Explore topic-wise InterviewSolutions in Class 12.

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your Class 12 knowledge and support exam preparation. Choose a topic below to get started.

51.

Sum of all terms in in G.P is 5 times the sum of odd terms. The common ratio is

Answer» <html><body><p>2<br/>3<br/>4<br/>5</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>
Discussion
52.

For a real number r let [r] denote the largest integer less than or equal to r. Let agt1 be a real number which is not an integer and let k be the smallest positive integer positive integer such that [a^(k)]gt[a]^(k). Thenwhich of the following statements is always true?

Answer» <html><body><p>`kle2([a]+1)^(2)`<br/>`kle2([a]+1)^(4)`<br/>`kle2^([a]+1)` <br/>`<a href="https://interviewquestions.tuteehub.com/tag/kle-3698020" style="font-weight:bold;" target="_blank" title="Click to know more about KLE">KLE</a>(1)/(a-[a])+1`</p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :By <a href="https://interviewquestions.tuteehub.com/tag/talking-662965" style="font-weight:bold;" target="_blank" title="Click to know more about TALKING">TALKING</a> <a href="https://interviewquestions.tuteehub.com/tag/different-951434" style="font-weight:bold;" target="_blank" title="Click to know more about DIFFERENT">DIFFERENT</a> values of a &amp; k. <br/> options (B) is possible.</body></html>
Discussion
53.

If bara,barb and barc are non coplanar vectors such that barb times barc=barb then

Answer» <html><body><p>`|bara|=1`<br/>`|barb|=1`<br/>`|bara|+|barb|+|barc|=3`<br/><a href="https://interviewquestions.tuteehub.com/tag/none-580659" style="font-weight:bold;" target="_blank" title="Click to know more about NONE">NONE</a> of these</p>Answer :A::<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>::<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>
Discussion
54.

A line y=mx +1 intersects the circle (x-3)^2+(y+2)^2=25 at the points P and Q . If the midpoint of the line segment PQ has x-coordinate -(3)/(5), then which one of the following options is correct ?

Answer» <html><body><p>`6 le m <a href="https://interviewquestions.tuteehub.com/tag/lt-537906" style="font-weight:bold;" target="_blank" title="Click to know more about LT">LT</a> 8` <br/>`-3le m lt -1` <br/>`4le m lt 6` <br/>`2le m lt 4` </p>Solution :(Key idea : <a href="https://interviewquestions.tuteehub.com/tag/firstly-462152" style="font-weight:bold;" target="_blank" title="Click to know more about FIRSTLY">FIRSTLY</a> find the centre of the given circle and write the coordinate of mid point (A),of line sequment PQ, since `Acbot PQ` <a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a> use (slope of AC)x(slope of PQ)`=-1`. <br/> It is given that points P and Q are intersecting points of circle. <br/> `(x-3)^2+(y+2)^2=25` .....(i) <br/> Line `"" y=mx+1 "".....(ii)` <br/> And , the mid -point of PQ is A having x-coordinate `(-3)/(<a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>)` so y-coordinate is `1-(3)/(5)m`. <br/> So, `A(-(3)/(5),1-(3)/(5)M)`<br/> From the figure, <br/> `because AC <a href="https://interviewquestions.tuteehub.com/tag/bot-25566" style="font-weight:bold;" target="_blank" title="Click to know more about BOT">BOT</a> PQ` <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/41Y_SP_MATH_SP_2019_E01_003_S01.png" width="80%"/> <br/> `rArr` (slope of AC)x (slope of PQ)` =-1`.<br/> `rArr ((-2-1+(3)/(5m))/(3+(3)/(5)))xxm=-I` <br/> `rArr 3m^2-15m+18=0` <br/> `rArr m=2or 3`.</body></html>
Discussion
55.

If the median of the data 6,7,x-2,x,18 and 21 written in ascending order is 16, then the variance of that data is

Answer» <html><body><p>`30(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)/(5)`<br/>`31(1)/(3)`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/32-307188" style="font-weight:bold;" target="_blank" title="Click to know more about 32">32</a>(1)/(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/33-307818" style="font-weight:bold;" target="_blank" title="Click to know more about 33">33</a>(1)/(3)`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :B</body></html>
Discussion
56.

In the experiment of tossing a coin n times, if the variable X denotes the number of heads and P(X=4),P(X=5),P(X=6) are in arithmetic progression then find n.

Answer» <html><body><p>11<br/>12<br/>13<br/>14</p>Answer :D</body></html>
Discussion
57.

Assuming the validity of the operations on the r.h.s. find dy/dt y = sqrt[[sin x + sqrt{{sin x + sqrt((sin x + ........)}])}]

Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :`y = {sqrt [<a href="https://interviewquestions.tuteehub.com/tag/sin-1208945" style="font-weight:bold;" target="_blank" title="Click to know more about SIN">SIN</a> + sqrt {sin x +1........]}}`<br/> sqrt(sin x + y) <br/> <a href="https://interviewquestions.tuteehub.com/tag/implies-1037962" style="font-weight:bold;" target="_blank" title="Click to know more about IMPLIES">IMPLIES</a> y^2 + sin x + y implies <a href="https://interviewquestions.tuteehub.com/tag/2y-301307" style="font-weight:bold;" target="_blank" title="Click to know more about 2Y">2Y</a> (dy)/(<a href="https://interviewquestions.tuteehub.com/tag/dx-960990" style="font-weight:bold;" target="_blank" title="Click to know more about DX">DX</a>) = cos x + dy/dx <br/> implies (2y-1) dy/dx = cos x implies dy/dx = cos x/(2y-1)`</body></html>
Discussion
58.

The value of P for which both the roots of the equation4x^(2)-20Px +(25P^(2)+15P-66)=0 are less than 2, lies in

Answer» <html><body><p>`((4)/(5), <a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)` <br/>`(2, <a href="https://interviewquestions.tuteehub.com/tag/oo-583684" style="font-weight:bold;" target="_blank" title="Click to know more about OO">OO</a>)` <br/>`(-<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>, (4)/(5))` <br/>`(-oo, -1)` </p>Answer :d</body></html>
Discussion
59.

Evaluate the following determinates |{:(1,omega),(omega,-omega):}| where omega is the cube root of unity

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a></body></html>
Discussion
60.

If the lines x-2y+3=0, 3x+ky+7=0 cut the coordinate axes in concylic points, then k=

Answer» <html><body><p>only I<br/>only II<br/>both I and II<br/>neither I nor II</p>Answer :A</body></html>
Discussion
61.

The tangent at a point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets directrics at Q and Q. A circle is drawn assuming PQ as diameter. Statement-1 This circle passes through the foci of the ellipse because Statement-2 PQ subtends 90^(@) at the corresponding focus.

Answer» <html><body><p>Statement 1 is True, Statement -<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a> is True, Statement -2 is a <a href="https://interviewquestions.tuteehub.com/tag/correct-409949" style="font-weight:bold;" target="_blank" title="Click to know more about CORRECT">CORRECT</a> exlpanation for Statement 1<br/>Statement 1 is True, Statement -2 is True, Statement -2 is NOT a correct exlpanation for Statement 1<br/>Statement-1 is True Statement-2 is <a href="https://interviewquestions.tuteehub.com/tag/false-459184" style="font-weight:bold;" target="_blank" title="Click to know more about FALSE">FALSE</a><br/>Statement-1 is False, Statement-2 is True</p>Answer :A</body></html>
Discussion
62.

If A = [(0,1),(1,0) ]then A^(2) is equal to :

Answer» <html><body><p>`[(0,1),(1,0)]` <br/>`[(1,0),(1,0)]`<br/>`[(1,0),(0,1)]`<br/>`[(0,1),(0,1)]` </p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :A</body></html>
Discussion
63.

If (1+x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + "….." + C_(n)x^(n), then C_(0) - (C_(0) + C_(1)) +(C_(0) + C_(1) + C_(2)) - (C_(0) + C_(1) + C_(2) + C_(3))+"….."(-1)^(n-1) (C_(0) + C_(1) + "……" + C_(n-1)) is (where n is even integer and C_(r) = .^(n)C_(r))

Answer» <html><body><p>a positive value<br/>a negative value<br/>divisible by `<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>^(n-1)`<br/>divisible by `2^(n)`</p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :For `n = 2m`, the given expression is <br/> `C_(<a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a>)-(C_(0)+C_(1))+(C_(0)+C_(1)+C_(2))-(C_(0)+C_(1)+C_(2)+C_(3))+"....."(-1)^(n-1)(C_(0)+C_(1)+"....."+C_(n-1))` <br/> `= C_(0)-(C_(0)+C_(1))+(C_(0)+C_(1)+C_(2))-(C_(0)+C_(1)+C_(2)+C_(3))+"....."-(C_(0)+C_(1)+"...."+C_(2m-1))` <br/> `= - (C_(1)+C_(3)+C_(<a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>)+"...."+C_(2m-1))` <br/> `= - (C_(1)+C_(3)+C_(5)+"......."+C_(n-1)) = -2^(n-1)`</body></html>
Discussion
64.

If the remainders obtained when a polynomial f(x) is divided with x, x-1, x+1 respectively are 1, -2, 3 then find the remainder when f(x) is divided with x^(3)-x ?

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(-<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)(<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>^(2)+5x-2)`</body></html>
Discussion
65.

Compute the following : (i) [{:(a,b),(-b,a):}]+[{:(a,b),(b,a):}] (ii) [{:(a^(2)+b^(2),b^(2)+c^(2)),(a^(2)+c^(2),a^(2)+b^(2)):}]+[{:(2ab,2bc),(-2ac,-2ab):}] (iii)[{:(-1,4,-6),(8,5,16),(2,8,5):}]+[{:(12,7,6),(8,0,5),(3,2,4):}] (iv) [{:(cos^(2)x,sin^(2)x),(sin^(2)x,cos^(2)x):}]+[{:(sin^(2)x,cos^(2)x),(cos^(2)x,sin^(2)x):}]

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :(i) `=[{:(2a,2b),(0,2a):}]`<br/> (<a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a>) `=[{:((a+b)^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>),(b+c)^(2)),((a-c)^(2),(a-b)^(2)):}]`<br/> (<a href="https://interviewquestions.tuteehub.com/tag/iii-497983" style="font-weight:bold;" target="_blank" title="Click to know more about III">III</a>) `=[{:(11,11,0),(16,5,21),(5,10,9):}]` <br/> (<a href="https://interviewquestions.tuteehub.com/tag/iv-501699" style="font-weight:bold;" target="_blank" title="Click to know more about IV">IV</a>) `=[{:(1,1),(1,1):}]`</body></html>
Discussion
66.

The world bank measures the amount of land devoted to agriculture among all 196 countriesin the world. The results from 9 of the countries are given in the table above. The median percent of of agrilcultural land for all 196 countriesin 34.95%. What is the difference between the median percent of agricultural land for these 9 countries and the median for all 196 countries?

Answer» <html><body><p>0.0115<br/>0.0419<br/>0.0965<br/>0.1995</p>Answer :A</body></html>
Discussion
67.

Find the Principle values of the following : tan^(-1)(-sqrt(3))

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(-<a href="https://interviewquestions.tuteehub.com/tag/pi-600185" style="font-weight:bold;" target="_blank" title="Click to know more about PI">PI</a>)/<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>`</body></html>
Discussion
68.

Evaluate : (i) Lim_(nrarroo) sum_(r=0)^(nrarr1) (1)/(sqrt(n^(2)-r^(2))) , (ii)Lim_(nrarroo) 3/n[1+sqrt((n)/(n+3))+sqrt((n)/(n+6))+sqrt((n)/(n+9))+"....."+sqrt((n)/(n+3(n-1)))] (iii) lim_(nrarroo) (sum_(r=1)^(2n) (3nr^(2)+2n^(2)r))

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :N//A</body></html>
Discussion
69.

A pair of dice is rolled. What is the probability that neither die shows a 2 given that they sum to 7.

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>)`</body></html>
Discussion
70.

How many 4 digit numbers are there, without repetition of digits, If each number is divisible by 5 ?

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :952</body></html>
Discussion
71.

Reshma wishes to mix types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs. 60/kg and Food Q costs Rs. 80/kg. Food P contains 3 units/kg of vitamin A and 5 units/kg of Vitamin B while food Q contains 4 units/kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/rs-625947" style="font-weight:bold;" target="_blank" title="Click to know more about RS">RS</a>. <a href="https://interviewquestions.tuteehub.com/tag/160-277205" style="font-weight:bold;" target="_blank" title="Click to know more about 160">160</a></body></html>
Discussion
72.

If (1+x+x^2+____x^100) (1-x+x^2-x^3+___+x^150) =a_0+a_1x+a_2x^2+____ +a_250 x^250 Then the value of a_0+a_2 + a_4+____ + a_250 is equal to ___

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :<a href="https://interviewquestions.tuteehub.com/tag/put-11868" style="font-weight:bold;" target="_blank" title="Click to know more about PUT">PUT</a> x=1 we get `<a href="https://interviewquestions.tuteehub.com/tag/101-266127" style="font-weight:bold;" target="_blank" title="Click to know more about 101">101</a> <a href="https://interviewquestions.tuteehub.com/tag/xx-747671" style="font-weight:bold;" target="_blank" title="Click to know more about XX">XX</a> 1 = a_0+a_1+a_2`____+`a_(250)` <br/> Put x=-1 we get `1xx151=a_0-a_1+a_2` ___`a_250` <br/> `252=2(a_0+a_2+____a_250)` <br/> `a_0+a_2+a_4`+___+`a_250`= <a href="https://interviewquestions.tuteehub.com/tag/126-271371" style="font-weight:bold;" target="_blank" title="Click to know more about 126">126</a></body></html>
Discussion
73.

If log_(e)5, log_(e)(5^(x) -1) and log_(e)(5^(x)-(11)/(5)) are in A.P then the values of x are

Answer» <html><body><p>`log_(5) <a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a> and log_(5)<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>`<br/>`log_(3)4 and log_(4)3`<br/>`log_(3) 4 and log_(3)5`<br/>`log_(5)<a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a> and log_(5)<a href="https://interviewquestions.tuteehub.com/tag/7-332378" style="font-weight:bold;" target="_blank" title="Click to know more about 7">7</a>`</p>Answer :A</body></html>
Discussion
74.

Three numbers are chosen at random without replacement from {1,2,3,….8}. The probability that their minimum is 3, given that their maximum is 6, is

Answer» <html><body><p>`(3)/(<a href="https://interviewquestions.tuteehub.com/tag/8-336412" style="font-weight:bold;" target="_blank" title="Click to know more about 8">8</a>)`<br/>`(1)/(5)`<br/>`(1)/(4)`<br/>`(2)/(5)`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html>
Discussion
75.

Let W(x,y) =x ^(2) + xy+y ^(2) and x = sin t, y = cos t in t in (0, 2pi) verify the above theorem.

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :The <a href="https://interviewquestions.tuteehub.com/tag/theorem-706777" style="font-weight:bold;" target="_blank" title="Click to know more about THEOREM">THEOREM</a> is <a href="https://interviewquestions.tuteehub.com/tag/verified-2323104" style="font-weight:bold;" target="_blank" title="Click to know more about VERIFIED">VERIFIED</a></body></html>
Discussion
76.

Compute the length of the segment of the straight line rho= a sec (varphi- (pi)/(3)) between varphi= 0 and varphi=(pi)/(2)

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(<a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a> <a href="https://interviewquestions.tuteehub.com/tag/sqrt3-3056952" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT3">SQRT3</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>) a`</body></html>
Discussion
77.

If veca=(3hati-hatj)/(sqrt(10)) and vecb=(hati+3hatj+hatk)/(sqrt(11)), then the value of (2veca+vecb)".[(veca xx vecb)xx(veca-3vecb)]

Answer» <html><body><p>5<br/>7<br/>8<br/>9</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html>
Discussion
78.

Integrate the following functions (sin^-1x)^2

Answer» <html><body><p></p>Solution :`<a href="https://interviewquestions.tuteehub.com/tag/int-11513" style="font-weight:bold;" target="_blank" title="Click to know more about INT">INT</a> (sin^-1 x)^2 <a href="https://interviewquestions.tuteehub.com/tag/dx-960990" style="font-weight:bold;" target="_blank" title="Click to know more about DX">DX</a> = int 1 <a href="https://interviewquestions.tuteehub.com/tag/xx-747671" style="font-weight:bold;" target="_blank" title="Click to know more about XX">XX</a> (sin^-1 x)^2 dx` <br/> =`(sin^-1 x)^<a href="https://interviewquestions.tuteehub.com/tag/2x-301182" style="font-weight:bold;" target="_blank" title="Click to know more about 2X">2X</a>- int 2 sin^-1 x 1/sqrt(1-x^2) x dx` <br/> =`x (sin^-1x)^2 + int (-2x)/sqrt(1-x^2) xx sin^-1x dx` <br/> =`x (sin^-1x)^2+ int (-2x)/sqrt(1-x^2) dx - int (1/sqrt(1-x^2) int (-2x)/sqrt(1-x^2) dx) dx` <br/> =`x(sin^-1x)^2+ sin^-1x xx 2 sqrt(1-x^2)- int1/sqrt(1-x^2) 2sqrt(1-x^2) dx` <br/> =`x (sin^-1 x)^2 +2 sqrt(1-x^2) sin^-1 x- 2x+c`</body></html>
Discussion
79.

Refers to question 15.Determine the maximum distance that the man can travel.

Answer» <html><body><p><br/></p>Solution :Referring to solution 15, we have <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_NCERT_EXE_MATH_XII_C12_S01_020_S01.png" width="&lt;klux&gt;80&lt;/klux&gt;%"/> <br/> <a href="https://interviewquestions.tuteehub.com/tag/maximise-2172432" style="font-weight:bold;" target="_blank" title="Click to know more about MAXIMISE">MAXIMISE</a> Z=x+y subject to <br/> `2x+3y le 120, 8x+5y le 400, x ge 0, y ge 0` <br/> On solving we get `8x +5y=400 and 2x+3y=120 we get ` <br/> `(30)/(7),(80)/(7)` and (0,40) <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_NCERT_EXE_MATH_XII_C12_S01_020_S02.png" width="80%"/> <br/> <a href="https://interviewquestions.tuteehub.com/tag/hence-484344" style="font-weight:bold;" target="_blank" title="Click to know more about HENCE">HENCE</a> the maximum distance that the man can <a href="https://interviewquestions.tuteehub.com/tag/travel-1426745" style="font-weight:bold;" target="_blank" title="Click to know more about TRAVEL">TRAVEL</a> is `54(2)/(7)<a href="https://interviewquestions.tuteehub.com/tag/km-1064498" style="font-weight:bold;" target="_blank" title="Click to know more about KM">KM</a>`.</body></html>
Discussion
80.

int e^(2x) (2sinx + cosx) dx =

Answer» <html><body><p>`e^(2x)` <a href="https://interviewquestions.tuteehub.com/tag/sinx-1210519" style="font-weight:bold;" target="_blank" title="Click to know more about SINX">SINX</a> + <a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a><br/>`e^(2x)` cosx + c<br/>`2e^(2x)` <a href="https://interviewquestions.tuteehub.com/tag/sin-1208945" style="font-weight:bold;" target="_blank" title="Click to know more about SIN">SIN</a> 2x + c<br/>`2e^(2x)`cosx + c</p>Answer :A</body></html>
Discussion
81.

If A+B+C=90^(@) then (cos 2A+cos 2B+cos 2C-1)/(sin A sin B sin C)=

Answer» <html><body><p>2<br/>4<br/>3<br/>1</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html>
Discussion
82.

If int(dx)/(1+e^(x))=x+f(x)+C , then f(x) is equal to

Answer» <html><body><p>`log (<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a> + <a href="https://interviewquestions.tuteehub.com/tag/e-444102" style="font-weight:bold;" target="_blank" title="Click to know more about E">E</a>^(x))` <br/>`log (1)/(1+e^(x))`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a> log(1 + e^(x))` <br/>`(x+e^(x))/(1+e^(x))`</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html>
Discussion
83.

The mid point of the chord x+2y+3=0 of the hyperbola x^(2)-y^(2)=4 is

Answer» <html><body><p>(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>,<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)<br/>(2,1)<br/>(-3,0)<br/>(1,-2)</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :D</body></html>
Discussion
84.

At what points in the interval [0, 2pi], does the function sin (2x) attain its maximum value ?

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>=(<a href="https://interviewquestions.tuteehub.com/tag/pi-600185" style="font-weight:bold;" target="_blank" title="Click to know more about PI">PI</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a>)` and `(<a href="https://interviewquestions.tuteehub.com/tag/5pi-1900435" style="font-weight:bold;" target="_blank" title="Click to know more about 5PI">5PI</a>)/(4)`</body></html>
Discussion
85.

If the angle between the two equal circles with centres (-2,0),(2,3) is 120^@then the radius of the circle is

Answer» <html><body><p>5<br/>3<br/>1<br/>2</p>Answer :A</body></html>
Discussion
86.

If bar(a) = overset(^)(i) + overset(^)(j) - overset(^)(k), bar(b) = 2 overset(^)(i) + 3 overset(^)(j) + 2 overset(^)(k), bar(c ) = - overset(^)(i) + overset(^)(j) +3 overset(^)(k) then the volume of tetrahedron is

Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a> <a href="https://interviewquestions.tuteehub.com/tag/sq-1223093" style="font-weight:bold;" target="_blank" title="Click to know more about SQ">SQ</a>. unit<br/>2 sq. unit<br/>3 <a href="https://interviewquestions.tuteehub.com/tag/cubic-940181" style="font-weight:bold;" target="_blank" title="Click to know more about CUBIC">CUBIC</a> unit<br/>4 cubic unit.</p>Answer :A</body></html>
Discussion
87.

The tangents drawn from the origin x^(2)+y^(2)-2rx-2hy+h^(2)=0 are per-pendicular if

Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/h-1014193" style="font-weight:bold;" target="_blank" title="Click to know more about H">H</a>=<a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a>+<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>`<br/>`h=-r`<br/>`r^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)+h^(2)=1`<br/>`r^(2)=h^(2)`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :D</body></html>
Discussion
88.

The real values of 'a' for which the quadratic equation 2x^2 - (a^3 + 8a - 1) x + a^2 - 4a = 0 possess roots of opposite sign is given by:

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`<a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a> <a href="https://interviewquestions.tuteehub.com/tag/lt-537906" style="font-weight:bold;" target="_blank" title="Click to know more about LT">LT</a> a lt <a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a>`</body></html>
Discussion
89.

In the spacethe equationby + cz + d = 0represents a plane perpendicular to the

Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/yoz-2342044" style="font-weight:bold;" target="_blank" title="Click to know more about YOZ">YOZ</a> - <a href="https://interviewquestions.tuteehub.com/tag/plane-1155510" style="font-weight:bold;" target="_blank" title="Click to know more about PLANE">PLANE</a> <br/><a href="https://interviewquestions.tuteehub.com/tag/zox-2345322" style="font-weight:bold;" target="_blank" title="Click to know more about ZOX">ZOX</a> - plane <br/><a href="https://interviewquestions.tuteehub.com/tag/xoy-747554" style="font-weight:bold;" target="_blank" title="Click to know more about XOY">XOY</a> - plane <br/>None of these </p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :A</body></html>
Discussion
90.

k-^n C_1 (k-1)+^n C_2 (k-2)-…..+(-1)^n ""^n C_n (k-n)=

Answer» <html><body><p>0<br/><a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a><br/>`-1`<br/>none</p>Answer :A</body></html>
Discussion
91.

Locus of perpendicular from center upon normal to the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1 is

Answer» <html><body><p>`(x^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)-+y^(2))^(2)((a^(2))/(x^(2))+(b^(2))/(y^(2))) =(a^(2)-b^(2))^(2)`<br/>`(x^(2)+y^(2))^(2)((a^(2))/(x^(2))-(b^(2))/(y^(2)))=(a^(2)+b^(2))^(2)`<br/>`(x^(2)+y^(2))^(2) ((x^(2))/(a^(2))-(y^(2))/(b^(2))) =(a^(2)+b^(2))^(2)`<br/>None of these </p>Solution :Let the <a href="https://interviewquestions.tuteehub.com/tag/foot-994954" style="font-weight:bold;" target="_blank" title="Click to know more about FOOT">FOOT</a> of perpendicular from center upon any normal be `P(h,k)` Then <a href="https://interviewquestions.tuteehub.com/tag/equation-974081" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATION">EQUATION</a> of normal to hyperbola is <br/> `(y-k) =- (h)/(k) (x-h)` <br/> or `<a href="https://interviewquestions.tuteehub.com/tag/hx-492904" style="font-weight:bold;" target="_blank" title="Click to know more about HX">HX</a> + ky = h^(2) +k^(2)` (1) <br/> Also normal at any point `<a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a>(a sec theta, tan theta)` on the hyperbola is <br/> `(ax)/(sec theta) +(by)/(tan theta) = a^(2) + b^(2)` (2) <br/> Comparing ratio coefficients of equations (1) and (2), <br/> We get `((a)/(sec theta))/(h)=((b)/(tan theta))/(k) =(a^(2)+b^(2))/(h^(2)+k^(2))` <br/> `rArr sec theta = (a(h^(2)+k^(2)))/(h(a^(2)+b^(2)))` and `tan theta = (b(h^(2)+k^(2)))/(k(a^(2)+b^(2)))` <br/> Squaring and subtracting `(x^(2)+y^(2))^(2) ((a^(2))/(x^(2))-(b^(2))/(y^(2))) = (a^(2)+b^(2))^(2)`</body></html>
Discussion
92.

If a,b,c are rational , the roots of equationx^2-2ax+(a^2-b^2+2bc-c^2)=0 are :

Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/rational-613044" style="font-weight:bold;" target="_blank" title="Click to know more about RATIONAL">RATIONAL</a> <br/>irrational<br/>equal<br/>imaginary </p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :A</body></html>
Discussion
93.

Match the following. I. int (1)/(sqrt(4-x^(2)))dx= "" a) (1)/(2) Sinh^(-1))(x)/(2)+c II. int (1)/(sqrt(4+x^(2)))dx= "" b)Cosh^(-1)(x)/(2)+c III. int (1)/(x^(2)-4))dx= "" c) "Sin"^(-1)(x)/(2)+c

Answer» <html><body><p>a,<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>,c<br/>b,c,a<br/>c,a,b<br/>a,c,b</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a></body></html>
Discussion
94.

|{:(sin35^@,-cos35^@),(sin55^@,cos55^@):}|=.........

Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a><br/>0<br/>`-1`<br/>2</p>Answer :A</body></html>
Discussion
95.

A vector vecr is inclined to x-axis at 45^(@) and to y-axis at 60^(@). If |vecr|=8 units find vecr.

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :N/A</body></html>
Discussion
96.

The scatterplot above shows the numbers of people diagnosed with melanoma, in ten - thousands, from 1940 to 1970. Based on the data shown in the figure, which of the following values is closest to the range of the number of incidences of melanoma between 1945 and 1950?

Answer» <html><body><p>5000<br/>10000<br/>17000<br/>36000</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>
Discussion
97.

Given PV=C (constant). The percentage of increase in V corresponding to an increase 1% in the value of P is

Answer» <html><body><p>0<br/>1<br/>-1<br/>2</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>
Discussion
98.

A bag contain 6 white and 4 red balls if 3 balls are drawn at random the probability of getting 1 red ball and 2 white balls is

Answer» <html><body><p>`1/2`<br/>`2/3`<br/>`3/10`<br/>`2/15`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>
Discussion
99.

Find the value of the integral underset(-pi//2)overset(pi//2)int sin^(2) theta . Cos^(7)theta d theta

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(<a href="https://interviewquestions.tuteehub.com/tag/32-307188" style="font-weight:bold;" target="_blank" title="Click to know more about 32">32</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/fract-1t-3-315-307072" style="font-weight:bold;" target="_blank" title="Click to know more about 315">315</a>)`</body></html>
Discussion
100.

Evalute the following integrals int (1)/(x) sqrt((x - 1)/(x + 1))dx =

Answer» <html><body><p>`cosh^(-1)<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a> - sec^(-1) ` x + <a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a><br/>`cosh^(-1) x + sec^(-1) ` x + c<br/>`<a href="https://interviewquestions.tuteehub.com/tag/sinh-2272520" style="font-weight:bold;" target="_blank" title="Click to know more about SINH">SINH</a>^(-1) x - sec^(-1)` x + c<br/>`sinh^(-1) x - "cosec"^(-1) ` x + c</p>Answer :A</body></html>
Discussion