28278 + Interview Questions in Maths in Class 12 Page 544 InterviewSolution

27151.	Integrate the following functions. int(x^(2)+1)/(x^(4)+1)dx
Answer» Answer :`(1)/(sqrt2)TAN^(-1)((x^(2)-1)/(sqrt2x)+C)`

Discussion

27152.	Which of the following , taken by itself, would be decreasing the rate at which energy is transferred by a way travelling along a straight ?
Answer» reducing the linear MASS density of the string by one half double the wavelength of the wave doubling the tension in the string. doubling the amplitude of the wave. Solution :AB `((dE)/(dt))_(AV)=(1)/(2)muvomega^(2)A^(2)=(1)/(2)mu((f)/(LAMBDA))omega^(2)A^(2)=(1)/(4pi)mu(omega^(2))/(lambda)A^(2)` `((dE)/(dt))_(av)=(1)/(2)SQRT(Tmu)omega^(2)A^(2)` `v=sqrt((T)/(mu))`

Discussion

27153.	The ratio in which the point Q(5,4,-6) divides the line joining the points P(3,2,-4) and R(9,8,-10) is
Answer» `2:1` `1:3` `2:3` `1:2` ANSWER :D

Discussion

27154.	Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find (i) P(A cap B) (ii) P(A cup B) (iii) P(A\|B) (iv) P(B\|A)
Answer» ANSWER :(i) 0.12, (II) 0.58, (III) 0.3, (IV) 0.4

Discussion

27155.	If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability (1)/(2))
Answer» ANSWER :`(3)/(16)`

Discussion

27156.	If x e ^(xy) = y + sin ^(2) x, thenat x =0, (dy)/(dx) =
Answer» 1 2 `1/2` 0 Answer :A

Discussion

27157.	Find the area enclosed with in the curve y=x^(2), y=x^(3)
Answer» ANSWER :`(1)/(12)`

Discussion

27158.	An equailateral triangle is inscribed in the parabola y^(2)=4ax whose vertex is at the vertex of the parabola . The length of its side is
Answer» `2sqrt(3)`a `4sqrt(3)`a `8sqrt(3)`a `16sqrt(3)`a Answer :C

Discussion

27159.	A cylindrical tank of radius 10m is being filled with wheat at the rate of 314 cubic metre per hour. The depth of the wheat is increasing at the rate of
Answer» 1 m/h 0.1 m/h 0.1 m/h 0.5 m/h Answer :A

Discussion

27160.	For events A and B if P(A) = 0.7, P(B) = 0.5 and P(A cap B)= 0.3 then find P(A \|B).
Answer» ANSWER :`(3)/(8)`

Discussion

27161.	Let H be a hyperbola of eccentricity 3. A normal to the hyperbola meets the transverse axis and the conjugate axis at P and Q, respectively. If locus of midpoint of PQ is a hyperbola of eccentricity elt then er is equal to
Answer» ANSWER :1.06

Discussion

27162.	(Manufacturing Problem) A manufacturer considers that men and women workers are equally efficient and so he pays tehm at the same rate.He has 30 and 17 units of workers(male and femlae) and capital respectively, which he uses to produce two types of goods A and B.To produe one unit of A, 2 workers and 3 units of capital are required whie 3 workers and 1 unit of capital are required to produce one unit of B. If A and B are priced at ₹. 100 and₹.120 per unit respectively, how should he use his resources to maximise the total revenue?Form the above as an LPP and solve graphically.
Answer» Answer :The maximum TOTAL revenue is OBTAINED when 3 units of GOODS A and 8 units of GOOD B be produced.

Discussion

27163.	If P(A) = 0.4, P(B)=0.5, P(C) =0.6, P(AcapB) = 0.2, P(BcapC) = 0.3, P(CcapA) = 0.25, P(AcapBcapC) = 0.1 then P(AcupBcupC) =
Answer» ANSWER :0.85

Discussion

27164.	Let f be a continuous function satisfying f (x+y) = f (x) + f (y), for each x, y in R and f(1) = 2 then int(f(x)tan^(-1)x)/((1+x^(2))^(2))dx is equal to
Answer» cannot be DETERMINED explicity `C-(tan^(-1)x)/(2(1+x^(2)))+(1)/(4)tan^(-1)x+f(x)/(1+(f(x))^2)` `C-(1)/((1+x^(2)))tan^(-1)x+(1)/(2)tan^(-1)x+(x)/(2(1X^(2)))` `C-(1)/((1+x^(2)))tan^(-1)x+(1)/(2)tan^(-1)x+(x)/(2(1+x^(2)))` Answer :D

Discussion

27165.	Find the shortest distance between the ellipse x^(2) + 2y^(2) = 2 and the circle x^(2)+y^(2)-3x-2sqrt(2)y+4=0
Answer» ANSWER :`(SQRT(3)-1)/(2)`

Discussion

27166.	How many geometrical isomers are possible for the given complex ? Pt(gly)Cl_(2)BrI]^(-) [If your answer is 2 then write the answer as 0002.]
Answer» Solution :`]PT(gly)Cl_(2)BrI]^(-)toM(AB)c_(2)de`

Discussion

27167.	Find area of the triangle with vertices at the point given in each of the following: ( -2,-3) , (3,2) ,( -1,-8)
Answer» ANSWER :` 15 `

Discussion

27168.	sec^(2) (tan^(-1) 4) + cosec^(2) (cot ^(-1) 3) =?
Answer» 30 29 27 25 Answer :C

Discussion

27169.	Two unit squares are chosen at random on a chess board. Find the probability that they have a side in common.
Answer» ANSWER :`(1)/(18)`

Discussion

27170.	A solution is to be kept between 68^@ F and 77^@ F. what is the range in temperature in degree Celsius (C) if the Celsius/ Fahrenheit (F) conversion formula is given by F = 9/5 C + 32?
Answer» Answer :The temperature in DEGREE CELSIUS MUST be in the RANGE between `20^@C and 25^@ C`

Discussion

27171.	If I_(n) = int_(0)^(1) (1- x^(5) )^(n) dx, then (I_(21) )/( I_(20) ) is equal to
Answer» ANSWER :`1.01`

Discussion

27172.	If two circles touching both the axes intersect at two points P and Q where P=(3,1) then PQ=
Answer» `SQRT(2)` `2sqrt(2)` `3sqrt(2)` `4sqrt(2)` ANSWER :B

Discussion

27173.	Sand is pouring from a pipe at the rate of 12 cm^(3)//s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4cm?
Answer» ANSWER :`(1)/( 48pi)` cm/sec

Discussion

27174.	If veca and vecb are parallel vector, then [(veca,vecb,vecc)] is equal to
Answer» 2 -1 1 0 Solution :N/A

Discussion

27175.	For the function f(x)= x + (1)/(x), x in [1, 3] the value of c for mean value theorem is
Answer» 1 `SQRT3` 2 None of these Answer :B

Discussion

27176.	if (4,k) and (2,3) are conjugate points with respect to the circle x^(2) + y^(2) = 17 then find k.
Answer» ANSWER :`3`

Discussion

27177.	If f:RrarrR_(1)f(x) is a differentiable bijective function, then which of the following may be true.
Answer» `(f(x)-x)f''(x)LT0,AAx in R` `(f(x)-x)f''(x)GT0,AAx in R` If `f(x)-x)f''(x)gt0,THENF(x)=f^(-1)(x)` has no solution If `f(x)-x)f''(x)gt0, then f(x)=f^(-1)(x)` has atleast a REAL solution Answer :B::C

Discussion

27178.	Find the absolute maximum value and the absolute minimum value of thefunctions in the given intervals: f(x) = (x-1)^(2) +3, x in[-3 ,1)
Answer» Answer :ABSOLUTE minimum VALUE = 19, absolute MAXIMUM value = 3

Discussion

27179.	From a point P(x_(1),y_(1)) on the straight line 4x-3y+14=0 two tangents PA and PB are drawn to the circles x^(2)+y^(2)=16 and x^(2)+y^(2)+8x-6y+12=0, then
Answer» PA=PB PA=3PB 3PA=PB none Answer :A

Discussion

27180.	Find the absolute maximum value and the absolute minimum value of thefunctions in the given intervals: f(x) = 4x -(1)/(2) x^(2) , x in [-2,(9)/(2)]
Answer» Answer :ABSOLUTE minimum value = – 10, absolute MAXIMUM value = 8

Discussion

27181.	The two adjacent sides of a parallelogram are 2hati-4hatj+5kandhati-2hatj-3hatk. Find the unit vector parallel to its diagonal Also , find its area.
Answer» ANSWER :`(1)/(7)(3hati-6hatj+2hatk);11sqrt(5)`

Discussion

27182.	If two dice are thrown and at least one of the dice shows 5.then the probability that the sum is 10 or more is
Answer» `(1)/(6)` `(4)/(11)` `(3)/(11)` `(2)/(11)` Solution :A = Eventof showing5 and atleastone dice`= (1,5) , (2,5),(3,5), (4,5), (5,5),(6,5), (5,1) ,(5,2),(5,3),(5,4), (5,6)` N (A) = 11 . and n(s) ` = 6 XX 6 = 36` B = Eventof Showingshows10 or morewhenat lest onedice SHOWN 5. ` = (5,5) ,(5,6),(6,5)` n(B) = 3 . `rArr n(A nn B) = 3` Now, `P((B)/(A)) = (P(AnnB))/(P(A))` . `=((n(AnnB))/(n(S)))/((n(A))/(n(S))) = ((3)/(36))/((11)/(36)) = (3)/(11)`

Discussion

27183.	Assertion(A ) :thenumberof rootsof x^4+2x^3 -7x^2 -8x +12=0Reason (R ) :Everyalgebraicequationofdegree n hasn rootsandnomore.
Answer» BOTHA and RaretrueR ISTHE correctexplanationof A both AandRare TRUEAND Ris notcorrectexplanationof A Ais trueand Risfalse A isfalseand Ristrue Answer :A

Discussion

27184.	Let I_(n)=int_(0)^(pi//2) cos^(n)x cos nx dx. Then, I_(n):I_(n+1) is equal to
Answer» `3:1` `2:3` `2:1` `3:4` ANSWER :C

Discussion

27185.	Let f(x)=[x]= Greatest integer less than or equal to x and k be an integer. Then, which one of the following in not correct?
Answer» `lim_(xtok^-)f(x)=K-1` `lim _(xtok)f(x)=k` `lim _(xtok)f(x)"exists"` `lim_(xtok)f(x)` does not EXIST Solution :We have, `f(x)=[x]` `THEREFORE ("LHS at" x =k)` `=lim_(xtok^-)f(x)=lim_(hto0)=lim_(hto0)f(k-h)=lim_(hto0)[h-k]` `=lim_(hto0)k-1=k-1[because k-1ltk-hltk-hlt ktherefore [k-h]=k-1]` `therefore (RHL "at" x=k)` `=lim_(xto0)f(x)=lim_(hto0)f(k-h)=lim_(hto0)[k+h]` `=lim_(hto0)k=k[because klt k+hlt k+1therefore [k+h]=k]` Clearly, `lim_(xt0k^+)f(x) ne lim_(xtok^+)f(x). So, lim_(xtok)f(x)` does not exist.

Discussion

27186.	H(x) increase as f(x) decreases for all real values ofx if
Answer» `a in (0,3)` `a in (-2,2)` `[3,oo)` none of these Solution :h(x) increases as f(x) decreases for all VALUES of x if `3a(f(x))^(2)-2 AF(x)+le for all x in R` or `33a LT 0and 4a^(2)-12ale 0` or `a lt 0 and a in [0,3]` So , such AIS possible

Discussion

27187.	Find the mean deviation from the mean for the set ofobservations 1,2,3,
Answer» ANSWER :1

Discussion

27188.	When three cards are drawn at random from a well shuffled pack of cards, then what is the probability that all of them are from the different suits?
Answer» `(""^(13)C_(3))/(""^(52)C_(3))` `(4.(""^(13)C_(1)""^(13)C_(1)""^(13)C_(1)))/(""^(52)C_(3))` `(3""^(13)C_(3)""^(13)C_(1)""^(13)C_(1))/(""^(52)C_(3))` None of these Answer :B

Discussion

27189.	Derivative of tan^(-1)x w.r. to cot^(-1)x is ……. Where x in R
Answer» `-1` 1 `(1)/(1 + X^(2))` `-(1)/(1 + x^(2))` ANSWER :A

Discussion

27190.	Let f(x) = int_(0)^(x)(dt)/(sqrt(1+t^(2))) and g(x)be the inverse of f(x), then which one of the followingholds good ?
Answer» `2G" = G^(2)` `2g" = 3G^(2)` `3g" = 2g^(2)` `3g" = g^(2)` SOLUTION :N//A

Discussion

27191.	(i) Find the length of the chord intercepted by the circle x^(2)+y^(2)-8x-2y-8=0 on the line x+y+1=0 (ii) Find the length of the chord intercepted by the circle x^(2)+y^(2)+8x-4y-16=0 on the line 3x-y+4=0 (iii) Find the length of the chord formed by x^(2)+y^(2)=a^(2) on the line xcos alpha +y sin alpha=p
Answer» ANSWER :(i) `2sqrt(7)` (ii) `2sqrt(26)` (III) `2sqrt(a^(2)-p^(2))`

Discussion

27192.	int_(0)^(1)[2x]dx where [] is the greatest integer function :
Answer» 1 `(1)/(4)` `(1)/(3)` `(1)/(2)`. ANSWER :D

Discussion

27193.	IFalpha,betaare therootsofax^2 + bx+ c=0and s_(n)= alpha ^n + beta ^nthen\|(3,1+S_1,1+S_2),(1+S_1,1+S_2,1+S_3),(1+s_(2),1+s_3,1+S_4)\|=
Answer» 0 `((B^2- 4AC )(a+b+c)^2)/(a^4)` `(b^2-4ac)/(a^4)` `((a+b+c)^2)/(a^4)` ANSWER :B

Discussion

27194.	Let the terms a_(1),a_(2),a_(3),…a_(n) be in G.P. with common ratio r. Let S_(k) denote the sum of first k terms of this G.P.. Prove that S_(m-1)xxS_(m)=(r+1)/rSigmaSigma_(i le itj le n)a_(i)a_(j)
Answer» Solution :We have `a_(1)+a_(2)+…+a_(m))^(2)` `=a_(1)^(2)+a_(2)^(2)+…+a_(m)^(2)+2(a_(1)a_(2)+a_(2)a_(3)+…)` `THEREFORE[(a_(1)(1-r^(m)))/(1-r)]^(2)=(a_(1)^(2)(1-r^(2m)))/(1-r^(2))+2underset(1leiltjlen)(SigmaSigma)a_(i)a_(j)` `rArr2underset(1leiltjlen)(SigmaSigma)a_(i)a_(j)=(a_(1)^(2)(1-r^(m))^(2))/((1-r)^(2))-(a_(1)^(2)(1-r^(2m)))/(1-r^(2))` `=(a_(1)^(2)(1-r^(m)))/((1-r)^(2)(1+r))2(r-r^(m))` `=(2R)/(1+r){a_(1)cdot((1-r^(m-1)))/(1-r)}{(a_(1)(1-r^(m)))/(1-r)}` `=S_(m-1)xxS_(m)`

Discussion

27195.	Solve (x^(2)+y^(2))dy=xydx
Answer» ANSWER :`CE^(X^(2))/(2Y^(2))`

Discussion

27196.	A: If (5+ sqrt(24))^n=I+F where, I, n are positive integers, 0 lt F lt 1 then I is an odd integer and (I+F)(1-F)=1. R : If (a+sqrtb)^=I+F where I, n are positive integers, 0 lt F lt1, a^2 - b=1 then i) I is an odd positive integer ii) (I+F)(1-F)=1.
Answer» Both A and R are true and R is the CORRECT EXPLANATION of A Both A and R true but R is not correct explanation of A A is true but R is false A is false but R is true Answer :A

Discussion

27197.	The simplest formular of a compound containing 50% of element X (atomic mass 10) and 50% pf element Y (atomic mass 20) is :-
Answer» XY `X_(2)Y` `XY_(3)` `X_(2)Y_(3)` ANSWER :A

Discussion

27198.	Write the Macleaurin series expansion of the following functions: (i)e^(x)(ii) sin x (iii) cos x (iv) log (1-x):-1 lt x lt 1(v) tan ^(-1)(x),-1 lt x lt 1(iv) cos ^(2)x
Answer» Answer :`=1-(2X^(2))/(\|_ul(2))+(2^(3)x^(4))/(\|_ul(4))`

Discussion

27199.	IFA+B+C =pi , thentan ((A)/(2))tan ((B)/(2)) + tan (B/2)tan(C/2) + tan(C/2 )tan ((A)/(2))is
Answer» `PI /6` `3` `2` `1` ANSWER :D

Discussion

27200.	Solve the inequality P(x)=x^(3)-4x^(2)+x+4 gt0.
Answer» Solution :USE a calculator to GRAPH `y=P(x)` and find its (approximate) ZEROS: `-0.814,1.471, and 3.343`. Observe that the graph of `y=P(x)` is above the x-axis for -0.814`ltxlt1.471` or `x GT 3.343`.

Discussion

Explore topic-wise InterviewSolutions in .

Integrate the following functions. int(x^(2)+1)/(x^(4)+1)dx

Which of the following , taken by itself, would be decreasing the rate at which energy is transferred by a way travelling along a straight ?

The ratio in which the point Q(5,4,-6) divides the line joining the points P(3,2,-4) and R(9,8,-10) is

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find﻿ (i) P(﻿A cap B)﻿ (ii) P(A cup B)﻿ (iii) P(A|B)﻿ (iv) P(B|A)﻿

If each element of a second order determinant is either zero or one, what is the﻿ probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being﻿ assumed with probability﻿ (1)/(2))

If x e ^(xy) = y + sin ^(2) x, thenat x =0, (dy)/(dx) =

Find the area enclosed with in the curve y=x^(2), y=x^(3)

An equailateral triangle is inscribed in the parabola y^(2)=4ax whose vertex is at the vertex of the parabola . The length of its side is

A cylindrical tank of radius 10m is being filled with wheat at the rate of 314 cubic metre per hour. The depth of the wheat is increasing at the rate of

For events A and B if P(A) = 0.7, P(B) = 0.5 and P(A cap B)= 0.3 then find P(A |B).

Let H be a hyperbola of eccentricity 3. A normal to the hyperbola meets the transverse axis and the con­jugate axis at P and Q, respectively. If locus of mid­point of PQ is a hyperbola of eccentricity elt then er is equal to

If P(A) = 0.4, P(B)=0.5, P(C) =0.6, P(AcapB) = 0.2, P(BcapC) = 0.3, P(CcapA) = 0.25, P(AcapBcapC) = 0.1 then P(AcupBcupC) =

Let f be a continuous function satisfying f (x+y) = f (x) + f (y), for each x, y in R and f(1) = 2 then int(f(x)tan^(-1)x)/((1+x^(2))^(2))dx is equal to

Find the shortest distance between the ellipse x^(2) + 2y^(2) = 2 and the circle x^(2)+y^(2)-3x-2sqrt(2)y+4=0

How many geometrical isomers are possible for the given complex ? Pt(gly)Cl_(2)BrI]^(-) [If your answer is 2 then write the answer as 0002.]

Find area of the triangle with vertices at the point given in each of the following: ( -2,-3) , (3,2) ,( -1,-8)

sec^(2) (tan^(-1) 4) + cosec^(2) (cot ^(-1) 3) =?

Two unit squares are chosen at random on a chess board. Find the probability that they have a side in common.

A solution is to be kept between 68^@ F and 77^@ F. what is the range in temperature in degree Celsius (C) if the Celsius/ Fahrenheit (F) conversion formula is given by F = 9/5 C + 32?

If I_(n) = int_(0)^(1) (1- x^(5) )^(n) dx, then (I_(21) )/( I_(20) ) is equal to

If two circles touching both the axes intersect at two points P and Q where P=(3,1) then PQ=

Sand is pouring from a pipe at the rate of 12 cm^(3)//s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4cm?

If veca and vecb are parallel vector, then [(veca,vecb,vecc)] is equal to

For the function f(x)= x + (1)/(x), x in [1, 3] the value of c for mean value theorem is

if (4,k) and (2,3) are conjugate points with respect to the circle x^(2) + y^(2) = 17 then find k.

If f:RrarrR_(1)f(x) is a differentiable bijective function, then which of the following may be true.

Find the absolute maximum value and the absolute minimum value of thefunctions in the given intervals: f(x) = (x-1)^(2) +3, x in[-3 ,1)

From a point P(x_(1),y_(1)) on the straight line 4x-3y+14=0 two tangents PA and PB are drawn to the circles x^(2)+y^(2)=16 and x^(2)+y^(2)+8x-6y+12=0, then

Find the absolute maximum value and the absolute minimum value of thefunctions in the given intervals: f(x) = 4x -(1)/(2) x^(2) , x in [-2,(9)/(2)]

The two adjacent sides of a parallelogram are 2hati-4hatj+5kandhati-2hatj-3hatk. Find the unit vector parallel to its diagonal Also , find its area.

If two dice are thrown and at least one of the dice shows 5.then the probability that the sum is 10 or more is

Assertion(A ) :thenumberof rootsof x^4+2x^3 -7x^2 -8x +12=0Reason (R ) :Everyalgebraicequationofdegree n hasn rootsandnomore.

Let I_(n)=int_(0)^(pi//2) cos^(n)x cos nx dx. Then, I_(n):I_(n+1) is equal to

Let f(x)=[x]= Greatest integer less than or equal to x and k be an integer. Then, which one of the following in not correct?

H(x) increase as f(x) decreases for all real values ofx if

Find the mean deviation from the mean for the set ofobservations 1,2,3,

When three cards are drawn at random from a well shuffled pack of cards, then what is the probability that all of them are from the different suits?

Derivative of tan^(-1)x w.r. to cot^(-1)x is ……. Where x in R

Let f(x) = int_(0)^(x)(dt)/(sqrt(1+t^(2))) and g(x)be the inverse of f(x), then which one of the followingholds good ?

int_(0)^(1)[2x]dx where [] is the greatest integer function :

IFalpha,betaare therootsofax^2 + bx+ c=0and s_(n)= alpha ^n + beta ^nthen|(3,1+S_1,1+S_2),(1+S_1,1+S_2,1+S_3),(1+s_(2),1+s_3,1+S_4)|=

Let the terms a_(1),a_(2),a_(3),…a_(n) be in G.P. with common ratio r. Let S_(k) denote the sum of first k terms of this G.P.. Prove that S_(m-1)xxS_(m)=(r+1)/rSigmaSigma_(i le itj le n)a_(i)a_(j)

Solve (x^(2)+y^(2))dy=xydx

A: If (5+ sqrt(24))^n=I+F where, I, n are positive integers, 0 lt F lt 1 then I is an odd integer and (I+F)(1-F)=1. R : If (a+sqrtb)^=I+F where I, n are positive integers, 0 lt F lt1, a^2 - b=1 then i) I is an odd positive integer ii) (I+F)(1-F)=1.

The simplest formular of a compound containing 50% of element X (atomic mass 10) and 50% pf element Y (atomic mass 20) is :-

Write the Macleaurin series expansion of the following functions: (i)e^(x)(ii) sin x (iii) cos x (iv) log (1-x):-1 lt x lt 1(v) tan ^(-1)(x),-1 lt x lt 1(iv) cos ^(2)x

IFA+B+C =pi , thentan ((A)/(2))tan ((B)/(2)) + tan (B/2)tan(C/2) + tan(C/2 )tan ((A)/(2))is

Solve the inequality P(x)=x^(3)-4x^(2)+x+4 gt0.

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find (i) P(A cap B) (ii) P(A cup B) (iii) P(A|B) (iv) P(B|A)

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability (1)/(2))

Let H be a hyperbola of eccentricity 3. A normal to the hyperbola meets the transverse axis and the conjugate axis at P and Q, respectively. If locus of midpoint of PQ is a hyperbola of eccentricity elt then er is equal to