100525 + Interview Questions in GENERAL QA IN GENERAL AWARENESS

1.	How did the King of Monaco earn his special revenue?
Answer» By allowing a gaming house to be run in Monaco.

Discussion

2.	By whom was the Earth University inspired?
Answer» Rabindranath Tagore.

Discussion

3.	Rearrange the jumbled segments to form a meaningful sentence.Earth / University / Democracy / the earth / teaches
Answer» The Earth University teaches Earth democracy.

Discussion

4.	What is the population of the Monaco Kingdom?
Answer» About seven thousand people.

Discussion

5.	Briefly describe the kingdom of Monaco mentioned in too dear?
Answer» Monaco was called a toy kingdom because it had such a tiny landmass that if all the land in the kingdom were divided, there would not be even an acre for each of its seven thousand inhabitants. The commodities taxed in Monaco were tobacco, wine, and spirit The people also paid a poll tax.

Discussion

6.	Whose beauty, according to Romeo, is too rich for use?
Answer» According to Romeo, it is Juliet’s beauty that is too rich for use.

Discussion

7.	What was the rumasur rife in partipindpuram.
Answer» When the king was born, the astrologers foretold that one day the Tiger King would actually would have to die. A great miracle took place. An astonishing phrase emerged from the lips of the tenday old Jilani Jung Jung Bahadur. He said, “All those who are born will one day have to die. There would be some sense if you could tell us the manner of that death.” At this the chief astrologer said that the prince was born in the hour of Bull. The Tiger and the Bull are enemies, therefore, the death would come from the Tiger. At this the crown prince thundered, “Let tigers beware!” This rumour was quite rife in Pratibandapuram. When the crown prince came of age of twenty, the state came to his hands. Then he also heard about this rumour.

7.

What was the rumasur rife in partipindpuram.

Answer»

When the king was born, the astrologers foretold that one day the Tiger King would actually would have to die. A great miracle took place. An astonishing phrase emerged from the lips of the tenday old Jilani Jung Jung Bahadur. He said, “All those who are born will one day have to die. There would be some sense if you could tell us the manner of that death.”

At this the chief astrologer said that the prince was born in the hour of Bull. The Tiger and the Bull are enemies, therefore, the death would come from the Tiger. At this the crown prince thundered, “Let tigers beware!” This rumour was quite rife in Pratibandapuram. When the crown prince came of age of twenty, the state came to his hands. Then he also heard about this rumour.

Discussion

8.	What is the population of the Kingdom of Monaco?
Answer» About seven thousand

Discussion

9.	Who accompanied Don Gonzalo when he came to the park in A Sunny Morning’?
Answer» Dona Laura accompanied Don Ganzalo when he came to the park in a Sunny morning

Discussion

10.	Name the movement which took place in the Himalayan region to save trees.
Answer» ‘Chipko’ is the non-violent movement that began in the Himalayan region to save the trees.

Discussion

11.	Mention any one of the places through which the foot walks in To the Foot from its Child’.
Answer» Throughout its life, the foot keeps walking without respite. It walks through fields, mines, markets, and ministries until death.

Discussion

12.	Who is the caretaker of Don Gonzalo in the play ‘A Sunny Morning’?
Answer» Juanito is the caretaker of Don Gonzalo in the play ‘A Sunny Morning.

Discussion

13.	How many acres of land did Basavaiah encroach?
Answer» 200 acres of land did Basavaiah encroach.

Discussion

14.	If the potential difference across the ends of a conductor is doubled, the current flowing through it getsA. doubledB. halvedC. four timesD. no change
Answer» Correct Answer - A doubled

Discussion

15.	Ocean thermal energy is due to :A. pressure difference at different level in the oceanB. temperature difference at different levels in the oceanC. Energy stored by the waves in the oceanD. Tides rising out of the ocean
Answer» Correct Answer - B Temperature difference at different levels in the ocean

Discussion

16.	In Which state Rolegan siddhi is:(a) Karnataka (b) Maharashtra(c) Tamil Nadu (d) Andhra Pradesh
Answer» Rolegan siddhi is Maharashtra.

Discussion

17.	Which city of Australia is planned by WALTER BERLY GRIFFIN in 1912.(a) Canbera (b) Sydney(c) Melbourne (d) None of these
Answer» Canbera city of Australia is planned by WALTER BERLY GRIFFIN in 1912.

Discussion

18.	Maracaibo port is situated in which of the following country:-(A) Veneguela (B) Iran (C) Japan (D) Canada
Answer» Maracaibo port is situated in Veneguela.

Discussion

19.	Which one of the following continent has largest road density and number of vehicles?(A) North America (B) Europe (C) Africa (D) Australia
Answer» North America continent has largest road density and number of vehicles.

Discussion

20.	Which one following types of activities are related to word Manufacturing?(A) Primary (B) Secondary (C) Tertiary (D) Quaternary
Answer» Secondary activities are related to word Manufacturing.

Discussion

21.	The size of population in lower age group is larger in countries where:(a) Birth rate is high (b) Birth rate is low(c) Death rate is high (d) Death rate is low
Answer» The size of population in lower age group is larger in countries where Death rate is low.

Discussion

22.	In which country the base of the age-sex pyramid is broad and apex is narrow in?(a) Developed countries (b) Developing countries(c) under developed countries(d) None of the above
Answer» The base of the age-sex pyramid is broad and apex is narrow in Developing countries.

Discussion

23.	Which one of the following countries has the highest density of population ?(a) Bangladesh (b) Pakistan(c) Sri Lanka (d) India
Answer» Bangladesh has the highest density of population.

Discussion

24.	The temperate grassland of Australia are called:(a) Prairies (b) Pampas(c) Downs (d) Steppes
Answer» The temperate grassland of Australia are called Downs.

Discussion

25.	Which one of the schools of thought first developed possibilism?(a) German school of Geography(b) Russian school of Geography(c) French school of Geography(d) British school of Geography
Answer» French school of Geography the schools of thought first developed possibilism.

Discussion

26.	Ecosystem has two components which are(a) Animals (b) Trees and weeds(c) Frogs and men (d) Abiotic and biotic
Answer» Ecosystem has two components are Abiotic and biotic.

Discussion

27.	Ecosystem consists of biotic components comprising living organisms and abiotic components comprising physical factors like temperature, rainfall, wind, soil and minerals. Ecosystems can be natural or can be artificial (manmade). I. Biotic components of ecosystems are: a) Plants b) Animals c) Microorganisms d) All II. Abiotic components are: a) Living b) Non- living c) Borderline between living and non- living d) None III. Examples of natural ecosystems are: a) Forestsb) Ponds c) Lakes d) All IV. Examples of artificial ecosystems are: a) Gardens b) Aquarium c) Crop- fields d) All V. Several ecosystems combine to form: a) Lithosphereb) Atmospherec) Hydrosphere d) Biome
Answer» (i) (d) (ii) (b) (iii) (d) (iv) (d) (v) (d)

27.

Ecosystem consists of biotic components comprising living organisms and abiotic components comprising physical factors like temperature, rainfall, wind, soil and minerals. Ecosystems can be natural or can be artificial (manmade). I. Biotic components of ecosystems are: a) Plants b) Animals c) Microorganisms d) All II. Abiotic components are: a) Living b) Non- living c) Borderline between living and non- living d) None III. Examples of natural ecosystems are: a) Forestsb) Ponds c) Lakes d) All IV. Examples of artificial ecosystems are: a) Gardens b) Aquarium c) Crop- fields d) All V. Several ecosystems combine to form: a) Lithosphereb) Atmospherec) Hydrosphere d) Biome

Answer»

(i) (d)

(ii) (b)

(iii) (d)

(iv) (d)

(v) (d)

Discussion

28.	Mastery orientation can be encouraged by1. focusing on students individual effort.2. comparing students successes with each other.3. assigning lot of practice material as home assignments.4. taking unexpected tests.
Answer» Correct Answer - Option 1 : focusing on students individual effort. Mastery Orientation: Mastery orientation is defined as having the goal of learning and mastering the task according to self-set standards. The learner is focused on developing new skills, improving, and acquiring additional knowledge. Mastery-orientated students find satisfaction with the work and are not influenced by external performance indicators such as grades. Students who have mastery goals tend to engage in activities that will increase their knowledge. They pay more attention, are more likely to process information at a higher level, and are not afraid to ask for help. Mastery orientation is described as a focus on learning and improvement. Mastery orientation focuses on learning, not grades; improvement, not appearances; competency, not competition. This person wants to understand and grow, not just prove how smart he or she is. Students who are more mastery motivated see learning as incremental. They believe abilities can be improved with practice and that they have control over their learning, These students exhibit academic behaviors that positively impact their learning successes. These behaviors include persevering through difficult tasks and using feedback to improve their performance. In mastery orientation, classroom emphasis is not on the outcome, but on the process and the progress. Students are recognized for improved performance and feedback is geared toward improvement. Reward systems are less extrinsic and more intrinsic. A systematic classroom program for influencing students to adopt a mastery goal mindset is TARGET. TARGET is concerned with task, authority, recognition, grouping, evaluation, and time Conclusion: Students’ motivational goal orientation is important to their successes as students as well as in the workplace. Students who adopt mastery goals with the growth mindset are more likely to develop a love for learning and that intrinsic motivation to learn is important to students’ academic growth – including their successful acquisition of skills. Teachers’ own beliefs, the feedback they choose to use, the time they give to students to complete tasks, the choices of tasks they give students, and the credence they give to students’ thoughts about learning experiences all play a role in shaping a students’ mindset toward learning. So, for mastery orientation, focussing on a student's individual effort is more important than comparing him with others, assigning a task, or unexpected test conduction. Hence, option (1) is correct.

28.

Mastery orientation can be encouraged by1. focusing on students individual effort.2. comparing students successes with each other.3. assigning lot of practice material as home assignments.4. taking unexpected tests.

Answer» Correct Answer - Option 1 : focusing on students individual effort.

Mastery Orientation:

Mastery orientation is defined as having the goal of learning and mastering the task according to self-set standards. The learner is focused on developing new skills, improving, and acquiring additional knowledge.
Mastery-orientated students find satisfaction with the work and are not influenced by external performance indicators such as grades. Students who have mastery goals tend to engage in activities that will increase their knowledge. They pay more attention, are more likely to process information at a higher level, and are not afraid to ask for help.
Mastery orientation is described as a focus on learning and improvement. Mastery orientation focuses on learning, not grades; improvement, not appearances; competency, not competition. This person wants to understand and grow, not just prove how smart he or she is.
Students who are more mastery motivated see learning as incremental. They believe abilities can be improved with practice and that they have control over their learning, These students exhibit academic behaviors that positively impact their learning successes. These behaviors include persevering through difficult tasks and using feedback to improve their performance.
In mastery orientation, classroom emphasis is not on the outcome, but on the process and the progress. Students are recognized for improved performance and feedback is geared toward improvement. Reward systems are less extrinsic and more intrinsic.
A systematic classroom program for influencing students to adopt a mastery goal mindset is TARGET. TARGET is concerned with task, authority, recognition, grouping, evaluation, and time

Conclusion: Students’ motivational goal orientation is important to their successes as students as well as in the workplace. Students who adopt mastery goals with the growth mindset are more likely to develop a love for learning and that intrinsic motivation to learn is important to students’ academic growth – including their successful acquisition of skills. Teachers’ own beliefs, the feedback they choose to use, the time they give to students to complete tasks, the choices of tasks they give students, and the credence they give to students’ thoughts about learning experiences all play a role in shaping a students’ mindset toward learning. So, for mastery orientation, focussing on a student's individual effort is more important than comparing him with others, assigning a task, or unexpected test conduction. Hence, option (1) is correct.

Discussion

29.	Assertion: Red data book has a record of all animals. Reason: Endangered species are not need to be noticed. a. Both assertion and reason are true, and reason is the correct explanation of assertion. b. Both assertion and reason are true, but reason is not the correct explanation of assertion. c. Assertion is true but reason is false d. Both assertion and reason are false.
Answer» d. Both assertion and reason are false.

Discussion

30.	Assertion: Penetration of sperm into ovum is a chemical process. Reason: Acrosome of sperm secretes a lytic enzyme hyaluronidase which dissolves vitelline membrane of ovum. a. Both assertion and reason are true, and reason is the correct explanation of assertion. b. Both assertion and reason are true, but reason is not the correct explanation of assertion. c. Assertion is true but reason is false d. Both assertion and reason are false.
Answer» a. Both assertion and reason are true, and reason is the correct explanation of assertion.

Discussion

31.	If there were a population of bacteria living in temperate waters, and if the water temperature were to be increased by global warming, most of these bacteria would die, but the few variants resistant to heat would survive and grow further. I. Some variants survived due to: a) Healthy structure b) Variations c) Adaptability d) None II. Variation occurs due to: a) DNA copying always have some variations b) Species desire to change c) Bio- chemical reaction similarity d) None III. Variations leads to: a) Survival of species b) Survival of individual c) Both a and b d) None IV. Variation and evolution are interrelated a) True b) Falsec) Cannot be said d) None V. Variation is prominent in: a) Unicellular organism b) Multicellular organism c) Both a and bd) None
Answer» (i) (b) (ii) (a) (iii) (c) (iv) (a) (v) (b)

31.

If there were a population of bacteria living in temperate waters, and if the water temperature were to be increased by global warming, most of these bacteria would die, but the few variants resistant to heat would survive and grow further. I. Some variants survived due to: a) Healthy structure b) Variations c) Adaptability d) None II. Variation occurs due to: a) DNA copying always have some variations b) Species desire to change c) Bio- chemical reaction similarity d) None III. Variations leads to: a) Survival of species b) Survival of individual c) Both a and b d) None IV. Variation and evolution are interrelated a) True b) Falsec) Cannot be said d) None V. Variation is prominent in: a) Unicellular organism b) Multicellular organism c) Both a and bd) None

Answer»

(i) (b)

(ii) (a)

(iii) (c)

(iv) (a)

(v) (b)

Discussion

32.	Assertion: Insects visit flowers to gather honey. Reason: Attraction of flowers prevents the insects from damaging other parts of the plant. a. Both assertion and reason are true, and reason is the correct explanation of assertion. b. Both assertion and reason are true, but reason is not the correct explanation of assertion. c. Assertion is true but reason is false d. Both assertion and reason are false.
Answer» d. Both assertion and reason are false

Discussion

33.	Assertion: A cell divides to give rise to two cells. Reasons: This is a basic event in reproduction in which cells use chemical reactions to build copies of their DNA.a) Both A and R are true, and R is correct explanation of the assertion. b) Both A and R are true, but R is not the correct explanation of the assertion. c) A is true, but R is false.d) A is false, but R is true
Answer» a) Both A and R are true, and R is correct explanation of the assertion.

Discussion

34.	Assertion: UAA. UAG and UGA terminate protein synthesis. Reason: They are not recognised by tRNA. a. Both assertion and reason are true, and reason is the correct explanation of assertion. b. Both assertion and reason are true, but reason is not the correct explanation of assertion. c. Assertion is true but reason is false. d. Both assertion and reason are false
Answer» a. Both assertion and reason are true, and reason is the correct explanation of assertion.

Discussion

35.	Assertion: Some organisms can make organic compounds like sugar and starch from inorganic substances using the radiant energy of the sun in the presence of chlorophyll Reasons: These organisms are called producers which include all green plants and certain bacteria which can produce food by photosynthesis.a) Both A and R are true, and R is correct explanation of the assertion. b) Both A and R are true, but R is not the correct explanation of the assertion. c) A is true, but R is false.d) A is false, but R is true
Answer» a) Both A and R are true, and R is correct explanation of the assertion.

Discussion

36.	Let `y=f(x)` be satisfying differential equation `e^(-x^(2))(dy)/(dx)=2xy^(2)` such that `f(0)=(1)/(2)` Q. Which of the following statement is correct about `f(x)`?A. `f(x)` is unboundedB. `f(x)` is bijectiveC. `f(x)` is oddD. None of these.
Answer» Correct Answer - A `int(dy)/(y^(2))=int2xe^(x^(2))dx` `-(1)/(y)=e^(x^(2))+C` point `(0.(1)/(2))` lies on the curve `implies-2=1+C` `impliesC=-3` Hence `-(1)/(y)=e^(x^(2))-3` `impliesf(x)=(1)/(3-e^(x^(2)))` Hence, `f(x)` is even which means that it cannot be objective Also, denominator of `f(x)` becomes zero which implies that it cannot be bounded.

Discussion

37.	Let `y=f(x)` be satisfying differential equation `e^(-x^(2))(dy)/(dx)=2xy^(2)` such that `f(0)=(1)/(2)` Q. Which of the following statement is correct about `f(x)`?A. `int_(0)^(1)f(x)dxlt(I)/(2)`B. Range of `f(x)` is `(0,(1)/(2)]`C. `(e+1)int_(0)^(1)f(x)dxgt1`D. None of these.
Answer» Correct Answer - C `f(x)` is increasing in `(0.,1)` and `f(0)=(1)/(2)` `impliesint_(0)^(1)f(x)dxgt(1)/(2)` And `implies(e+1)int_(0)^(1)f(x)dxgt(e+1)/(2)gt1` Hence (C) option is correct.

Discussion

38.	Consider two planes `P_(1):2x-3y++z=-5` and `P_(2):x-4y-14z=5` if a line L whose points `A-=(-7,y_(1),z_(1))` lie on plate `P_(1)` and points `B-=(X_(2),y_(2),z_(2))` and `C-=(x_(3),y_(3),z_(3))` lies on plate `P_(2)` has equation `(x+7)/(a)=(y-y_(1))/(-b)=(z-z_(1))/(c)` where a,b,c `epsilonN` and `a+b+c` is minimum. Q. The minimum value of `a+b+c` isA. 3B. 4C. 5D. 6
Answer» Correct Answer - D Line `L:(x+7)/(a)=(y-y_(1))/(-b)=(z-z_(1))/(c)` `(-7,y,z_(1))` lie on plane `P_(1)` `implies-3y_(1)+z_(1)=9` ,…(1) Line L lies on plate `P_(2)` `impliesa+4b+14c=0` ..(2) Also `(-7,y_(1),z_(1))` lies on `P_(2)` `implies-4y_(1)-14z_(1)=12` .. (3) Form (1) and (3) Line passes through `(-7,-3,0)` Least value of a,b,c is `a=2,b=3,c=1` (from (2))

Discussion

39.	Consider two planes `P_(1):2x-3y++z=-5` and `P_(2):x-4y-14z=5` if a line L whose points `A-=(-7,y_(1),z_(1))` lie on plate `P_(1)` and points `B-=(X_(2),y_(2),z_(2))` and `C-=(x_(3),y_(3),z_(3))` lies on plate `P_(2)` has equation `(x+7)/(a)=(y-y_(1))/(-b)=(z-z_(1))/(c)` where a,b,c `epsilonN` and `a+b+c` is minimum. Q. The point A is `(p,q,r)` then `p-q+r` isA. 3B. `-3`C. `4`D. `-4`
Answer» Correct Answer - D Line `L:(x+7)/(a)=(y-y_(1))/(-b)=(z-z_(1))/(c)` `(-7,y,z_(1))` lie on plane `P_(1)` `implies-3y_(1)+z_(1)=9` ,…(1) Line L lies on plate `P_(2)` `impliesa+4b+14c=0` ..(2) Also `(-7,y_(1),z_(1))` lies on `P_(2)` `implies-4y_(1)-14z_(1)=12` .. (3) Form (1) and (3) Line passes through `(-7,-3,0)` Least value of a,b,c is `a=2,b=3,c=1` (from (2))

Discussion

40.	`vecalpha` and `vecbeta` are two unit vectos and `vecr` is a vector such that `vecr,vecalpha=0` and `sqrt(2)(vecrxxvecbeta)=3(vecrxxvecalpha)-vecbeta`, then `(1)/(\|vecr\|^(2))` equal
Answer» Correct Answer - 7 `vecr.hatbeta=0` (taking dot on both the sides of the given equation and using `vecr.vecalpha=0`) `sqrt(2)vecrxx(vecrxxhatbeta)=3vecrxx(vecrxxhatalpha)-vecrxxhatbeta` `impliessqrt(2)((vecr.hatbeta)vecr-(vecr.vecr)hatbeta)=3((vecr.hatalpha)-vecrxxhatbeta` `sqrt(2)((vecr.hatbeta)vecr-(vecr.vecr)hatbeta)=3((vecr.hatalpha)vecr-(vecr.vecr)hatalpha)-vecrxxhatbeta` `implies-sqrt(2)\|vecr\|^(2)hatbeta=-3\|vecr\|^(2)hatalpha-vecrxxhatbeta` `implies3\|vecr\|^(2)hatalpha=-vecrxxhatbeta+sqrt(2)\|vecr\|^(2)hatbeta` `implies9\|vecr\|^(4)=\|vecr\|^(2)+2\|vecr\|^(4)` `implies\|vecr\|=(1)/(sqrt(7))`

Discussion

41.	Let `veca=hati+hatj+hatk,vecb=2hati+3hatk,vecc=hati-hatj` and `vecd=6hati+2hatj+3hatk`. If `vecd=x(vecbxxvecc)+y(veccxxveca)+z(vecaxxvecb)` where x, y and z are scalars then the value of `x+y+z` is k. the number of prime factors of 5k is.
Answer» Correct Answer - 2 `veca.vecd=x[vecavecbvecc]` `x=(veca.vecd)/([vecavecbvecc]),y=(vecbvecd)/([vecavecbvecc]),z=(veccvecd)/([vecavecbvecc])` `((veca+vecb+vecc).vecd)/([vecavecbvecc])=(34)/(5)`

Discussion

42.	If `y= 3x+c` is a tangent to the circle `x^2+y^2-2x-4y-5=0` , then `c` is equal to :A. `(-2, 3)`B. `(4, -1)`C. `(2, -3)`D. `(4, 1)`
Answer» Correct Answer - A::D Equation of given circle `x^(2) + y^(2) - 2x - 4y - 5 = 0` `rArr (x-1)^(2) + (y - 2)^(2) = 0` Equation of tangent `y = 3x + c` Length of the perpendicular from centre `=` radius `\|(3-2+c)/(sqrt(3^(2)+1^(2)))\| = sqrt(10) rArr c = 9.-11` If `c = 9` then point of contact is `(-2,3)` if `c = -11` then point of contact is `(4, 1)`

Discussion

43.	Number of different paths of shortest distance from `A` and `B` to in the grid which do not pass through `M`, is A. `.^(11)C_(5)-.^(6)C_(3)`B. `262`C. `442`D. `.^(11)C_(5)-[.^(6)C_(3)xx.^(5)C_(2)]`
Answer» Correct Answer - B::D Total path.[number of paths passing through `M`] `= .^(11)C_(5)-[.^(6)C_(3)xx.^(5)C_(2)] = 462 - 20 xx 10 = 262`

Discussion

44.	`(sin^(3)x)/(1 + cosx) + (cos^(3)x)/(1 - sinx) =`A. `sqrt(2)cos((pi)/(4) - x)`B. `sqrt(2)cos((pi)/(4) + x)`C. `sqrt(2)sin((pi)/(4) - x)`D. `sqrt(2)sin((pi)/(4) + x)`
Answer» Correct Answer - A::D `(sin^(3)x)/(1+cosx)+(cos^(3)x)/(1-sinx)` `rArr ((1-cosx)sin^(3)x)/((1-cosx)(1+cosx))+((1+sinx)cos^(3)x)/((1+sinx)(1-sinx))` `rArr (1 - cosx)sinx + (1+sinx)cos x` `rArr sin x + cos x rArr sqrt(2)cos((pi)/(4) - x) = sqrt(2)sin ((pi)/(4) + x)`

Discussion

45.	If `tan1^(@).tan2^(@).tan^(@)"………tan89^(@) = 4x^(2) + 2x` then the value of `x` isA. `sin"(pi)/(5)`B. `cos"(pi)/(5)`C. `sin"(pi)/(10)`D. `cos"(4pi)/(5)`
Answer» Correct Answer - C::D `tan1^(0).tan2^(0).tan3^(0)"……"tan89^(0) = 4x^(2) + 2x = 1` `rArr 4x^(2) + 3=2x - 1 = 0 rArr x(-1 +-sqrt(5))/(4)` `rArr (sqrt(5) - 1)/(4) = sin (pi)/(10)` or `-((sqrt(5) + 1)/(4)) = cos(4pi)/(5)`

Discussion

46.	If `(tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y`. Then which of the following may be true(A) `(x+y)/(tan1)=-2`(B) `(tan^(-1)x)/(1-tan^(-1)y)=2`(C) `(x+y)/(tan1)=2`(D) `(x+y)/(cot1)=1`A. `(x+y)/(tan1)=-2`B. `(tan^(-1)x)/(1-tan^(-1)y)=2`C. `(x+y)/(tan1)=2`D. `(x+y)/(cot1)=1`
Answer» Correct Answer - A `a^(3)+b^(3)+c^(3)=3abc` `impliesa+b+c=0` or `a=b=c` `impliestan^(-1)x+tan^(-1)y=1` or `tan^(-1)x=tan^(-1)y=-1` `impliesx=y=-tan1` or `(x+y)/(1-xy)=tan1` `(x+y)/(tan1)=-2`

Discussion

47.	f:RrarrR is a function satisfying `f(x+5)gef(x)+5 and f(x+1)lef(x)+1`. Given `f(1)=1` and `g(x)=f(x)+1-x, g(2009)` is equal toA. `2009`B. `2008`C. `1`D. None of these
Answer» Correct Answer - C `f(x+5)gef(x)+5 ….(i)` and `f(x+1)lef(x)+1 …(ii)` or `f(x)ge f(x+1)-1….(iii)` `implies f(x+5)gef(x)+5gef(x+1)-1+5` or `f(x+5)ge f(x+1)+4…..(iv)` `impliesf(x+5)ge f(x+4)+1` and `therefore (x+1)ge f(x)+1….(v)` `("replacing" x by x-4)` from (ii) and (v) `implies f(x+1)=f(x)+1....(vi)` `therefore f(1)=1` from (vi), f(2), f(3)=3 etc. f(2009) =2009 `therefore g(2009)=f(2009)+1-2009=1`

Discussion

48.	`tanA +tanB + tanC = tanA tanB tanC` ifA. `A + B + C= pi`B. `A + B + C= 2pi`C. `A + B + C= npi`D. `A + B + C= pi//2`
Answer» Correct Answer - A

Discussion

49.	Circumradius of a `Delta ABC` is 2, O is the circumcentre, H is the orthocentre then- `1/64(AH^2+BC^2)(BH^2+AC^2)(CH^2+AB^2)` is equal toA. 64B. 16C. `1/64`D. 1
Answer» Correct Answer - 1 `AH^(2)+BC^(2)=4R^(2)cos^(2)A+4Rsin^(2)A=4R^(2)` `rArr1/64(AH^(2)+BC^(2))(BH^(2)+AC^(2))(CH^(2)+AB^(2))` `(64R^(6))/64=R^(6)=64`

Discussion

50.	Two balls are rolling on a flat smooth table. One ball has velocity components `sqrt(3) hat(j)` and `hat(i)` while the other has components `2 hat(i)` and `2 hat(j)`. If both start moving simultaneously from the same point, the angle between their paths is-A. `15^(@)`B. `30^(@)`C. `45^(@)`D. `60^(@)`
Answer» Correct Answer - A Velocity of one ball `vec(v)_(1)=hat(i)+sqrt(3)hat(j)` Velocity od second ball `vec(v)_(2)=2hat(i)+2hat(j)` Angle between their path: `cos theta=(vec(v)_(1).vec(v)_(2))/(v_(1)v_(2))=(2+2sqrt(3))/((2)(2sqrt(2)))=(1+sqrt(3))/(2sqrt(2))rArr theta=15^(@)`

Discussion

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