28278 + Interview Questions in Maths in Class 12

1.	If 3x + 8 gt 2, then the smallest integer value of 5x + 12 is
Answer» 1 2 3 4 Answer :C

Discussion

2.	IfDelta = {:[( a_11, a_12, a_113),( a_21,a_22,a_23) ,(a_31,a_32, a_33) ]:} and A_y is Cofactors of a_ijthen value of Deltais given by
Answer» ` a_11 A_31+ a_12A_32+a_13A_33` ` a_11A_11+a_12A_21+a_13A_31` ` a_21A_11+a_22A_12+a_23A_13` `a_11A_11+a_21A_21+a_31A_31` ANSWER :D

Discussion

3.	Evaluate the definite integrals int_(0)^(2)(6x+3)/(x^(2)+4)dx
Answer» ANSWER :`3LOG2+(3PI)/8`

Discussion

4.	Kyle can choose between blue, black, and brown pants, white, yellow, or pink shirts, and whether or not he wears a tie to go with his shirt. How many days can Kyle go without wearing the same combination twice?
Answer» ANSWER :18

Discussion

5.	The number of value(s) of x satisfying 1-log_(g)(x+1)^(2)=1/2log_(sqrt(3))((x+5)/(x+3)) is
Answer» SOLUTION :`1-log(3^(2))(x+1)^(2)=1/2log_(3^(1//2))((x+5)/(x+3))` `=1-2/2log_(3)\|x+1\|2/2=log_(3)((x+5)/(x+3))` `=log_(3)(3/(\|x+1\|))=log_(3)((x+5)/(x+3))` `implies3/(\|x+1\|)=(x+5)/(x+3)` Case I1 `x+1gt0impliesxgt-1` `implies3(x+3)=(x+1)(x+5)` `impliesx^(2)+3x-4=0` `impliesx=-4` or `x=1` `x=-4` rejected `(xgt-1)` `:.x=1` Case II `x+1lt0impliesxlt-1` `3(x+3)-1(x+1)(x+5)` `impliesx^(2)+9x+14=0` `impliesx=-2` or `x=-7` `:.` Set of value of `x` `={-7, -2, 1}`

Discussion

6.	Find the centre of the conic 14x^(2) - 4xy + 11y^(2) - 44x - 58y +71=0
Answer» ANSWER :`= ( 2,3)`

Discussion

7.	Consider the following Statements p : A tumbler is half empty. A tumbler is half full. Then, thee combination form of"p if and only if q"is
Answer» a TUMBLER is half empty and half full a tumbler is half empty if and only if it is half full Both (a) and (B) NONE of the these Answer :B

Discussion

8.	If I = int xsin^(-1){(1)/(2)sqrt((2a-x)/(a))dx=Kx^(2)sin^(-1){(1)/(2)sqrt((2-x)/(a))}+(1)/(2a){t^((5)/(2))+4a^(2)t^((1)/(2))-(4a)/(3)t^((3)/(2))} + C , t = 2a + x, then K is equal to
Answer» ANSWER :`0.50`

Discussion

9.	underset(x rarr oo)(lim) (x^(2))/(e^(x)) is
Answer» 2 0 `OO` 1 Answer :B

Discussion

10.	Find the ellipse whose vertices are (2,-2) (2,4) and e=1//3
Answer» ANSWER :`((x-2)^(2))/(8)+((y-1)^(2))/(0)=1`

Discussion

11.	x and y are the sides of two squares such that y=x-x^(2). Find the rate of change of the area of second square with respect to the area of first square.
Answer» ANSWER :`2X^(2)-3x+1`

Discussion

12.	The radical centre of the three circles described on the three sides of a triangle as diameter is ......... of the triangle
Answer» the ORTHOCENTRE the circumcentre the INCENTRE the centroid of the triangle ANSWER :A

Discussion

13.	Find the equation of the parabola which is symmetric about y-axis, and passes through the point (2,-3) .
Answer» ANSWER :`y^(2)-2x-3y+4=0`

Discussion

14.	A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 minutes from the angle of depression of the car to change from 30^(@) "to" 45^(@), then after this, the time taken (in minutes) by the car to reach the foot of the tower, is
Answer» `9 (1 + SQRT(3))` `18 (sqrt(3) - 1)` `(9)/(2) (sqrt(3) - 1)` `18 (1 + sqrt(3)` ANSWER :A

Discussion

15.	Find the probability of getting. (i) a prime number when a die is rolled. (ii) sum 9 when two dice are rolled. (iii) sum atleast 10 when two dice are rolled.
Answer» Answer :`(i) (1)/(2)` `(ii) (1)/(9)` `(III) (11)/(12)`

Discussion

16.	If the normal at P on the hyperbola meets the transverse axis at G, S is a foci andthe eccentricity of the hyperbola then SG : SP is equal to
Answer» a b e `1//e` ANSWER :C

Discussion

17.	Define linear combination of vectors.
Answer» ANSWER :`BAR(a_1),bar(a_2),bar(a_3),……….(a_n)`.

Discussion

18.	The value of int_(-1)^(1) (2\|x\| - \|x\|^3)dx is :
Answer» 3 `3/2` `0` `3/4` ANSWER :B

Discussion

19.	f : (0, pi)to R, f(x)=2x+cot x. Find the intervals in which f(x) is strictly increasing or strictly decreasing.
Answer» ANSWER :DECREASE in `(0,(pi)/(4))`, increase in `((pi)/(4),(3PI)/(4))`, decrease in `((3pi)/(4),pi)`

Discussion

20.	Evaluate the integrals by using substitution int_(0)^(1)x/(x^(2)+1)dx
Answer» ANSWER :`1/2log2`

Discussion

21.	If alpha=5/(2!xx3)+(5xx7)/(3!xx3^(2))+(5xx7xx9)/(4!xx3^(3))+...," then "alpha^(2)+4alpha=
Answer» 21 23 25 27 Answer :B

Discussion

22.	Three distinguishable dice are rolled. In how many ways we can get a total 15?
Answer» ANSWER :10

Discussion

23.	vec(a)=hatj-hatk and vec( c )=hati-hatj-hatk. The vector vec(b) is such that vec(a) xx vec(b)+vec( c )=0 and vec(a)*vec(b)=3 then vec(b) = ………..
Answer» `-hati+hatj-2hatk` `2hati-hatj+2hatk` `hati-hatj-2hatk` `hati+hatj-2hatk` ANSWER :A

Discussion

24.	If f(x) = underset(nrarroo)limn^(2)(x^(1//n)-x^(1//(n+1))),xgt0 then int x f(x) dx is equal to
Answer» `X^(2)//2` 0 `x^(2)log x - (1)/(2) x^(2) + C` none of these Answer :D

Discussion

25.	Cosine of the angle between the lines overliner=5hati-hatj+4hatk+lamda(hati+2hatj+2hatk)and overliner=7hati+2hatj+2hatk+mu(3hati+2hatj+6hatk)is
Answer» 0 `(1)/(2)` `(19)/(21)` `(1)/(3)` Answer :C

Discussion

26.	f : R to R : f (x) = x^(3)is
Answer» ONE-one and onto one-one and into many - one and onto many -one and into Answer :A

Discussion

27.	Show that the function given by f(x)=e^(2x) is increasing on R.
Answer» ANSWER :`2E^(2X)GT 0`

Discussion

28.	Examine the existence of the following limits:lim_(xto0) cosecx
Answer» Solution :L.H.L.`=lim_(xto0-)` COSECX `=lim_(hto0)` COSEC(-h) `=lim_(hto0)` -1/sin h`=-infty` R.H.L.`=lim_(hto0+)`cosecx `=lim_(hto0)`cosec(h)=`infty` As L.H.L.neR.H.L. the LIMIT does not exist.

Discussion

29.	Choose the correct answer. The general solution of a differential equation e^x dy + (y e^x + 2x) dx = 0 is...a) x e^x + x^2 = cb) x e^y + y^2 = cc) x e^y + y^2 = cd) y e^x + x^2 = c
Answer» `X e^x + x^2 = C` `x e^y + y^2 = c` `y e^x + x^2 = c` `y e^x + x^2 = c` ANSWER :C

Discussion

30.	y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A,B (a,0), and c are concyclic. Tangents to the parabola y^(2)=4x at A and C intersect at point D and tangents to the parabola y^(2)=-8(x-a) intersect at point E. Then the area of quadrilateral DAEC is
Answer» `96sqrt(2)` `48sqrt(3)` `54sqrt(5)` `36sqrt(6)` Solution :(1) Solving the fiven parabolas , we have -8(x-1)=4x `orx=(2A)/(3)` Therefore, the INTERSECTION are `(2a//3,pmsqrt(8a//3))`. Now, OABC is cyclic quadrilateral. Hence, `angleOAB` must be a right angle. So, Slope of `OAxx` Slope of AB=-1 `or(sqrt(8a//3))/(2a//3)xx(sqrt(8a//3))/(a-(2a//3))=-1` `ora=12` Therefore, the coordinates of A and B are `(8,4sqrt(2))and(8,-4sqrt(2))`, respectively. So, Length of COMMON chord `=8sqrt(2)` Area of quadrilateral `=(1)/(2)OBxxAC` `=(1)/(2)xx12xx8sqrt(2)` `48sqrt(2)` Tangent to the parabola `y^(2)=4xat(8,4sqrt(2))" is "4sqrt(2)y=2(x+8)orx-2sqrt(2)y+8=0`, which meets the x-axis at D(-8,0). Tangent to the parabola `y^(2)=-8(x-12)at(8,4sqrt(2))" is "4sqrt(2)y=-4(x+8)+96orx+sqrt(2)y=16=0`, which meets the x-axis at E(16,0). Hence, Area of quadrilateral `DAEC=(1)/(2)DExxAC` `(1)/(2)xx24xx8sqrt(2)` `=96sqrt(2)`

Discussion

31.	Integrate the following functions x logx
Answer» SOLUTION :`intx logx dx = INT logx xx X dx` =`logx xx x^2/2 - int 1/x xx x^2/2 dx` `(x^2logx)/2 -1/2 int x dx` =`(x^2logx)/2 -1/2 x^2/2 +c` =`x^2/2 logx - x^2/4 +c`

Discussion

32.	Integrate the following rational functions : int((x^(3)-1)/(x^(3)+1))dx
Answer» ANSWER :`X-log\|x\|-tan^(-1)x+(1)/(2)log\|x^(2)+1\|+c`

Discussion

33.	If f : R to R is a continuous defined by f(x)=[x]cos ((2x-1)/(2))pi, where [x] denotes the greatest integer function, then f is
Answer» DISCONTINUOUS only at non-zero INTEGRAL VALUES of x continuous only at y continuous only at x discontinuous only ANSWER :C

Discussion

34.	A dice is tossed twice. Find probability of getting a number greater than 3 on each toss.
Answer» ANSWER :`(1)/(4)`

Discussion

35.	Number of Irrational terms in the expansion of (2^(1/3)+3^(1/2)+5^(1/6))^(10) is equal to :-
Answer» Solution :Total TERMS= `.^(12)C_(2) = 66` , Number of rational terms = 3 Irrational terms = 66 - 3 = 63 terms.

Discussion

36.	Accoding to kelper's law if a planet revolves around the sun, its trajectory is elliptical with sun sweeps equal areas is equal interyals of time. Given the ratio f magnetitude of maximum velocity (u) to minimum velocity (v) of planet as 3 and shortance distance between plonet and sun is (a)/(2). Elccentricity of elliptical orbit is
Answer» `(2)/(3)` `(2)/(4)` `(2)/(1)` `(1)/(SQRT(2))` ANSWER :C

Discussion

37.	Accoding to kelper's law if a planet revolves around the sun, its trajectory is elliptical with sun sweeps equal areas is equal interyals of time. Given the ratio f magnetitude of maximum velocity (u) to minimum velocity (v) of planet as 3 and shortance distance between plonet and sun is (a)/(2). Time taken by planet two revolves once is (ka)/(u) then k is
Answer» `PI` `2 SQRT(3)pi` `(sqrt(3))/(2) pi` none of these Answer :B

Discussion

38.	Accoding to kelper's law if a planet revolves around the sun, its trajectory is elliptical with sun sweeps equal areas is equal interyals of time. Given the ratio f magnetitude of maximum velocity (u) to minimum velocity (v) of planet as 3 and shortance distance between plonet and sun is (a)/(2). If velocity at the end of axis of the elliptical orbit is v. then magnetiduce of u, v,vare in
Answer» A.P H.P G.P none of these Answer :C

Discussion

39.	If Tan theta_(1)=k cot theta_(2) then(cos (theta_(1)+theta_(2)))/(cos (theta_(1)-theta_(2)))=
Answer» `(1+k)/(1-k)` `(1-k)/(1+k)` `(k+1)/(k-1)` `(k-1)/(k+1)` ANSWER :B

Discussion

40.	The standard deviation is not affected by the change of
Answer» ORIGIN SCALE origin and scale NONE of these ANSWER :A

Discussion

41.	int1/(x+sqrt(x^(2)-x+1))dx=Plog(x+sqrt(x^(2)-x+1))+Qlog(2x-1+2sqrt(x^(2)-x+1))+R(3/(2x-1+2sqrt(x^(2)-x+1)))+c Then the values of P, Q, R are
Answer» `2, 3/2, 1/2` `2, -3/2, 1/2` `2, -3/2, -1/2` NONE of these Answer :C

Discussion

42.	If the general solution of sin x + 3 sin 3x + sin 5 x = 0 " is " x = y then the set of all values of cos y is
Answer» `{-1,-(SQRT(3))/(2),(sqrt(3))/(2),1}` `{-1,(1)/(2),1}` `{-(sqrt(3))/(2),0,1,(sqrt(3))/(2)}` `{-1,-(1)/(2),(1)/(2),1}` ANSWER :D

Discussion

43.	If a variable line, 3x + 4y -lambda = 0 is such that the two circles x^(2)+y^(2)-2x-2y+1=0 and x^(2)+y^(2)-18x-2y+78=0 are not its opposite sides, then the set of all values of lambda is the interval
Answer» [13, 23] [2,17] [12,21] [23,31] Solution :The GIVEN circle, `x^(2)+y^(2)-2x-2y+1=0""...(i)` and `x^(2)+y^(2)-18x-2y+78=0,""...(ii)` are on the opposite side of the variable line `3x+4y-lambda = 0`. Their centres also lie in the opposite sides of the varible line. `RARR[3(1)+4(1)-lambda][3(9)+4(1)-lambda]lt0` [`therefore ` the points ` P(x_(1), y_(1)) and Q (x_(2), y_(2))` lie on the opposite sides of the line AX + by + c =0, `if (ax_(1)+by_(1)+c)(ax_(2)+by_(2)+c)lt0]` `rArr (lambda-7)(lambda-31)lt0` `rArr lambdain(7, 31)""...(iii)` Also, we have `\|(3(1)+4(1)-lambda)/(5)\|gesqrt(1+1-1)` `(therefore" Distance of centre from the given line is greater than the radius, i.e., " (ax_(1)+by_(1)+c)/(sqrt(a^(2)+b^(2)))GE R)` `rArr \|7-lambda\| ge5rArrlambdain(-oo,2] uu [12,oo)""(iv)` and`\|(3(9)+4(1)-lambda)/(5)\|gesqrt((81+1-78))` `rArr\|lambda-31\|ge10` `rArrlambdain(-oo,21]uu[,oo)""...(v)` From Eqs. (iii), (iv) and (v), we get `lambda in [12, 21]`

Discussion

44.	A point moves in a plane so that its distances PA and PB from the two fixed points A and b in the plane satisfy the relationPA - PB =k( k ne 0,)then the locus of Pis
Answer» a PARABOLA an elipse a hyperbola a BRANCH of a hyperbola Answer :C

Discussion

45.	If (2x^(2)+5)/((x+1)^(2)(x-3))=(A)/(x+1)+(B)/((x+1)^(2))+(C)(x-3) then A=
Answer» `- (15)/(4)` `15/4` `9/16` `- 9/16` ANSWER :C

Discussion

46.	Consider the following statements A is relative error in the area of a square when the relative error in its side os 0.4 B is relative error in the volume of a sphere when the relative error in its radius is 0.3 C is relative error in the surface area of a closed cylinder whose height is equal to its radius, when the relative error in its height is 0.2 D is approximate error in y = x ^(2)+ x-3 when x =2 and delta x =0.1 The ascending order of the values of errors in these statements is
Answer» B,C,A,D A,C,B,D C,D,A,B D,A,C,B Answer :C

Discussion

47.	Letf(x) = underset( n rarr oo)("Lim")underset( n=1)overset( n ) ( sum) 3^(n-1) sin^(3) ""(x)/(3^(n)) and g(x) = x- 4f(x) . Evaluate underset( x rarr 0)("Lim") ( 1+ g(x))^("cotx")
Answer» ANSWER :`g(X) = sin x ` and l =E

Discussion

48.	n whole numbers are randomly chosen and multiplied. Now, match the following lists.{:("List I","List II"),("a. The probability that the last digit is 1, 3, 7, or 9 is","p. "(8^(n)-4^(n))/(10^(n))),("b. The probability that the last digit is 2, 4,6, 8 is ","q. "(5^(n) - 4^(n))/(10^(n))),("c. The probability that the last digit is 5 is","r. " (4^(n))/(10^(n))),("d. The probability that the last digit is zero is","s. "(10^(n) - 8^(n) - 5^(n) + 4^(n))/(10^(n))):}
Answer» `{:("a","b","C","d"),("q","s","s","R"):}` `{:("a","b","c","d"),("r","q","q","p"):}` `{:("a","b","c","d"),("q","p","p","s"):}` `{:("a","b","c","d"),("q","s","p","r"):}` Solution :a. The required event will occur if last digit in all the chosen numbers is 1, 3, 7, or 9. Therefore, the required probability is `(4//10)^(n)`. b. The required probability is EQUAL to the probability that the last digit is 2, 4, 6, 8 and is given by P(last digit is 1, 2, 3, 4, 6, 7, 8, 9) -P (last digit is 1, 3, 7, 9) = `(8^(n) - 4^(n))/(10^(n))` c. P(1, 3, 5, 7, 9) - P(1, 3, 7, 9) = `(5^(n) - 4^(n))/(10^(n))` d. The required probability is `P(0, 5) - P(5) = ((10^(n) - 8^(n))-(5^(n) - 4^(n)))/(10^(n))` `P(0, 5) - P(5) = ((10^(n) - 8^(n))-(5^(n) - 4^(n)))/(10^(n))`

Discussion

49.	If x ge 0, y ge 0, 2x+y le10 and x+2y ge 10 then the minimum value of f=x+y is
Answer» 4 5 0 2 Answer :D

Discussion

50.	If int_(0)^(oo) (log(1+x^(2)))/(1+x^(2))dx=kint_(0)^(oo) (log(1+x))/(1+x^(2))dx, then k=
Answer» 4 8 `PI` `2PI` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If 3x + 8 gt 2, then the smallest integer value of 5x + 12 is

IfDelta = {:[( a_11, a_12, a_113),( a_21,a_22,a_23) ,(a_31,a_32, a_33) ]:} and A_y is Cofactors of a_ijthen value of Deltais given by

Evaluate the definite integrals int_(0)^(2)(6x+3)/(x^(2)+4)dx

Kyle can choose between blue, black, and brown pants, white, yellow, or pink shirts, and whether or not he wears a tie to go with his shirt. How many days can Kyle go without wearing the same combination twice?

The number of value(s) of x satisfying 1-log_(g)(x+1)^(2)=1/2log_(sqrt(3))((x+5)/(x+3)) is

Find the centre of the conic 14x^(2) - 4xy + 11y^(2) - 44x - 58y +71=0

Consider the following Statements p : A tumbler is half empty. A tumbler is half full. Then, thee combination form of"p if and only if q"is

If I = int xsin^(-1){(1)/(2)sqrt((2a-x)/(a))dx=Kx^(2)sin^(-1){(1)/(2)sqrt((2-x)/(a))}+(1)/(2a){t^((5)/(2))+4a^(2)t^((1)/(2))-(4a)/(3)t^((3)/(2))} + C , t = 2a + x, then K is equal to

underset(x rarr oo)(lim) (x^(2))/(e^(x)) is

Find the ellipse whose vertices are (2,-2) (2,4) and e=1//3

x and y are the sides of two squares such that y=x-x^(2). Find the rate of change of the area of second square with respect to the area of first square.

The radical centre of the three circles described on the three sides of a triangle as diameter is ......... of the triangle

Find the equation of the parabola which is symmetric about y-axis, and passes through the point (2,-3) .

Find the probability of getting. (i) a prime number when a die is rolled. (ii) sum 9 when two dice are rolled. (iii) sum atleast 10 when two dice are rolled.

If the normal at P on the hyperbola meets the transverse axis at G, S is a foci andthe eccentricity of the hyperbola then SG : SP is equal to

Define linear combination of vectors.

The value of int_(-1)^(1) (2|x| - |x|^3)dx is :

f : (0, pi)to R, f(x)=2x+cot x. Find the intervals in which f(x) is strictly increasing or strictly decreasing.

Evaluate the integrals by using substitution int_(0)^(1)x/(x^(2)+1)dx

If alpha=5/(2!xx3)+(5xx7)/(3!xx3^(2))+(5xx7xx9)/(4!xx3^(3))+...," then "alpha^(2)+4alpha=

Three distinguishable dice are rolled. In how many ways we can get a total 15?

vec(a)=hatj-hatk and vec( c )=hati-hatj-hatk. The vector vec(b) is such that vec(a) xx vec(b)+vec( c )=0 and vec(a)*vec(b)=3 then vec(b) = ………..

If f(x) = underset(nrarroo)limn^(2)(x^(1//n)-x^(1//(n+1))),xgt0 then int x f(x) dx is equal to

Cosine of the angle between the lines overliner=5hati-hatj+4hatk+lamda(hati+2hatj+2hatk)and overliner=7hati+2hatj+2hatk+mu(3hati+2hatj+6hatk)is

f : R to R : f (x) = x^(3)is

Show that the function given by f(x)=e^(2x) is increasing on R.

Examine the existence of the following limits:lim_(xto0) cosecx

Choose the correct answer. The general solution of a differential equation e^x dy + (y e^x + 2x) dx = 0 is...a) x e^x + x^2 = cb) x e^y + y^2 = cc) x e^y + y^2 = cd) y e^x + x^2 = c

y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A,B (a,0), and c are concyclic. Tangents to the parabola y^(2)=4x at A and C intersect at point D and tangents to the parabola y^(2)=-8(x-a) intersect at point E. Then the area of quadrilateral DAEC is

Integrate the following functions x logx

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

If f : R to R is a continuous defined by f(x)=[x]cos ((2x-1)/(2))pi, where [x] denotes the greatest integer function, then f is

A dice is tossed twice. Find probability of getting a number greater than 3 on each toss.

Number of Irrational terms in the expansion of (2^(1/3)+3^(1/2)+5^(1/6))^(10) is equal to :-

If Tan theta_(1)=k cot theta_(2) then(cos (theta_(1)+theta_(2)))/(cos (theta_(1)-theta_(2)))=

The standard deviation is not affected by the change of

int1/(x+sqrt(x^(2)-x+1))dx=Plog(x+sqrt(x^(2)-x+1))+Qlog(2x-1+2sqrt(x^(2)-x+1))+R(3/(2x-1+2sqrt(x^(2)-x+1)))+c Then the values of P, Q, R are

If the general solution of sin x + 3 sin 3x + sin 5 x = 0 " is " x = y then the set of all values of cos y is

If a variable line, 3x + 4y -lambda = 0 is such that the two circles x^(2)+y^(2)-2x-2y+1=0 and x^(2)+y^(2)-18x-2y+78=0 are not its opposite sides, then the set of all values of lambda is the interval

A point moves in a plane so that its distances PA and PB from the two fixed points A and b in the plane satisfy the relationPA - PB =k( k ne 0,)then the locus of Pis

If (2x^(2)+5)/((x+1)^(2)(x-3))=(A)/(x+1)+(B)/((x+1)^(2))+(C)(x-3) then A=

Letf(x) = underset( n rarr oo)("Lim")underset( n=1)overset( n ) ( sum) 3^(n-1) sin^(3) ""(x)/(3^(n)) and g(x) = x- 4f(x) . Evaluate underset( x rarr 0)("Lim") ( 1+ g(x))^("cotx")

If x ge 0, y ge 0, 2x+y le10 and x+2y ge 10 then the minimum value of f=x+y is

If int_(0)^(oo) (log(1+x^(2)))/(1+x^(2))dx=kint_(0)^(oo) (log(1+x))/(1+x^(2))dx, then k=