28278 + Interview Questions in Maths in Class 12

1.	If a*(b times c)=3 then
Answer» `C(a TIMES B)=-3` `a(c times b)=-3` `b(a times c)=3` `(a times c)b=3` ANSWER :B

Discussion

2.	If X is a poisson distribution such that P(X=1)=P(X=2)then,P(X=4)=
Answer» `1/3e^(2)` `2/3e^(2)` `4/3e^(2)` none Answer :B

Discussion

3.	If x+y ge 1, x ge y, 0 le x le 1, y ge 0 then the minimum value of f=3x+2y is
Answer» 1 2 2.5 3 Answer :C

Discussion

4.	Differentiate the functions given in Exercises 1 to 11 w.r.t. x. (x+(1)/(x))^(x)+x^((1+(1)/(x)))
Answer» ANSWER :`(X+(1)/(x))^(x)[(x^(2)-1)/(x^(2)+1)+LOG(x+(1)/(x))]+x^(1+(1)/(x))((x+1-logx)/(x^2))`

Discussion

5.	According to Boil's law PV = C, where V = 600 cm^(3), P = 150 SI/cm^(2) and (dP)/(dt)=20 SI//cm^(2). Find (dV)/(dt).
Answer» ANSWER :`80 CM^(3)`/MIN

Discussion

6.	int_(-pi//4)^(pi//4)((x+pi//4)/(2-cos2x))dx=
Answer» `(8pi sqrt(3))/(5)` `(2PI sqrt(3))/(9)` `(4 pi^(2)sqrt(3))/(9)` `(pi^(2))/(6sqrt(3))` ANSWER :D

Discussion

7.	If f(x) = 2x secx + x and g(x) =3 tanx thenin interval x in (0, pi//2) is
Answer» `F(X) GT g(x)` `f(x) lt g(x)` `f(x)=g(x)` NONE of these Answer :A

Discussion

8.	Evaluate :1 + 3x + 6x ^(2) + 10 x ^(3)+……. upto infinite term, whre \|x\| lt 1.
Answer» ANSWER :`(1)/((1 + X ) ^(3)) `

Discussion

9.	If \|{:(n^(2),(n+1)^(2),(n+2)^(2)),((n+1)^(2),(n+2)^(2),(n+3)^(2)),((n+2)^(2),(n+3)^(2),(n+4)^(2)):}\|=Deltaand\|(1,-4,7),(-2,3,-5),(3,x,-3)\|=2Delta+1, then x=
Answer» 3 4 5 6 Answer :A

Discussion

10.	(cos""(pi)/(6)+isin""(pi)/(6))^(1//2)+(cos""(pi)/(6)-isin""(pi)/(6))^(11//2)
Answer»

Discussion

11.	Lists I, II and III contains conics, equation of tangents to the conics and points of contact, respectively. If the tangent to a suitable conic (List I) at (sqrt3(1)/(2)) is found to be sqrt3x+2y=4. then which of the following options is the only CORRECT combination?
Answer» (II) (iii) (R) (IV) (iv) (S) (IV) (iii) (S) (II) (iv) (R) Solution :Tangent is `(SQRT3,(1)/(2))` is `sqrt3x+2y=4` Since slope of tangent at `(sqrt3,(1)/(2))` is `-ve`, possible curves are (I) and (II) only (draw the diagram and verify). ALSO, given equation of tangent cannot match with `my=x^(2)x+a`. So, comparing eq. (I) with `y=mx+asqrt(x^(2)+1)`, we get `a=2` and `m=(-sqrt3)/(2)`. THEREFORE, equation of CURVE is `(x^(2))/(4)+y=1`. The corresponding point of CONTACT is `((-a^(2)m)/(sqrt(a^(2)m^(2)+1)),(1)/(sqrt(a^(2)m^(2)+1)))`

Discussion

12.	Evaluate the following integral int (2x + 1)/(x(x^(2) + 4)^(2)) dx
Answer» ANSWER :`(1)/(16) LOG x - (1)/(32) log (x^(2) + 4) + (1)/(8 (x^(2) + 4)) + (1)/(8) tan^(-1) ((x)/(2)) + (1)/(4) ((x)/(4 + x^(2))) + c `

Discussion

13.	Lists I, II and III contains conics, equation of tangents to the conics and points of contact, respectively. If a tangent to a suitable conic (List I) is fond to be y = x+8 and its point of contact is (8, 16), then which of the following options I sthe only CORRECT combination?
Answer» (II) (i) (P) (III) (i0) (Q) (II) (iv) (R) (I) (ii) (Q) Solution :TANGENT at (8, 16) is `y=x+8` Since the SLOPE of tangent is `+ve`, possible curve will be `y^(2)=4AX`. Hence, equation of tangent is `my=m^(2)x+a` and point of contact is `((a)/(m^(2)),(2a)/(m))`.

Discussion

14.	Integrate the following : int3x^2dx
Answer» SOLUTION :`int3x^2dx`=`3x^3/3+C`=`x^3+C`

Discussion

15.	Lists I, II and III contains conics, equation of tangents to the conics and points of contact, respectively. For a=sqrt2 if a tangent is drawn to a suitable conic (List I) at the point of contact (-1,1), which of the following options is the only CORRECT combination for obtaining its equation?
Answer» (II) (ii) (Q) (III) (i) (P) (I) (i) (P) (I) (ii) (Q) Solution :For `a=sqrt2` and POINT `(-1,1)` on the CURVE, the only possible curve is `x^(2)+y^(2)=a^(2)` Equation of tangent is `y=mx+asqrt(m^(2)+1)` and point of CONTACT is `((-ma)/(sqrt(x^(2)+1)),(a)/(sqrt(m^(2)+1)))`.

Discussion

16.	If A is any square matrix then AA' is a ……….Matrix.
Answer» Symmetric Skew symmetric Identity Diagonal Answer :A

Discussion

17.	Find out wrongly matched pair.
Answer» Tuber-Potato Leaf buds-Banana Offsets-Water Hyacinth Rhizome-Ginger Answer :B

Discussion

18.	Compute : [(1,0),(1,0)][(0,0),(1,0)]
Answer» ANSWER :`[(0,0),(0,0)]`

Discussion

19.	A vehicle registration numebr consists of 2 letters of English alphabet followed by 4 digits,where the first digit in not zero.Then the total number of vehicles with distinct registration number is
Answer» `26^(2)xx10^(4)` `""^(26)P_(2)xx""^(10)P_(4)` `""^(26)P_(2)xx13xx""^(6)P_(6)` `26^(2)xx9xx10^(3)` ANSWER :D

Discussion

20.	Evaluate the following definite integrals . int_(a)^(b)xdx
Answer» ANSWER :`1/2(B^(2)-a^(2))`

Discussion

21.	Evaluate : (i) intsin3xsin2xdx (ii) intcos3xsin2xdx (iii) intcos4xcosxdx (iv) intsin^(3)xcos^(3)xdx
Answer» Solution :(i) Using 2 sin a sin b = cos (a-b)-cos(a+b), we have `intsin3xsin2xdx=(1)/(2)int2sin3xsin2xdx` `=(1)/(2)int(cosx-cos5x)DX` `=(1)/(2)intcosxdx-(1)/(2)cos5xdx` `=(1)/(2)sinx-(sin5x)/(10)+C`. (ii) Using 2 cos a sin b = sin (a+b)-sin(a-b), we get `intcos3xsin2xdx=(1)/(2)int2cos3xsin2xdx` `=(1)/(2)int(sin5x-sinx)dx` `=(1)/(2)intsin5xdx(1)/(2)intsinxdx` `=(-cos5x)/(10)+(cosx)/(2)+C`. (iii) Using 2 cos a cos b = cos (a+b)+cos(a-b), we get `intcos4xcosxdx=(1)/(2)int2cos4xcosxdx` `=(1)/(2)int(cos5x+cos3x)dx` `=(1)/(2)intcos5xdx+(1)/(2)intcos3xdx` `=(sin5x)/(10)+(sin3x)/(6)+C`. (iv) `intsin^(3)xcos^(3)xdx=intsin^(3)xcos^(2)xcosxdx` `=intsin^(3)x(1-sin^(2)x)cosxdx` `=intt^(3)(1-t^(2))DT," where"sinx=t` `=intt^(3)dt-intt^(5)dt=(t^(4))/(4)-(t^(6))/(6)+C` `=(1)/(4)sin^(4)-(1)/(6)sin^(6)x+C`.

Discussion

22.	Find the equations of the circles for which the points given below are the end points of a diameter. (1,2), (4,6)
Answer» Answer :` x ^(2) + y ^(2) - 5x - 8Y + 16 =0 `

Discussion

23.	The value of (2 (sin2 theta-2 cos^(2)theta-1))/(cos theta-sin theta-cos 3 theta +sin 3 theta)=
Answer» `cos THETA` `SEC theta` `cosec theta` `sin theta` ANSWER :C

Discussion

24.	Mean and variance of binomial distribution are 3 and 2 respectively then parameter n is ………..
Answer» 9 3 8 6 Answer :A

Discussion

25.	The set (A//B)uu(B//A) is equal to
Answer» `[A//(ANNB)]NN[B//(AnnB)]` `(AUUB)//(AnnB)` `A//(AnnB)` `bar(AnnB)//AuuB` ANSWER :B

Discussion

26.	Findint ( x^(3)-2x+3)/(x^(2)+x-2) dx .
Answer» ANSWER :`(x^(2))/(2) - x + LOG \| (x+2)^(1//3) (x - 1)^(1//3) \| + c`

Discussion

27.	A vertical dam has the form of a trapezoid whose upper base is 70m long, the lower one 50m, and the altitude 20m. Find the force of water pressure experienced by the dam
Answer» ANSWER :`11333 (1)/(3)`

Discussion

28.	Let A, B, C be angles of a triangle ABC and let D=(5pi+A)/(32), E=(5pi+B)/(32), F=(5pi+C)/(32), then : (where D, E, F ne (n pi)/(2), n in I, I denote set of integers)
Answer» `cotD cotE+cotEcotF+cotDcotF=1` `cotD+cotE+cotF=cotDcotEcotF` `TAND tanE+tanE tanF+tanF tanD=1` `tanD+tanE+tanF=tanD tanE tanF` ANSWER :B::C

Discussion

29.	If a point P is moving such that the length of tangents drawn from P to x^(2) + y^(2) - 2x + 4 y - 20= 0"___"(1). and x^(2) + y^(2) - 2x - 8 y +1= 0"___"(2). are in the ratio 2:1 Then show that the equation of the locus of P is x^(2) + y^(2) - 2x - 12 y +8= 0
Answer» ANSWER :` X^(2)+ y^(2) -2X -12Y +8=0 `

Discussion

30.	The maximum value of Delta=\|{:(1,1,1),(1,1-sintheta,1),(1+costheta,1,1):}\| is (theta is real number)".........."
Answer» `1/2` `sqrt3/2` `SQRT2` `(2SQRT3)/4` ANSWER :A

Discussion

31.	Compute the length of the astroid : x= a cos^(3) t, y= a sin^(3)t
Answer» ANSWER :6A

Discussion

32.	The radical centre of the circles x^(2) + y^(2) + a_(r)x + b_(r)y + c - 0 , r - 1,2,3is (a,b)
Answer» (a,B) (b.a) (0,0) NONE ANSWER :C

Discussion

33.	If the tangent at the point P on the circle x^(2)+y^(2)+6x+6y=2 meet the line 5x-2y+6=0 at a point Q on y-axis then PQ=
Answer» `10` `15` `25` `5` ANSWER :D

Discussion

34.	Discuss the continuity of the functions at the points given against them. If a function is discontinuous, determine whether the discontiunity is removable. In this case, redefine the function, so that it becomes continuous : {:(f(x)=(e^(5x)-e^(2x))/(sin3x)",", "for" x ne0),(=1",", "for" x=0):}}at x=0.
Answer» ANSWER :`F(0)=2`

Discussion

35.	Find dy/dx, x=at^2,y=2at and find the value at=1/2
Answer» SOLUTION :`x=at^2,y=2AT` Then dx/dt=2at,dy/dt=2A` `RARR `dy/dx=(2a)/(2at)=1/t` `therefore dy/dx]_(r=1/2)=1/(1/2)=2`

Discussion

36.	Method of integration by parts : inte^(2x)*x^(4)dx=(e^(2x))/(2)f(x)+c then f(x)=.....
Answer» `(1)/(2)x^(4)-2x^(3)+3x^(2)-3x+(3)/(2))` `(x^(4)-x^(3)+2x^(2)-3x+2)` `(x^(4)-2x^(3)+3x^(2)-3x+(3)/(2))` `(x^(4)-2x^(3)+2x^(2)-3x+(3)/(2))` ANSWER :C

Discussion

37.	Evaluate the following inegrals int(1)/(sqrtx^(2)-3)dx
Answer» ANSWER :`LOG\|(X+sqrt(x^(2)-3))/(sqrt(3))\|+c`

Discussion

38.	The value of lim_(xrarr0)\|x\|/x is
Answer» 1 -1 0 Does not exist Answer :D

Discussion

39.	Consider a logarithmic equation log(x^(4)+1)=log(kx)(x^(2)+3x+1)….(i) {:(,"Column-I",,"Columnn-II",),(,"Values of k",,"No. of solutions of (i)",),((A),k=2,(P),0,),((B),k=-6,(Q),1,),((C),k=-12,(R),2,),((C),k=4,(S),4,),(,,(T),"even number",):}
Answer» ANSWER :A::B::C::D

Discussion

40.	If cos alpha, cos beta, cos gamma are the direction cosines fo a vector veca, then cos 2alpha + cos 2beta + cos 2gamma is equal to
Answer» a.2 b.3 C.`-1` d.0 Answer :C

Discussion

41.	(i) Find the equation of director circle of 9x^(2) + 25 y^(2)=225 (ii) Find the equation of auxiliary circle of 9x^(2) + 1 6 y^(2) =144
Answer» ANSWER :`X^(2)+y^(2)=34`

Discussion

42.	A : If 4Sin^(-1)x+Cos^(-1)x=pi then the value of 4Cos^(-1)x+Sin^(-1)x" is "3pi//2 R : If a Cos^(-1)x+bSin^(-1)x=k then the value of bCos^(-1)x+aSin^(-1)x" is "(a+b)pi/2-k
Answer» Both A and R are TRUE and R is the CORRECT EXPLANATION of A Both A and R are 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

43.	Differentiate w.r.t x the function sin^(-1) (x sqrtx), where 0 le x le 1
Answer» ANSWER :`(3)/(2) SQRT((X)/(1-x^(3)))`

Discussion

44.	Three balls are drawn at random from collection of 7 white, 12 green and 4 red balls, The probability that each ballis of different colours is……….
Answer» `(.^(7)C_(1)xx.^(12)C_(1)xx.^(4)C_(1))/(.^(23)C_(3))` `(8)/(253)` `(4)/(253)` `(1)/(253)` ANSWER :A

Discussion

45.	Evaluate the following integrals : (i) int(cosx)/(2sinx+3cosx)dx (ii) int(2sinx+cosx)/(7sinx-5cosx)dx ,br. (iii) int(5sinx+6)/(2cosx+sinx+3)dx
Answer» Solution :`(i)` We have `cosx=K(2sinx+3cosx)+m(2cosx-3sinx)` `impliescosx=(2k-3m)sinx+(3k+2m)cosx` Equating the COEFFICIENTS `sinx` and `cosx` from both sides `3k+2m=1` `2k-3m=0` when `k=(3)/(13)` and `m=(2)/(13)` Thus `int(cosx)/(2sinx+3cosx)DX=(3)/(13)intdx+(2)/(13)int((2cosx-3sinx))/(2sinx+3cosx)dx` `=(3)/(13)x+(2)/(13)ln\|2sinx+3cosx\|` `(ii)` Let `2sinx+cosx=k(7sinx-5cosx)+m(7cosx+5sinx)` `implies2sinx+cosx=(7k+5m)sinx+(7m-5k)cosx` `implies7k+5m=2` and `7m-5k=1` when `m=(17)/(74)` and `k=(9)/(14)` Thus `int(2sinx+cosx)/(7sinx-5cosx)dx=(9)/(74)intdx+(17)/(74)int(7cosx+5sinx)/(7sinx-5cosx)dx` `=(9)/(14)x+(17)/(74)ln\|7sinx-5cosx\|+C` `(iii)` Let`5sinx+6=k(2cosx+sinx+3)+m(-2sinx+cosx)+n` `implies5sinx+6=(2k+m)cosx+(k-2m)sinx+3k+n` `implies2k+m=0`, `k-2m=5`, `3k+n=6` `impliesk=1`, `n=3`, `m=-2` Thus `int(5sinx+6)/(2cosx+sinx+3)dx=intdx-2int((cosx-2sinx))/(2cosx+sinx+3)dx+3int(1)/(2cosx+sinx+3)dx` `=x-2ln\|2cosx+sinx+3\|+3l_(1)`, say `l_(1)=int(1)/((2cosx+sinx+3)dx=int(1)/(2((1-tan^(2).(x)/(2))/(1+tan^(2).(x)/(2)))+(2tan.(x)/(2))/(1+tan^(2).(x)/(2))+3)dx` `=int(1+tan^(2).(x)/(2))/(2-2tan^(2).(x)/(2)+2tan.(x)/(2)+3+3tan^(2).(x)/(2))dx` `=int(sec^(2).(x)/(2))/(5+2tan.(x)/(2)+tan^(2).(x)/(2))dx` Let us put `tan.(x)/(2)=u` so that `sec^(2).(x)/(2)dx=2du` `=int(2)/(4+(1+u)^(2))du` `=2*(1)/(2)tan^(-1)((1+u)/(2))+C` `=tan^(-1)((tan.(x)/(2)+1)/(2))+C` Hence the given integral is `int(5sinx+6)/(2cosx+sinx+3)dx=x-2ln\|2cosx+sinx+3\|+3tan^(-1)((sin.(x)/(2)+cos.(x)/(2))/(2cos.(x)/(2)))+C`

Discussion

46.	Find the values of 'a' in equation 'a+0.65 (n+1) which gives value of effective nuclear charge experience by last electron of 2^(nd) period elements. (wheren is number of electrons in 2^(nd) shell)
Answer» ANSWER :`1.30`

Discussion

47.	Find the equation of the circle which cuts each of the following circles orthogonally. x^2+y^2+3x+2y+1=0 x^2+y^2-x+6y+5=0 x^2+y^2+5x-8y+15=0
Answer» ANSWER :`x^2+y^2-6x-4y-14=0`

Discussion

48.	Findthe sumto 50 terms of 1+(2)(3)+4+(5)(6)+7+(8)(9)+….
Answer» ANSWER :`49675`

Discussion

49.	The orthocentre of the triangle formed by the lines x = 0, y = 0 and x + y = 1 is
Answer» `((1)/(2), (1)/(2))` `((1)/(3), (1)/(3))` (0, 0) `((1)/(4), (1)/(4))` ANSWER :C

Discussion

50.	If the slope of the line joining the points (3, 4) and (-2, a) is equal to (-2)/(5) then the value of a is equal to
Answer» 6 4 3 2 Answer :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

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Evaluate the following integral int (2x + 1)/(x(x^(2) + 4)^(2)) dx

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If a point P is moving such that the length of tangents drawn from P to x^(2) + y^(2) - 2x + 4 y - 20= 0"___"(1). and x^(2) + y^(2) - 2x - 8 y +1= 0"___"(2). are in the ratio 2:1 Then show that the equation of the locus of P is x^(2) + y^(2) - 2x - 12 y +8= 0

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Compute the length of the astroid : x= a cos^(3) t, y= a sin^(3)t

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(i) Find the equation of director circle of 9x^(2) + 25 y^(2)=225 (ii) Find the equation of auxiliary circle of 9x^(2) + 1 6 y^(2) =144

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Differentiate w.r.t x the function sin^(-1) (x sqrtx), where 0 le x le 1

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Findthe sumto 50 terms of 1+(2)(3)+4+(5)(6)+7+(8)(9)+….

The orthocentre of the triangle formed by﻿ the lines x = 0, y = 0 and x + y = 1 is

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