28278 + Interview Questions in Maths in Class 12

1.	Show that the area of the region bounded by (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (ellipse) is pi ab. Also deduce the area of the circle x^(2)+y^(2)=a^(2)
Answer» ANSWER :`piab`

Discussion

2.	Integrate the function (x-1)/(x^(2)-2x-5)
Answer»

Discussion

3.	p (2,3,-4) ,vecb =2 hati - hatj + 2 hatk Cartesian equation of a planepassing through the point with position vector b and perpendicular to the vector vec(OPQ) being the origin is :
Answer» `2X -y + 2z + 7=0` `2x -y + 2z -7 =0` `2x + 3Y-4 z + 7=0` `2x + 3y - 4Z -7=0` ANSWER :C

Discussion

4.	If the first three terms in the binomial expansion of (1+bx)^n in ascending powers of x are 1,6x and 16x^2 respectively then b + n =
Answer» A) `28/3` B) `15/2` C) `29/3` D) `17/3` ANSWER :C

Discussion

5.	Expresssqrt2+ i =r cos theta +ir sin thetacomplex numbers in the polar form.
Answer» SOLUTION :where R`SQRT(a^2+b^2)=sqrt((sqrt2)^2+1^2)=sqrt3` `"and theta=TAN^(-1)(b/a)=tan^(-1)(1/sqrt2)` `:.sqrt2+i=sqrt3(costheta=isintheta),where tan` theta=1/sqrt2`

Discussion

6.	If veca,vecb and vecc are unit vectors such that veca+vecb+vecc=vec0 then the value of veca.vecb+vecb.vecc+vecc.veca isa) 1 b) 0 c) 3 d) -3/2
Answer» 1 0 3 `-3/2` ANSWER :D

Discussion

7.	Let S be the set of real numbers. For a, b in S, relation R is defined by aRb iff \|a-b\|lt 1 then R is
Answer» only REFLEXIVE only SYMMETRIC only TRANSITIVE reflexive & symmetric ANSWER :D

Discussion

8.	O is the origin and lines OA, OB and OC have direction cosines l_(r),m_(r)andn_(r)(r=1,2 and3). If lines OA', OB' and OC' bisect angles BOC, COA and AOB, respectively, prove that planes AOA', BOB' and COC' pass through the line (x)/(l_(2)+l_(2)+l_(3))=(y)/(m_(1)+m_(2)+m_(3))=(z)/(n_(1)+n_(2)+n_(3)).
Answer» Solution :If `theta` is the `angleBCO`, then the direction consines of OA' `("bisector of "angleBOC)" " are" "(l_(2)+l_(3))/(2cos(theta//2)),(m_(2)+m_(3))/(2cos(theta//2))` `(n_(2)+n_(3))/(2cos(theta//2))` or the direction ratios of OA' are `l_(2)+l_(3),m_(2)+m_(3)andn_(2)+n_(3)` ALSO, the direction cosines of OA are `l_(1),m_(1)andn_(1)`. Hence, the equation of plane AOA' is `\|{:(X,y,z),(l_(2)+l_(3),m_(2)+m_(3),n_(2)+n_(3)),(l_(1),m_(1),n_(1)):}\|=0` Applying `R_(2)toR_(2)+R_(3)`, we get the equation of plane AOA' as `\|{:(x,y,z),(l_(1)+l_(2)+l_(3),m_(1)+m_(2)+m_(3),n_(1)+n_(2)+n_(3)),(l_(1),m_(1),n_(1)):}\|=0` For all values of r, the point `(l_(1)+l_(2)+l_(3))r,(m_(1)+m_(2)+m_(3))and(n_(1)+n_(2)+n_(3))r)` LIES on plane AOA'. Hence, the line `(x)/(l_(1)+l_(2)+l_(3))=(y)/(m_(1)+m_(2)+m_(3))=(z)/(n_(1)+n_(2)+n_(3))=r` lies on plane AOA'. Similarly, this line lies on planes BOB' and COC' also. Hence, all the three planes, AOA' BOB' and COC', pass through the line.

Discussion

9.	The set of values of x which satisfy 5x+2 lt 3x+8 and (x+2)/(x-1) lt 4 is
Answer» (2, 3) `(-oo, 1) UU(2, 3)` `(-oo, 1)` (1, 3) Answer :B

Discussion

10.	The normal at a point (bt_1^(2) , 2bt_1)on a parabola meets the parabola again in the point (bt_2^(2) , 2bt_2)then
Answer» ` t_2 =-t_1 +(2)/( t_1) ` ` t_2= t_1 +(2)/( t_1) ` ` t_2 =t_1 +(2)/(t_1) ` ` t_2=-t_1- (2)/(t_1) ` ANSWER :D

Discussion

11.	int(x)/(9-4x^2)dx
Answer» ANSWER :`-1/8logabs(9-4x^(2))+C`

Discussion

12.	obtain the equation of hyperbola in each of the following cases: centre at (0,0) transverse axis along x-axis of length 4 and focus at (2sqrt5,0).
Answer» Solution :Here 2a=4 c=`2SQRT5` `THEREFORE` a=2 `therefore` b^2=c^2-a^2=20-4=16 `therefore` EQN of the ellipse is`x^2/a^2-y^2/b^2=1` or `x^2/4-y^2/16=1`

Discussion

13.	Prove that lim x_(n)=2, if x_(n)=(2n+3)//(n+1). Find the number of the term beginning with which the inequality \|(2n+3)//(n+1)-2\| le epsi, where e=0.1, 0.01, 0.001, is fulfilled.
Answer» Answer :The INEQUALITY `\|(2n+3)/(n+1)-2\| LT e` is satisfied for `n GT N=E (1/e-1)`. At e=0.1 the inequality if FULFILLED beginning with n=10, at e=0.01 beginning with n=100, at e=0.001 beginning with n=100.

Discussion

14.	Let P be a point on an ellipse whose parameter is (pi)/(3) . The sum and differences of the focal distances of P is 8 and 3 then the eccentricity of the ellipse is
Answer» `sqrt(3)/(4)` `3/8` `3/4` `sqrt(3)/(2sqrt(2))` ANSWER :C

Discussion

15.	dy/dx + y/x = x^(2) isfind integrating factor.
Answer»

Discussion

16.	Select the correct answer:Degree of differential equation of log(dy/dx)^2=3x+4y is
Answer» `0` `1` `2` not defined Answer :D

Discussion

17.	Solve the following differential equations sin^(2) x(dy)/(dx) + y = cot x
Answer» Answer :`y E^(-cot X) = (1+ cotx) C^(-cot x) + c`

Discussion

18.	Select the CORRECT order of ionisation energy ?
Answer» PB gt SN TL gt B Al gt Ga P gt N

Discussion

19.	veca,vecb,veccbe three vectors such that V_1=[vecavecbvecc]=1 and V_2=[(vecaxxvecb)xxvecc(vecbxxvecc)xxveca(veccxxveca)xxvecb]then the value of sum_(r=1)^(6)V_1^r+V_1V_2^r is
Answer» 3 12 6 24 Solution :`V_1=1,V_2=0` ( `because` COPLANAR VECTORS )

Discussion

20.	Let a=2hati+hatk, b=hati+hatj+hatk and c=hati-3hatj+7hatk. If r is a vector such that rxxb=cxxb and r.a-0, then value of r.b is
Answer» 7 `-7` `-5` 5 Solution :Let `r=xhat(i)+yhat(j)+zhat(k)` Given `rxxb=cxxb` `rArr (xhat(i)+yhat(j)+zhat(j))XX(HAT(i)+hat(j)+hat(k))` `=(4hat(i)-3hat(j)+7hat(k))xx(hat(i)+hat(j)+hat(k))` `rArr (y-Z)hat(i)-(x-z)hat(j)+(x-y)hat(k)=-10hat(i)+3hat(j)+7hat(k)` `because\|{:(hat(i),hat(j),hat(j)),(x,y,z),(1,1,1):}\|=hat(i)(y-z)-hat(j)(x-z)+hat(k)(y-z)` `rArr\|{:(hat(i),hat(j),hat(j)),(4,-3,7),(1,1,1):}\|=hat(i)(-10)-hat(j)(-3)+hat(k)(7)` `rArr y-z=-10,-(x-z)=3,x-y=7` `rArr y-z=-10,-x+z=3,x-y=7`....(i) and `r.a=0` `rArr (xhat(i)+yhat(j)+zhat(k)).(2hat(i)+hat(k))` `rArr 2x+z=0` ......(ii) From EQS.(i) and (ii) , we get `x=-1,y=-8,z=2` `therefore r.b=(-hat(i)-8hat(j)+2hat(k)).(hat(i)+hat(j)+hat(k))` `=-1-8+2=-7`.

Discussion

21.	If p, q,r are in A. P. then the line px + qy + r=0 passes through a fixed point
Answer» `(1,2)` `(-1,2)` `(1, -2)` `(-1, -2)` ANSWER :C

Discussion

22.	Show that f(x)=tan^(-1)(sin x + cos x) is an increasing function in (0, (pi)/(4)).
Answer» ANSWER :`X in (0, (PI)/(4))`

Discussion

23.	If P(A\|B) gt P(A), then which of the following is correct:
Answer» `P(B\|A) LT P(B)` `P(A nn B) lt P(A). P(B)` `P(B\|A) GT P(B)` P(B\|A) = P(B) ANSWER :c

Discussion

24.	One kind of cake requires 200g of flour and 25g of fat and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1kg of fat assuming that there is no shortage of other ingredients used in making the cakes.
Answer» SOLUTION :NA

Discussion

25.	Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(1)(d)/(dx)(sin^(-1)""(2x)/(1+x^(2)))dx=..........
Answer» 0 `PI` `(pi)/(2)` `(pi)/(4)` ANSWER :C

Discussion

26.	The product of any matrix by the scalar …….. Is the null matrix .
Answer» ANSWER :By multipling each ELEMENT of MATRIX by ZERO we GET zero matrix .

Discussion

27.	(x + y )(dy)/(dx) = 1
Answer» ANSWER :`(X + y + 1) = CE^(y)`

Discussion

28.	Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f(x) = 2x^(3) - 9x^(2) + 12x + 5 in the interval [0, 3]. Then
Answer» 1 5 4 9 Answer :A

Discussion

29.	If the roots of x^(2)+px+12=0 are in the ratio 1:3, then p =
Answer» `pm9` `PM3` `PM6` `pm8` ANSWER :d

Discussion

30.	Find the probability that 2 particular persons never sit together, when n persons sit in a row.
Answer» ANSWER :`1-(2)/(N)`

Discussion

31.	If the distance between the planes Ax-2y+z=d and the plane containing the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-2)/(3)=(y-3)/(4)=(z-4)/(5)is sqrt(6), then \|d\| is :
Answer» 3 4 5 6 Solution :Equation of the PLANE containingthe GIVEN lines is. `\|{:(x-1,y-2,z-3,),(2,3,4,),(3,4,5,):}\|=0impliesx-2y+z=0` since this plane MUST be parallel to the plane `Ax-2y+z=d`, we GET `A=1`As distance between the PLANES is `sqrt(6)`. we get `(\|d\|)/(sqrt(1+4+1))sqrt(6)implies\|d\|=6`

Discussion

32.	The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1), (1, 1) and (1, 0) is
Answer» `1+sqrt(2)` `1-sqrt(2)` `2+sqrt(2)` `2-sqrt(2)` ANSWER :D

Discussion

33.	** is a binary operation on the set Q. a""b=(a)/2+b/(3)then find 1/(2) "" 4/(5).
Answer» SOLUTION :N/A

Discussion

34.	The normal to a circle S =0 at P (1,3) is x + 2y -7 and it has another normal at Q(3,5) which is the polar of the pointA(7, -(1)/(2)) with respect to the circle x ^(2) + y ^(2)- 4x + 6y -12 =0. Then the equation of the circle S =0 is
Answer» `x ^(2) + y ^(2) -10X -2Y + 6=0` `x ^(2) + y ^(2) - 5x -2y + 1=0` `x ^(2) + y ^(2) - 8X + 2y -8=0` `x ^(2) + y ^(2) -7x + 3y -12=0` ANSWER :A

Discussion

35.	The latus rectum LL^(') subtends a right angle at the centre of the ellipse, then its eccentricity is
Answer» `(SQRT(3)+1)/(2)` `(sqrt(2)+1)/(2)` `(sqrt(3)-sqrt(2))/(2)` `(sqrt(5)-1)/(2)` Answer :D

Discussion

36.	Let I_(n) =int _(1) ^(e^(2))(ln x)^(n) dt (x ^(2)), then the vlaue of 2I_(n)+nI_(n-1) equals to:
Answer» 0 `2e ^(2)` `E ^(2)` `1` Answer :B

Discussion

37.	A 30"cm" long metal rod expands by 0.0650"cm" when its temperature is raised from 0^(@)C to 100^(@)C. A second rod of different metal and of the same length expands by 0.0350"cm" for the same rise in temperature. A third composite rod, also 30"cm" long, is made-up of pieses of each of the above metals placed end to end and expands by 0.0580"cm" when temperature is increased from 0^(@)C to 100^(@)C. Find the length of the longer portion of the composite bar in cm at 0^(@)C.
Answer» Solution :`alpha_(1)=(0.065)/(30xx100)` `alpha_(2)=(0.035)/(30xx100)` `Deltal=l_(1)a_(1)DELTAT+(30-l_(1))alpha_(2)DeltaT` `0.058=l_(1)XX(0.065)/(3000)+(30-l_(1))xx(0.035)/(3000)` `1.74=0.065l_(1)+1.05-0.035l_,` `0.69=+0.03l_(1)` `l_(1)=23" cm ",l_(2)=7" cm "`

Discussion

38.	If a is a non-zero vector of magnitude'a'and lambda a non-zero scalar, then lambda oversetrarra is a unit vector if:a)lambda = 1b)lambda = -1c)a=\|lambda\|d)a =1/(\|lambda\|)
Answer» `LAMBDA = 1` `lambda = -1` `a=\|lambda\|` `a =1/(\|lambda\|)` ANSWER :D

Discussion

39.	A person on a ship sailing north sees two lighthouses which are 6 km apart, in a line due west . After an hour's tailing one of them bears south west and the other southern south west. The ship is travelling at a rate of
Answer» 12 km/hr 6 km/hr `3sqrt2` km/hr `(6+3sqrt2)` km/hr ANSWER :D

Discussion

40.	Show that sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x, (1)/(sqrt2)le x le 1.
Answer» ANSWER :`2COS^(-1)X`

Discussion

41.	Integrate the following functions : (xcosx)^(2)
Answer» Answer :`(x^(3))/(6)+(1)/(4)x^(2)SIN2X+(1)/(4)xcos2x-(1)/(8)sin2x+c`

Discussion

42.	If 2x+y ge 10, x+2y ge 10, x ge 0, y ge 0 then the minimum valueof f=x+y is
Answer» 2 5 10 `20//3` ANSWER :D

Discussion

43.	The numberofrectanglesformedin achessboardis
Answer» ANSWER :1296

Discussion

44.	Let A=[(2,4),(3,2)], B=[(1,3),(-2,5)], C=[(-2,5),(3,4)] Find each of the following: (i) A+B (ii) A-B (iii) 3A-C (iv) AB (v) BA
Answer» Answer :`(i) A+B=[(3,7),(1,7)] (II) A-B=[(1,1),(5,-3)]` `(III) 3A-C=[(8,7),(6,2)] (IV) AB=[(-6,26),(-1,19)] (V) BA=[(11,10),(11,2)]`

Discussion

45.	If (sec^(8)theta)/(a) + (tan ^(8)theta)/(b) = (1)/(a+b) then for every real value of sin ^(2) theta,find relation between a + b ?
Answer» ANSWER :`=> AB LE 0`

Discussion

46.	Let f(x) = x^(3) - 8x^(3) + 22x^(2) - 24x and g(x) = {{:(min f(x)",",x le t le x + 1 -1 le x le 1),(x - 10",",x ge 1):} Discuss the continuity and differentiability of g(x) in [-1, oo)
Answer» ANSWER :X = 1

Discussion

47.	Integration using rigonometric identities : int cos^(5)xdx=....
Answer» `sinx-(2)/(3)sin^(3)x+(1)/(5)sin^(5)x+C` `sinx+(2)/(3)sin^(3)+(1)/(5)sin^(5)x+c` `sinx-(2)/(3)sin^(3)x-(1)/(5)sin^(5)+c` NONE of these Answer :A

Discussion

48.	Statement 1: The value of cot^(-1)((7)/(4))+cot^(-1)((19)/(4))+...+cot^(-1)((4r^(2)+3)/(4))+... upto infinity istan^(-1)(2). Statement 2: sum_(r=1)^(n)"tan"(x_(r)-x_(r-1))/(1+x_(r-1)x_(r))=tan^(-1)x_(n)-tan^(-1)x_(0).
Answer» Statement-1 is TRUE, Statement-2 is True and Statement-2 is a CORRECT EXPLANATION forStatement-1. Statement-1 is True, Statement-2 is True and Statement-2 is NOT a correct explanation forStatement-1. Statement-1 is True, Statement-2 is FALSE. Statement-1 is False, Statement-2 is True. Answer :A

Discussion

49.	Match the items of List-I with those of List-II The correct matching is
Answer» `{:("A","B","C","D"),("I","IV","II","III"):}` `{:("A","B","C","D"),("IV","III","I","II"):}` `{:("A","B","C","D"),("IV","I","III","II"):}` `{:("A","B","C","D"),("IV","I","II","III"):}` ANSWER :D

Discussion

50.	theta is said to be well behaved if it lies in interval [0,(pi)/(2)]. They are intelligent if they make domain of f +g and g equal. The vlaue of theta for which h (theta) is defined are handosome. Let f (x)= sqrt(thetax ^(2) -2 (theta^(2) -3) x-12theta,) g (x)=ln (x^(2) -49), h (theta) ln [int_(0)^(theta) 4 cos ^(2)t dt - theta ^(2)], where theta isin radians. Complete set of alues of theta which are intelligent is :
Answer» `[(6)/(7) , (7)/(2)]` `(0, (PI)/(3)]` `[(1)/(4), (6)/(7)]` `[(1)/(2), (pi)/(2)]` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Show that the area of the region bounded by (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (ellipse) is pi ab. Also deduce the area of the circle x^(2)+y^(2)=a^(2)

Integrate the function (x-1)/(x^(2)-2x-5)

p (2,3,-4) ,vecb =2 hati - hatj + 2 hatk Cartesian equation of a planepassing through the point with position vector b and perpendicular to the vector vec(OPQ) being the origin is :

If the first three terms in the binomial expansion of (1+bx)^n in ascending powers of x are 1,6x and 16x^2 respectively then b + n =

Expresssqrt2+ i =r cos theta +ir sin thetacomplex numbers in the polar form.

If veca,vecb and vecc are unit vectors such that veca+vecb+vecc=vec0 then the value of veca.vecb+vecb.vecc+vecc.veca isa) 1 b) 0 c) 3 d) -3/2

Let S be the set of real numbers. For a, b in S, relation R is defined by aRb iff |a-b|lt 1 then R is

The set of values of x which satisfy 5x+2 lt 3x+8 and (x+2)/(x-1) lt 4 is

The normal at a point (bt_1^(2) , 2bt_1)on a parabola meets the parabola again in the point (bt_2^(2) , 2bt_2)then

int(x)/(9-4x^2)dx

obtain the equation of hyperbola in each of the following cases: centre at (0,0) transverse axis along x-axis of length 4 and focus at (2sqrt5,0).

Prove that lim x_(n)=2, if x_(n)=(2n+3)//(n+1). Find the number of the term beginning with which the inequality |(2n+3)//(n+1)-2| le epsi, where e=0.1, 0.01, 0.001, is fulfilled.

Let P be a point on an ellipse whose parameter is (pi)/(3) . The sum and differences of the focal distances of P is 8 and 3 then the eccentricity of the ellipse is

dy/dx + y/x = x^(2) isfind integrating factor.

Select the correct answer:Degree of differential equation of log(dy/dx)^2=3x+4y is

Solve the following differential equations sin^(2) x(dy)/(dx) + y = cot x

Select the CORRECT order of ionisation energy ?

veca,vecb,veccbe three vectors such that V_1=[vecavecbvecc]=1 and V_2=[(vecaxxvecb)xxvecc(vecbxxvecc)xxveca(veccxxveca)xxvecb]then the value of sum_(r=1)^(6)V_1^r+V_1V_2^r is

Let a=2hati+hatk, b=hati+hatj+hatk and c=hati-3hatj+7hatk. If r is a vector such that rxxb=cxxb and r.a-0, then value of r.b is

If p, q,r are in A. P. then the line px + qy + r=0 passes through a fixed point

Show that f(x)=tan^(-1)(sin x + cos x) is an increasing function in (0, (pi)/(4)).

If P(A|B) gt P(A), then which of the following is correct:

One kind of cake requires 200g of flour and 25g of fat and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1kg of fat assuming that there is no shortage of other ingredients used in making the cakes.

Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(1)(d)/(dx)(sin^(-1)""(2x)/(1+x^(2)))dx=..........

The product of any matrix by the scalar …….. Is the null matrix .

(x + y )(dy)/(dx) = 1

Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f(x) = 2x^(3) - 9x^(2) + 12x + 5 in the interval [0, 3]. Then

If the roots of x^(2)+px+12=0 are in the ratio 1:3, then p =

Find the probability that 2 particular persons never sit together, when n persons sit in a row.

If the distance between the planes Ax-2y+z=d and the plane containing the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-2)/(3)=(y-3)/(4)=(z-4)/(5)is sqrt(6), then |d| is :

The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1), (1, 1) and (1, 0) is

** is a binary operation on the set Q. a"*"b=(a)/2+b/(3)then find 1/(2) "*" 4/(5).

The normal to a circle S =0 at P (1,3) is x + 2y -7 and it has another normal at Q(3,5) which is the polar of the pointA(7, -(1)/(2)) with respect to the circle x ^(2) + y ^(2)- 4x + 6y -12 =0. Then the equation of the circle S =0 is

The latus rectum LL^(') subtends a right angle at the centre of the ellipse, then its eccentricity is

Let I_(n) =int _(1) ^(e^(2))(ln x)^(n) dt (x ^(2)), then the vlaue of 2I_(n)+nI_(n-1) equals to:

If a is a non-zero vector of magnitude'a'and lambda a non-zero scalar, then lambda oversetrarra is a unit vector if:a)lambda = 1b)lambda = -1c)a=|lambda|d)a =1/(|lambda|)

A person on a ship sailing north sees two lighthouses which are 6 km apart, in a line due west . After an hour's tailing one of them bears south west and the other southern south west. The ship is travelling at a rate of

Show that sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x, (1)/(sqrt2)le x le 1.

Integrate the following functions : (xcosx)^(2)

If 2x+y ge 10, x+2y ge 10, x ge 0, y ge 0 then the minimum valueof f=x+y is

The numberofrectanglesformedin achessboardis

Let A=[(2,4),(3,2)], B=[(1,3),(-2,5)], C=[(-2,5),(3,4)] Find each of the following: (i) A+B (ii) A-B (iii) 3A-C (iv) AB (v) BA

If (sec^(8)theta)/(a) + (tan ^(8)theta)/(b) = (1)/(a+b) then for every real value of sin ^(2) theta,find relation between a + b ?

Let f(x) = x^(3) - 8x^(3) + 22x^(2) - 24x and g(x) = {{:(min f(x)",",x le t le x + 1 -1 le x le 1),(x - 10",",x ge 1):} Discuss the continuity and differentiability of g(x) in [-1, oo)

Integration using rigonometric identities : int cos^(5)xdx=....

Statement 1: The value of cot^(-1)((7)/(4))+cot^(-1)((19)/(4))+...+cot^(-1)((4r^(2)+3)/(4))+... upto infinity istan^(-1)(2). Statement 2: sum_(r=1)^(n)"tan"(x_(r)-x_(r-1))/(1+x_(r-1)x_(r))=tan^(-1)x_(n)-tan^(-1)x_(0).

Match the items of List-I with those of List-II The correct matching is

** is a binary operation on the set Q. a""b=(a)/2+b/(3)then find 1/(2) "" 4/(5).