100525 + Interview Questions in GENERAL QA IN GENERAL AWARENESS

1.	Let `g(x)= ax + b ` , where ` a lt 0 ` and g is defined from [1,3] onto [0,2] then the value of ` cot ( cos^(-1) (\|sin x \| + \|cos x\|) + sin^(-1)(-\|cos x \| - \|sinx\|)) ` is equal to :A. `g(1)`B. `g(2)`C. `g(3)`D. `g(1)+g(3)`
Answer» Let g(x)=ax+b, where `a lt 0` and g is defined from [1,3] onto [0,2] then the value of `cot(cos^(-1)(\|sinx\|+\|cos x\|)+sin^(-1)(-\|cosx\|-\|sinx\|))` is equal to (A) g (B) g(2) (C*)g(3) (D)g(1)+g(3) Consider `F(s)=cot(cos^(-1)(\|sinx\|+\|cos x\|)+sin^(-1)(-\|cosx\|-\|sinx\|))` But `\|sinx\|+\|cosx\| in [1,sqrt(2)]AA x in R` `:. F(x)=cot(cos^(-1)(1)+sin^(-1)(-1))=cot(0-(pi)/(2))=0=g(3)" " `(AsF(x)=0,`AAx in D_(F)`)

Discussion

2.	If `f(x)=sum_(r=0)^(20) .^(20)C_(r) (In (1+x))^(r),g(x)=sum_(r=0)^(20)(-1)^(r).^(20)C_(r)(1+3sinx)^(20-r)` then,A. `sum_(r=0)^(oo)(g(pi//6))^(r)=(6^(20))/(2^(20)-1)`B. `sum_(r=0)^(oo)(g(pi//6))^(r)=(6^(30))/(2^(20)-1)`C. If `h (x)=[f(x)]^(1//20)` then `sum_(r=0)^(oo) [h(x^(2^(r)))-1]` (where `\|x\|lt1)=-In(1-x)`D. `h(x)=[f(x)]^(1//20)` then `sum_(r=0)^(oo) [h(x^(2^(r)))-1]` where `\|x\|lt1)=In(1-x)`
Answer» Correct Answer - A::C ac

Discussion

3.	Which of the following functions have the same period ?A. `f(x)=sin^(2)(x) +cos^(4)x+2`B. `g(x)=(1)/(f(sin x))+(1)/(f(cos x))` where `f(x)=(1)/(sqrt(1-x^(2)))`C. `h(x)=(\|sin x\|+\|cos x\|)/(\|sinx-cosx\|)`D. `k(x)=cos(cos x)+cos(sin x)`
Answer» ABD A,B,D each have a period `pi//2`, and C has a period `pi`

Discussion

4.	Let `p(x)` be a polynomial of degree 6 with leading coefficient unity and `p(-x)=p(x)AAxepsilonR`. Also `(p(1)+3)^(2)+p^(2)(2)+(p(3)-5)^(2)=0` then `sqrt(-4-p(0))` is….
Answer» Correct Answer - 6 `[6]` `p(x)=(x^(2)-4)(x^(4)-10x^(2)+10)`

Discussion

5.	Let f: defined from `(1//4,oo) to R^(+) as, f(x)=log_(1//4)(x-(1)/(4))+(1)/(2)log_(4)(16x^(2)-8x+1)` Statement-1: f(x) is neither injective nor surjective . Statement-1: f(x) is a constant function.A. Statement-1 is true, statement -2 is true and statement -2 is correct explantion for statement-1.B. Statement-1 is true, statement -2 is true and statement -2 is NOT correct explantion for statement-1.C. Statement-1 is true, statement-2 is falseD. Statement-1 is false, statement-2 is true
Answer» B `f(x)=log_(1//4)(x-(1)/(4))+(1)/(2) log_(4)16+(1)/(2) log_(4)(x^(2)-(x)/(2)+(1)/(16))(x gt(1)/(4))` `=log_(1//4)(x-(1)/(4))+1+log_(4)(x-(1)/(4))` `=-log_(4)(x-(1)/(4))+log_(4)(x-(1)/(4))+1` `=1 implies ` f is constant hence f is many one as well into. Also range is a singelton `implies` f is constant but a constant function can be any thing `implies` not the explanation.

Discussion

6.	If `lim_(n->oo)[((2009)^2010)^n+((2010)^2009)^n]^(1/n)` is equal to `a^b` where `a,b in N` then `a-b` is equal to:
Answer» Correct Answer - 1 `[1]`

Discussion

7.	The value of `x, x in (2,oo)` where `f (x) = sqrt(x sqrt(8x-16))+ sqrt(x- sqrt(8x-16))` is not differentiable is:
Answer» Correct Answer - 4 `[4]`

Discussion

8.	`A` and `B` are two square matrices such that `A^(2)B=BA` and if `(AB)^(10)=A^(k)B^(10)` then the value of `k-1020` is.
Answer» Correct Answer - 3 `[3]`

Discussion

9.	`Delta I_(1)I_(2)I_(3)` is an excentral triangle of an equilateral triangle `Delta ABC` such that `I_(1)I_(2)=4` unit, if `DeltaDEF` is pedal triangle of `DeltaABC`, then `(Ar(Delta I_(1)I_(2)I_(3)))/(Ar (DeltaDEF))=`
Answer» Correct Answer - 4 `[4]`

Discussion

10.	If two points `P & Q` on the hyperbola ,`x^2/a^2-y^2/b^2=1` whose centre is C be such that CP is perpendicularal to `CQ and a lt b`1 ,then prove that `1/(CP^2)+1/(CQ^2)=1/a^2-1/b^2`.
Answer» Correct Answer - 4 `[4]`

Discussion

11.	We need a loan to start the company and we need a company to get the loan. It’s a ______ situation. A) calls the shots B) chew things over C) chicken D) call his bluff E) chicken and egg
Answer» Correct option is E) chicken and egg

Discussion

12.	Let `S={(x,y),x^(2)+y^(2)-6x-8y+21le0}` then `"max"{(12x)/7-(5y)/7,(x,y)inS}+"min" {1/2(x^(2)+y^(2)+1)+(x-y),(x-y)inS}` `-"min"{(sqrt(3)y+\|x-3\|)/(\|x-3\|),(x,y)inS}`
Answer» Correct Answer - 6 `[6]` `6+4-4`

Discussion

13.	She always likes to think things through very carefully. She likes to ______. A) chicken and egg B) chicken C) chew things over D) call his bluff E) call it quits
Answer» Correct option is C) chew things over

Discussion

14.	If the equation `x^(3)-3x+1=0` has three roos `x_(1),x_(2),x_(3)` where `x_(1)ltx_(2)ltx_(3)` then the value of `({x_(1)}+{x_(2)}+{x_(3)})` is ({.} F.P. of `x`).
Answer» Correct Answer - 1 `[1]`

Discussion

15.	Whatever we do, we are going to come out badly. It’s a ______ situation. A) a can of worms B) carry the can C) chicken D) can’t win E) chicken and egg
Answer» Correct option is D) can’t win

Discussion

16.	The total number of three-digit numbers, with one digit repeated exactly two times, is
Answer» If 0 taken twice then ways = 9 If 0 taken once then ⁹C₂ x 2 = 18 If 0 not taken then ⁹C₁ ⁸C₁.3 = 216 Total = 243

16.

The total number of three-digit numbers, with one digit repeated exactly two times, is

Answer»

If 0 taken twice then ways = 9

If 0 taken once then ⁹C₂ x 2 = 18

If 0 not taken then ⁹C₁ ⁸C₁.3 = 216

Total = 243

Discussion

17.	If the mean deviation about the mean of the numbers 1, 2, 3, ..., n, where n is odd, is (5(n + 1))/n then n is equal to____
Answer» Mean deviation about mean of first n natural numbers is \(\frac{n^2-1}{4n}\) ∴ n = 21

17.

If the mean deviation about the mean of the numbers 1, 2, 3, ..., n, where n is odd, is (5(n + 1))/n then n is equal to____

Answer»

Mean deviation about mean of first n natural numbers is \(\frac{n^2-1}{4n}\)

∴ n = 21

Discussion

18.	Let `a_k = .^nC_k` for `0 lt= k lt= n` and `A_k = [(a_(k-1),0), (0,a_k)]` for `1 lt= k lt= n` and `B=sum_(k=1)^(n-1)A_k * A_(k+1) = [(a,0), (0,b)]`
Answer» Correct Answer - 1 `A_(k).A_(k+1)=[(a_(k-1), 0),(0,a_(k))][(a_(k),0),(0,a_(k+1))]` `A_(k).A_(k+1)=[(a_(k-1).a_(k), 0),(0,a_(k)a_(k+1))]` `A_(k).A_(k+1)=[(.^(n)C_(k-1) .^(n)C_(k), 0),(0, .^(n)C_(k) .^(n)C_(k+1))]` `B=[(sum_(k=1)^(n=1).^(n)C_(k-1).^(n)C_(k),0),(0,sum_(k=1)^(n-1).^(n)C_(k).^(n)C_(k+1))]=[(a,0),(0,b)]` `a=b=.^(2n)C_(n-1-n)`

Discussion

19.	If `alpha_(1),alpha_(2),alpha_(3), alpha_(4)` are the roos of `x^(4)+2x^(3)+bx^(2)+cx+d=0` such that `alpha_(1)-alpha_(3)=alpha_(4)-alpha_(2)`, then `b-c` is equal to__________
Answer» Correct Answer - 1 `(x^(4)+2x^(3)+bx^(2)+cx+d)=(x-alpha_(1))(x-alpha_(2))(x-alpha_(3))(x-alpha_(4))=(x^(2)+px+q)(x^(2)+px+r)` `=x^(4)+2px^(3)+(q+r+p^(2))x^(2)+(pr+pq)x+qr` `(2p)^(3)-4(2p)(q+r+p^(2))+8(pq+pr)=0` `2^(3)-4xx2xxb+8c=0` `impliesb-c=1`

Discussion

20.	I wish you _______. I’m sure you would enjoy joining us. A) could come B) had come C) may come D) would come
Answer» Correct option is B) had come

Discussion

21.	For once on the face of the Earth let’s not speak in any language, let’s stop for one second, and not move our arms so much. It would be an exotic moment without rush, without engines, we would all be together in a sudden strangeness. i The poet uses the word “let’s” to ____ a) initiate a conversation between the poet and the readers. b) invite readers as part of the poem’s larger call to humanity. c) welcome readers into the world of the poem and its subject. d) address readers as fellow members of the human race. ii Margaret Atwood said, “Language divides us into fragments, I wanted to be whole.” Choose the option that correctly comments on the relationship between Margaret Atwood’s words and the line from the above extract – “let’s not speak in any language” a) Atwood endorses Neruda’s call to not speak in any language. b) Atwood justifies Neruda’s request to not engage in any speaking. c) Atwood undermines Neruda’s intent to stop and not speak in any language. d) Atwood surrenders to Neruda’s desire for silence and not speak in any language. iii Why do you think the poet employs words like “exotic” and “strangeness”? a) To highlight the importance of everyone being together suddenly for once. b) To emphasize the frenetic activity and chaos that usually envelops human life. c) To indicate the unfamiliarity of a sudden moment without rush or without engine. d) To direct us towards keeping quiet and how we would all be together in that silence. iv Choose the option that correctly matches the idioms given in Column A with their meanings in Column B.Colulmn ACollumn B1. On the face of the earth(i) in existence2. What on earth(ii) To do all possible to accomplish something3. Move heaven and earth(iii) To express surprise or shock4. To salt of the earth(iv) To be good and worthlya) 1 – (i); 2 – (iv); 3 – (iii); 4 – (ii) b) 1 – (i); 2 – (iii); 3 – (ii); 4 – (iv)c) 1 – (ii); 2 – (i); 3 – (iv); 4 – (iii) d) 1 – (iv); 2 – (ii); 3 – (iii); 4 – (i)
Answer» i – d ; ii – c ; iii – b ; iv – b i- B ii- A iii- B iv-B 1. A 2. A 3. B 4. B

21.

For once on the face of the Earth let’s not speak in any language, let’s stop for one second, and not move our arms so much. It would be an exotic moment without rush, without engines, we would all be together in a sudden strangeness. i The poet uses the word “let’s” to ____ a) initiate a conversation between the poet and the readers. b) invite readers as part of the poem’s larger call to humanity. c) welcome readers into the world of the poem and its subject. d) address readers as fellow members of the human race. ii Margaret Atwood said, “Language divides us into fragments, I wanted to be whole.” Choose the option that correctly comments on the relationship between Margaret Atwood’s words and the line from the above extract – “let’s not speak in any language” a) Atwood endorses Neruda’s call to not speak in any language. b) Atwood justifies Neruda’s request to not engage in any speaking. c) Atwood undermines Neruda’s intent to stop and not speak in any language. d) Atwood surrenders to Neruda’s desire for silence and not speak in any language. iii Why do you think the poet employs words like “exotic” and “strangeness”? a) To highlight the importance of everyone being together suddenly for once. b) To emphasize the frenetic activity and chaos that usually envelops human life. c) To indicate the unfamiliarity of a sudden moment without rush or without engine. d) To direct us towards keeping quiet and how we would all be together in that silence. iv Choose the option that correctly matches the idioms given in Column A with their meanings in Column B.Colulmn ACollumn B1. On the face of the earth(i) in existence2. What on earth(ii) To do all possible to accomplish something3. Move heaven and earth(iii) To express surprise or shock4. To salt of the earth(iv) To be good and worthlya) 1 – (i); 2 – (iv); 3 – (iii); 4 – (ii) b) 1 – (i); 2 – (iii); 3 – (ii); 4 – (iv)c) 1 – (ii); 2 – (i); 3 – (iv); 4 – (iii) d) 1 – (iv); 2 – (ii); 3 – (iii); 4 – (i)

Answer»

i – d ;

ii – c ;

iii – b ;

iv – b

i- B

ii- A

iii- B

iv-B

1. A

2. A

3. B

4. B

Discussion

22.	Someone is going to have to take responsibility for this disaster. Who is going to ______. A) can’t win B) carry the can C) chicken D) a can of worms E) chicken and egg
Answer» Correct option is B) carry the can

Discussion

23.	I don’t think she _____. Call her again. A) can have heard B) might have heard C) must hear D) can be heard
Answer» Correct option is B) might have heard

Discussion

24.	If `k_(1)` and `(k_(2)gtK+k_(2))` are two non-zero integral values of `k` for which the cubic equation `x^(3)+3x^(2)+k=0` has all integer roots, then the value of `k_(1)-k_(2)` is equal to_______
Answer» Correct Answer - 8 `x^(3)+3x^(2)+k=0 to alpha, beta, gamma` `alpha+beta+gamma=-3, alpha beta +beta gamma+gamma alpha=0, alpha beta gamma=-k` `alpha^(2)+beta^(2)+gamma^(2)=9` `because alpha,beta, gamma epsilonIimpliesalpha^(2)=9, beta^(2)=0, gamma^(2)=0` or `alpha^(2)=4, beta^(2)=4, gamma^(2)=1` `alpha^(2)=4, beta^(2)=4, gamma^(2)=1` Possible roots: `+-3, 0, 0, +-2, +-2, +-1` But `alpha beta+beta gamma +gamma alpha=0` So, possible roots are `3, 0, 0, -3, 0, 0, 2, 2, -1, -2, -2 , 1` Possible non-zero valuesof `k` are `-4` and 4

Discussion

25.	If `A, B, C` are the angles of triangle `ABC` and `tan A, tan B, tan C` are the roots of the equation `x^(4)-3x^(3)+3x^(2)+2x+5=0`, if the fourth root of the equation is `tan D` then find `3tan D`.
Answer» Correct Answer - 5 Let the fourth root of the equation be `tan D` Now `A + B + C = pi` Consider `tan (A + B + C + D)` `= (sumtanA-sumtanAtanBtanC)/(1-sumtanAtanB+IItanA)` `= (3 - (-2))/(1 - 3 + 5) = (5)/(3) rArr tan(pi + D) = tan D = (5)/(3)`

Discussion

26.	Let’s face it, he decides. He’s the boss so he’s the one that ______. A) called it a day B) calls the shots C) call it quits D) chicken E) call his bluff
Answer» Correct option is B) calls the shots

Discussion

27.	I’m sure that there is a lot of corruption in that country. If we order an internal audit we may be opening ______. A) carry the can B) chicken C) can’t win D) chicken and eggE) a can of worms
Answer» Correct option is E) a can of worms

Discussion

28.	Don’t you think we should go ______ our plans again? A) down B) through C) on
Answer» Correct option is B) through

Discussion

29.	If a point moves in a straigth line in such a manner that its retardation is porportional to its speed, the distance covered (x) is associated with speed (v) is -A. `x prop V`B. `x prop V^(2)`C. `X prop V^(3)`D. `x prop - V`
Answer» Correct Answer - B f = at `(dv)/(dt) = at` `intdv=int"at "dt` `v-x =(at^(2))/(2)` `v = x+(at^(2))/(2)`

Discussion

30.	Mark the correct statements:A. The magnitude of the velocity of a particle is equal to its speed.B. The magnitude of average velocity in an interval is equal to its average speed in that interval.C. It is possible to have a situation in which the speed of a particle is always zero but the average speed is not zero.D. It is possible to have a situation in which the speed of the particle is never zero but the average speed in an interval is zero.
Answer» Correct Answer - C `v = (dx)/(dt)` = slope of x-t graph is same for both.

Discussion

31.	Figure shows position-time graph of two cars A and B. A. Car A is faster than car B.B. Car B is faster than car A.C. Both cars are moving with same velocity.D. Both cars have positive acceleration.
Answer» Correct Answer - C After t = 2 second the acceleration of football is increasing `therefore` C has to be correct alternative

Discussion

32.	A football is rolling down a hill of unknown shape. The speed of the football at different times is noted as given below (Football always remains in contact with hill) : `{:("Time",,,"Instantaneous speed"),(0 sec,,," "0),(1 sec,,," "4m//s),(2 sec,,," "8 m//s),(3 sec,,," "16m//s),(4 sec,,," "24 m//s):}` The correct shape of the hill is depicted in :A. B. C. D.
Answer» Correct Answer - B `a=x^(2)+3x` `v(dv)/(dx) = x^(2)+3x` `vdv = (x^(2)+3x)dx` `(v^(2))/(2)=(x^(3))/(3)+(3x^(2))/(2)+c` `v^(2)=(2)/(3)x^(3)+3x^(2)+c` `v=sqrt((2)/(3)x^(3)+3x^(2)+c)`

Discussion

33.	Find the minimum height h so that ball just completes the circular motion on the surface when it is released from rest as shown in the diagram (All surfaces are smooth) A. `h = (5)/(2)R`B. h = 2RC. `h = (2)/(5)R`D. h = 3R
Answer» Correct Answer - D Since there is no change in kinetic energy of stone, the total work done on stone in any duration is zero.

Discussion

34.	The following figure shows the velocity time graph of a body. According to this at the point B- A. The force is zeroB. The force is in the direction of the motionC. The force is in opposite direction of the motionD. It is only the gravitational force
Answer» Correct Answer - D `a=-kv` `(dv)/(dx)=-kv` `intdv=-intk" "dx` `v=-kx.........+c`

Discussion

35.	At t = 0 a projectile is fired from a point O(taken as origin) on the ground with a speed of `50 m//s` at an angle of `53^(@)` with the horizontal. It just passes two points A & B each at height 75 m above horizontal as shown The horizontal separation between the points A and B isA. 30 mB. 60 mC. 90 mD. None
Answer» Correct Answer - D `v_(1)sintheta_(1)=v_(2)sintheta_(2)` Time of flight `T=(2xsintheta)/(g)` `T_(1)=(2v_(1)sintheta_(1))/(g)=(2v_(2)sintheta_(2))/(g)=T_(2)` Maximum height `H_("max")=(x^(2)sin^(2)theta)/(2g)=((xsintheta))/(2g)` `H_("max")=((v_(1)sintheta_(1))^(2))/(2g)=((v_(2)sintheta_(2)))/(2g)=H_("2max")` `vec(a)_("rel")=-ghat(j)+ghat(j)=0` `because vec(a)_("rel")=0` & time of flight is same the trajectory of one w.r.t. other is a straight line.

Discussion

36.	The acceleration (a) of moving particle varies with displacement according to the following relation ` a = X^(2)+3X`, Then correct relation between velocity and displacement is :-A. `V=sqrt((X^(2))/(3)+(3X^(2))/(2)+C)`B. `V=sqrt((2)/(3)X^(3)+3X^(2)+C)`C. `V=((2)/(3)X^(3)+3X^(2)+C)`D. `V = 2x + 3`
Answer» Correct Answer - C `vec(a)=(dvec(v))/(dt)` is negative, but `vec(v)` = positive implies `vec(a)` and `vec(v)` are in opposite direction

Discussion

37.	Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are `v_(1)` and `v_(2)` at angle `theta_(1)` and `theta_(2)` respectively from the horizontal, then answer the following question If `v_(1) = v_(2)` and `theta_(1) gt theta_(2)`, then choose the incorrect statementA. Particle 2 moves under the particle 1B. The slope of the trajectory of particle 2 with respect to 1 is always positiveC. Both the particle will have the same range if `theta_(1) gt 45^(@)` and `theta_(2) lt 45^(@)` and `theta_(1) + theta_(2) = 90^(@)`D. none of these
Answer» Correct Answer - A `x=v costheta t = 50 xx(3)/(5) xx2=60m` `y=usinthetat-(1)/(2)g t^(2)= 50xx(4)/(5)xx2-(1)/(2)xx10xx2^(2)=60m` `d=sqrt(x^(2)+y^(2))` `=sqrt(60^(2)+60^(2))=60sqrt(2)m`

Discussion

38.	Our family is quite ______ united family.A) IsB) aC) theD) an
Answer» Correct option is B) a

Discussion

39.	The committee decided to award the prize to you and ______. A) I B) we C) his D) me
Answer» Correct option is D) me

Discussion

40.	What word is used for the meat of a pig when it’s used as meat?
Answer» Correct answer is pork

Discussion

41.	Young sheep’s meat is called ______.
Answer» Correct answer is lamb

Discussion

42.	The flesh of a fully grown sheep is called ______.
Answer» Correct answer is mutton

Discussion

43.	Roosters, hens, ducks, and turkeys when bred for food or for their eggs are collectively known as ______.
Answer» Correct answer is poultry

Discussion

44.	Which one of the following will accelerate phosphorus cycle?(1) Volcanic activity(2) Weathering of rocks(3) Rain fall and storms(4) Burning of fossil fuels
Answer» (2) Weathering of rocks

Discussion

45.	At which stage of life the oogenesis process is initiated?(1) Embryonic development stage(2) Birth(3) Adult(4) Puberty
Answer» (1) Embryonic development stage

Discussion

46.	Roe and Caviar are the eggs of ______.
Answer» Correct answer is fish

Discussion

47.	The flesh of a deer used for eating is known as ______.
Answer» Correct answer is - venison

Discussion

48.	Match the plant with the kind of life cycle it exhibits:List-IList-II(a) Spirogyra(i) Dominant diploid sporophyte vascular plant, with highly reduced male or female gametophyte(b) Fern(ii) Dominant haploid free-living gametophyte(c) Funaria(iii) Dominant diploid sporophyte alternating with reduced gametophyte calledprothallus(d)Cycas(iv) Dominant haploid leafygametophyte alternating with partially dependentmulticellular sporophyteChoose the correct answer from the options given below:(1) (a)-(ii), (b)-(iii). (c)-(iv), (d)-(i)(2) (a)-(iii), (b)-(iv),(c)-(i), (d)-(ii)(3) (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)(4) (a)-(iv), (b)-(i), (c)-(ii), (d)-(iii)
Answer» (1) (a)-(ii), (b)-(iii). (c)-(iv), (d)-(i)

Discussion

49.	Addition of more solutes in a given solution will:(1) lower its water potential(2) make its water potential zero(3) not affect the water potential at all(4) raise its water potential
Answer» (1) lower its water potential

Discussion

50.	The collective word for the flesh of animals such as rabbits, pigeons and deer hunted for sport or food is ______.
Answer» Correct answer is game

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let `g(x)= ax + b ` , where ` a lt 0 ` and g is defined from [1,3] onto [0,2] then the value of ` cot ( cos^(-1) (|sin x | + |cos x|) + sin^(-1)(-|cos x | - |sinx|)) ` is equal to :A. `g(1)`B. `g(2)`C. `g(3)`D. `g(1)+g(3)`

Which of the following functions have the same period ?A. `f(x)=sin^(2)(x) +cos^(4)x+2`B. `g(x)=(1)/(f(sin x))+(1)/(f(cos x))` where `f(x)=(1)/(sqrt(1-x^(2)))`C. `h(x)=(|sin x|+|cos x|)/(|sinx-cosx|)`D. `k(x)=cos(cos x)+cos(sin x)`

Let `p(x)` be a polynomial of degree 6 with leading coefficient unity and `p(-x)=p(x)AAxepsilonR`. Also `(p(1)+3)^(2)+p^(2)(2)+(p(3)-5)^(2)=0` then `sqrt(-4-p(0))` is….

If `lim_(n->oo)[((2009)^2010)^n+((2010)^2009)^n]^(1/n)` is equal to `a^b` where `a,b in N` then `a-b` is equal to:

The value of `x, x in (2,oo)` where `f (x) = sqrt(x sqrt(8x-16))+ sqrt(x- sqrt(8x-16))` is not differentiable is:

`A` and `B` are two square matrices such that `A^(2)B=BA` and if `(AB)^(10)=A^(k)B^(10)` then the value of `k-1020` is.

`Delta I_(1)I_(2)I_(3)` is an excentral triangle of an equilateral triangle `Delta ABC` such that `I_(1)I_(2)=4` unit, if `DeltaDEF` is pedal triangle of `DeltaABC`, then `(Ar(Delta I_(1)I_(2)I_(3)))/(Ar (DeltaDEF))=`

If two points `P & Q` on the hyperbola ,`x^2/a^2-y^2/b^2=1` whose centre is C be such that CP is perpendicularal to `CQ and a lt b`1 ,then prove that `1/(CP^2)+1/(CQ^2)=1/a^2-1/b^2`.

We need a loan to start the company and we need a company to get the loan. It’s a ______ situation. A) calls the shots B) chew things over C) chicken D) call his bluff E) chicken and egg

Let `S={(x,y),x^(2)+y^(2)-6x-8y+21le0}` then `"max"{(12x)/7-(5y)/7,(x,y)inS}+"min" {1/2(x^(2)+y^(2)+1)+(x-y),(x-y)inS}` `-"min"{(sqrt(3)y+|x-3|)/(|x-3|),(x,y)inS}`

She always likes to think things through very carefully. She likes to ______. A) chicken and egg B) chicken C) chew things over D) call his bluff E) call it quits

If the equation `x^(3)-3x+1=0` has three roos `x_(1),x_(2),x_(3)` where `x_(1)ltx_(2)ltx_(3)` then the value of `({x_(1)}+{x_(2)}+{x_(3)})` is ({.} F.P. of `x`).

Whatever we do, we are going to come out badly. It’s a ______ situation. A) a can of worms B) carry the can C) chicken D) can’t win E) chicken and egg

The total number of three-digit numbers, with one digit repeated exactly two times, is

If the mean deviation about the mean of the numbers 1, 2, 3, ..., n, where n is odd, is (5(n + 1))/n then n is equal to____

Let `a_k = .^nC_k` for `0 lt= k lt= n` and `A_k = [(a_(k-1),0), (0,a_k)]` for `1 lt= k lt= n` and `B=sum_(k=1)^(n-1)A_k * A_(k+1) = [(a,0), (0,b)]`

If `alpha_(1),alpha_(2),alpha_(3), alpha_(4)` are the roos of `x^(4)+2x^(3)+bx^(2)+cx+d=0` such that `alpha_(1)-alpha_(3)=alpha_(4)-alpha_(2)`, then `b-c` is equal to__________

I wish you _______. I’m sure you would enjoy joining us. A) could come B) had come C) may come D) would come

Someone is going to have to take responsibility for this disaster. Who is going to ______. A) can’t win B) carry the can C) chicken D) a can of worms E) chicken and egg

I don’t think she _____. Call her again. A) can have heard B) might have heard C) must hear D) can be heard

If `k_(1)` and `(k_(2)gtK+k_(2))` are two non-zero integral values of `k` for which the cubic equation `x^(3)+3x^(2)+k=0` has all integer roots, then the value of `k_(1)-k_(2)` is equal to_______

If `A, B, C` are the angles of triangle `ABC` and `tan A, tan B, tan C` are the roots of the equation `x^(4)-3x^(3)+3x^(2)+2x+5=0`, if the fourth root of the equation is `tan D` then find `3tan D`.

Let’s face it, he decides. He’s the boss so he’s the one that ______. A) called it a day B) calls the shots C) call it quits D) chicken E) call his bluff

I’m sure that there is a lot of corruption in that country. If we order an internal audit we may be opening ______. A) carry the can B) chicken C) can’t win D) chicken and eggE) a can of worms

Don’t you think we should go ______ our plans again? A) down B) through C) on

If a point moves in a straigth line in such a manner that its retardation is porportional to its speed, the distance covered (x) is associated with speed (v) is -A. `x prop V`B. `x prop V^(2)`C. `X prop V^(3)`D. `x prop - V`

Figure shows position-time graph of two cars A and B. A. Car A is faster than car B.B. Car B is faster than car A.C. Both cars are moving with same velocity.D. Both cars have positive acceleration.

Find the minimum height h so that ball just completes the circular motion on the surface when it is released from rest as shown in the diagram (All surfaces are smooth) A. `h = (5)/(2)R`B. h = 2RC. `h = (2)/(5)R`D. h = 3R

The following figure shows the velocity time graph of a body. According to this at the point B- A. The force is zeroB. The force is in the direction of the motionC. The force is in opposite direction of the motionD. It is only the gravitational force

The acceleration (a) of moving particle varies with displacement according to the following relation ` a = X^(2)+3X`, Then correct relation between velocity and displacement is :-A. `V=sqrt((X^(2))/(3)+(3X^(2))/(2)+C)`B. `V=sqrt((2)/(3)X^(3)+3X^(2)+C)`C. `V=((2)/(3)X^(3)+3X^(2)+C)`D. `V = 2x + 3`

Our family is quite ______ united family.A) IsB) aC) theD) an

The committee decided to award the prize to you and ______. A) I B) we C) his D) me

What word is used for the meat of a pig when it’s used as meat?

Young sheep’s meat is called ______.

The flesh of a fully grown sheep is called ______.

Roosters, hens, ducks, and turkeys when bred for food or for their eggs are collectively known as ______.

Which one of the following will accelerate phosphorus cycle?(1) Volcanic activity(2) Weathering of rocks(3) Rain fall and storms(4) Burning of fossil fuels

At which stage of life the oogenesis process is initiated?(1) Embryonic development stage(2) Birth(3) Adult(4) Puberty

Roe and Caviar are the eggs of ______.

The flesh of a deer used for eating is known as ______.

Addition of more solutes in a given solution will:(1) lower its water potential(2) make its water potential zero(3) not affect the water potential at all(4) raise its water potential

The collective word for the flesh of animals such as rabbits, pigeons and deer hunted for sport or food is ______.