2 = 24

So y = √24 or - √24

y = 2√6 or -2√6

Hence the numbers are 12 and 2√6 or 12 and -2√6

42.

The difference between squares of two numbers is 120. The square of smallernumber is twice the greater number. Find the numbers.i)

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Let the numbers be x and y where x>y so,

x^2 - y^2 = 120.....(1)

y^2 = 2 x.....(2)

Putting (2) in (1), we get

x^2 - 2x = 120

x^2 - 2x - 120 = 0

x^2 - 12x + 10x - 120 = 0

x(x -12) +10(x - 12) = 0

(x-12)(x+10) = 0

So x can be 12 or -10, but we are given that the square of smaller number is twice the larger number, therefore the square of any number cant be negative,

Thus x cant take value of -10

So x = 12, so y^2 = 2 (12)

y^2 = 24

So y = √24 or - √24

y = 2√6 or -2√6

Hence the numbers are 12 and 2√6 or 12 and -2√6

43.

EXERCISE 1.1. Is gero a ational number? Can you write i in he fowhere p andg are integersis zero a rational number? Can you write it in the formand q #0?

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44.

-an.cach and three shirts marked atretailer wants toget aprofitof10% aftergiving a discount of 12.5 %on an article. What shbe the marked price of the article whose cost price is 1470?d8HOTS

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45.

tan A tan B+ tan A cot B7. For A B 90, prove that vsin A sec Bs= sec A.OR7. Prove the resultseco-tanosec θ + tan θ1-2sec θ , tan θ + 2 tan2 θ

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46.

2. For what value of p, x - b is a zero of the polynomial -(a+ bs ap-e

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47.

interest lof', Jul(3) Rs 1736 (4) Rs 1680(1) Rs 1765 (2) Rs 17473. A sum of money on compound interest becomes 8 times in 3 years. Findthe rate of interest(3) 40% (4) 60%(180%(2) 100%amounts to Bs 3840 in 2 years and

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The answer to your question is 40%

48.

4. of 50 is equal to45a) 30b) 40c) 50

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(4/5) of 50 is (4/5) x 50 =40

thx

49.

1500 is divided between A, B and C in the ratio 1: 3:5. Bs share isl750

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Let the ratio be x so,

A, B, C will get x, 3x, 5x parts

According to questionx + 3x + 5x = 1500

9x = 1500

x = 1500/9 = 500/3

So, B will get 3x = 3 × 500/3 = ₹ 500

50.

5. 50% of 3 kg =

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