28278 + Interview Questions in Maths in Class 12

1.	Integrate the following functions. int(x^(2)-1)/(x^(4)+x^(2)+1)dx
Answer» Answer :`(1)/(2)log\|(X^(2)-x+1)/(x^(2)+x+1)\|+c`

Discussion

2.	How many middle terms are there in the expansion of (2x + 3y)^128
Answer» ANSWER :ONE

Discussion

3.	Mean of the numbers 1,2,3,…,n with respective weights 1^(2) + 1, 2^(2) + 2, 3^(2) + 3,…,n^(2)+n is
Answer» `(3N+2)/(2)` `(3n+1)/(4)` `(2N+1)/(3)` `(3n(n+1))/(2(2n +1))` ANSWER :B

Discussion

4.	The solution of y dx - xdy + 3x^(2) y^(2) e^(x^(3))dx = 0 is
Answer» `(y)/(X) + E^(x^(3)) = C` `(y)/(x) - e^(x^(3)) = c` `(x)/(y) + e^(x^(3)) = c` `(x)/(y) - e^(x^(3)) = c` ANSWER :C

Discussion

5.	If \|bar(x)\|=\|bar(y)\|=1 and bar(x)_\|_bar(y), then \|bar(x)-bar(y)\| =……………
Answer» `SQRT(2)` `sqrt(3)` 1 0 Answer :A

Discussion

6.	Show that the points (1, 2, -1), (2, 5, 1) and (0, -1, -3) are collinear.
Answer» are collinear are vertices of a parallelogram vertices of a RHOMBUS vertices of a RECTANGLE ANSWER :B

Discussion

7.	obtain the equation of hyperbola in each of the following cases: centre (1,-2) transverse axis parallel to x-axis of length 6 and conjugate axis of length 10.
Answer» Solution :CENTRE (1,-2) transverse axis parallel to x-axisof length 6 conjugate axis of length 10 .`THEREFORE` 2a=6 , 2b=10 `therefore` a=3 , b=5, h=1 , k=-2 `therefore` EQN of the hyperbola `(x-h)^2/a^2-(y-k)^2/b^2=1` or `(x-1)^2/9-(y-2)^2/25=1`

Discussion

8.	Integration by partial fraction : int(dx)/(x^(4)-1)=....+c
Answer» `(1)/(4)log\|(X+1)/(x-1)\|` `(1)/(4)log\|(x+1)/(x-1)\|-(1)/(2)TAN^(-1)x` `(1)/(2)log\|(x^(2)-1)/(x+1)\|` `(1)/(4)log\|(x+1)/(x-1)\|-(1)/(2) "tan"^(-1)(x)/(2)` ANSWER :B

Discussion

9.	Find adjoint of each of the matrices{:[( 1,-1,2),( 2,3,5),( -2,0,1) ]:}
Answer» ANSWER :` {:(2,1,-11),( -12,5,-1),(6,2,5):}`

Discussion

10.	Using the properties of determinants, prove the following It 2s=a+b+c then \|{:(a^2,(s-a)^2,(s-a)^2),((s-b)^2,b^2,(s-b)^2),((s-c)^2,(s-c)^2,c^2):}\|=2s^3(s-a)(s-b)(s-c)
Answer» ANSWER :`2s^3(s-a)(s-b)(s-c)`

Discussion

11.	Find the number of points with integral coordinates that lie in the interior of the region common to the circle x^(2) + y^(2) = 16 and the parabola y^(2) = 4x.
Answer» ANSWER :16

Discussion

12.	Evaluate int{(e^(2logx)+e^(3logx))/(x+x^2)}dx.
Answer» SOLUTION :`INT(E^(2Inx)+e3Inx)/(x+x^2)dx=int(e^(Inx^3)+e^(Inx^3))/(x+x^2)dx=int(x^2+x^3)/(x+x^2)dx=intxdx=x^2/2+C`

Discussion

13.	If A(1,1,1),C(2,-1,2)the vector equationof theline vec(AB)is vec(r) = (hat(i) + hat(j) + hat(k)) + t(6hat(i) -3hat(j) + 2hat(k))and d is theshrotest distanceof the point C form vec(AC)then
Answer» `B(6,-3,2)` `B(5,-4,1)` `d = SQRT(2)` `d = sqrt(6)` ANSWER :C

Discussion

14.	Plane meets the coordinateaxes in P,Q,R respectively .If the centroidof trianglePQR is (1,1/2,1/3) , then the equation of plane is .
Answer» `2x+4y+3z=5` `x+2y+3z=3` `x+4y+6z=-5` `2x-2y+6z=3` ANSWER :B

Discussion

15.	Find the asymptotes of the following curves: f(x) = (x^(2))/(x+1)
Answer» ANSWER :`x=2`

Discussion

16.	Evaluate the following definite integrals . int_(0)^(5)(x+1)dx
Answer» ANSWER :`35/2`

Discussion

17.	Prove that sum_(k = 1)^(n) k. ""^(k)P_(n + 1) -1.
Answer» <P> Answer :`sum_(k = 1)^(N) k. ""^(k)P_(n + 1) -1`.

Discussion

18.	The partial fractions of (1)/(x^(2)(x+2)) are
Answer» `- (1)/(4X)+(1)/(2x^(2))+(1)/(4(x+2))` `(1)/(4x)+(1)/(2x^(2))+(1)/(4(x+2))` `- (1)/(4x)+(1)/(x^(2))+(1)/(4(x+2))` `(1)/(4x)-(1)/(2x^(2))+(1)/(4(x+2))` Answer :A

Discussion

19.	Let hata,vecb and vecc be the non-coplanar unit vectors. The angle between hatb and hatc is alpha "between" hatc and hata is beta and "between" hata and hatb is gamma. If A(hatacos alpha),B(hatbcosbeta) and C(hatc cosgamma), then show that in triangle ABC, (\|hataxx(hatbxxhatca)\|)/(sinA)=(\|hatbxx(hatcxxhata)\|)/sinB = (\|hatcxx(hataxxhatb)\|)/sinC=(prod\|hataxx(hat xx hatc\|))/(sumsin alpha-cosbeta. cos gammahatn_(1)) where hatn_(1)=(hatbxxhatc)/(\|hatbxxhatc\|),hatn_(2)=(hatcxxhata)/(\|hatcxxhata\|)and hatn_(3)=(hataxxhatb)/(\|hataxxhatb\|)
Answer» Solution :From the sine rule, we GET `(AB)/(sin C)=(AC)/(sinB)=(BC)/(sinA)= ((AB)(BC)(CA))/(2DeltaABC)` `BC=\|vec(BC)\|=\|hatc COS gamma=-hatbcosbeta\|=\|(hata.hatb)hatc-(hatc.hata)hatb\|=\|(hataxx(hatbxxhatc))\|` `AC = \|vec(AC)\|=\|hatbxx(hatcxxhata)\|and AB = \|vec(AB)\|=hatcxx(hataxx hatb)\|` `DeltaABC=1/2\|vec(BC)xxvec(BA)\|` `=1/2 \|(hatc cosgamma-hatb cos BETA)xx(hata COSALPHA-hatbcosbeta)\|` `=1/2 \|(hatc xxhata)cosalpha cosgamma+(hatbxxhatc)cosalphacosbeta+(hata xx hatb)cos beta cos alpha\|` `2DeltaABC=\|sumhatn_(1)sinalphacosbeta cosgamma\|` `(\|hataxx(hatbxxhatc)\|)/sinA=(\|hatbxx(hatcxxhata)\|)/sinB=(\|hatcxx(hataxxhatb)\|)/sin C = (prod\|hata xx(hatbxx hatc)\|)/(\|sum sinalpha COSBETA cosgamma hatn_(1)\|)`

Discussion

20.	Statement 1 The sum of the focal distances of a point on the ellipse 4x^(2)+5y^(2)-16x-30y41=0 is 2sqrt5. Statement 2 The equation 4x^(2)+5y^(2)-16x-30y+41=0 can be expressed as 4(x-2)^(2)+5(y-3)^(2)=20.
Answer» Statement I is true, statement II is true: statement II is a CORRECT explanation for statement I Statement I is true, statement II is true, statement II is not a correct explanation for statement I statement I is true, statement II is FALSE statement I is false, statement II is true Answer :B

Discussion

21.	If a_(1), a_(2) , ……. A_(n) are in H.P., then the expression a_(1)a_(2) + a_(2)a_(3) + ….. + a_(n - 1)a_(n) is equal to
Answer» `N(a_(1) - a_(n))` `(n - 1) (a_(1) - a_(n))` `na_(1),a_(n)` `(n - 1)a_(1)a_(n)` ANSWER :D

Discussion

22.	int_(0)^(oo) (dx)/((1+x^(2))^(4))=
Answer» `(3pi)/(26)` `(7pi)/(28)` `(5PI)/(32)` `(9 pi)/(24)` ANSWER :C

Discussion

23.	If (5z_2)/(11z_1) is purely imaginary, then the value of \|(2z_(1)+3z_(2))/(2z_(1)-3z_(2))\| is
Answer» `(37)/(33)` `2` `1` `3` ANSWER :C

Discussion

24.	Ifalpha , beta , gammaare the rootsof x^4 -4x^2 -x+2=0 find thevaluesofsumalpha^2 betaandsum(1)/(alpha^2)
Answer» ANSWER :`(I )-3 "" (II ) (17)/(4)`

Discussion

25.	Evaluate int_(0)^(2)e^(x)dx as the limit of a sum.
Answer» ANSWER :`E^(B) - e^(a)`

Discussion

26.	Solve the differential equation y e^(x/y) dx = (x e^(x/y) + y^(2))dy ( y ne 0).
Answer» ANSWER :`E^((X)/(y)) = y + C`

Discussion

27.	Let (S) denotes the number of ordered pairs (x,y) satisfying (1)/(x)+(1)/(y)=(1)/(n),Aax,y,n in N. Q. sum_(r=1)^(10)S(r) equals\
Answer» 47 48 49 50 Solution :`because1^(2)toS(1)=1,2^(2)toS(2)=3,3^(2)toS(3)=3`, `4^(2) to 2^(4)to S(4)=5,5^(2)toS(5)=3,S(6)=9` `S(7)=3,S(8)=7,S(9)=5 and S(10)=9`[from above] `therefore underset(R=1)overset(10(sum)S(r)=S(1)+S(2)+S(3)+S(4)+S(5)+S(6)+S(7)+S(8)+S(9)+S(10)` `=1+3+3+5+3+9+3+7+5+9=48`

Discussion

28.	Evaluate the following determinates (i) \|{:("3","-1","-2"),(0,0,"-1"),(3,"-5","0"):}\|
Answer» ANSWER :-12

Discussion

29.	The negation of (pvv~q)^^q is
Answer» `(~PVVQ)^^~Q` `(p^^~q)VVQ` `(~p^^q)vv~q` `(p^^~q)vv~q` ANSWER :C

Discussion

30.	y = sin^(-1)(2xsqrt(1 - x^2)), -1/(sqrt2) lt x lt 1/(sqrt2)
Answer» ANSWER :`(2)/(SQRT(1-x^(2)))`

Discussion

31.	If 10 person are seated at a round table, then what is the probability that two particular persons sit together?
Answer» Solution :Here, 10 PERSON are seated round table. Total no. of ways in which 10 persons can sit along a round table = (10-1)!=9! `therefore`Total no. of elementary events = 9! Now if we regard two particular person as ONE person, then we will be left with only 9 persons. These 9 persons can be seated along a round table in (9-1)=8! ALSO, those two particular persons can be arranged among themselves in 2! ways `therefore`No. of favourable elementary events = `8!xx2!` THUS, required probability `= (8!xx2!)/(9!)=2/9`

Discussion

32.	If 1m ((2z+1)/(iz+1))=3, then locus of z is
Answer» A circle A parabola A STRAIGHT line None of these Answer :A

Discussion

33.	Find the approximate value off(5.001), where f(x) = x^(3) – 7x^2 + 15.
Answer» ANSWER :`–34.995`

Discussion

34.	Consider the parabola x^(2) +4y = 0. Let P(a,b) be any fixed point inside the parabola and let S be the focus of the parabola. Then the minimum value at SQ +PQ as point Q moves on the parabola is
Answer» `\|1 -a\|` `\|ab\|+1` `SQRT(a^(2)+b^(2))` `1-b` Solution : Let the foot of perpendicular from Q to the directrix be N. `SQ + PQ = QN + PQ` is minimum when P, Q and N are COLLINEAR. So, minimum value of `SQ + PQ = PN = 1 -b`

Discussion

35.	STATEMENT-1: The line 2009x+2010y+2011=0 where 2009a+2011c=0 passes through the point ((a)/(b),(b)/(c )), where abc ne 0. STATEMENT-2: If 2009a+2010+2011c=0, then the straight line ax+by+c=0, abc ne 0 passes through ((2009)/(2011),(2010)/(2011)).
Answer» Statement-1 is TRUE, Statemetn-2 is True, Statemetn-2 is a CORRECT explanation for Statement-5 Statement-1 is True, Statemetn-2 is True, Statement-2 is NOT a correct explanation for Statement-5 Statement-1 is True, Statement-2 is False Statement-1 is False, Statement-2 is True ANSWER :B

Discussion

36.	Find the rate of change of the area of a circle with respect to its radius r when r=6cm.
Answer»

Discussion

37.	Let vec(u),vec(v) and vec(w) be such that \|vec(u)\|=1,\|vec(v)\|=2,\|vec(w)\|=3. If the projection vec(v) along vec(u) is equal to that of vec(w) along vec(u) and vec(v),vec(w) are perpendicular to each orher, then \|vec(u)-vec(v)+vec(w)\| equals ............... .
Answer» 2 `SQRT(7)` `sqrt(14)` 14 Answer :C

Discussion

38.	Sum to n terms the series 1 + (1+ 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4).......
Answer» ANSWER :`(N (n +1) ( n +2))/( 6)`

Discussion

39.	If Nis the setof alllnaturalnumbersthenwhichof the followingis true
Answer» `f(x)= 3X -2` DOESNOT mapN to N `f(x)=x^2 +1` does notmap N to N `x to x^2 - 3x +1`doesnot mapN to N `x to( x (x+1))/( 2) ` does not mapN to N Answer :C

Discussion

40.	If barx =18, bary=100, Var(X)=196, Var(Y) = 400 and p(X,Y) = 0.8, find the regressionlines. Extimate the value of y when x = 70 and that of x when y = 90.
Answer» SOLUTION :N/A

Discussion

41.	If f'(x)=(2x)/((1+x^(2))^(2)) , find f(x).
Answer»

Discussion

42.	Evalute the following integrals int(2x^(2) -3 " sin x " + 5 sqrt(x))dx
Answer» Answer :`(2)/(3)X^(3)+3cosx+(10)/(3)x^(+3//2)+C`

Discussion

43.	If 2f''(x)=sinx-49sin7x, find f(x).
Answer»

Discussion

44.	If f'(x)=3sinx-4cosx, find f(x).
Answer»

Discussion

45.	"Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domains of f and g.
Answer» Solution :Let `F(X) =sqrtx, G(x) =1 -x^2` `:.` Dom `f=R_+ U_(0) =R_0`,Dom g =R

Discussion

46.	A and B are two events such that P(A) gt 0, P(B) ne 1 then P(barA\|barB) is equal to
Answer» <P>1- P(A\|B) `1- P(barA\|B)` `(1- P(A UUB))/(P(B))` `(P(barA))/(P(B))` ANSWER :C

Discussion

47.	25 ml of a solution containing HCl and H_(2)SO_(4) required 10 ml of 1 M NaOH solution for complete neutralization. 20 ml of the same acid mixture on being treated with excess of AgNO_(3) gives Report your answer as (x+y)xx1000.
Answer» Solution :Let molarity of HCL is x and `H_(2)SO_(4)` is y `{:(m" mole""mmole "),( x xx25""+""2yxx25=10xx1),(""underbrace("")),("" m" mole of "[H^(+)]):}` ApplyingPOAC Applying POAC `(20xxx)/(1000)=(0.1435)/(143.5)=10^(-3)` `x=(1)/(20)=0.05M` `y=(8.75)/(50)=0.175M` ` therefore(x+y)xx1000=(0.05+0.175)xx1000=225`

Discussion

48.	The number of vectors of unit length perpendicular to the vectors bar(a)=2bar(i)+bar(j)+2bar(k) and bar(b)=bar(j)+bar(k) is ………….
Answer» Only ONE Only TWO Only three INFINITE Answer :B

Discussion

49.	Let P, Q, R, S be points on the plane with position vectors -2hat(i)-hat(j),4hat(i),3hat(i)+3hat(j),-3hat(i)+2hat(j) respectively. The quadrilateral PQRS must be a
Answer» PARALLELOGRAM, which is NEITHER a RHOMBUS nor a rectangle square rectangle, but not a square rhombus, but not a square Answer :A

Discussion

50.	Let A = {1,2,3}. Then number of equivalence relations containing (1,2) is
Answer» 1 2 3 4 Solution :N/A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

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

How many middle terms are there in the expansion of (2x + 3y)^128

Mean of the numbers 1,2,3,…,n with respective weights 1^(2) + 1, 2^(2) + 2, 3^(2) + 3,…,n^(2)+n is

The solution of y dx - xdy + 3x^(2) y^(2) e^(x^(3))dx = 0 is

If |bar(x)|=|bar(y)|=1 and bar(x)_|_bar(y), then |bar(x)-bar(y)| =……………

Show that the points (1, 2, -1), (2, 5, 1) and (0, -1, -3) are collinear.

obtain the equation of hyperbola in each of the following cases: centre (1,-2) transverse axis parallel to x-axis of length 6 and conjugate axis of length 10.

Integration by partial fraction : int(dx)/(x^(4)-1)=....+c

Find adjoint of each of the matrices{:[( 1,-1,2),( 2,3,5),( -2,0,1) ]:}

Using the properties of determinants, prove the following It 2s=a+b+c then |{:(a^2,(s-a)^2,(s-a)^2),((s-b)^2,b^2,(s-b)^2),((s-c)^2,(s-c)^2,c^2):}|=2s^3(s-a)(s-b)(s-c)

Find the number of points with integral coordinates that lie in the interior of the region common to the circle x^(2) + y^(2) = 16 and the parabola y^(2) = 4x.

Evaluate int{(e^(2logx)+e^(3logx))/(x+x^2)}dx.

If A(1,1,1),C(2,-1,2)the vector equationof theline vec(AB)is vec(r) = (hat(i) + hat(j) + hat(k)) + t(6hat(i) -3hat(j) + 2hat(k))and d is theshrotest distanceof the point C form vec(AC)then

Plane meets the coordinateaxes in P,Q,R respectively .If the centroidof trianglePQR is (1,1/2,1/3) , then the equation of plane is .

Find the asymptotes of the following curves: f(x) = (x^(2))/(x+1)

Evaluate the following definite integrals . int_(0)^(5)(x+1)dx

Prove that sum_(k = 1)^(n) k. ""^(k)P_(n + 1) -1.

The partial fractions of (1)/(x^(2)(x+2)) are

Statement 1 The sum of the focal distances of a point on the ellipse 4x^(2)+5y^(2)-16x-30y41=0 is 2sqrt5. Statement 2 The equation 4x^(2)+5y^(2)-16x-30y+41=0 can be expressed as 4(x-2)^(2)+5(y-3)^(2)=20.

If a_(1), a_(2) , ……. A_(n) are in H.P., then the expression a_(1)a_(2) + a_(2)a_(3) + ….. + a_(n - 1)a_(n) is equal to

int_(0)^(oo) (dx)/((1+x^(2))^(4))=

If (5z_2)/(11z_1) is purely imaginary, then the value of |(2z_(1)+3z_(2))/(2z_(1)-3z_(2))| is

Ifalpha , beta , gammaare the rootsof x^4 -4x^2 -x+2=0 find thevaluesofsumalpha^2 betaandsum(1)/(alpha^2)

Evaluate int_(0)^(2)e^(x)dx as the limit of a sum.

Solve the differential equation y e^(x/y) dx = (x e^(x/y) + y^(2))dy ( y ne 0).

Let (S) denotes the number of ordered pairs (x,y) satisfying (1)/(x)+(1)/(y)=(1)/(n),Aax,y,n in N. Q. sum_(r=1)^(10)S(r) equals\

Evaluate the following determinates (i) |{:("3","-1","-2"),(0,0,"-1"),(3,"-5","0"):}|

The negation of (pvv~q)^^q is

y = sin^(-1)(2xsqrt(1 - x^2)), -1/(sqrt2) lt x lt 1/(sqrt2)

If 10 person are seated at a round table, then what is the probability that two particular persons sit together?

If 1m ((2z+1)/(iz+1))=3, then locus of z is

Find the approximate value off(5.001), where f(x) = x^(3) – 7x^2 + 15.

Consider the parabola x^(2) +4y = 0. Let P(a,b) be any fixed point inside the parabola and let S be the focus of the parabola. Then the minimum value at SQ +PQ as point Q moves on the parabola is

STATEMENT-1: The line 2009x+2010y+2011=0 where 2009a+2011c=0 passes through the point ((a)/(b),(b)/(c )), where abc ne 0. STATEMENT-2: If 2009a+2010+2011c=0, then the straight line ax+by+c=0, abc ne 0 passes through ((2009)/(2011),(2010)/(2011)).

Find the rate of change of the area of a circle with respect to its radius r when r=6cm.

Let vec(u),vec(v) and vec(w) be such that |vec(u)|=1,|vec(v)|=2,|vec(w)|=3. If the projection vec(v) along vec(u) is equal to that of vec(w) along vec(u) and vec(v),vec(w) are perpendicular to each orher, then |vec(u)-vec(v)+vec(w)| equals ............... .

Sum to n terms the series 1 + (1+ 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4).......

If Nis the setof alllnaturalnumbersthenwhichof the followingis true

If barx =18, bary=100, Var(X)=196, Var(Y) = 400 and p(X,Y) = 0.8, find the regressionlines. Extimate the value of y when x = 70 and that of x when y = 90.

If f'(x)=(2x)/((1+x^(2))^(2)) , find f(x).

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

If 2f''(x)=sinx-49sin7x, find f(x).

If f'(x)=3sinx-4cosx, find f(x).

"Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domains of f and g.

A and B are two events such that P(A) gt 0, P(B) ne 1 then P(barA|barB) is equal to

25 ml of a solution containing HCl and H_(2)SO_(4) required 10 ml of 1 M NaOH solution for complete neutralization. 20 ml of the same acid mixture on being treated with excess of AgNO_(3) gives Report your answer as (x+y)xx1000.

The number of vectors of unit length perpendicular to the vectors bar(a)=2bar(i)+bar(j)+2bar(k) and bar(b)=bar(j)+bar(k) is ………….

Let P, Q, R, S be points on the plane with position vectors -2hat(i)-hat(j),4hat(i),3hat(i)+3hat(j),-3hat(i)+2hat(j) respectively. The quadrilateral PQRS must be a

Let A = {1,2,3}. Then number of equivalence relations containing (1,2) is