28278 + Interview Questions in Maths in Class 12

1.	The tangent at a point P(acos theta,bsin theta) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the auxillary circle in two points. The chord joining them subtends a right angle at the centre. Find the eccentricity of the ellipse:
Answer» ANSWER :`(SIN alpha+beta)/(sin (alpha+beta))`

Discussion

2.	Solve : [{:(x^(2)),(y^(2)):}]+2[{:(2x),(3y):}]=3[{:(7),(-3):}].
Answer» ANSWER :`x=-7,y=-3orx=3,y=-3`.

Discussion

3.	Write the value of x for which d/dx"tan"^-1((2x)/(1-x^2))=2/(1+x^2)
Answer» SOLUTION :`d/dx"TAN"^-1((2x)/(1-X^2))=2/(1+x^2)`for `x in R-{-1,1}

Discussion

4.	Find the sum of all 4 - digited numbers that can be formed using 1,3,4,5,7 without repetition.
Answer» ANSWER :533280

Discussion

5.	Equation of the tangent and normal to the curve x=(1)/(t), y=t-(1)/(t) at the pint t=2 on it are respectively
Answer» `5x-y=4 , x+5y+7=0` `x-5y=4, 5x+y+7=0` `5x+y=4, x-5y +7=0` `x+5y=4, 5x-y+7=0` ANSWER :C

Discussion

6.	A variable plane passes through a fixed point (alpha,beta,gamma) and meets the coordinate axes in A,B, and C. let P_(1)P_(2)" and "P_(3) be the planes passing through A,B,C and parallel to the coordinate planes YZ,ZX,XY respectively . Then, the locus of the points of intersection of the planes P_(1)P_(2)" and "P_(3)is
Answer» `alphax+betay+gammaz=1` `(alpha)/x,(beta)/y+(gamma)/z=1` `ax_(2)+betay^(2)+gammaz^(2)=1` `alphabetax+betagammay+alphagammaz=1` ANSWER :B

Discussion

7.	Solve the differential equation y dx + ( x-y"e^(y) ) dy = 0
Answer» ANSWER :`XY= ( y-1) E^(y) + C`

Discussion

8.	Evalute the following integrals int (5 x - 3) sqrt(x^(2) - 6x + 13) dx
Answer» ANSWER :`(5)/(3)(x^(2)-6x+13)^(3//2)+6(x-3)sqrt(x^(2)-6x+13)+24sinh^(-1)((x-3)/(2))+C`

Discussion

9.	The probability that Australia wins a match against India in a cricket game is given to be (1)/(3). If india and Australia play 3 matches, what is the probability that, i) Australia will loose all the three matches ? ii) Australia will win atleast one match ?
Answer» ANSWER :`(1)/(9)`

Discussion

10.	If theta is angle between two vectors vec(a) and vec(b) then vec(a).vec(b)ge 0 only when …….
Answer» `0lt THETA LT (PI)/(2)` `0 le theta le (pi)/(2)` `0 lt theta lt pi` `0 le theta le pi` Answer :B

Discussion

11.	Match the following lists:
Answer» Solution :a. `F(X+pi//2)=cos(\|sin(x+pi//2)\|-\|cos(x+pi//2)\|)` `=cos (\|cosx\|-\|-SINX\|)` `=cos(\|cosx\|-\|sinx\|)` `=cos(\|sin x\|-\|cosx\|)` `=f(x)` b. `f(x+pi//2)=cos[tan(x+pi//2)+cot(x+pi//2)].` `cos[tan(x+pi//2)-cot(x+pi//2)]` `=cos[-cotx-tanx]cos[-cotx+tanx]` `=cos(tanx+cotx)cos(tanx-cotx)` `=f(x)` c. The period of `sin^(-1)(sinx) " is " 2pi.` The period of `e^(tanx) " is " pi`. Thus, the period of `f(x)" is " LCM (2pi,pi)=2pi.` d. The given function is `f(x)=sin^(3)x sin 3x` `=((3sinx-sin 3x)/(4)) sin 3x` `=(3)/(8) (cos 2x-cos 4x)-(1)/(8)(1-cos6x)` Thus, the period of `f(x) " is " pi.`

Discussion

12.	Insert 4 H.M between 3/4 and (3)/(19).
Answer» ANSWER :`H _(4) = (3)/(16)`

Discussion

13.	Find \|vecaxxvecb\|, if veca=hati-7hatj+7hatkandvecb=3hati-2hatj+2hatk.
Answer» ANSWER :`19sqrt(2)`

Discussion

14.	If the complex numbers z_(1), z_(2)" and "z_(3) denote the vertices of an isoceles triangle, right angled at z_(1), " then "(z_(1)-z_(2))^(2)+(z_(1)-z_(3))^(2) is equal to
Answer» `0` `(z_(2)+z_(3))^(2)` `2` `(z_(2)- z_(3))^(2)` ANSWER :D

Discussion

15.	Find the general solution of the differential equation (dy)/(dx) = (1 + x^(2))(1 + y^(2))
Answer» ANSWER :`TAN^(-1)y = x + (x^(3))/(3) + C`

Discussion

16.	If overline(a)overline(b), overline(c )are unit vectors satisfying the relation overline(a) +b +sqrt(3)overline( c) =0, then the angle between a and b is
Answer» `(pi)/(6)` `(pi)/(4)` `(pi)/(3)` `(pi)/(2)` Answer :C

Discussion

17.	If n isa positiveinteger , then 5^(2n +2) - 24 n-25isdivisibleby
Answer» 574 575 674 576 Answer :D

Discussion

18.	The value of 'a' for which one root of the quadraticequation(a^(2)-5a +3) x^(2)+(3a-1) x+2=0 is twice the other is
Answer» `2//3` `1//3` `-2//3` `-1//3` ANSWER :a

Discussion

19.	A focal chord of the parabola y^(2)=4axmeets it at P and Q . If S is the focus then (1)/(SP)+(1)/(SQ) =
Answer» a 1/a 2a 2/a Answer :B

Discussion

20.	The value of the expression tan(1/2"cos"^(-1)2/sqrt5)is
Answer» `2-sqrt5` `sqrt5-2` `(sqrt5-2)/2` `5-sqrt2` ANSWER :B

Discussion

21.	The sum of first 26 terms of an A.P. a_(1),a_(2),a_(3),.. if a_(2)+a_(6)+a_(9)+a_(18)+a_(21)+a_(25)=165, is
Answer» 705 715 725 735 Answer :B

Discussion

22.	underset(xrarr0)lim(xe^(x)-sinx)/(x) is equal to
Answer» 1)3 2)1 3)0 4)2 Answer :C

Discussion

23.	Find the relation between the slopes of marginal revenue curve and the average revenue curve, for the demandfunction p = a- bx
Answer» ANSWER :`-2A`

Discussion

24.	If three number are drawn at random successively without replacement from a set S = {1, 2, . . . . 10}, then the probability that the minimum of the chosen number is 3 or their maximum is 7 .
Answer» `(11)/(40)` `(5)/(40)` `(3)/(40)` `(1)/(40)` ANSWER :A

Discussion

25.	A mirror and a source of light are situated at origin O & at a point on OX respectively. A ray of light from sources strikes the mirror along x-axis & reflected. If the DRs of normal to plane are lt1-1,1gt, then DCs of reflected ray are
Answer» `(:(1)/(3),(2)/(3),(2)/(3):)` `(:(-1)/(3),(-2)/(3),(2)/(3):)` `(:(-1)/(3),(-2)/(3),(-2)/(3):)` None Solution :For B to win: PR or `overset(RBR)(BR R)` `{:("Black",,"Red",,"B(n)",,,),(1,,2,,B(1)=1,,,overset(A(n))A(1)=0),(2,,2,,B(2)=(2)/(4).(1)/(3)+(2)/(4).(2)/(3).(1)/(2)+(2)/(4).(2)/(3).(1)/(2),,,),(3,,2,,B(3)=(2)/(5).(1)/(4)+(2)/(5).(3)/(4).(1)/(3)+(3)/(5).(2)/(4).(1)/(3),,,),(n,,2,,B(n)=(2)/(n+2).(1)/(n+1)+(2)/(n+2).(n)/(n+1).(1)/(n)+(n)/(n+2).(2)/(n+2).(1)/(n),,,):}` `therefore B(n) = (6)/((n+1)(n+2))` `A(n)=1-B(n)=((n-1)(n+4))/((n+1)(n+2))` `pi[A(n)]=(6xx(n+2)(n+3)(n+4))/(3xx4xx5.n(n+1)(n+2))`

Discussion

26.	The set of points where the function f given by f(x)= \|2x-1\| sin x is differentiable is x in ……….
Answer» R `R- {(1)/(2)}` `(0, oo)` none of these Answer :B

Discussion

27.	vec(a),vec(b) and vec( c ) are non zero vectors. (vec(a)xx vec(b))xx vec( c )=(1)/(3)\|vec(b)\|\|vec( c )\|vec(a). If the acute angle between the vectors vec(b) and vec( c ) is theta then sin theta = ……………
Answer» `(1)/(3)` `(SQRT(2))/(3)` `(2)/(3)` `(2sqrt(2))/(3)` ANSWER :D

Discussion

28.	Form the differential equation representing the family of ellipse having foci on x-axis and centre at the origin.
Answer» ANSWER :`X(DY)/(DX) - y = 0`

Discussion

29.	A = (2+ 1) (22 + 1) (2 + 1)..... (2^(2048) + 1) The value of (A + 1)^(1//2048)is
Answer» ANSWER :4

Discussion

30.	If A,B,C,D are the lengths of subtangents to the curves 1) sqrtx+sqrty=3 at (4,1) 2) x^2y^2=1 at (-1,1) 3) y=(x+1)/x at (1,2) 4) x^2+xy+y^2=7 at (1,-3) then the descending order of A,B,C,D is
Answer» A,B,C,D D,C,B,A A,B,D,C C,B,D,A Answer :B

Discussion

31.	If C_k is the coefficient of x^k in the expansion of (1 + x)^2005 and if a,d are real numbers then sum_(k = 0)^(2005) (a + kd).C_k =
Answer» `(2A + 2005d)2^2004` `(2a + 2005d)2^2005` `(2a + 2004D)2^2005` `(2a + 2004d)2^2005` ANSWER :A

Discussion

32.	Let the mapping f:NN rarr NNdefined by f(x) = {(x+1", when" x in NN", an odd"),(x-1 ", when" x in NN", an even"):} The mapping f will be ___
Answer» many-ONE and into one-one and onto many -one and onto bijective mapping Answer :B

Discussion

33.	If x + y = 1, prove that sum_(r=0)^(n) r""^(n)C_(r) x^(r ) y^(n-r)= nx.
Answer» SOLUTION :We have `UNDERSET(R=0)OVERSET(n)sumr.^(n)C_(r)X^(r )y^(n-r) =underset(r=1)overset(n)sumn.^(n-1)C_(r-1)x^(r-1)x^(1)y^(n-r)` ` = nx underset(r=1)overset(n)sum .^(n-1)C_(r-1)x^(r-1)y^((n-1)-(r-1))` `= nx(x+y)^(n-1)` ` = nx , [:' x + y = 1]`

Discussion

34.	If (x_i y_i) ,i =1,2,3,4are concylic points on xy= 4 then x_1x_2x_3x_4 =
Answer» 4 `-4` `-16` `16` ANSWER :D

Discussion

35.	If a fair coin is tossed 10 times, find the probability of (i) exactly six heads (ii) at least six heads (iii) at most six heads
Answer» Answer :(i) `(105)/(512)`, (ii) `(193)/(512)` and (iii) `(53)/(64)`

Discussion

36.	A :sin theta + sin (pi+ theta ) + sin ( 2pi + theta ) ......... + sin (10pi + theta ) = sin theta R :sin theta + sin (pi + theta ) + sin (2 pi + theta ) ........ + sin(n pi + theta ) = sin thetaif n is even
Answer» A is TRUE , R is true and R is CORRECT explanation of A A is true , R is TRUEAND R is not correct explanation of A A is true , R is false A is false , R is true ANSWER :A

Discussion

37.	hat(i). ( hat(k) xx hat(j)) + hat(j) .(hat(i) xx hat(k) ) + hat(k). ( hat(j) xx hat(i) ) + hat(i). (hat(i) xx hat(j) ) + hat(j) . ( hat(j) xx hat(k) ) =...........
Answer» `-1` `1` `3` `-3` ANSWER :D

Discussion

38.	Find the second order derivatives of the functions e^(x) sin 5x
Answer» Answer :`2e^(X) [5 cos 5X-12 SIN 5x]`

Discussion

39.	Distance between the lines 5x + 3y-7 = 0 and 15x +9y + 14 = 0 is
Answer» `(35)/(SQRT(34))` `(1)/(sqrt(34))` `(35)/(3sqrt(34))` `(35)/(2sqrt(34))` Answer :C

Discussion

40.	The locus of the points representing the complex numbers z for which absz-2=abs((z-i)-abs(z+5i)=0 is
Answer» A circle with CENTRE at the origin A STRAIGHT line passing through the origin The single point (0, -2) None of these Answer :C

Discussion

41.	Evaluate int_(-1)^(3/2)abs(xsinpix)dx
Answer» ANSWER :`(3)/(PI)+(1)/(pi^(2))`

Discussion

42.	Evaluate the following integrals (ii) int_(0)^(a)(a^(2)x-x^(3))dx
Answer» ANSWER :`(a^(4))/(4)`

Discussion

43.	If cosalpha and cosbeta are the roots of 4x^(2)-3=0,then what is the value ofsecalphaxxsecbeta ?
Answer» `-(4)/(3)` `(4)/(3)` `(3)/(4)` `-(3)/(4)` ANSWER :A

Discussion

44.	Evaluate int_(0)^(infty)(tan^(-1)ax- tan^(-1)x)/(x)dx where a is a parameter.
Answer» ANSWER :`=(PI)/(2)`

Discussion

45.	If the determinant of the matrix A = [{:(0,a,b),(-a,0,beta),(-b,alpha,0):}]is zero for all a,b then alpha+beta=
Answer» 0 1 `-1` 2 Answer :A

Discussion

46.	Evaluate the following definite integrals as limit of sums. int_(-1)^(1)e^(x)dx
Answer» ANSWER :`E-(1)/(e)`

Discussion

47.	Let a = hat I + hatj +hatk, vec b = hati-hatj+hatk and c be a unit vector bot to vecaand coplanar with veca and vecb, then it is given by
Answer» `1/sqrt6(2hati - HATJ+ HATK)` `1/sqrt2(hatj + hatk)` `-1/sqrt6(hati-2hatj-hatk)` `1/2(hatj-hatk)` ANSWER :A

Discussion

48.	If the sum of 12^(th) and 22^(nd) terms of an A.P is 100, then the sum of the first 33 terms of the A.P is
Answer» 1700 1650 3300 3400 Answer :B

Discussion

49.	Find all those roots of the equation z^12 – 56z^6 – 512= 0 whose imaginary part is positive.
Answer» ANSWER :`pm1+isqrt(3),(PM(SQRT(3)+i))/(sqrt(2)),sqrt(2)i`

Discussion

50.	If p, q are the roots of the equationx^(2)+px +q=0, then
Answer» p = 1, Q = -2 p = 0, q = 1 p = -2, q = 0 p = -2, q = 1 Answer :a

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The tangent at a point P(acos theta,bsin theta) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the auxillary circle in two points. The chord joining them subtends a right angle at the centre. Find the eccentricity of the ellipse:

Solve : [{:(x^(2)),(y^(2)):}]+2[{:(2x),(3y):}]=3[{:(7),(-3):}].

Write the value of x for which d/dx"tan"^-1((2x)/(1-x^2))=2/(1+x^2)

Find the sum of all 4 - digited numbers that can be formed using 1,3,4,5,7 without repetition.

Equation of the tangent and normal to the curve x=(1)/(t), y=t-(1)/(t) at the pint t=2 on it are respectively

Solve the differential equation y dx + ( x-y"e^(y) ) dy = 0

Evalute the following integrals int (5 x - 3) sqrt(x^(2) - 6x + 13) dx

The probability that Australia wins a match against India in a cricket game is given to be (1)/(3). If india and Australia play 3 matches, what is the probability that, i) Australia will loose all the three matches ? ii) Australia will win atleast one match ?

If theta is angle between two vectors vec(a) and vec(b) then vec(a).vec(b)ge 0 only when …….

Match the following lists:

Insert 4 H.M between 3/4 and (3)/(19).

Find |vecaxxvecb|, if veca=hati-7hatj+7hatkandvecb=3hati-2hatj+2hatk.

If the complex numbers z_(1), z_(2)" and "z_(3) denote the vertices of an isoceles triangle, right angled at z_(1), " then "(z_(1)-z_(2))^(2)+(z_(1)-z_(3))^(2) is equal to

Find the general solution of the differential equation (dy)/(dx) = (1 + x^(2))(1 + y^(2))

If overline(a)overline(b), overline(c )are unit vectors satisfying the relation overline(a) +b +sqrt(3)overline( c) =0, then the angle between a and b is

If n isa positiveinteger , then 5^(2n +2) - 24 n-25isdivisibleby

The value of 'a' for which one root of the quadraticequation(a^(2)-5a +3) x^(2)+(3a-1) x+2=0 is twice the other is

A focal chord of the parabola y^(2)=4axmeets it at P and Q . If S is the focus then (1)/(SP)+(1)/(SQ) =

The value of the expression tan(1/2"cos"^(-1)2/sqrt5)is

The sum of first 26 terms of an A.P. a_(1),a_(2),a_(3),.. if a_(2)+a_(6)+a_(9)+a_(18)+a_(21)+a_(25)=165, is

underset(xrarr0)lim(xe^(x)-sinx)/(x) is equal to

Find the relation between the slopes of marginal revenue curve and the average revenue curve, for the demandfunction p = a- bx

If three number are drawn at random successively without replacement from a set S = {1, 2, . . . . 10}, then the probability that the minimum of the chosen number is 3 or their maximum is 7 .

A mirror and a source of light are situated at origin O & at a point on OX respectively. A ray of light from sources strikes the mirror along x-axis & reflected. If the DRs of normal to plane are lt1-1,1gt, then DCs of reflected ray are

The set of points where the function f given by f(x)= |2x-1| sin x is differentiable is x in ……….

vec(a),vec(b) and vec( c ) are non zero vectors. (vec(a)xx vec(b))xx vec( c )=(1)/(3)|vec(b)||vec( c )|vec(a). If the acute angle between the vectors vec(b) and vec( c ) is theta then sin theta = ……………

Form the differential equation representing the family of ellipse having foci on x-axis and centre at the origin.

A = (2+ 1) (22 + 1) (2 + 1)..... (2^(2048) + 1) The value of (A + 1)^(1//2048)is

If A,B,C,D are the lengths of subtangents to the curves 1) sqrtx+sqrty=3 at (4,1) 2) x^2y^2=1 at (-1,1) 3) y=(x+1)/x at (1,2) 4) x^2+xy+y^2=7 at (1,-3) then the descending order of A,B,C,D is

If C_k is the coefficient of x^k in the expansion of (1 + x)^2005 and if a,d are real numbers then sum_(k = 0)^(2005) (a + kd).C_k =

Let the mapping f:NN rarr NNdefined by f(x) = {(x+1", when" x in NN", an odd"),(x-1 ", when" x in NN", an even"):} The mapping f will be ___

If x + y = 1, prove that sum_(r=0)^(n) r""^(n)C_(r) x^(r ) y^(n-r)= nx.

If (x_i y_i) ,i =1,2,3,4are concylic points on xy= 4 then x_1x_2x_3x_4 =

If a fair coin is tossed 10 times, find the probability of﻿ (i) exactly six heads﻿ (ii) at least six heads﻿ (iii) at most six heads﻿

A :sin theta + sin (pi+ theta ) + sin ( 2pi + theta ) ......... + sin (10pi + theta ) = sin theta R :sin theta + sin (pi + theta ) + sin (2 pi + theta ) ........ + sin(n pi + theta ) = sin thetaif n is even

hat(i). ( hat(k) xx hat(j)) + hat(j) .(hat(i) xx hat(k) ) + hat(k). ( hat(j) xx hat(i) ) + hat(i). (hat(i) xx hat(j) ) + hat(j) . ( hat(j) xx hat(k) ) =...........

Find the second order derivatives of the functions e^(x) sin 5x

Distance between the lines 5x + 3y-7 = 0﻿ and 15x +9y + 14 = 0 is

The locus of the points representing the complex numbers z for which absz-2=abs((z-i)-abs(z+5i)=0 is

Evaluate int_(-1)^(3/2)abs(xsinpix)dx

Evaluate the following integrals (ii) int_(0)^(a)(a^(2)x-x^(3))dx

If cosalpha and cosbeta are the roots of 4x^(2)-3=0,then what is the value ofsecalphaxxsecbeta ?

Evaluate int_(0)^(infty)(tan^(-1)ax- tan^(-1)x)/(x)dx where a is a parameter.

If the determinant of the matrix A = [{:(0,a,b),(-a,0,beta),(-b,alpha,0):}]is zero for all a,b then alpha+beta=

Evaluate the following definite integrals as limit of sums. int_(-1)^(1)e^(x)dx

Let a = hat I + hatj +hatk, vec b = hati-hatj+hatk and c be a unit vector bot to vecaand coplanar with veca and vecb, then it is given by

If the sum of 12^(th) and 22^(nd) terms of an A.P is 100, then the sum of the first 33 terms of the A.P is

Find all those roots of the equation z^12 – 56z^6 – 512= 0 whose imaginary part is positive.

If p, q are the roots of the equationx^(2)+px +q=0, then

If a fair coin is tossed 10 times, find the probability of (i) exactly six heads (ii) at least six heads (iii) at most six heads

Distance between the lines 5x + 3y-7 = 0 and 15x +9y + 14 = 0 is