28278 + Interview Questions in Maths in Class 12

1.	Integrate the following functions: (cos2x+2 sin^2 x)/cos^2x
Answer» SOLUTION :`(cos2x+2 sin^2x)/cos^2x)` `=(1-2sin^2x+2sin^2x)/cos^2x = sec^2x` THEREFORE `INT (cos2x+2sin^2x)/cos^2x) = tanx+c`

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2.	Find the area of the region bounded by the curve y^(2) = 4xand line x=3.
Answer» ANSWER :`=8sqrt(3)` SQ. UNITS.

Discussion

3.	If A,B,C are mutually exclusive and exhaustive events such that P(A)=2P(B)=3P(C ) then P(BuuC)=
Answer» `(6)/(11)` `(5)/(11)` `(4)/(11)` `(7)/(11)` ANSWER :B

Discussion

4.	Consider the three vectors p, q, r such that p=hat(i)+hat(j)+hat(k) and q=hat(i)-hat(j)+hat(k) , ptimesr=q+cp and p*r=2 Q. If y is a vector satisfying (1+c)y=ptimes(qtimesr), then the vectors x, y and r
Answer» are collinear are coplanar represent the coterminus EDGES of a TETRAHEDRON whose volume is c CU. Units represent the coterminus edges of a parallelopiped whose volume is c cu. Units Answer :C

Discussion

5.	Drawa rough sketch of thegivencurvey=1 +\|x+1\|,x =-3 , x =3 , y=0and findthe areaof theregionbounded by them , usingintegration
Answer» ANSWER :`=16` SEQ . UNIT

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6.	Consider the function f(x) =(x^(3))/(4)-sin pi x+3
Answer» f(x) does not attain VALUE within the INTERVAL [-2,2] f(x) takes on the value `2 (1)/(3)` in the interval `[-2,2]` f(x) takes on the value `3(1)/(4)` in the interval [-2,2] f(x) takes no value no value p `1LT p lt 5` in the interval [-2,2] Answer :B::C

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7.	Write the absolute maximum and absolute minimum of the function f(x)=x/\|x\| in [-2, 2].
Answer» SOLUTION :

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8.	In triangle ABC, angle A gt pi/2. A A_(1) and A A_(2) are the medium and altitude, espectively. If angle B A A_(1)= angle A _(1) A A_(2)=angle A _(2) AC, then sin^(3)""A/3 . Cos ""A/3is equal to
Answer» `(3A^(3))/(16b^(2)c)` `(3a^(3))/(64b ^(2)c)` `(3a^(2))/(4b^(2)c)` `(3a^(3))/(12 b^(2)c)` ANSWER :D

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9.	If a xx I + 2a - 5j = 0 then a =
Answer» 2I + k I + 2k 2j + k j + 2k Answer :C

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10.	sinh (ix) is equal to
Answer» `i SIN X` `sinix` `-i sin x` `i sin IX` ANSWER :a

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11.	If P(A) = 2/3, P(B) = 4/9 " and " P(AcapB)=4/5, then find the value of P(AcupB) " and " P(A'capB').
Answer» <P> SOLUTION :`P(ACUPB)=38/45 " and " P(A'capB')=7/45`

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12.	Solve the following system of linear equation by matrix method. x-y+2z=1 2y-3z=1 and 3x-2y+4z=2.
Answer» ANSWER :x=0, y = 5 and Z = 3

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13.	Integrate the following functions : intsqrt(4x^(2)-5)dx
Answer» ANSWER :`xsqrt(X^(2)-(5)/(4))-(5)/(4)log\|x+sqrt(x^(2)-(5)/(4))\|+C`

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14.	Prove that : int_(pi//4)^(3pi//4) (x)/(1+sin x)dx=pi(sqrt(2)-1)
Answer»

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15.	Find the equation of the circle passing through the points (3,4) (3,2) ,(1,4)
Answer» ANSWER :` X^(2) + y ^(2)-4X -6Y +11=0 `

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16.	A pair of fair dice are rolled till a sum of 2 or 3 is obtained. Find the probability of getting sum 2 before getting sum 3.
Answer» ANSWER :`(1)/(3)`

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17.	int_(pi//2)^(pi//2)e^(sin^(2)x).sin^(2n+1)xdx=
Answer» 2e 0 1 `e/2` ANSWER :B

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18.	From 5 apples, 4 mangoes & 3 bananas, in how many ways we can select atleast two fruits of each variety if fruits of same species are identical?
Answer» ANSWER :24

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19.	Centres of circles touching both the axes and also the line 3x+4y-12=0 is
Answer» (1,1), (6,6), (-2,2) and (3,-3) (1,-1) and (6,-6) (-1,1) and (-6,6) (-1,-1) and (-6,-6) ANSWER :A

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20.	If hata, hatb are unit vectors and vec c is such that vec c=veca xx vec c +vecb, then the maximum value of[veca vecb vec c] is :
Answer» 1 `(1)/(2)` 2 `(3)/(2)` ANSWER :B

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21.	Which one of the following must equal p + q , if x - y = p and 2x + 3y = q ?
Answer» `X + y` `3x - 2y` `2X -3Y` `3x + 2y` Answer :D

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22.	If A and B are mutually exclusive events, given that P(A)=3/5,P(B)=1/5, then P(A or B) is
Answer» ANSWER :`2/25`

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23.	bar(d)=lambda(bar(a)xx bar(b))+mu(bar(b)xx bar( c ))+v(bar( c )xx bar(a)) and [bar(a)bar(b)bar( c )]=(1)/(8) then lambda+mu+v = …………..
Answer» `bar(d)(bar(a)+bar(B)+bar( C ))` `2BAR(d).(bar(a)+bar(b)+bar( c ))` `4bar(d).(bar(a)+bar(b)+bar( c ))` `8bar(d)(bar(a)+bar(b)+bar( c ))` Answer :D

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24.	Find the angle between the linesvecr = (3 + lambda)hati + 2(1 + lambda)hatj + 2(1 – 2lambda)hatkand vecr=5hatj-2hatk+mu(3hati+2hatj-6hatk).
Answer» ANSWER :ANGLE `theta=cos^(-1)((19)/(21))`

Discussion

25.	which of the following lines are asymptotes for the graph of y=(3x^2-13x-10)/(x^2-4x-5) ? I. x=-1 II. x=5 III. Y=3
Answer» I only II only I and II I and III Solution :Factor the NUMERATOR and denominator: `((3x+2)(x-5))/((x+1)(x-5))`, Since the x-5 DIVIDE out, the only vertical asymptote is at x=-1. Since the degree of the numerator and denominator are equal, y approaches 3 as x approaches`+-oo`, so y=3 is a HORIZONTAL asymptote. [9]

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26.	The minimum radius of the circle which contains the threecircles, x^(2)+y^(2)-4y-5=0,x^(2)+y^(2)+12x+4y+31=0 and x^(2)+y^(2)+6x+12y+36=0 is
Answer» `(7)/(18)sqrt(900)+3` `(sqrt(845))/(9)+4` `(5)/(36)sqrt(949)+3` none of these Solution :`S_(1)-=x^(2)+y^(2)-4y-5=0` `S_(2)-=x^(2)+y^(2)+12x+4y+31=0` and `S_(3) -=x^(2)+y^(2)+6x+12y+36=0` `C_(1) -= (0,2),r_(1)=3` `C_(2) -= (-6,-2), r_(2)=3` `C_(3) -= (-3,-6) , r_(3)=3` All circles have the same radius, THERADIUS of the CIRCLE touching all the circles is `CP=C C_(1)=C_(1)P+3` Let `C(h,k)` be the center of the required circle. Then, `C C_(1)= C C_(2) = C C_(3)`or `C C_(1)^(2) = C C_(2)^(2)= C C_(3)^(2)` or `(h-0)^(2)+(k-2)^(2)=(h+6)^(2)+(k+2)^(2)` `=(h+3)^(2)+(k+6)^(2)` or `-4k+4=12h+4k+40=6h+12k+45` or `3h+2k+9=0` and `6h-8k-5=0` Solving, we get `h=(-31)/(18),k=(-23)/(12)` `:. C C_(1)=sqrt((0+(31)/(18))^(2)+(2+(23)/(12))^(2))=(5)/(36)sqrt(949)` Now, `CP =C C_(1)+3=(5)/(36)sqrt(949)+3`

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27.	For the vectors A(-1,-2,3) and B(1,2,-1) the direction cosines of vec(AB) are ……………
Answer» `(1)/(3),(2)/(3),(-2)/(3)` 2, 4, -4 `(2)/(sqrt(6)),(4)/(sqrt(6)),(-4)/(sqrt(6))` `(-1)/(3),(-2)/(3),(2)/(3)` ANSWER :A

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28.	Find the coefficient of x^(-7)" in "((2x^(2))/(3)-(5)/(4x^(5)))^(7)
Answer» ANSWER :` - 4375/324`

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29.	Distance from the point (-3,2,5) to the point where the line (x+3)/2= (y-2)/2=(z-5)/2 meets the plane x+y +2z = 3 is
Answer» `7/18` `8/17` `17/8` `18/7` ANSWER :D

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30.	Show that the function f(x)=\|cosx\| is a continuous function.
Answer» Solution :Write `g(X)=cosx`and`H(x)=\|x\|.` Then g and h are CONTINUOUS functions `therefore(hog)(x)=h(g(x))=h(cosx)=\|cosx\|` is a continuous function i.e.,f(x) is a continuous function.

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31.	Find the equation of all lines having slope 2 which are tangents to the curve y=(1)/(x-3), x ne 3.
Answer» ANSWER :`(x-3)^(2)GT 0`

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32.	Compute the integrals :int_(1) ^(15) "arc tan " sqrt(sqrt(x) - 1)dx
Answer» ANSWER :`(16 PI)/(3) - 2 sqrt(3)`

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33.	A point charge ..................
Answer» Solution :LET a vessel is closed by a disc of radius 'R'. Then the flux linked with the closed vessel will be `phi=Q/epsi_(0)` Now flux linked with the disc will be `phi_("disc")=Q/(2 epsi_(0)) (1- x/sqrt(x^(2)+R^(2)))` `phi_("total")=phi_("disc")+phi_("vessel")` `phi_("vessel")=Q/(2 epsi_(0)) (1+ x/sqrt(x^(2)+R^(2)))`

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34.	There are 2n things out of which 'n' are alike and 'n' are different, the number of ways of selecting 'n' things is
Answer» `""^(2N)C_(N)` `2^(n)-1` `2^(n)` n Answer :C

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35.	A point charge .................
Answer» SOLUTION :As sphere is grounded, its NET potential must be 0, Hence `(KQ)/x+(Kq)/R=0` `(QR)/x=q` `i=(dq)/(dt)=+(QR)/x^(2) xx (dx)/(dt)` `i=(QRV)/x^(2)`

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36.	A person gets Rs. 2 if head comes and loses Rs. 5 when a tail comes then how much money can he expect in the long run per game, when an unbiased coin in tossed twice.
Answer» ANSWER :3 (LOSS)

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37.	The volume of a cube is increasing at a rate of 8 cubie centimeters per second. How fast is the surface area increasing when the length of the edge is 12 cm?
Answer» ANSWER :`(8)/(3) "CM"^(2)` /sec

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38.	Evaluate intx^(2) cos x dx
Answer» ANSWER :`(X^(2)-2)sinx+2xcosx+c`

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39.	Write in the simplest form of tan^(-1)sqrt((1-cosx)/(1+cosx)),0ltxltpi
Answer» ANSWER :`x/2`

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40.	The value of lim_(n to oo)((n!)/(n^(n))^(2n^(4+1))/(5n^(5)+1)) is equal
Answer» e `(2)/(e)` `((1)/(e))^(2)/(5)` NONE of these ANSWER :C

Discussion

41.	Indicate which of the following is a tautology .
Answer» <P>`(~p VV Q) ~ (p vv ~q)` `(~p vv ~q) to p vv q` `(p vv ~q) ^^ (p vv q)` `(~p vv ~q) vv (p vv q)` ANSWER :D

Discussion

42.	There are 25 girls and 15 boys in class XI and 30 boys and 20 girls in class XII. If a student chosen from a class, selected at random, happens to be a boy, find the probability that he has been chosen from class XII.
Answer» <P> Solution :LET `E_1`= The student is choosen from class XI. `E_2` The student is choosen from class XII. A= The student is a boy.`P(E_1)=P(E_2)=1/2` `P(A//E_1)=15/40=3/8` P(A//E_2)=30/50=6/10` We WENT to find `P(E_2//A)`. By Baye.s theoren `P(E_2\|A)=(P(E_2)P(A//E_2))/(P(E_1)P(A//E_1)+P(E_2)P(A//E_2))` `=(1/2cdot 6/10)/(1/2cdot3/8+1/2cdot6/10)=(6/10)/((15+24)/40)=24/39=8/13`

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43.	AA\|x\|le1,cos^(-1)(-x)=
Answer» `cos^(-1)(x)` `PI=cos^(-1)(x)` `pi - cos^(-1)(x)` `(pi)/2-cos^(-1)(x)` ANSWER :C

Discussion

44.	If the position vectors of the vertices of Delta ABC are 3hati+hatj+2hatk, hati-2hatj+7hatk and -2hati+3hatj+5hatk, then the DeltaABC is
Answer» right angled and isosceles right angled, but not isosceles isosceles but not right angled equilateral Solution :Given vertices are `A(3hati+hatj+2hatk),B(hati-2hatj+7hatk)andC(-2hati+3hatj+5hatk)`. Now, `AB=(hati-2hatj+7hatk)-(3hati+hatj+2hatk)` `=-2hati-3hatj+5hatk` `THEREFORE \|AB\|=sqrt(4+9+25)=sqrt(38)` Similarly, `\|BC\|=\|CA\|=sqrt(38)` `therefore \|AB\|=\|BC\|=\|CA\|=sqrt(38)` HENCE, triangle is an equilateral triangle.

Discussion

45.	Statement 1: If a circle S = 0 intersects a hyperbola xy =4at four points , Three of them are (2,2) , (4,1)and ( 6, 2//3)then coordinates of the fouth points are (1//4 , 16 ) Statement 2: If a circle S=0 intersects a hyperbola xy= c ^(2)att_1, t_2, t_3 , t_4thent_1.t_2.t_3.t_4=1.Then correct statement is
Answer» Both the STATEMENT are TRUE and II is the CORRECT explanation of I Both the statement are True but Statement II is Not the correct explanation of Statement I. statement -I is True and Statement -II is False statement -I is False and statement -II is True Answer :D

Discussion

46.	If I_(n) = int Cot^(n)xdx then I_(4) + I_(6) =
Answer» ` - (Cot^(5)x)/(5)` `Cot^(5)` x `(1)/(5) Cot^(5)` x `-(1)/(5) Cot^(5) x - (1)/(3)Cot^(3)` x ANSWER :A

Discussion

47.	Evalute the following integrals int (x^(2) - 1)/(x^(4) + x^(2) + 1) dx
Answer» Answer :`(1)/(2 SQRT(3)) LOG \| (x^(2) - sqrt(3) x + 1)/(x^(2) + sqrt(3X) + 1) \| + c `

Discussion

48.	[(1+ cos((pi)/(12))+ i sin ((pi )/(12)))/(1+ cos((pi)/(12))-i sin((pi)/(12)))^(72)]
Answer» 0 `-1` `1` `1/2` ANSWER :C

Discussion

49.	Which of the following is a contradiction?
Answer» <P>`(p ^^ Q) ^^ (~(p VV q))` `p vv (~p ^^ q)` `( p to q) to p` NONE of these ANSWER :A

Discussion

50.	Let veca,vecb,vecc be three mutually perpendicular vectors having same magnitude and vecr is a vector satisfying vecaxx((vecr-vecb)xxveca)+vecbxx((vecr-vecc)xxvecb)+veccxx((vecr-veca)xxvecb)=vec0, then vecr is equal to
Answer» `1/3(veca+vecb+vecc)` `1/2(veca+vecb+vecc)` `3/2(veca+vecb+vecc)` `2(veca+vecb+vecc)` SOLUTION :NA

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Integrate the following functions: (cos2x+2 sin^2 x)/cos^2x

Find the area of the region bounded by the curve y^(2) = 4xand line x=3.

If A,B,C are mutually exclusive and exhaustive events such that P(A)=2P(B)=3P(C ) then P(BuuC)=

Consider the three vectors p, q, r such that p=hat(i)+hat(j)+hat(k) and q=hat(i)-hat(j)+hat(k) , ptimesr=q+cp and p*r=2 Q. If y is a vector satisfying (1+c)y=ptimes(qtimesr), then the vectors x, y and r

Drawa rough sketch of thegivencurvey=1 +|x+1|,x =-3 , x =3 , y=0and findthe areaof theregionbounded by them , usingintegration

Consider the function f(x) =(x^(3))/(4)-sin pi x+3

Write the absolute maximum and absolute minimum of the function f(x)=x/|x| in [-2, 2].

In triangle ABC, angle A gt pi/2. A A_(1) and A A_(2) are the medium and altitude, espectively. If angle B A A_(1)= angle A _(1) A A_(2)=angle A _(2) AC, then sin^(3)""A/3 . Cos ""A/3is equal to

If a xx I + 2a - 5j = 0 then a =

sinh (ix) is equal to

If P(A) = 2/3, P(B) = 4/9 " and " P(AcapB)=4/5, then find the value of P(AcupB) " and " P(A'capB').

Solve the following system of linear equation by matrix method. x-y+2z=1 2y-3z=1 and 3x-2y+4z=2.

Integrate the following functions : intsqrt(4x^(2)-5)dx

Prove that : int_(pi//4)^(3pi//4) (x)/(1+sin x)dx=pi(sqrt(2)-1)

Find the equation of the circle passing through the points (3,4) (3,2) ,(1,4)

A pair of fair dice are rolled till a sum of 2 or 3 is obtained. Find the probability of getting sum 2 before getting sum 3.

int_(pi//2)^(pi//2)e^(sin^(2)x).sin^(2n+1)xdx=

From 5 apples, 4 mangoes & 3 bananas, in how many ways we can select atleast two fruits of each variety if fruits of same species are identical?

Centres of circles touching both the axes and also the line 3x+4y-12=0 is

If hata, hatb are unit vectors and vec c is such that vec c=veca xx vec c +vecb, then the maximum value of[veca vecb vec c] is :

Which one of the following must equal p + q , if x - y = p and 2x + 3y = q ?

If A and B are mutually exclusive events, given that P(A)=3/5,P(B)=1/5, then P(A or B) is

bar(d)=lambda(bar(a)xx bar(b))+mu(bar(b)xx bar( c ))+v(bar( c )xx bar(a)) and [bar(a)bar(b)bar( c )]=(1)/(8) then lambda+mu+v = …………..

Find the angle between the linesvecr = (3 + lambda)hati + 2(1 + lambda)hatj + 2(1 – 2lambda)hatkand vecr=5hatj-2hatk+mu(3hati+2hatj-6hatk).

which of the following lines are asymptotes for the graph of y=(3x^2-13x-10)/(x^2-4x-5) ? I. x=-1 II. x=5 III. Y=3

The minimum radius of the circle which contains the threecircles, x^(2)+y^(2)-4y-5=0,x^(2)+y^(2)+12x+4y+31=0 and x^(2)+y^(2)+6x+12y+36=0 is

For the vectors A(-1,-2,3) and B(1,2,-1) the direction cosines of vec(AB) are ……………

Find the coefficient of x^(-7)" in "((2x^(2))/(3)-(5)/(4x^(5)))^(7)

Distance from the point (-3,2,5) to the point where the line (x+3)/2= (y-2)/2=(z-5)/2 meets the plane x+y +2z = 3 is

Show that the function f(x)=|cosx| is a continuous function.

Find the equation of all lines having slope 2 which are tangents to the curve y=(1)/(x-3), x ne 3.

Compute the integrals :int_(1) ^(15) "arc tan " sqrt(sqrt(x) - 1)dx

A point charge ..................

There are 2n things out of which 'n' are alike and 'n' are different, the number of ways of selecting 'n' things is

A point charge .................

A person gets Rs. 2 if head comes and loses Rs. 5 when a tail comes then how much money can he expect in the long run per game, when an unbiased coin in tossed twice.

The volume of a cube is increasing at a rate of 8 cubie centimeters per second. How fast is the surface area increasing when the length of the edge is 12 cm?

Evaluate intx^(2) cos x dx

Write in the simplest form of tan^(-1)sqrt((1-cosx)/(1+cosx)),0ltxltpi

The value of lim_(n to oo)((n!)/(n^(n))^(2n^(4+1))/(5n^(5)+1)) is equal

Indicate which of the following is a tautology .

There are 25 girls and 15 boys in class XI and 30 boys and 20 girls in class XII. If a student chosen from a class, selected at random, happens to be a boy, find the probability that he has been chosen from class XII.

AA|x|le1,cos^(-1)(-x)=

If the position vectors of the vertices of Delta ABC are 3hati+hatj+2hatk, hati-2hatj+7hatk and -2hati+3hatj+5hatk, then the DeltaABC is

If I_(n) = int Cot^(n)xdx then I_(4) + I_(6) =

Evalute the following integrals int (x^(2) - 1)/(x^(4) + x^(2) + 1) dx

[(1+ cos((pi)/(12))+ i sin ((pi )/(12)))/(1+ cos((pi)/(12))-i sin((pi)/(12)))^(72)]

Which of the following is a contradiction?

Let veca,vecb,vecc be three mutually perpendicular vectors having same magnitude and vecr is a vector satisfying vecaxx((vecr-vecb)xxveca)+vecbxx((vecr-vecc)xxvecb)+veccxx((vecr-veca)xxvecb)=vec0, then vecr is equal to