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.

Q17. Differentiate sin (cosx²) w.r.t. x

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2.

Differentiate (sin 2x)" + sin-1 V3x with respect to x.

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wrong answer

3.

Differentiate sin 2x w.r. to x by Ist Principle.

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4.

35. Differentiate sin x w.r.t x form first principles

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5.

Differentiate wrt x\sqrt{\frac{(1+\sin 2 x)}{(1-\sin 2 x)}}

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thank you very much

6.

integrate wrt x9xe^3x

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7.

36. The sum of the roots of 3x2 +5x 2 is

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thanx

8.

22. Find the domain of the following functions :yo li) log(4x – 3) Elielog(9 - x2)

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9.

Find the storm AP the sum is 36product is 1620

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10.

Different sinx wrt x from 1 principle.

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11.

Different sinx wrt x from 1 principle.1.

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12.

.Q-19 Prove that : 3 cos 68º.cosec22°43º. tan 47º. tan 12°tan 600 tan 780-6-V3

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3 cos 68. cosec 22 - 1/2 tan 43 . tan 47. tan 12. tan 60 . tan 78

⇒3 sin 22 . cosec 22 - 1/2 cot 47 .tan 47 .cot 78 .√3 . tan 78

(since cos 68 = sin 22, tan 43 = cot 47,tan 12 = cot 78 and tan 60 =√3)

⇒3 * 1/cosec 22 * cosec 22 - 1/2 cot 47 * 1/cot 47 . cot 78 . 1/cot 78 *√3

⇒3 -√3/2

⇒(6 -√3)/ is the answer 2

13.

\operatorname { tan } \frac { \pi } { 12 } + \operatorname { tan } \frac { \pi } { 6 } + \operatorname { tan } \frac { \pi } { 12 } \operatorname { tan } \frac { \pi } { 6 } = 1

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14.

65. The angle between the pair of tangents drawn tothe ellipse 3x2 +2y 5 from the point12(a) tan(b) tan (6/5)ortan"(12)(d) tan-1(12.5)

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x^2/5/3+y^2/5/2=1y=mx+-√5m^2/3+5/2passing through (1,2)4m^2+24m-9=0M1+m2=-6and m1m2=-9/4tan^2A=(m1+m2)^2-4m1m2/(1+m1m2)^2=144/5tanA=12/√5A=tan^-1(12/√5)

15.

If(cosx) -(cos y) find ay

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16.

9 x \sqrt { 5 } + \operatorname { log } _ { x } 5 x = \frac { 9 } { 4 } + \operatorname { log } _ { x } ^ { 2 } \sqrt { 5 }

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17.

( 0 \operatorname { log } 5 + \operatorname { log } ( 5 x + 1 ) = \operatorname { log } ( x + 5 ) + 1

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18.

Differentiate the followi. (i) sin 2x

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19.

Differentiate the following from the firstprinciple:-11. sin-1(2x)2. tan2

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20.

If x = acose and y = bsinθ then find ay whereθ is a parameter.d2dx2

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Use parametric differentiation to do it first calculate dy/d(theta) =bcos() now dx/d(theta)=-asin() now y`=-bcos/asin and then dy`/d(theta)= -b/a×(-sin^2-cos^2)/sin^2=bcosec^2/a now d^2y/dx^2=(bcosec^2/a)-asin=-b/a^2 cosec^3

21.

First term of an arithmetic progress is 1, last term is 11 and sum 36. Find thenumber ofterms and common difference.

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please find the common difference

22.

Doind the sum ofindicated number ofterms in each ofthe following A.Ps(i) 16, 11.6 , 23 termsTHIs(ii) 0.5,-1.0,-1.5, ...., 10 terms4' 2

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23.

3.following are zeroes of the poly(oi p(vii)期 H-1, -73,-34. Find the zeno of the polynomial in each of the follapx)x-5(v) p(x)= 3xa+d,c#0,c,dare realnumbers.mi) p(1)Remainder Theorems consider two numbers 15 and 6. You know that vtient 2 and remainder 3. Do you remember h153(6 x 2)+3e that the remainder 3 is less than the di12 (6x 2)+0t is the remainder here? Here the remaindeof 12 or 12 is a multiple of 6.ow, the question is: can we divide one polynomi

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24.

Find ay, whendx1. x = at?, y = 2at

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x = at²

y = 2at

dy/dx

d(2at)/ d(at²)

divide by dt

d(2at)dt/dt d(at²)

2a/ 2at

1/t

25.

llcos:sin-1:2,thenfindthevalueof4cos θ + 2 sin θ10.From the given figure, prove that θ +0-90Also prove that there are two other rightangled triangles. Find sina, cos β andtan .1520129E16

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26.

Product of its zero respectively1/4,1

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Any quadratic equation having a and b as zeroes can be written as

x² - ( a + b)x + ab = 0

x² - ( 1/4 + 1) x + 1/4 × 1 = 0

x² - 5x/4 + 1/4 = 0

4x² - 5x + 1 = 0

27.

ayFind-, if x = a( θ + sin θ ), y = a(1 + cos θ ).ax

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28.

it sina 0 - 3 sin a caso then plonethat tan olar 12

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1+sin^2 theta=3 sintheta cos theta (we know that sin^2 theta + cos^2 theta =1)

= ( sin^2 theta + cos^2 theta ) + sin ^2 theta = 3 sin theta cos theta

= sin^2 theta + cos^2 theta + sin ^2 theta = 3 sin theta cos theta

= cos^2 theta + 2 sin^2 theta = 3 sin theta cos theta

On dividing by cos^2 theta, we get

= 1 + 2 tan^2 theta = 3 tan theta

Let tan theta = b

2b^2 - 3b + 1 = 0

= (2b-1)(b-1) = 0

b = 1 or 1/2

So, tan theta = 1 or 1/2.

29.

\frac { 1 - \operatorname { cos } \theta + \operatorname { sin } \theta } { 1 + \operatorname { cos } \theta + \operatorname { sin } \theta } \text { interms of } \operatorname { tan } \frac { \theta } { 2 }

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(1-cosx+sinx)/(1+cosx+sinx)=(2sin^2x/2+2sinx/2cosx/2)/(2cos^2x/2+2sinx/2cosx/2)=2sinx/2(sinx/2+cosx/2)/2cosx/2(sinx/2+cosx/2)=tanx/2

30.

wwwma1. Find ten rational numbers between andles

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it's shortcut. hope u like this answer

31.

log x5.dxx2

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32.

y=\frac{x^{2}-1}{x^{2}+1} wrt x

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33.

(vii) Differentiate sin-1 (3x 4x3) with respectto х.

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34.

3 Differentiate sin (cos(x)) with respect to x.ition for

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35.

le 9.6. Differentiate sin 2x w.r. to x by Ist Principle.

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36.

2. What are the different ways in which infectiousdiseases can spread ?

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37.

Prove that if the number ofterms of an A. P. is odd then the middle term is the A M.between the first and last terms

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i) Let the 1st term of the AP be 'a' and its common difference be 'd'

ii) As the number of terms are odd, the nth term is (2n + 1)

iii) Hence nth term (last tern) is: a + (2n + 1 - 1)d = a + 2nd

iv) So Arithmetic mean between 1st & last term is:(a + a + 2nd)/2 = 2(a + nd)/2 = a + nd

v) The middle term of (2n + 1)th term is: (2n + 1 + 1)/2 = (n + 1)Hence middle term is (n + 1)th term = a + (n + 1 - 1)d = a + nd

Thus from steps (iv) & (v),

Middle term = AM of 1st and last terms.

38.

AT WHICH SUM WILL THE SIMPLEINTEREST AT THE RATE OF 3 3/4, PERANNUM BE 210 IN 2 1/3

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Sum = (100 * 210)/(15/4 * 7/3)

= 21000 * 4/35

= 2400.

39.

If the divisor, gootient and remainder are.10o, 28 and zero respectively then thedividend is

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use dividend=quotient*divisor+remainder Answer is 2800

quotient*divisor=dividend28*100=2800

use dividend=quotient*divisor+remainder answer is 2800

quotient*divisor= divident28*100=2800

the answer is 2800 use this answer

dividend is 2800 becoz it is due to dividend=divisor*quotient

quotient*divisor=dividend 28*100=2800

100×28=2800divisor× quotient=divident

use formula : Dividend= divisor*quotient + remainder then answer would be 100*28+0=2800

dividend=divisor*quotient+remainder= 100*28+0=2800+0=2800

Divident=quotient*divisor +remainder Formula is a=bq+r And answer is 2800

Let divident be xas we know, x÷100=28now, we transposed 100 in to R. H. S. then we get, x=28*100x=2800

2800 is the answer of this question

twenty eight hundred

28 X 100 + 0= 2800 dividend

quotient*divisor=divident 28*100=2800

quotient*fivisor=divident 28*100=2800

2800dividend=divisor*quotient+remainder

dividend =answer is 2800

dividend=quotient*divisor+remainder answer is 2800

dividend =divisor × qutent + remainderdividend=100×28+0=2800

dividend=quotienti division+remainder answer is 2800

the correct Answer is 2800

is. question answer zero

if the divisor qootient and remainder are 100,28 and zero respectively then the dividend is

100*28+0 = 2800 so the dividend is 2800

use divide =quentent divisor+reminder and answer is 2800

use dividend=quotient*divisor+ remainderanswer is 2800

2800 is the right answer

quotient ×divisor =divident 28×100=2800

use dividend = quotient*divisor+remainderanswer is 2800

use dividend=question*divisor+remainder Answer is 2800

2800 is. the answer

By using Dividend= Divisor* Quotient + Remainder , dividend = 100*28+0= 2800

2800 is the right answer........

the dividend is 2800

28*100=2800 is right answer

Dividend_is_2800 Becoz_it_DueDividend=Divisor*Quotientcorrect_answer

divident=divisor*quotient+remainder2800

this answer is 1000%sure 2800

2800 is the answer of the question

2800 is the answer i am correct

28×100=2800quotient*divison=dividend

the answer is 2800 it's correct answer

if the divisor qootien and remainder are 100,28 and zero respectively then the dividend is

dividend is 3.5714285714

The divine r is 3.5714285714

dividend=divisor * quotient +remainderthen we get dividend= 100*28+0 =2800+0 =2800

quotient ❌ divisor= dividend 28❌100= 2800

28×100dividend =divisor*quotient+remainder

2800 as dividend= diviser* quotient+ reminder

2800 is the correct answer

28*100dividend =divisor *quotient +reminder

use dividend=divisor×quotient+remainder therefore answer is 2800

my answer is 2800 bro am I right

use divided = question*divisor+remainder answer is 2800

Dividend=divisor×quotient+remainder =100×28+0dividend=2800 ✓

I don't know about it

right answer is 2800

2800 is the answer quotient *divisor +reminder

100*28=2800this is right answer.

use dividend=quotient*dividor+remainder answer is 2800

dividend=divisor*quotient+remainder,so,100*28+0=2800

28*100=2800 use is Answers

Dividend=Queficient *divisor+remainder 2800

if the divisor qootint and remainder are 100,28 and

answer is 2800 and so on

Dividend=quotient*divisor+remainder answer is 2800

2800 divided answer this question on my mind

40.

कि के मे. न हे कर से केक,(x —2)(x + 3)(x - 3)(x + 4) =40 AN e की प्रकृति ज्ञातकीजिए। (2013, 16, 17)o e TFTR=TTTIT

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41.

if tan A=5/12 find sinA+cosA_tanA/cosA+cosecA_cotA

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42.

find the value of sina interms of cosa

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43.

Zero Marks: 0 In all other cases.unita digit of the lent positive integer which when divided by 6, 7, 8, 9 and 12 lesremainder 1 is

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44.

Find ay , when x-e2t . cos t , y = e2t, sin t .dx

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45.

A test인42. Studenta-H 6 ad-there studenagiver E ClasA2 S tudenn서o manY

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Number of stidents that passed= 42 * 6/7 = 36 students

Number of students that failed= 42 - 36 = 6.

46.

)If y = log cos x2, then x =at ay has the value :dx

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47.

o) Find the average of the first 10 multiples of 15.

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15,30,45,60,75,90,105,130,135,150so average=(15+30+45+60+75+90+105+120+135+150)/10=825/10=82.5

48.

EXAMPLE 4.37Differentiate (sin)+ wrt

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49.

Find the sum of first 10 multiples of 6.

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Herea= 6d= 6n= 10so Sn= n/2(2a+(n-1)d)

= 5(12+54)66*5= 330

50.

EXAMPLE 3.15Differentiate sin'z by first principle.

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