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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 95351. |
If in the expansion of `(1/x+xtanx)^(5)` and `xgt0` the ratio of `4^(th)` term to the `2^(nd)` term is `2/27 pi^(4)`, the value of `[x]` can be (where `[.]` is greatest integer function) |
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Answer» Correct Answer - 1 `(T_(4))/(T_(2))=2/27pi^(4)impliesx^(2)tanx=1/(3sqrt(3))pi^(2)` `implies x=(pi)/3` |
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| 95352. |
if `veca` and `vecb` non-zero ad non-collinear vectors, thenA. `veca xx vecb=[vecavecbhati]hati+[vecavecbhatj]hatj+[vecavecbhatk]hatk`B. `vecavecb=(veca.hati)+(vecahatj)(vecb.hatj)+(veca.hatk)(vecb.hatk)`C. if `vecu=hata-(hata.hatb)hatb` and `vecv=hata xx hatb`, then `|vecv|=|vecu|`D. if `vecc=vecaxx(vecaxxvecb),` then `vecc.veca=0` |
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Answer» Correct Answer - A::B::C::D (A) `bar(a)xxbar(b)=a_(1)hat(i)+a_(2)hat(j)+a_(3)hat(k)` Take dot with `hat(i)` `[bar(a)bar(b)hat(i)]=a_(1)` Similarly `a_(2)=[bar(a)bar(b)hat(j)]` `a_(3)=[bar(a)bar(b)hat(k)]` (B) take `bar(a)=a_(1)hat(i)+a_(2)hat(j)+a_(3)hat(k)` `bar(b)=b_(1)hat(i)+b_(2)hat(j)+b_(3)hat(k)` (C) `|bar(mu)|=sqrt(|hat(a)|^(2)+(hat(a).hat(b))^(2)|hat(b)|^(2)-2(hat(a).hat(b))(hat(a).hat(b))` `|bar(mu)|= sqrt(1+(hat(a).hat(b))^(2)-2(hat(a).hat(b))^(2))=|sintheta|` `barv=|sintheta|` (D) `bar(c).bar(a)=0` (obvious) |
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| 95353. |
if `veca` and `vecb` non-zero ad non-collinear vectors, thenA. `vecaxxvecb=[vecavecbhati]hati+[vecavecbhatj]hatj+[vecavecbhatk]hatk`B. veca.vecb=(veca.hati)(vecb.hati)+(veca.hatj)(vecb.hatj)+(veca.hatk)(vecb.hatk)`C. if `vecu=hata-(hata.hatb)hatb` and `vecv=hataxxhatb` then `|vecv|=|vecu|`D. if `vecc=vecaxx(vecaxxvecb)`, then `vecc.veca=0` |
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Answer» Correct Answer - A::B::C::D (A). `vecaxxvecb=a_(1)hati+a-(2)hatj+a_(3)hatk` Take dot with `hati` `[overline(a)overline(b)hati]=a_(1)` similarly `a_(2)=[overline(a)overline(b)hatj]` `a_(2)=[overline(a)overline(b)hatk]` (B) take `overline(a)=a_(1)hati+a_(2)hatj+a-(3)hatk` `overline(b)=b_(1)hati+b_(2)hatj+b_(3)hatk` (C) `|overline(u)|=sqrt(|hata|^(2)+(hata.hatb)^(2)|hat(b)|^(2)-2(hata.hatb)(hat(a).hat(b)))` `|overline(u)|=sqrt(1+(hata.hatb)^(2)-2(hata.hatb)^(2))=|sintheta|` `vecv=|sintheta|` (D). `vecc.veca=0` (obvious) |
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| 95354. |
The number of ways of choosing triplet `(x , y ,z)`such that `zgeqmax{x, y}a n dx ,y ,z in {1,2, n ,n+1}`isa. `^n+1C_3+^(n+2)C_3`b. `n(n+1)(2n+1)//6`c. `1^2+2^2++n^2`d. `2((^(n+2)C_3))_(-^(n+2))C_2`A. .^(n+1)C_(2)+^(n+2)C_(3)`B. `(1)/(6)n(n+1)(2n+1)`C. `1^(2)+2^(2)+….+n^(2)`D. `2(` .^(n+2)C_(3))-^(n+2)C_(2)` |
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Answer» Correct Answer - A::B::C::D if `z=1` so `x,y=1` `x,yto{1,2}` number of ways `=2^(2)` `z=3` `x,y in {1,2,3}` Number of ways `=3^(2)` similarly`n^(2)` `1^(2)+2^(2)…n^(2)` |
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| 95355. |
The present population of a city is 363000. If it increases by 10% every year, then what was the population 2 years ago? |
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Answer» Present Population of city = 363000 Rate of increase in population annually = 10% Let the populations 1 year ago be x. Now, x + 10% of x = 363000 x + 10/100 * x = 363000 x + x/10 = 363000 (10x + x )/10 = 363000 11x/10 = 363000 11x = 363000 x 10 x = 3630000/11 x = 330000 The population 1 year ago will be 330000. The population 2 year ago will be 2 x 330000 = 660000 |
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| 95356. |
The average of six consecutive odd numbers P,Q,R,S,T and U is 116.what is the product of R and T. |
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Answer» Assuming that the numbers are not only consecutive, but fall in the alphabetical order given. Since 116 is the average, and there are 6 numbers given, 3 must fall on either side of 116. That means that the following should be true: P:111 Q:113 R:115 S:117 T:119 U:121 Therefore the product of R and T, or R * T, would be 115 * 119 = 13,685. |
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| 95357. |
The population of a town increase by 10% annually. If the present population is 22000, find it population a year ago. |
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Answer» Present population of town = 22000 Rate of increase in population annually = 10% Let the population 1 year ago be x . Now, (x + 10% of x) = 22000 (x + x/10) = 22000 11x/10 = 22000 x = 22000 x 10/11 x = 20000 So, The population 1 year ago will be 20000. |
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| 95358. |
. The population of a town is 176400, If it increases annually at 5 %,what will be its population 2 years hence? What was it 2 years ago ? |
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Answer» if the population is x. new population after one year=>`x+x/20=(21x)/20` new population after one more year=`(21x)/20+1/20xx(21x)/20=(441x)/400` here x=176400 therefore new population after 2 years=>194481 now if `(441x)/400=176400` then x=`160000` |
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| 95359. |
If the points `A(1, 0, -6), B(3, p, q) and C(5, 9, 6)` are collinear,find the value of `p and q`. |
| Answer» Given points:`A(1,0,-6)``B(3,p,q)``C(5,9,6)``vecA = overset(^^)(i) - 6overset(^^)(k) ``vecB = 3overset(^^)(i) +poverset(^^)(j) + qoverset(^^)(k)``vecC = 5overset(^^)(i) + 9overset(^^)(j) + 6overset(^^)(k)``vec(AB) = vecB - vecA = 2overset(^^)(i) + poverset(^^)(j) + 15overset(^^)(k)``vec(AC) = vecC - vecA = 4overset(^^)(i) + 9overset(^^)(j) + 12overset(^^)(k)``vec(AB) = lambda*vec(AC)``2overset(^^)(i) + poverset(^^)(j) + 15overset(^^)(k) = lambda*(4overset(^^)(i) + 9overset(^^)(j) + 12overset(^^)(k))`Comparing coefficients:`overset(^^)(i) : 2 = 4lambda rArr lambda = 1/2``overset(^^)(j): p = 9lambda rArr p = 9/2``overset(^^)(k): q+6 = 12lambda rArr q + 6 = 6 rArr q = 0` | |
| 95360. |
A tangent to the ellipse `x^2 / a^2 + y^2 / b^2 = 1` touches at the point P on it in the first quadrant & meets the coordinate axes in A & B respectively. If P divides AB in the ratio `3: 1` reckoning from the x-axis find the equation of the tangent. |
| Answer» equation of tangent at any point on eclipse`(x cos theta)/a+(ysin theta)/b=1`co-ordinates of A`(a/costheta,0)`co-ordinates of B`(0,b/sin theta)`P is between A and B with ratio 3:1So, P`(a/(4cos theta), (3b)/(4sintheta))`=P`(a cos theta, b sin theta)``a/(4cos theta)=acostheta``cos^2theta =1/4``costheta=-1/2``sin theta=sqrt3/2`equation of tangent will be`x/(2a)+(xysqrt3)/(2b)=1``bx+aysqrt3=2ab` | |
| 95361. |
A tangent at a point P on the curve cuts the x-axis at A and B is the foot of perpendicular from P on the x axis. If the midpoint of AB is fixed at `(alpha,0)` for any point P, find the differential equation and hence find the curve. |
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Answer» here, ` y=f(x)` `Y - y = dy/dx*(X-x)` putting Y=0`-y = dy/dx*(X-x)` `X= x- y*dy/dx` C is the mid point of AB let coorinates of C as `(alpha,0)` `C(alpha,0) = ((x+x - y*(dy/dx))/2 , 0)` `2*alpha = 2*x - y*dx/dy` `y*dx/dy = 2*(x- alpha)` this is differential eqn integrating both sides `int dx/(2*(x-alpha)) = int dy/y` `1/2 * ln(x-alpha) = y + c` `ln(x- alpha) = 2*y +2*c` `ln(x-alpha) = 2*y + k` `x-alpha = e^(2*y+k)` `x= alpha + e^(2y+k)` |
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| 95362. |
Two circles of radii a and b (a < b) touch externally. Length of the direct common tangent from the point of intersection of the direct common tangents to the smaller circle is |
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Answer» `/_ ABM~~/_PQM` (AAA) `(BM)/(QM)=(AB)/(PQ)=b/a` `(BQ+QM)/QM=b/a` -(1) AX=AB-XB =b-a In `/_AXP` BQ=PX=`sqrt(AP^2-AX^2)` =`sqrt((a+b)^2-(b-a)^2)` =`sqrt(4ab)` =`2sqrt(ab)` from eqation 1 `(2 sqrt(ab)+QM)/(QM)=b/a` `(2 sqrt(ab))/(QM) +1=b/a` `(2 sqrt(ab))/(QM)=(b-a)/a` QM=`(2a sqrt(ab))/(b-a)` |
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| 95363. |
T is a point on the tangent to a parabola `y^2= 4ax` at its point `P. TL and TN` are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Then (A)SL=2(TN) (B) 3(SL)=2(TN) (C) SL=(TN) (D) 2(SL)=3(TN) |
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Answer» `y^2=4ax` Tangent at `P:x+at^2` Let`T(x_1,y_1)` lies on tangent `ty_1=x_1+at^2` `m_(SP)=(2at-0)/(at^2-a)-(2t)/(t^2-1)` `m_(sp)*m_(tl)=-1` `(2t)/(t^2-1)*m_(tl)=-1` `m_(tl)=(1-t^2)/(2t)` Equation of TL `y-y_1=(1-t^2)/(2t)*(x-x_1)` SL is perpendicular on line TC `D_1=SL=|((-2ty_1+a(t^2-1)-x_1(t^2-1))/(sqrt(4t^2+(t^2-1)^2)))|` solving this `SL=x_1+a` perpendicular distance `D_2=TN=(x_1+a)/(sqrt(1^2+0^2))=x_1+a` `SL+TN+x_1+a` |
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| 95364. |
(0)/(0)=2 |
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Answer» Reduce Zero Numerator `0 = 2` Statement Is False `0 = 2` |
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| 95365. |
PB is a line segment on a number line. It has endpoints at -2 and 12. what is the coordinate of its midpoint |
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Answer» =(-2 + 12)/2 |
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| 95366. |
Let S be a non-empty subset of R. Consider the following statement: P: There is a rational number x Î S such that x > 0.Which of the following statements is the negation of the statement P ?(1) There is no rational number x ∈ S such that x £ 0(2) Every rational number x ∈ S satisfies x £ 0(3) x ∈ S and x £ 0 x is not rational(4) There is a rational number x ∈ S such that x £ 0 |
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Answer» (2) Every rational number x ∈ S satisfies x £ 0 P: there is a rational number x ∈ S such that x > 0 ~P: Every rational number x ∈ S satisfies x £ 0 |
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| 95367. |
Sum of three consecutive numbers is 3003. Find the lowest number.1. 9982. 9993. 10004. 1001 |
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Answer» Correct Answer - Option 3 : 1000 Calculations: Let the numbers be (x – 1), x, (x + 1) According to problem, x – 1 + x + x + 1 = 3003 ⇒ 3x = 3003 ⇒ x = 1001 Lowest number = x – 1 ⇒ 1001 – 1 = 1000 ∴ Required lowest number is 1000 |
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| 95368. |
A person was asked to state his age in years. His reply was, 'Take my age 4 years hence, multiply it by 3 and then subtract 4 times my age three years ago and you will know how old I am'. What was the age of the person?1. 15 years2. 18 years3. 12 years4. 24 years5. 6 years |
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Answer» Correct Answer - Option 3 : 12 years Given: Take my age 4 years hence, multiply it by 3 and then subtract 4 times my age three years ago Calculation: Let the age of the person be x years According to the question, ⇒ x = 3(x + 4) – 4(x – 3) ⇒ x = 3x + 12 – 4x + 12 ⇒ 2x = 24 ⇒ x = 12 years ∴ The age of the person was 12 years. |
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| 95369. |
Find the antonym of word:Liberate A) rescue B) confine C) deliver D) divorce |
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Answer» Correct option is B) confine |
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| 95370. |
Despite his dislike of Jack, he had always ______ him if some other boy at school attacked him. A) kept up with B) carried out C) settled down D) stood up for |
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Answer» Correct option is D) stood up for |
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| 95371. |
The police accused him _____ going through a red light. A) of B) for C) in D) through |
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Answer» Correct option is A) of |
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| 95372. |
The situation had occurred _____ a misunderstanding. A) for B) of C) with D) because of |
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Answer» Correct option is D) because of |
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| 95373. |
I tried to get through to him, but I couldn’t ______ his misunderstanding. A) catch on B) clear up C) work up to D) catch up with |
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Answer» Correct option is B) clear up |
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| 95374. |
Fill in the blanks with the appropriate articles and prepositions given in brackets:our opinión this dispute has arisen through .......... regrettable misunderstanding clue to .......... backwardness ....... your ideas. |
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Answer» In, a, the, of |
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| 95375. |
Write an essay of about 18-20 sentences on Gender Discrimination – a challenge to social justice. |
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Answer» Gender is a concept that is used to describe men and women. This denotes not only the biological features of man or woman, it includes the cultural, behavioural, and social layers of life. It includes the status of each in the social hierarchy. It is common to understand gender from the woman’s perspective only. Gender is used to study issues related to women. Women and children are the ones who are usually left 1 behind in the society. Women have been j discriminated against since ages. Gender discrimination is present all over the world. But the nature of discrimination is not same everywhere, it is a complex whole of numerous social issues. It is great social evil and a bane even in this age of Artificial Intelligence. India is a predominantly patriarchal society, generally preference is given for male child. Hence gender based foeticide is a common practice in India. This has led to skewed gender ratio in India. There is inequality in women accessing education, ownership, economic activities as well as social activities. Gender discrimination is evident in family structure too. It is shocking to see that 2011, the ratio of female and male was 933 females to 1000 males. The governments of India have implemented many laws to curb gender inequalities. Yet gender equality is still a mirage. Laws and punishment seem to have no effect and women are still being discriminated. The only solution to gender discrimination seems to be awareness about gender bias. But it will take a long time for this awareness to transform into a social change. While it is true that today woman have proved their worth in every field, there are still millions of women who face discrimination at every juncture of life. There is a great need for further empowering women so that they can lead an enriched life free of discrimination. |
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| 95376. |
Write an essay in about 150 -200 words on the 'Decision making is a challenge'. |
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Answer» Decision making is a process that plays a vital role in our daily lives. Some decisions are not very important whereas other imperative decisions, when cautiously carried out, can change the path of our lives. When faced with a crisis, one of the major issues is deciding the right thing. Decision making can be quite complicated and challenging in some cases. It is hence essential to gather as much information from different sources and assess all possible alternatives to the problem or situation at hand before making a decision. Doing so will permit us to land at the best possible result for the problem. Such decisions can’t be an overnight one. It takes a couple of months to investigate and consult with friends, family and university professors to make a decision. Low cost tuition fee and the course time are also a big influence in taking decisions. An advantage of such decisions can only be an outcome of research and discussion and there is no conflict in that. This significantly decreases the probability of risk in any decision making. If a decision is made correct and one is quite pleased with the way it is turning out to be then one has crossed all barriers. It is imperative that one makes decisions in consultation with parents opinions and check on other surveys and researches to avoid challenges. |
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| 95377. |
Where did Kubla Khan make his pleasure dome? a. Tehran b. Istanbul c. Xanadu d. Taipei |
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Answer» Answer is: c. Xanadu |
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| 95378. |
Where did the author first meet Frau Frieda? a. Vietnam b. Vienna c. Venice d. Vancouver |
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Answer» Answer is: b. Vienna |
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| 95379. |
Write an essay on "The value of discipline" in about 150 words. |
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Answer» Discipline Discipline is a basic necessity of life. The proper growth of life is impossible if there is no discipline in it. Discipline is necessary in every sphere of life. It is necessary in schools and colleges. Students should be respectful to their teachers. The teacher should show proper respect to the principal. This surely helps in the progress of a institution. Discipline makes life harmonious and useful. Discipline is a must in the shaping of human character. It trains our mind. Man by temperament does not like restraints. Discipline gives restraint. It fixes spell of work and play. It shows us correcting our paths of life. It teaches us how to discharge our duties. Our unbridled sentiments are controlled by the force of discipline. Discipline costs nothing but pays rich dividends. It is a key to success in all sphere of life. Its value should never be under-estimated. |
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| 95380. |
In the essay ‘The mark on the wall’ what was the mark on the wall in reality? (a) a swatted fly (b) mark made by a nail (c) a snail (d) a tomb |
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Answer» Correct answer is (c) a snail |
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| 95381. |
J. Krishnamurti, does not say this in his essay ‘Understanding Freedom and discipline’: (a) In order to be truly free, one must break down the walls of tradition. (b) Discipline is imposed both externally and internally. (c) Intelligence demands breaking away from tradition. (d) Being concerned about one’s looks means one is sensitive. |
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Answer» Correct answer is (d) Being concerned about one’s looks means one is sensitive |
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| 95382. |
According to Milton, the best tribute that future generations has given to Shakespeare is___ a. His readers’ bodies constitute the permanent space in which Shakespeare peacefully lies.b. His works have won great awards. c. His works had pleased Queen Elizabeth. d. Great monument built in his honour. |
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Answer» a. His readers’ bodies constitute the permanent space in which Shakespeare peacefully lies. |
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| 95383. |
Read the extract given below and answer the questions that follow.Surely, Shakespeare is wicked, the map a bad example, With ships and sun and love tempting them to steal For lives that slyly turn in their cramped holes From fog to endless night? On their slag heap, these children ‘ Wear skins peeped through by bones and spectacles of steel With mended glass, like bottle bits on stones(a) Why is Shakespeare described as wicked? (b) Explain, “from fog to endless night.” (c) What does the reference to ‘slag heap’ mean? (d) How do they live in their holes? |
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Answer» (a) Shakespeare has been described as ‘wicked’ because the children are not aware of his literary genius. In their school, hardly any learning takes place, as they are troubled by hunger, despair and failed aspirations. (b) With reference to the passage, ‘from fog to endless night’ refers to early morning to late night. It means that every day is the same for the slum children. (c) The bloodless bodies of the poor children are referred to as ‘slag heap’. (d) They live like rats in their cramped little holes. Their houses are small, dirty and congested. Fog and darkness dominate their lives. |
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| 95384. |
What does Milton not suggest in the poem ‘To Shakespeare’? (a) Not necessary to build a monument for Shakespeare. (b) Shakespeare will be an inspiration for generations to come. (c) Shakespeare’s followers will build him an ornate mausoleum. (d) Shakespeare’s work’s brilliance has not been understood properly |
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Answer» Correct answer is (c) Shakespeare’s followers will build him an ornate mausoleum. |
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| 95385. |
What do the shadows represent in the poem ‘A Lecture upon the Shadows’? (a) Superstitions (b) Young Love (c) Pessimism (d) Discord and disagreements |
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Answer» Correct answer is (d) Discord and disagreements |
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| 95386. |
Which ceremony in the story ‘I Sell my Dreams’ is being compared to Neruda’s sacred siesta? (a) Breaking the bell ceremony (b) Releasing the dove ceremony (c) Japanese rice wine ceremony (d) Japanese tea ceremony |
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Answer» Correct answer is (d) Japanese tea ceremony |
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| 95387. |
Which signboard would the writer have chosen for his 1992 undertaking, in Jibhi Valley?A. option 1B. option 2C. option 3D. option 4 |
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Answer» Correct answer is: D. option 4 |
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| 95388. |
Select the option that lists what we can conclude from the text.(1) people of Jibhi Valley practiced sustainable tourism.(2) the people of Jibhi valley gradually embraced tourism.(3) tourists never revisited Jibhi Valley.(4) the writer was an enterprising person.A. (1) and (2) are true.B. (2), (3) and (4) are true.C. (2) and (4) are true.D. (1), (3) and (4) are true. |
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Answer» Correct answer is: C. (2) and (4) are true. |
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| 95389. |
Which quote summarises the writer’s feelings about the pace of growth of tourism in JibhiValley?A. We kill all the caterpillars, then complain there are no butterflies. - John MarsdenB. Nature will give you the best example of life lessons, just open your eyes and see. – Kate Smith 4C. We do not see nature with our eyes, but with our understanding and our hearts. - William HazlettD. I’d rather be in the mountains thinking of God than in church thinking of the mountains. - John Muir |
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Answer» Correct answer is: A. We kill all the caterpillars, then complain there are no butterflies. - John Marsden |
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| 95390. |
Our traditions are very ANCIENT and our people are proud of them. A) present B) old C) modern D) real E) young |
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Answer» Correct option is C) modern |
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| 95391. |
On which part of the face is highlighter applied? |
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Answer» cheekbones and under the eyebrows. |
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| 95392. |
Packaging tours is an innovative business concept that was first introduced in the mid of century. (a) Sixteenth (b) Eighteenth (c) Nineteenth (d) Twentieth |
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Answer» (c) Nineteenth Nineteenth is an innovative business concept that was first introduced in the mid of century. |
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| 95393. |
Define Traditions. |
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Answer» A tradition (also called a custom) is anything which lots of people do, and have done for a long time. A custom is more about practices, while culture is more about ideas or a group of customs. |
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| 95394. |
Give one word: The skin that overlies the nail plate . |
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Answer» Perionychium |
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| 95395. |
Define the concept of freedom tours. |
Answer»
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| 95396. |
Differentiate between Man-made and Natural Tourism products. |
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Answer» Natural tourism product- These are more closely associated with natural environment. These include natural resources such as area’s climate, its setting, landscape and natural environment. Natural resources are frequently the most important elements in a destination’s attraction. Man-made tourism products are created by man for pleasure, leisure or business. These includes culture, traditions, entertainment, business. |
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| 95397. |
Expand PBX ______ |
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Answer» Expand PBX – PRIVATE BRANCH EXCHANGE. |
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| 95398. |
How many copies are there in a message slip? |
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Answer» Three copies |
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| 95399. |
What information is required to access the client’s requirement for makeup? |
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Answer» Occasion, time for makeup and age of client for makeup. |
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| 95400. |
scientists will break ______ in their search for new sources of energy. A) up B) through C) out |
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Answer» Correct option is B) through |
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