28278 + Interview Questions in Maths in Class 12

1.	The production cos of x computers for a company over one year is $175x+$150,000 . To minimize production costs in a given year to $465,000 , how many computers can the company make in that year ?
Answer» 857 1725 1800 2657 Answer :C

Discussion

2.	int[(1)/((x+a)^(3)(x+b)^(5))]^(1//4)dx=
Answer» `(1)/((b-a))((x+b)/(x+a))^(1//4)+C` `-(1)/((b-a))((x+a)/(x+b))^(1//4)+c` `(4)/(b-a)((x+a)/(x+b))^(3//4)+c` `(4)/(b-a)((x+a)/(x+b))^(1//4)+c` ANSWER :D

Discussion

3.	If X ~ B(10, 0.6) then find mean and variance of X.
Answer» ANSWER :`6, 2.4`

Discussion

4.	If tan^(-1)x + tan^(-1)y=4pi//5, then cot^(-1)x + cot^(-1)y is equal to
Answer» 1.`pi` 2.`(pi)/(5)` 3.`(2pi)/(5)` 4.`(3PI)/(5)` Answer :B

Discussion

5.	There are n straight lines in a plane, no two of which are parallel and no three pass through the same point. Theirpointsof intersection are joined. The number of fresh lines thus formed is
Answer» `(N(n-1)(n-2)(n-3))/(8)` `(n(n+1)(n-2)(n-3))/(8)` `(n(n+1)(n+2)(n-3))/(8)` `(n(n+1)(n+2)(n+3))/(8)` ANSWER :A

Discussion

6.	Let a function f be defined by f(x)="x-\|x\|"/x for x ne 0 and f(0)=2. Then f is
Answer» CONTINUOUS nowhere continuous everywhere continuous for all X EXCEPT x =1 continuous for all x except x=0 ANSWER :D

Discussion

7.	Assertion (A): Three vectors are coplanar if one of them is expressible as a linear combination of the other two Reason (R) Any three coplanar vectors are linearly
Answer» Both A and R are TRUE and R is the correct explanation of (A) A is true but R is not correct explanation of A A is true but R is FALSE A is false but R is true Answer :B

Discussion

8.	The number of ways in which the letters of the word 'FRACTION' be arranged so that No two vowels come together is
Answer» `5! 3!` `6! 3!` `5! ""^(6)P_(3)` `8!` ANSWER :C

Discussion

9.	Check the injectivity and surjectivity of the following function . f:N rarr N cup {0}, f (n) = n+(-1)^(n).
Answer» SOLUTION :N/A

Discussion

10.	Let vec(a)=2hati+hatj-2hatk and vec(b)=hati+hatj. Let the vector vec( c ) is such that \|vec( c )-vec(a)\|=3,\|(vec(a)xx vec(b))xx vec( c )\|=3. The angle between vec( c ) and vec(a)xx vec(b) is 30^(@). Then vec(a).vec( c ) = ……………
Answer» `(1)/(8)` `(25)/(8)` 2 5 Answer :C

Discussion

11.	If the origin of a coordinate system is shifted to (-sqrt(2).sqrt(2)) and then the coordinate system is rotated anticlockwise through an angle 45^(@), the point P(1,-1) in the original system has new coordinates
Answer» `(SQRT(2),-2sqrt(2))` `(0,-2sqrt(2))` `(0,-2-sqrt(2))` `(0,-2+sqrt(2))` ANSWER :C

Discussion

12.	Ifz_(1),z_(2),z_(3) are three points lying on the circle \|z\|=2, then minimum value of \|z_(1)+z_(2)\|^(2)+\|z_(2)+z_(3)\|^(2)+\|z_(3)+z_(1)\|^(2)=
Answer» 6 12 15 24 Solution :`\|z\|=\|z_(2)\|=\|z_(3)\|=2` `because \|z_(1)+z_(2)+z_(3)\|^(2)ge0implies(z_(1)+z_(2)+z_(3))(barz_(1)+barz_(2)+barz_3)GE0` `impliessum\|z_(1)\|^(2)+sum(z_(1)barz_(2)+barz_(1)z_(2))ge0implies2sum\|z_(1)\|^(2)+sum(z_(1)barz_(2)+barz_(1)z_(2))gesum\|z_(1)\|^(2)` `implies\|z_(1)+z_(2)\|^(2)+\|z_(2)+z_(3)\|^(2)+\|z_(3)+z_(1)\|^(2)GE12 {because \|z_(1)\|=\|z_(2)\|=\|z_(3)\|=2}`

Discussion

13.	Find the centre and radius of the following circles : a(x^2 + y^2) - bx - cy = 0
Answer» SOLUTION : `a(x^2 + y^2) - BX - cy = 0` or, `x^2 + y^2 - (bx)a - (cy)/a = 0` `THEREFORE` 2g = -b/a, 2f = -c/a, c = 0 `therefore` g = -b/2a, f = -c/2a `therefore` CENTRE at (-g, -f) = (b/2a, c/2a) and radius = `sqrt(g^2 + f^2 - c) = sqrt((b^2)/(4a^2) + (c^2)/(4a^2))` = `sqrt((b^2 + c^2)/(2a))`

Discussion

14.	A homeowners' association limits the dimensions of the pools that it will allow in a particular subdivision. The bylaws state that permits will only be granted for pools shaped like rectangular prisms, for which the sum of the length of the pool and the perimeter of the vertical side containing the ladder cannot exceed 200 meters. the perimeters of the ladder side is determined using the width and the depth of the pool . IF a pool has a length of 75 meters and its width is 1.5 times its depth, which of the following shows the allowable depth a, in meters, of the pool?
Answer» `0 lt a lt 62 1/2` `0 lt a le 50` `0 lt a le 31 1/4` `0 lt a le 25` ANSWER :D

Discussion

15.	There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row is
Answer» `""^(12)C_(8)` `""^(12)P_(8)` `2xx""^(12)P_(8)` `2xx""^(12)C_(8)` Answer :B

Discussion

16.	int_(0)^(pi//2)(1)/(a^(2).sin^(2)x+b^(2).cos^(2)x)dx is equal to
Answer» 1.`(pi a)/(4B)` 2.`(pi a)/(2b)` 3`(pi b)/(4A)` 4.`(pi)/(2ab)` Answer :D

Discussion

17.	Shows that the following functions do not possess maximum or minimum. 4 - 3x + 3x^2 - x^3
Answer» SOLUTION :PROCESSED as in (III)

Discussion

18.	The number of values of alpha in [-10pi, 10pi] for which the equations (sin alpha)x-(cos alpha)y+3z=0, (cos alpha)x+(sin alpha)y-2z=0 and 2x+3y+(cos alpha)z=0 have nontrivial solution is
Answer» 10 20 40 15 Answer :B

Discussion

19.	Find the adjoint of A= [(1,2),(3,4)]
Answer» SOLUTION :ADJ A=[(4,-2),(-3,1)]

Discussion

20.	Which of the following reacts completely with SO_(2) without requiring a catalyst ?
Answer» `KI` `XeF_(2)` `SiO_(2)` `O_(2)` Answer :C

Discussion

21.	int(e^(x)(1-nx^(n-1)-x^(2n)))/((1-x^(n)) sqrt(1-x^(2n)))d=....+c
Answer» `E^(x) SQRT((1-x^(n))/(1+x^(n)))` `e^(x) sqrt((1+x^(n))/(1-x^(n)))` `e^(-x) sqrt((1-x^(n))/(1+x^(n)))` None of these Answer :B

Discussion

22.	If A=[(1,2,3),(2,3,1)] and B=[(3,-1,3),(-1,0,2)], then find 2A-B.
Answer» ANSWER :`[(-1,5,3),(5,6,0)]`

Discussion

23.	Find minors and cofactors of all the elements of the determinant \|{:(1,-2),(4,3):}\|
Answer» ANSWER :MINOR : `{:(M_(11)=3,M_(12)=4),(M_(21)=-2,M_(22)=1):}` COFACTOR : `A_(11)=(-1)^(1+1)M_(11)=(-1)^2(3)=3` `A_(12)=(-1)^(1+2)M_(12)=(-1)^3(4)=-4` `A_(21)=(-1)^(2+1)M_(21)=(-1)^3(-2)=2` `A_(22)=(-1)^(2+2)M_(22)=(-1)^4(1)=1

Discussion

24.	If a function f:RtoR is defined by f(x){{:(2x,xgt3),(x^(2),1lexle3),(3x,xlt1):} Then the value of f(-1)+f(2)+f(4) is
Answer» 9 14 5 none of these ANSWER :A

Discussion

25.	Consider the equation sec theta +cosec theta=a, theta in (0, 2pi) -{pi//2, pi, 3pi//2} If the equation has four distinct real roots, then
Answer» `\|a\| gt 2sqrt(2)` `\|a\| lt 2sqrt(2)` `a ge -2sqrt(2)` none of these Solution :We have equation `sec x + cosec x =a` To ANALYZE the roots of the equation, we draw the graph of function `y= sec x+ cosec x` and check how many times line `y=a` intersects this graph. Period of `y=sec x + cosec x` is `2PI`. So, we draw the graph of the function for `x in [0, 2pi]`. The garph of function can be easily drawn by drawing the graph of `y=sec x` and `y=cosec x` and then adding the values of `sec x` and `cosec x` by inspection. For example, in first quadrant, `sec x, cosec x gt 0`. Also, when x approaches to zero, `cosec x` approaches to infinity. So, `f(x)` approaches to infinity. Similarly, when x approaches to `pi//2 sec x` approaches to infinity. So, `f(x)` approaches to infinity. At `x=pi//4, f(x)` attains its LEAST value which is `2sqrt(2)`. With similar arguments, we can draw the graph of `y=f(x)` in intervals `(pi//2, pi), (pi, 3pi//2)` and `(3pi//2, 2pi)` We have FOLLOWING graph of `y=f(x)`. From the figure, we can say that `f(x)=a` has two distinct solution if line `y=a` cuts the graph `y=f(x)` between `y=2sqrt(2)` and `y=-2sqrt(2)` i.e., `\|a\| lt 2sqrt(2)`. If line `y=a`, cuts the graph of `y=f(x)` above `y=2sqrt(2)` and below `y=-2sqrt(2)`, then `f(x)=a` has FOUR distinct solutions. So, `\|a\| gt 2sqrt(2)`.

Discussion

26.	A manufacturer can sell x items per day at a price p rupees each, where p=125-(5)/(3)x. Thecost of production for x items is 500 + 13x + 0.2x^(2). Find how much he should producehave a maximum profit, assuming all items produces are sold.
Answer» SOLUTION :N/A

Discussion

27.	{:("Column A" , "The avearge temperature in New","ColumnB"),(, "Orland from January through",),(, "August is "36^(@)C."The minimum",),(,"and the maximum temeperatures",),(,"between September and December ",),(,"are"26^@C"and"36^(@)C"respectively.",),("The average temperature for the year", ,36^@C):}
Answer» If column A is larger If column B is larger If the columns are EQUAL If there is not ENOUGH information to decide Answer :B

Discussion

28.	If z_(1) , z_(2) , z_(3) are the vertices of an equilateral triangle with centroid at z_0 show that z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = 3 z_(0)^(2)
Answer» ANSWER :A::B::C

Discussion

29.	Solve the following linear programming problems graphically : Maximise Z = 50x + 15y subject to constraints 5x+y le 100, x+y le 60, x, y ge 0.
Answer» Answer :MAXIMUM Z = 1250 at (10, 50).

Discussion

30.	For what value of 'K', the system of equations kx+y+z=1, x+ky+z=k" and "x+y+kz=K^(2) has no solution ?
Answer» `0` `-1` `1` NONE of these Answer :D

Discussion

31.	If e^((dy)/(dx)) = x + 1 and y = 3 when x = 0, then y = (x + 1) ln (x + 1) + f (x), where f(x) =
Answer» `3 -X` `x - 3` `1 - x` `x - 1` ANSWER :A

Discussion

32.	Evaluate the definite integrals int_(0)^(1)(xe^(x)+sin(pix)/4)dx
Answer» ANSWER :`1+4/PI-(2SQRT2)/pi`

Discussion

33.	There are two circles in xy-plane whose equations are x^(2)+y^(2)-2x-3=0 and x^(2)+y^(2)-2x=0. A point (x,y) is choosen at random inside the larger circle. The the probability that the point has been taken from the smaller circle is
Answer» `1//4` `3//4` `1//2` `1//3` ANSWER :A

Discussion

34.	[(a+b,b+c,c+a)]=[(a,b,c)], then
Answer» `[(a,b,c)]=1` a, b, c are coplanar `[(a, b, c)]=-1` a, b, c are mutually perpendicular Solution :Given, `[a+b" "b+c" "c+a]=[ABC]` `rArr""(a+b){(b+c)xx(c+a)}=[abc]` ` IMPLIES(a+b).{bxxc+bxxa+cxxa}=[a" "b" "c][ :' cxxc =0]` `rArr""a(bxxc)+BB*b(cxxa)=[abc]` `rArr""[abc]+[abc]=[abc]""[bca]=[abc]]` `rArr""[abc]=0` `rArr"a, b"` and c are cojplanar.

Discussion

35.	Mean and variance of the binomial distribution is 4 and 3 respectively. Then ……….. is the probability for X = 6
Answer» `16C_(6) ((1)/(4))^(10)((3)/(4))^(6)` `16C_(6) ((1)/(4))^(6)((3)/(4))^(10)` `17C_(6) ((1)/(4))^(10)((3)/(4))^(4)` `12C_(6) ((1)/(4))^(6)((3)/(4))^(6)` Answer :B

Discussion

36.	Statement-1 : The variance of first n even natural numbers is (n^(2)-1)/(4) Statement-2 : The sum of first n natural number is (n(n+1))/(2) and the sum of the squares of first n natural number is (n(n+1)(2n+1))/(6).
Answer» Statement-1 is TRUE, statement-2 is true, statement-2 is a CORRECT EXPLANATION for statement-10 Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-10 Statement-1 is true, statement-2 is FALSE Statement-1 is false, statement-2 is true Answer :D

Discussion

37.	Find a point on the curve y= (x-3)^(2), where the tangent is parallel to the chord joining the points (3,0) and (4,1).
Answer» ANSWER :`((7)/(2), (1)/(4))`

Discussion

38.	Find the scalar product of the following pairs of vectors and the angle between them. hati-hatj and hatj+hatk
Answer» SOLUTION :Let `veca = hati-hatj, VECB = hatj+hatk` Then `\|veca\| = sqrt2, \|vecb\| = sqrt2` Now `veca.vecb = 1xx0-1xx1+0xx1 = 0-1+0 = -1` if `theta` is the ANGLE between `veca` and `vecb` then `theta = cos^(-1) ((veca.vecb)/(\|veca\|\|vecb\|))` =`cos^(-1)(-(1)/(sqrt2 sqrt2)) = cos^(-1) (-1/2) = (2pi)/3`.

Discussion

39.	the particular solution of(1 + x^(2))(dy)/(dx) + 2xy = (1)/(1 + x^(2)), y = 0 whenx= 1 is
Answer» Answer :`y (1 + X^(2)) = TAN^(-1)x - (PI)/(4)`

Discussion

40.	Solve by matrix Method: x+2y+3z=2 2x+3y+z=-1 x-y-z=-2
Answer» ANSWER :`-1/-11`

Discussion

41.	Find number of solutions of the equation sin^(-1)(\|log_(6)^(2)(cos x)-1\|)+cos^(-1)(\|3log_(6)^(2)(cos x)-7\|)=(pi)/(2), if x in [0, 4pi].
Answer» ANSWER :4

Discussion

42.	A set contains (2n + 1) elements. The number of subsets of the set which contain at most 'n' elements is
Answer» 2N `N^(2)` `2^(n^(2))` `2^(2n)` ANSWER :D

Discussion

43.	The probability that a teacher will conduct an unannounced test during any class meeting is 1//4. If a student of the class is absent twice, then the probability for the student to miss atleast one test is
Answer» `(3)/(16)` `(6)/(16)` `(1)/(16)` `(7)/(16)` ANSWER :D

Discussion

44.	A non-zero vector a is parallel to the line of intersection of the plane determined by the vectors hat(i),hat(i)+hat(j) and the plane determined by vectors hat(i),-hat(j),hat(i)+hat(k). The angle between a and (hat(i)-2hat(j)+2hat(k)) is
Answer» A`(PI)/(6)` B`(pi)/(4)` C`(pi)/(3)` D`(2pi)/(5)` Answer :D

Discussion

45.	Evaluate the following integrals : int_(1/4)^(1/2)(dx)/(sqrt(x-x^(2)))
Answer» ANSWER :`(PI)/(6)`

Discussion

46.	Thereciprocalequationis
Answer» classoneandx=1is a root classone andx=-1 is AROOT classtwoand`X= +-1` are roots classtwoandx=1 ISA rootbutnotx=-1 Answer :C

Discussion

47.	intsin^(-1)xdx=......+c
Answer» `COS^(-1)X` `xcos^(-1)x-sqrt(1-x^(2))` `xsin^(-1)x+sqrt(1-x^(2))` `xcos^(-1)x+sqrt(1-x^(2))` ANSWER :C

Discussion

48.	If A is the area of the loop given below than A is equal to
Answer» ANSWER :53

Discussion

49.	If (1 + x + x^2)^n = C_0 + C_1x + C_2x^2 + C_3x^3 + ……..C_nx^n then find C_0 + C_3 + C_6 + …….
Answer» ANSWER :`3^(n-1)`

Discussion

50.	Let omega ne 1 be a cube root of unity. Then the minimumof the set {\|a+bomega+c omega^2\|^2:a,b,c "distinct non -zero integers"} equals.............
Answer» Solution :Given , `OMEGA ne 1 ` be a CUBE root of unity, then ` \|a +b Omega +c Omega ^2\|^2` ` =(a+bOmega +cOmega^2)bar((a+bOmega +cOmega^2)),(because zbar(z)=\|z\|^2)` `=(a+bOmega +cOmega^2)(a+b bar(Omega)+2c bar(Omega)^2)` `=a^2+b^2+c^2+ab)(Omega^2+Omega)+b(Omega^2+Omega^4)+ac(Omega +Omega^2)"" ["as" Omega^3=1]` ` =a^2+b^2+c^2+ab)(-1)+bc(-1)+ac(-1)"" [" as" Omega+ Omega^2=-1,Omega^4=Omega]` `=a^2+b^2+c^2-ab-bc-ca` `=(1)/(2){(a-b)^2+(b-c)^2+(c-a)^2}` `because a, b and c` are DISTINCT non - zero integers, For minimum VALUE `a=1,b=2 and c=3` `THEREFORE \|a+b Omega +cOmega^2\|_("min")^(2)=(1)/(2){1^2+1^2+2^2}`. ` =(6)/(2) =300`.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The production cos of x computers for a company over one year is $175x+$150,000 . To minimize production costs in a given year to $465,000 , how many computers can the company make in that year ?

int[(1)/((x+a)^(3)(x+b)^(5))]^(1//4)dx=

If X ~ B(10, 0.6) then find mean and variance of X.

If tan^(-1)x + tan^(-1)y=4pi//5, then cot^(-1)x + cot^(-1)y is equal to

There are n straight lines in a plane, no two of which are parallel and no three pass through the same point. Theirpointsof intersection are joined. The number of fresh lines thus formed is

Let a function f be defined by f(x)="x-|x|"/x for x ne 0 and f(0)=2. Then f is

Assertion (A): Three vectors are coplanar if one of them is expressible as a linear combination of the other two Reason (R) Any three coplanar vectors are linearly

The number of ways in which the letters of the word 'FRACTION' be arranged so that No two vowels come together is

Check the injectivity and surjectivity of the following function . f:N rarr N cup {0}, f (n) = n+(-1)^(n).

Let vec(a)=2hati+hatj-2hatk and vec(b)=hati+hatj. Let the vector vec( c ) is such that |vec( c )-vec(a)|=3,|(vec(a)xx vec(b))xx vec( c )|=3. The angle between vec( c ) and vec(a)xx vec(b) is 30^(@). Then vec(a).vec( c ) = ……………

If the origin of a coordinate system is shifted to (-sqrt(2).sqrt(2)) and then the coordinate system is rotated anticlockwise through an angle 45^(@), the point P(1,-1) in the original system has new coordinates

Ifz_(1),z_(2),z_(3) are three points lying on the circle |z|=2, then minimum value of |z_(1)+z_(2)|^(2)+|z_(2)+z_(3)|^(2)+|z_(3)+z_(1)|^(2)=

Find the centre and radius of the following circles : a(x^2 + y^2) - bx - cy = 0

There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row is

int_(0)^(pi//2)(1)/(a^(2).sin^(2)x+b^(2).cos^(2)x)dx is equal to

Shows that the following functions do not possess maximum or minimum. 4 - 3x + 3x^2 - x^3

The number of values of alpha in [-10pi, 10pi] for which the equations (sin alpha)x-(cos alpha)y+3z=0, (cos alpha)x+(sin alpha)y-2z=0 and 2x+3y+(cos alpha)z=0 have nontrivial solution is

Find the adjoint of A= [(1,2),(3,4)]

Which of the following reacts completely with SO_(2) without requiring a catalyst ?

int(e^(x)(1-nx^(n-1)-x^(2n)))/((1-x^(n)) sqrt(1-x^(2n)))d=....+c

If A=[(1,2,3),(2,3,1)] and B=[(3,-1,3),(-1,0,2)], then find 2A-B.

Find minors and cofactors of all the elements of the determinant |{:(1,-2),(4,3):}|

If a function f:RtoR is defined by f(x){{:(2x,xgt3),(x^(2),1lexle3),(3x,xlt1):} Then the value of f(-1)+f(2)+f(4) is

Consider the equation sec theta +cosec theta=a, theta in (0, 2pi) -{pi//2, pi, 3pi//2} If the equation has four distinct real roots, then

A manufacturer can sell x items per day at a price p rupees each, where p=125-(5)/(3)x. Thecost of production for x items is 500 + 13x + 0.2x^(2). Find how much he should producehave a maximum profit, assuming all items produces are sold.

If z_(1) , z_(2) , z_(3) are the vertices of an equilateral triangle with centroid at z_0 show that z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = 3 z_(0)^(2)

Solve the following linear programming problems graphically : Maximise Z = 50x + 15y subject to constraints 5x+y le 100, x+y le 60, x, y ge 0.

For what value of 'K', the system of equations kx+y+z=1, x+ky+z=k" and "x+y+kz=K^(2) has no solution ?

If e^((dy)/(dx)) = x + 1 and y = 3 when x = 0, then y = (x + 1) ln (x + 1) + f (x), where f(x) =

Evaluate the definite integrals int_(0)^(1)(xe^(x)+sin(pix)/4)dx

There are two circles in xy-plane whose equations are x^(2)+y^(2)-2x-3=0 and x^(2)+y^(2)-2x=0. A point (x,y) is choosen at random inside the larger circle. The the probability that the point has been taken from the smaller circle is

[(a+b,b+c,c+a)]=[(a,b,c)], then

Mean and variance of the binomial distribution is 4 and 3 respectively. Then ……….. is the probability for X = 6

Statement-1 : The variance of first n even natural numbers is (n^(2)-1)/(4) Statement-2 : The sum of first n natural number is (n(n+1))/(2) and the sum of the squares of first n natural number is (n(n+1)(2n+1))/(6).

Find a point on the curve y= (x-3)^(2), where the tangent is parallel to the chord joining the points (3,0) and (4,1).

Find the scalar product of the following pairs of vectors and the angle between them. hati-hatj and hatj+hatk

the particular solution of(1 + x^(2))(dy)/(dx) + 2xy = (1)/(1 + x^(2)), y = 0 whenx= 1 is

Solve by matrix Method: x+2y+3z=2 2x+3y+z=-1 x-y-z=-2

Find number of solutions of the equation sin^(-1)(|log_(6)^(2)(cos x)-1|)+cos^(-1)(|3log_(6)^(2)(cos x)-7|)=(pi)/(2), if x in [0, 4pi].

A set contains (2n + 1) elements. The number of subsets of the set which contain at most 'n' elements is

The probability that a teacher will conduct an unannounced test during any class meeting is 1//4. If a student of the class is absent twice, then the probability for the student to miss atleast one test is

A non-zero vector a is parallel to the line of intersection of the plane determined by the vectors hat(i),hat(i)+hat(j) and the plane determined by vectors hat(i),-hat(j),hat(i)+hat(k). The angle between a and (hat(i)-2hat(j)+2hat(k)) is

Evaluate the following integrals : int_(1/4)^(1/2)(dx)/(sqrt(x-x^(2)))

Thereciprocalequationis

intsin^(-1)xdx=......+c

If A is the area of the loop given below than A is equal to

If (1 + x + x^2)^n = C_0 + C_1x + C_2x^2 + C_3x^3 + ……..C_nx^n then find C_0 + C_3 + C_6 + …….

Let omega ne 1 be a cube root of unity. Then the minimumof the set {|a+bomega+c omega^2|^2:a,b,c "distinct non -zero integers"} equals.............