28278 + Interview Questions in Maths in Class 12

1.	y' + 5y = 0
Answer» ANSWER :ORDER 1; DEGREE 1

Discussion

2.	Number of compounds having S-S linkage H_(2)S_(2)O_(3),H_(2)S_(2)O_(78),H_(2)S_(2)O_(5),H_(2)S_(4)O_(8),H_(2)S_(2)O_(4)
Answer» ANSWER :`4.00`

Discussion

3.	If the roots of x^(3)-kx^(2)+14x-8=0 are in geometric progression, then k=
Answer» -3 7 4 0 Answer :B

Discussion

4.	A coins is tossed three times,where E:atmost two tails, F: atleast one tail.Find P(E/F) in each case above.
Answer» Solution :Here,S = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} E={HHH,HHT,HTH,THH,TTH,THT,HTT} F= {HHT,HTH,THH,HTT,THT,TTH,TTT}`rArr` `EnnF = {HHT,HTH,THH,TTH,THT,HTT} therefore `P(EnnF)`=6/8and P(E) 7/8 THUS,P(E/F)=`(P(EnnF))/(P(F))`=6/8/7/8=6/7

Discussion

5.	Integrate the following functions : int(x^(3))/(1+x^(8))dx
Answer» ANSWER :`(1)/(4)TAN^(-1)(x^(4))+C`

Discussion

6.	Let p,q and r be real number (p ne q, r ne 0) such that the roots ofthe equation (1)/( x + p) + (1)/( x + q) = (1)/(r)are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to :
Answer» `(1)/(2) (p^(2) + q^(2))` `p^(2) + q^(2)` `2 (p^(2) + q^(2))` `p^(2) + q^(2) + r^(2)` ANSWER :D

Discussion

7.	Let z_(1) , z_(2) be two roots of the equation z^(2) + az + b = 0 , z being complex . Further assume that the origin z_(1) and z_(2) form an equilateral triangle , then
Answer» `a^(2) = B` `a^(2) = 2b` `a^(2) = 3B` `a^(2) = 4b` Answer :C

Discussion

8.	A business man gets a profit of Rs. 2800 with probability 0.5, loss of Rs. 5000 with probability 0.3. and neither profit nor loss with probability 0.2. Find mean of his income.
Answer» ANSWER :`-100`

Discussion

9.	Find (dy)/(dx) in the following y= sec^(-1) ((1)/(2x^(2)-1)), 0 lt x lt (1)/(sqrt2)
Answer» ANSWER :`(-2)/(1+ X^(2))`

Discussion

10.	What is the value of arg omega+ arg omega^2?
Answer» SOLUTION :`argomega=ARG omega^2=arg(omega.omega^2)` `=arg(omega^3)=arg(1)=2NPI` `:. "The PRINCIPAL ARGUMENT" =0.`

Discussion

11.	Find both the maximum value and the minimum value of f(x)=3x^(4)-8x^(3)+12x^(2)-48x+25 on the interval [0, 3].
Answer» ANSWER :`25, -39`

Discussion

12.	{:(" "Lt),(x rarr 3):} (1)/(x-3) int_(3)^(x)e^(t)dt=
Answer» `E^(3)` `1/e` `e^(2)` e Answer :A

Discussion

13.	If P is ((1)/(2)+i(sqrt(3))/(2)) and OP is rotated through an angle (pi)/(2) in the clockwise direction then the new position of P is :
Answer» `(1)/(2)i-i(SQRT(3))/(2)` `(-sqrt(3))/(2)-(1)/(2)` `-(1)/(2)i-i(sqrt(3))/(2)` `(sqrt(3))/(2)-(i)/(2)` ANSWER :D

Discussion

14.	If A and B are events such that P(AuuB)=(5)/(6), P(barA)=(1)/(4), P(B)=(1)/(3), then A and B are
Answer» MUTUALLY exclusive independent EXHAUSTIVE events exhaustive and independent Answer :B

Discussion

15.	A balloon is filled in such a way that its volume increases at the rate of 40 cm^(3)/min. when radius is 8 cm, the rate of increases in the surface area is ……………. cm^(2)/min.
Answer» 8 10 20 None of these ANSWER :B

Discussion

16.	Let S = sum _(r=1)^(30) (""^(30+r)C_(r) (2r-1))/(""^(30)C_(r)(30+r)),K=sum_(r=0)^(30) (""^(30)C_(r))^(2) and G=sum_(r=0)^(60) (-1)^(r)(""^(60)C_(r) )^(2) The value (SK_SG) is
Answer» 0 1 `2^(30)` `2^(60)` Solution :`because S = sum _(r=1)^(30) (""^(30+r)C_(r) (2r-1))/(""^(30)C_(r)(30+r))=sum_(r=0)^(30) (""^(30+r)C_(r))/(""^(30)C_(r))(1-(30-r+1)/(30+r))` `=sum_(r=0)^(30)[ (""^(30+r)C_(r))/(""^(30)C_(r)) -(""^(30+r)C_(r))/(""^(30)C_(r))CDOT ((30-r+1))/((30+r))]` `=sum_(r=0)^(30)[ (""^(30+r)C_(r))/(""^(30)C_(r)) -""^((30+r)/(r)cdot ^(29+r)C_(r-1))/(""^(30)C_(r))cdot ((30-r+1))/(30+r)]` `=sum_(r=0)^(30)[ (""^(30+r)C_(r))/(""^(30)C_(r)) -( ""^(29+r)C_(r-1))/(""^(30)C_(r-1)) ][because (""^(n)C_(r))/(""^(n)C_(r-1))=(n-r+1)/r]` For n = 30 `((31-r)/rcdot ""^(30)C_(r)=""^(30)C_(r-1))` `=(""^(30+30)C_(30))/ (""^(30)C_(30)) - (""^(29-1)C_(0))/(""^(30)C_(0))= ""^(60)C_(30)-1` `K = sum _(r=1) ^(30) (""^(30)C_(r))^(2) = ""^(60)C_(30) and G = sum_(r=0)^(60) (-1)^(r) (""^(60)C_(r))^(2)` `(""^(60)C_(0))^(2) - (""^(60)C_(1))^(2)+(""^(60)C_(2))^(2)-...+(""^(60)C_(60))=""^(60)C_(30)` [`because n=60` is EVEN ] `SK - SG = S (K- G) = (G- G) = 0 [ because K= G]`

Discussion

17.	Write the following functions in the simplest form : tan^(-1) sqrt((1-cos x)/(1+cos x)), 0 lt x lt pi
Answer» SOLUTION :`tan^(-1)SQRT((1-cos X)/(1+cos x)) = tan^(-1) sqrt((2sin^2 x//2)/(2cos^2 x//2)) = tan^(-1)(tan frac X2) =x/2`

Discussion

18.	Evalute the following integrals int x cos^(-1)xdx
Answer» Answer :`(1)/(4) [ (2x^(2) - 1) COS^(-1) x - x SQRT(1 -x^(2)) ]+ C `

Discussion

19.	Determine the intervals of concavity of the curve y=3 +sin x.
Answer» ANSWER :`x=npi`

Discussion

20.	The value of\|(veca,vecb,vec c),(vecavecp, vecbvecp, veccvecp),(vecavecq,vecbvecq, vec cvecq)\| is equal to :
Answer» `(vecp XX vecq)[veca xx vecb" "vecb xx vecc" "vecc xx veca]` `2(vecp xx vecq)[veca xx vecb" "vecb xx VEC c" " vec c xx veca ]` `4(vecp xx vecq)[veca xx vecb" "vecb xx vec c" " vec c xx veca]` `(vecp xx vecq) SQRT([veca xxvecb" " vecb xx vec c" "vec c xx veca])` Answer :D

Discussion

21.	Integrate the following functions e^(2x+3)
Answer» SOLUTION :`INT E^(2x+3) DX = e^(2x+3)/2+C` `int e^x dx = e^x +c`

Discussion

22.	Obtain the equation of straight lines : Passing through the points (2,3) and (-4,1) .
Answer» SOLUTION :Equation of the LINE is `y-y_1 = (y_2-y_1)/(x_2-x_1) (x-x_1)` or, `y-3 = (1-3)/(-4-2) (x-2)` or, `y-3 = (-2)/(-6) (x-2)` or, y-3 = 1/3 (x-2) or, 3y-9 = x-2 or, x-3y+7 = 0

Discussion

23.	If z = x + iy is a complex number such that Z^((1)/(3)) = a + ib, then the value of (1)/(a^(2) + b^(2)) ((x )/(a) + (y)/(b)) is equal to
Answer» `-1` `-2` 0 2 Answer :B

Discussion

24.	If two positive numbers are in the ratio 3 + 2sqrt(2) : 3 - 2sqrt(2), then the ratio between their A.M. and G.M. is
Answer» `6 : 1` `3 : 2` `2 : 1` `3: 1` ANSWER :D

Discussion

25.	Evaluate : int(sin x + cos x)/(9 + 16 sin 2x) dx.
Answer» ANSWER :`(1)/(40) log \|(5+4(sin X - COS x))/(5-4(sin x - cos x))\| + c`

Discussion

26.	By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(sin^(3/2)xdx)/(sin^(3/2)x+cos^(3/2)x)
Answer» ANSWER :`pi/4`

Discussion

27.	If phi (x) is a differentiable real valued function satisfying phi (x) +2phi le 1, then it can be adjucted as e^(2x)phi(x)+2e^(2x)phi(x)lee^(2x) or (d)/(dx)(e^(2)phi(x)-(e^(2x))/(2))le or (d)/(dx)e^(2x)(phi(x)-(1)/(2))le0 Here e^(2x) is called integrating factor which helps in creating single differential coefficeint as shown above. Answer the following question: If p(1)=0 and dP(x)/(dx)ltP(x) for all xge1 then
Answer» <P>`P(x)GT 0 forall x gt 1` P(x) is a constant function `P(x) lt 0 forall x gt 1` none of these Solution :`(DP(x))/(dx)GTP(x)` or `E^(-x)(dp(x))/(dx)-e^(-x)p(x)gt0` or `(d)/(dx)p(x)e^(-x)gt0` thus P(x) `e^(-x)` is and increasing function i.e `p(x)e^(-x)gt9(1)e^(-1)forallxge1` or `p(x)e^(-x)gt 0 forall xgt1 or p(x)gt0 forall x gt1`

Discussion

28.	The vertices of a triangle are A(3, 7), B(3, 4) and C(5, 4). The equation of the bisector of the angle /_ABC is
Answer» y=X+1 y = x - 1 y = 3X - 5 y = x Answer :A

Discussion

29.	If bara is a non-zero vector are two vectors such that bara xx barb= bara xx barc and bara.barb=bara.barc, then prove that barb=barc.
Answer» ANSWER :`:.BARB= BARC`.

Discussion

30.	Evaluate the definite integrals . underset(0)overset(a)int (a^(2)x-x^(3))dx
Answer» ANSWER :`(a^(4))/(4)`

Discussion

31.	If a = 2i + k, b = I + j + k, c = 4i - 3j + 7k. The vector r satisfying r xx b = c xx b and r.a = 0 is
Answer» I +8J + 2K I - 8j + 2k `-1 - 8j + 2k` I - 8j - 2k Answer :C

Discussion

32.	Resolve into Partial Fractions (iv) (x^(4))/((x-1)(x-2))
Answer» ANSWER :`X^(2)+3x+7- (1)/((x-1))+(16)/((x-2))`

Discussion

33.	Find the probability that in a family of 5 children, there will be exactly 3 male children.
Answer» ANSWER :`(5)/(16)`

Discussion

34.	The probability of the event A occuring is 0.5 and of B occurring is 0.3. If A and B are mutually exclusive events then the probability of neither A nor B occuring is
Answer» ANSWER :`0.2`

Discussion

35.	If int(dx)/(1+sinx)=tan((x)/(2)+a)+b, then..
Answer» `a=(PI)/(4),B=3` `a=-(pi)/(4),b=3` `a=(pi)/(4),b=` Arbitary CONSTANT `a=-(pi)/(4),b=` Arbitary constant Answer :D

Discussion

36.	Number of binary operations on the set {a,b} are
Answer» 10 16 20 8 Solution :N/A

Discussion

37.	(a+b).(a-b)+((a+b)(a-b)(a^2+b^2))/(2!)+((a+b)(a-b)(a^4+b^4+a^2b^2))/(3!)+.....=
Answer» `E^(a) +e^b` `e^(a+b)` `e^(a^2)-e^(b^3)` `e^(a^2)-e^(b^2)` ANSWER :C

Discussion

38.	Write the first three terms of the expansion of (1+(x^(2))/(2))^(-5)
Answer» SOLUTION :N/A

Discussion

39.	If 1,alpha,alpha^2,alpha^3,…,alpha^(n-1) be the n^(th) roots of unity, then prove that 1^p+alpha^p+(alpha^2)^p+(alpha^3)^p+…+(alpha^(n-1))^p={{:(0,if" "pnekn),(n,if" "p=kn):}" where p,k"epsilonN
Answer»

Discussion

40.	Let p and q be two statements and let r and s be the following statements: r : p harr q s: ~ q harr ~ p Then which of the following is not true
Answer» R `EQUIV`s `r ^^ s equiv` s `r VEE s equivs` `r NE s ` ANSWER :D

Discussion

41.	The probabilities that at least one of the events A and B occurs is 0.8 and the probabilitythat both events occur simultaneously is 0.25. Find the probability P(barA)+P(barB).
Answer» 0.95 0.05 0.5 None of these SOLUTION :N/A

Discussion

42.	If (1.05)^(50) = 11.658 then sum _(n = 1) ^(49) (1.05)^(n) equals
Answer» 208.34 212.12 212.16 213.16 Answer :C

Discussion

43.	the matrix S is rotation through an angle 45^(@) and G is th reflection about the line y=2x, then (SG)^(2) is equal to
Answer» 7I 5I 3I I Answer :D

Discussion

44.	If I(x)=intx^2(logx)^2dx and I(I)=0 then I(x)
Answer» `x^3/18[8(LOGX)^2-3logx]+7/18` `x^3/27[9(logx)^2+6logx]-2/27` `x^3/27[9(logx)^2+6logx+2]-2/27` `x^3/27[9(logx)^2+6logx-2]+2/27` ANSWER :C

Discussion

45.	Fromthe polynomial equation whose roots are1+I,1-I,-1+I,-1-I
Answer» ANSWER :`x^4+4=0`

Discussion

46.	If ab ne 0 and the sum of the coefficient of x^7 and x^4 in the expansion of ((x^2)/(a)-(b)/(x))^11 zero, then
Answer» a = B a + b = 0 ab = -1 ab = 1 ANSWER :D

Discussion

47.	If A and B are two events such that P (A) = 0.3, P (B) = 0.6 and P ((B)/(A)) = 0.5 find P (A cup B)
Answer» ANSWER :0.75

Discussion

48.	For the matrixA={:[( 3,2),( -1,2) ]:} .Find the numbers a and b such that A^(2) +aA+bI =O.
Answer» ANSWER :` a=-4,b=1`

Discussion

49.	The unit vector in the opposite direction of bar(x)+bar(y)-2bar(z) is ………… where bar(x)=(1,1,0),bar(y)=(0,1,1) and bar(z)=(1,0,1).
Answer» `((1)/(SQRT(6)),(-2)/(sqrt(6)),(1)/(sqrt(6)))` `((1)/(6),(-2)/(6),(1)/(6))` `((-1)/(sqrt(6)),(2)/(sqrt(6)),(-1)/(sqrt(6)))` `((-1)/(6),(2)/(6),(-1)/(6))` ANSWER :A

Discussion

50.	A firm has a marginal revenue function given MR=(a)/(x+b)-c ,where x is the output a, b, c are constants. Then demand function is given by p=(k)/(x)log((x+b)/(b))-c , where k is(i) a(ii) c(iii) 1(iv) -1
Answer» a C 1 `-1` ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

y' + 5y = 0

Number of compounds having S-S linkage H_(2)S_(2)O_(3),H_(2)S_(2)O_(78),H_(2)S_(2)O_(5),H_(2)S_(4)O_(8),H_(2)S_(2)O_(4)

If the roots of x^(3)-kx^(2)+14x-8=0 are in geometric progression, then k=

A coins is tossed three times,where E:atmost two tails, F: atleast one tail.Find P(E/F) in each case above.

Integrate the following functions : int(x^(3))/(1+x^(8))dx

Let p,q and r be real number (p ne q, r ne 0) such that the roots ofthe equation (1)/( x + p) + (1)/( x + q) = (1)/(r)are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to :

Let z_(1) , z_(2) be two roots of the equation z^(2) + az + b = 0 , z being complex . Further assume that the origin z_(1) and z_(2) form an equilateral triangle , then

A business man gets a profit of Rs. 2800 with probability 0.5, loss of Rs. 5000 with probability 0.3. and neither profit nor loss with probability 0.2. Find mean of his income.

Find (dy)/(dx) in the following y= sec^(-1) ((1)/(2x^(2)-1)), 0 lt x lt (1)/(sqrt2)

What is the value of arg omega+ arg omega^2?

Find both the maximum value and the minimum value of f(x)=3x^(4)-8x^(3)+12x^(2)-48x+25 on the interval [0, 3].

{:(" "Lt),(x rarr 3):} (1)/(x-3) int_(3)^(x)e^(t)dt=

If P is ((1)/(2)+i(sqrt(3))/(2)) and OP is rotated through an angle (pi)/(2) in the clockwise direction then the new position of P is :

If A and B are events such that P(AuuB)=(5)/(6), P(barA)=(1)/(4), P(B)=(1)/(3), then A and B are

A balloon is filled in such a way that its volume increases at the rate of 40 cm^(3)/min. when radius is 8 cm, the rate of increases in the surface area is ……………. cm^(2)/min.

Let S = sum _(r=1)^(30) (""^(30+r)C_(r) (2r-1))/(""^(30)C_(r)(30+r)),K=sum_(r=0)^(30) (""^(30)C_(r))^(2) and G=sum_(r=0)^(60) (-1)^(r)(""^(60)C_(r) )^(2) The value (SK_SG) is

Write the following functions in the simplest form : tan^(-1) sqrt((1-cos x)/(1+cos x)), 0 lt x lt pi

Evalute the following integrals int x cos^(-1)xdx

Determine the intervals of concavity of the curve y=3 +sin x.

The value of|(veca,vecb,vec c),(veca*vecp, vecb*vecp, vecc*vecp),(veca*vecq,vecb*vecq, vec c*vecq)| is equal to :

Integrate the following functions e^(2x+3)

Obtain the equation of straight lines : Passing through the points (2,3) and (-4,1) .

If z = x + iy is a complex number such that Z^((1)/(3)) = a + ib, then the value of (1)/(a^(2) + b^(2)) ((x )/(a) + (y)/(b)) is equal to

If two positive numbers are in the ratio 3 + 2sqrt(2) : 3 - 2sqrt(2), then the ratio between their A.M. and G.M. is

Evaluate : int(sin x + cos x)/(9 + 16 sin 2x) dx.

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(sin^(3/2)xdx)/(sin^(3/2)x+cos^(3/2)x)

The vertices of a triangle are A(3, 7),﻿ B(3, 4) and C(5, 4). The equation of the﻿ bisector of the angle /_ABC is﻿

If bara is a non-zero vector are two vectors such that bara xx barb= bara xx barc and bara.barb=bara.barc, then prove that barb=barc.

Evaluate the definite integrals . underset(0)overset(a)int (a^(2)x-x^(3))dx

If a = 2i + k, b = I + j + k, c = 4i - 3j + 7k. The vector r satisfying r xx b = c xx b and r.a = 0 is

Resolve into Partial Fractions (iv) (x^(4))/((x-1)(x-2))

Find the probability that in a family of 5 children, there will be exactly 3 male children.

The probability of the event A occuring is 0.5 and of B occurring is 0.3. If A and B are mutually exclusive events then the probability of neither A nor B occuring is

If int(dx)/(1+sinx)=tan((x)/(2)+a)+b, then..

Number of binary operations on the set {a,b} are

(a+b).(a-b)+((a+b)(a-b)(a^2+b^2))/(2!)+((a+b)(a-b)(a^4+b^4+a^2b^2))/(3!)+.....=

Write the first three terms of the expansion of (1+(x^(2))/(2))^(-5)

If 1,alpha,alpha^2,alpha^3,…,alpha^(n-1) be the n^(th) roots of unity, then prove that 1^p+alpha^p+(alpha^2)^p+(alpha^3)^p+…+(alpha^(n-1))^p={{:(0,if" "pnekn),(n,if" "p=kn):}" where p,k"epsilonN

Let p and q be two statements and let r and s be the following statements: r : p harr q s: ~ q harr ~ p Then which of the following is not true

The probabilities that at least one of the events A and B occurs is 0.8 and the probabilitythat both events occur simultaneously is 0.25. Find the probability P(barA)+P(barB).

If (1.05)^(50) = 11.658 then sum _(n = 1) ^(49) (1.05)^(n) equals

the matrix S is rotation through an angle 45^(@) and G is th reflection about the line y=2x, then (SG)^(2) is equal to

If I(x)=intx^2(logx)^2dx and I(I)=0 then I(x)

Fromthe polynomial equation whose roots are1+I,1-I,-1+I,-1-I

If ab ne 0 and the sum of the coefficient of x^7 and x^4 in the expansion of ((x^2)/(a)-(b)/(x))^11 zero, then

If A and B are two events such that P (A) = 0.3, P (B) = 0.6 and P ((B)/(A)) = 0.5 find P (A cup B)

For the matrixA={:[( 3,2),( -1,2) ]:} .Find the numbers a and b such that A^(2) +aA+bI =O.

The unit vector in the opposite direction of bar(x)+bar(y)-2bar(z) is ………… where bar(x)=(1,1,0),bar(y)=(0,1,1) and bar(z)=(1,0,1).

A firm has a marginal revenue function given MR=(a)/(x+b)-c ,where x is the output a, b, c are constants. Then demand function is given by p=(k)/(x)log((x+b)/(b))-c , where k is(i) a(ii) c(iii) 1(iv) -1

The value of|(veca,vecb,vec c),(vecavecp, vecbvecp, veccvecp),(vecavecq,vecbvecq, vec cvecq)| is equal to :

The vertices of a triangle are A(3, 7), B(3, 4) and C(5, 4). The equation of the bisector of the angle /_ABC is