28278 + Interview Questions in Maths in Class 12

1.	A,B,C are three angles of a triangle and "sin" (A+c/2)= n "sin" C/2 ("sin" C/2)/("cos"A/2 "cos"B/2)=
Answer» `2/(n+1)` `1/(n+1)` `-2/(n+1)` `1/(n+1)` ANSWER :A

Discussion

2.	The range of a random variable X is {1, 2, 3, ……..} and P(X=k)=(C^(k))/(lfloork) where k = 1, 2, 3,…. Find the value of C
Answer» ANSWER :`log_(E)2,((log_(e)2)^(2)+2log_(e)2)/(2)`

Discussion

3.	Evaluate :[2hati "" hatj "" hatk ] +[hati hatk hatj ] +[hatk hatj 2hati ]
Answer» ANSWER :` -1`

Discussion

4.	If the quadratic equation a_(1)x^(2)-a-(2)x+a_(3)=0 where a_(1),a_(2),a_(3) in N has two distinct real roots belonging to the interval (1,2) then least value of a_(1) is_______
Answer» Solution :`alpha+beta=(a_(2))/(a_(1)), alpha beta=(a_(3))/(a_(1)), alpha, beta epsilon (1,2)` `implies alpha-1, beta-1, 2-alpha, 2-beta epsilon (0,1)` A.M. `ge` G.M. `implies((alpha-1)+(2-alpha))/2 ge sqrt((alpha-1)(2-alpha))` `implies(alpha-1)(2-alpha) le 1/4` SIMILARLY `(beta-1)(2-beta) le 1/4` `0 lt (alpha-1)(2-alpha)(beta-1)(2-beta) lt 1/16` (Both can't equal to `1/4` simultaneously `(alpha !=beta)` `0 lt ((a_(3))/(a_(1))-(a_(2))/(a_(1))+1)(4-(2a_(2))/(a_(1))+(a_(3))/(a_(1))) lt 1/16` `0 lt ((a_(1)-a_(2)+a_(3))(4a_(1)-2a_(2)+a_(3)))/(a_(1)^(2)) lt 1/16` `(a_(1)^(2))/16 gt (a_(1)-a_(2)+a_(3)(4a_(1)-2a_(2)+a_(3))` `(a_(1)^(2))/16 gt f(1).f(2)implies(a^(2))/16 gt 1` `implies` Least integral alue of `a` is 5

Discussion

5.	Determine k and solve the equation 2x^3-6x^2+3x+k=0 if one of its roots is twicethe sum of the othertwo roots.
Answer» ANSWER :`k=9/4`

Discussion

6.	If f(x) = \|(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x-1))\|, using properties of determinant, find f(2x) - f(x).
Answer» ANSWER :`18 X^(2)(1-5x^(2))`

Discussion

7.	Find (i) inte^(x)(tan^(-1)x+1/(1+x^(2)))dx (ii) int((x^(2)+1)e^(x))/((x+1)^(2))dx
Answer» ANSWER :`(i)E^(x)TAN^(-1)+x+c, (ii) ((x-1)/(x+1))e^(x)+c`

Discussion

8.	f (x) = { (sin ^(3) x ^(2))/( {:(""x), ( 0"," x =-0):}), x ne 0 is
Answer» continous but not DERIVABLE at x =0 NEITHER continous nor differentiable at `x =0` CONTINUOUS and differentiable at `x =0` None of these ANSWER :C

Discussion

9.	A value of b for which the equations :x^(2) + bx - 1= 0, x^(2) + x + b = 0 Have one root in common is :
Answer» `-SQRT(2)` `-isqrt(3)` `isqrt(5)` `sqrt(2)` ANSWER :B

Discussion

10.	An endless inextensible string of length 15 m passes around two pins, A and B which are 5 m apart. This string is always kept tight and a small ring, R, of negligible dimensions, inserted in this string is made to move in a path keeping all segments RA, AB, RB tight (as mentioned earlier). The ring traces a path, given by conic. C, then:
Answer» CONIC C is an ellipse with eccentricity `(1)/(2)` Conic C is an HYPERBOLA with eccentricity 2 Conic C is an ellipse with eccentricity `(2)/(3)` Conic C is an hyperbola with eccentricity `(3)/(2)` ANSWER :A

Discussion

11.	int(dx)/(2sqrt(x)(1+x))=...
Answer» `(1)/(2)TAN^(-1) (SQRT(x))+c` `tan^(-1) (sqrt(x))+c` `2tan^(-1) (sqrt(x))+c` NONE of these Answer :B

Discussion

12.	If z_(1)" and "z_(2) are two complex numbers such that \|(z_(1)-z_(2))/(z_(1)+z_(2))\|=1 then
Answer» `z_(1)=kz_(2), K in R` `z_(1)= ikz_(2), k in R` `z_(1)=z_(2)` `z_(1)= BAR(z_2)` Answer :B

Discussion

13.	Four fair dicew are rolled and found that the numbers on the dice are in ascending order. Find the probability that one die shows 4.
Answer» ANSWER :`(2)/(3)`

Discussion

14.	If A = [(0,c,-b),(-c,0,a),(b,-a,0)] and B = [(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc,a^(2))]then AB is :
Answer» A B I O ANSWER :D

Discussion

15.	The volume of a spherical cap of height (a)/(2) cut off from the sphere of radius a is :
Answer» `(2)/(3)pia^3` `(pia^3)/(24)` `(5pia^3)/(24)` `4PI`. ANSWER :C

Discussion

16.	The vectors vec(AB) = 3 hati + 5 hatj + 4 hatk and vec(AC) = 5 hati - 5 hatj + 2 hatk are the sides of a triangle ABC. The length of the median through A is
Answer» ANSWER :5

Discussion

17.	By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(4))log(1+tanx)dx
Answer» ANSWER :`pi/8log2`

Discussion

18.	A committeeconsisting of at least three members is to be formed from a group of 6 boys and 6 girls suchthat it always has a boy and a girl. The number of ways to form such committee is
Answer» `2^(12) - 2^(7) - 13` `2^(11) - 2^(6) - 13` `2^(12) - 2^(7) - 35` `2^(11) - 2^(7) - 35` Answer :A

Discussion

19.	A circle passing through the vertex C ofa rectangle ABCD and touching its sides AB and AD at M and N, respectively. If the distance from C to the line segment MN is equal to 5 units, then find the area of the reactangle ABCD.
Answer» <P> Solution :Let us take AB and AD as coordinate axes. If r is the radius of CIRCLE , then equation of circle touching both the axes is `(x-r)^(2)+(y-r)^(2)=r^(2)` or `x^(2)+y^(2)-2rx-2ry+r^(2)=0` Let point C be (p,q) Equation of line MN is `x+y-r=0` DISTANCE of MN from C is 5 units. `:. (\|p+q-r\|)/(sqrt(2))=5` `implies (p+q-r)^(2)=50` Since (p,q) lies on the circle , we have `p^(2)+q^(2)-2rp-2rq+r^(2)=0` `implies (p+q-r)^(2)-2pq=0` `implies 50-2pq=0` `implies pq=25` Therefore, area of rectangle `25sq.` units.

Discussion

20.	Write the inverse trignometric function tan^(-1)(x/sqrt(a^(2)-x^(2)))\|x\|lta, in simplest form.
Answer» ANSWER :`SIN^(-1)(x//a)`

Discussion

21.	Equation of the circles \|z-1-i\|=1 & \|z-1+i\|=1 touches internally a circle of radius 2. The equation of the circle touching all the circles can be
Answer» `3zbarz+z+barz-1=0` `3zbarz-7(z+barz)+15=0` `zbarz-z-barz-3=0` `3zbarz+(z+barz)+1=0` Solution :GIVEN circle touches externally at real AXIS So, the centre `C` of the DESCRIBED circles lies on real axis which has radius `R` then `"CC"_(1)="CC"_(2)=1+r` `C_(1)C_(3)=C_(2)C_(3)=1` `"CC"_(3)=2-r` `:.(1+r)^(2)=1^(2)+(2-r)^(2)` `impliesr=2//3` `:.` Centre of described circle is `-1+2/3=(-1)/3` or `3-2/3=7/3` `:.` Required equation of circle are `\|z+1/3\|=2/3` & `\|z-7/3\|=2/3`

Discussion

22.	A sample space consists of 9 elementary outcomes outcomes E_(1), E_(2),…, E_(9) whose probabilities are:P(E_(1))=P(E_(2)) = 0.09, P(E_(3))=P(E_(4))=P(E_(5))=0.1P(E_(6)) = P(E_(7)) = 0.2, P(E_(8)) = P(E_(9)) = 0.06 If A = {E_(1), E_(5), E_(8)}, B= {E_(2), E_(5), E_(8), E_(9)} then (a) Calculate P(A), P(B), and P(A nnB).(b) Using the addition law of probability, calculate P(A uu B).(c ) List the composition of the event A uu B, and calculate P(A uu B) by adding the probabilities of the elementary outcomes. (d) Calculate P(barB) from P(B), also calculateP(barB) directly from the elementarty outcomes of B.
Answer» <P> Solution :(a) `P(A) = P(E_(1)) + P(E_(5)) + P(E_(8))` `=0.09 + 0.1 + 0.06 = 0.25` (b)`P(B) = P(E_(2)) + P(E_(5)) + P(E_(8)) = P(E_(9))` `= 0.09 + 0.1 + 0.06 + 0.06 = 0.31` `P(A UU B) = P(A) + P(B) - P(A NN B)` Now, `A nn B = {E_(5), E_(8)}` `therefore P(A nn B) = P(E_(5)) + P(E_(8)) = 0.1 + 0.06= 0.16` `therefore P(A uu B) = 0.25+ 0.31 - 0.16 = 0.40` (c )`A uu B = {E_(1), E_(2), E_(5), E_(8), E_(9)}` `P(A uu B) = P(E_(1)) + P(E_(2)) + P(E_(5)) + P(E_(8)) + P(E_(9))` `=0.09 + 0.09 + 0.1 +0.06 + 0.06 = 0.40` (d) `because P(bar(B)) = 1- P(B) = 1 - 0.31 = 0.69` and `bar(B) = {E_(1), E_(3), E_(4), E_(6), E_(7)}` `therefore P(bar(B)) = P(E_(1)) + P(E_(3)) + P(E_(4)) + P(E_(6)) + P(E_(7))` = 0.09 + 0.1 + 0.1 + 0.2 + 0.2 = 0.69

Discussion

23.	Find (dy)/(dx) in the following : y= sec^(-1) ((1)/(2x^(2)-1)), 0 lt x lt (1)/(sqrt(2)).
Answer» ANSWER :`-(2)/(SQRT(1-x^(2)))`

Discussion

24.	int(x^(4)-1)/(x^(2)(x^(4)+x^(2)+1)^(1//2))dx
Answer» ANSWER :`SQRT(X^(2)+(1)/(x^(2))+1+c)`

Discussion

25.	If y = cos x. Cos 2x . Cos 3x find (dy)/(dx)
Answer» Answer :`-cos X cos 2X cos 3X [tan x +2 tan 2x+3 tan 3x]`

Discussion

26.	Iff(x) isis a polynomialofdegreen withrationalcoefficients and 1 +2 I ,2 - sqrt(3)and 5arerootsoff(x)=0then theleastvalueof n is
Answer» 5 4 3 6 Answer :A

Discussion

27.	A balanced dice is tossed (2n + 1) times. Find probability of an event that number 1 OR 3 OR 4 comes up at most n times.
Answer» ANSWER :`(1)/(2)`

Discussion

28.	A insects initially at origin has to move from (0,0) to (6,6). It moves towards +ve x-axis or +ve y-axis. In each step it moves from (x,y) to (x+1,y) or (x,y+1). Find the number of different paths it canfollow to complete it's journey if it does not pass through any of the four points (3,1),(3,2),(4,1) and (4,2).
Answer» ANSWER :`469`

Discussion

29.	Probability that A speaks truth is (4)/(5). A coin is tossed. A reports that a head appears. The probability that actually there was head is
Answer» `(4)/(5)` `(1)/(2)` `(1)/(5)` `(2)/(5)` ANSWER :A

Discussion

30.	If the two equations x^2 - cx + d = 0 and x^2- ax + b = 0 have one common root and the second equation has equal roots, then 2 (b + d) =
Answer» ANSWER :AC

Discussion

31.	If the opposite vertices of a square are (-2, 3) and (8, 5), then the equations ofthe sides of that square are
Answer» `3x-2y+12=0, 3x+2y-14=0, 2x-3y+51=0, 2x+3y-31=0` `3x-2y+12=0, 3x-2y+14=0, 2x+3y-51=0, 2x+3y-31=0` `3x-2y+12=0, 3x+2y+14=0, 2x-3y+51=0, 2x+3y-31=0` `3x-2y+12=0, 3x-2y-14=0, 2x+3y-5=0, 2x+3y-31=0` ANSWER :D

Discussion

32.	If veca=2hati+hatj+4hatk and vecb=3hati-2hatj+hatk then veca.vecb=
Answer» 6 3 8 5 Answer :C

Discussion

33.	If area bounded by y=logx, y = x and x^(2)+y^(2)+2xy-k^(2)=0 is sq. units, then area bounded by y=e^(x),y=log x and x^(2)+y^(2)+2xy-k^(2)=0 will be
Answer» a SQ. UNITS `(a)/(2)` 2A sq. units none of these Answer :C

Discussion

34.	If (sqrt3-i)^n=2^n,b epsilon 1,the set of integers,then n is a multiple of
Answer» 6 10 9 12 Answer :D

Discussion

35.	If a=sqrt(2i), then which of the following is correct?
Answer» a= 1+ i `a=1-i` `a=-(SQRT2)i` NONE of these Answer :A

Discussion

36.	If y=(2)/(sqrt(a^(2)-b^(2)))tan^(-1) [sqrt((a-b)/(a+b))tan""(x)/(2)]
Answer» `(d^(2)y)/(dx^(2))""\|_(X=(pi)/(2))=` `(b)/(2a^(2))` `(b)/(a^(2))` `(2B)/(a)` ANSWER :B

Discussion

37.	A and B are independent events P(A cap B)= 0.5 and P(A)= 0.2 then P(B)= ……….
Answer» `(3)/(8)` `(2)/(3)` `(1)/(2)` `(2)/(5)` Answer :A

Discussion

38.	{:(,"List-I",,"List-II"),((A),~(p^^q)" equals",(i),~p^^~q),((B),~(pvvq)" equals",(ii),p^^(~q)),((C),pimpliesq=,(iii),~pvv~q),((D),~(pimpliesq)=,(iv),(~p)vvq):}
Answer» Answer :(A) `IFF` (III), (B) `iff` (i), (C ) `iff` (iv), (D) `iff` (II)

Discussion

39.	If bar(a)=(1,1,1),bar(b)=(4,-2,3) and bar( c )=(1,-2,1)then the vector of magnitude 6 in the direction of 2bar(a)-bar(b)+3bar( c ) is ……………..
Answer» `((1)/(3),(-2)/(3),(2)/(3))` (2, -4, 4) `(-2, 4, -4)` `((-1)/(3),(2)/(3),(-2)/(3))` Answer :B

Discussion

40.	Let the tangents drawn from the origin to the circle, x^(2)+y^(2)-8x-4y+16=0 touch it at the points A and B. Then (AB)^(2) is equal to :
Answer» `(3)/(25)` `(64)/(5)` `(52)/(5)` `(56)/(5)` ANSWER :B

Discussion

41.	sin{pi/3-sin^(-1)(-1/2)} is _____
Answer» `1/2` `1/3` `1/4` `1` ANSWER :D

Discussion

42.	Some standard forms of integration : intx^(2)sqrt(x^(6)-1)dx=.......+c
Answer» `(1)/(6)(x^(3)SQRT(x^(6)-1)+COS^(-1)x^(3))` `(1)/(6)(x^(3)sqrt(x^(6)-1)+SIN^(-1)x^(3))` `(1)/(6)(x^(3)sqrt(x^(6)-1)+log\|x^(3)+sqrt(x^(6)-1)\|)` `(1)/(6)(x^(3)sqrt(x^(6)-1)-log\|x^(3)+sqrt(x^(6)-1)\|)` Answer :D

Discussion

43.	Express the following differential equations in the form (dx)/(dy) = F((x)/(y)) (i) (1+e^((x)/(y)))dx + e^((x)/(y))(1-(x)/(y))dy = 0 (ii) xdy - ydx + y e^(-(2x)/(y)) dy = 0
Answer» ANSWER :(i) `(DX)/(dy) = (E^((X)/(y))[(x)/(y)-1])/(1+e^((x)/(y))) ` (ii) `(dx)/(dy) = (x)/(y)+e^(-2((x)/(y)))`

Discussion

44.	Find the derivatives w.r.t. x : (5x)/(root(3)(1-x^(2)))+sin^(2)(2x+3)
Answer» ANSWER :`(5(3-x^(2)))/(3(1-x^(2))^(4//3))+2 SIN(4x+6)`

Discussion

45.	If f(x)={(([x]-1)/(x-1)",",xne1),(0",",x=1):} then f(x) is
Answer» CONTINUOUS as WELL as DIFFERENTIABLE at X = 1 differentiable but not continuous at x = 1 ontinuous but not differentiable at x = 1 neither continuous nor differentiable at x = 1 Answer :D

Discussion

46.	Find the coordinates of the pole of the straight line (i) x+y+2=0 with respect to the circle x^(2)+y^(2)-4x+6y+2=0 (ii) 3x+4y-45=0 with respect to the circle x^(2)+y^(2)-6x-8y+5=0 (iii) x-2y+22=0 with respect to the circlex^(2)+y^(2)-5x+8y+6=0 (iv) ax+by+c=0 with respect to the circle x^(2)+y^(2)=r^(2)
Answer» <BR> Answer :(i) (-9,-24) (II) (6,8) (III) (2,-3) (iv) `(-(ar^(2))/c,(-br^(2))/c)`

Discussion

47.	Write the value of intxsec^2xdx.
Answer» SOLUTION :`intxsec^2xdx=xtanx-inttanx=xtanx-Insecx+c`

Discussion

48.	If f(x)=(sin^(-1)([x]+x))/"[x]" , [x] ne 0 =0, [x] = 0where [x] denotes the greatest integer less than or equal to x, then lim_(x to 0) f(x) is
Answer» 1 `-1` 0 none of these ANSWER :D

Discussion

49.	Let S denote the sum of the infinite series 1+(8)/(2!)+(21)/(3!)+(40)/(4!)+(65)/(5!) + ….. Then
Answer» `S LT 8` `S GT 12` `8 lt S lt 12` `S=8` Answer :C

Discussion

50.	C_3//4+C_5//6+C_7//8+….=
Answer» `((2^(n+1)-n^2-n -2))/(2(n+1))` `((2^(n+2)+n^2 +n-2))/(n+1)` `((3^(n+2)-n^2 -n-2))/(n+1)` none Answer :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A,B,C are three angles of a triangle and "sin" (A+c/2)= n "sin" C/2 ("sin" C/2)/("cos"A/2 "cos"B/2)=

The range of a random variable X is {1, 2, 3, ……..} and P(X=k)=(C^(k))/(lfloork) where k = 1, 2, 3,…. Find the value of C

Evaluate :[2hati "" hatj "" hatk ] +[hati hatk hatj ] +[hatk hatj 2hati ]

If the quadratic equation a_(1)x^(2)-a-(2)x+a_(3)=0 where a_(1),a_(2),a_(3) in N has two distinct real roots belonging to the interval (1,2) then least value of a_(1) is_______

Determine k and solve the equation 2x^3-6x^2+3x+k=0 if one of its roots is twicethe sum of the othertwo roots.

If f(x) = |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x-1))|, using properties of determinant, find f(2x) - f(x).

Find (i) inte^(x)(tan^(-1)x+1/(1+x^(2)))dx (ii) int((x^(2)+1)e^(x))/((x+1)^(2))dx

f (x) = { (sin ^(3) x ^(2))/( {:(""x), ( 0"," x =-0):}), x ne 0 is

A value of b for which the equations :x^(2) + bx - 1= 0, x^(2) + x + b = 0 Have one root in common is :

int(dx)/(2sqrt(x)(1+x))=...

If z_(1)" and "z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 then

Four fair dicew are rolled and found that the numbers on the dice are in ascending order. Find the probability that one die shows 4.

If A = [(0,c,-b),(-c,0,a),(b,-a,0)] and B = [(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc,a^(2))]then AB is :

The volume of a spherical cap of height (a)/(2) cut off from the sphere of radius a is :

The vectors vec(AB) = 3 hati + 5 hatj + 4 hatk and vec(AC) = 5 hati - 5 hatj + 2 hatk are the sides of a triangle ABC. The length of the median through A is

By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(4))log(1+tanx)dx

A committeeconsisting of at least three members is to be formed from a group of 6 boys and 6 girls suchthat it always has a boy and a girl. The number of ways to form such committee is

A circle passing through the vertex C ofa rectangle ABCD and touching its sides AB and AD at M and N, respectively. If the distance from C to the line segment MN is equal to 5 units, then find the area of the reactangle ABCD.

Write the inverse trignometric function tan^(-1)(x/sqrt(a^(2)-x^(2)))|x|lta, in simplest form.

Equation of the circles |z-1-i|=1 & |z-1+i|=1 touches internally a circle of radius 2. The equation of the circle touching all the circles can be

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

int(x^(4)-1)/(x^(2)(x^(4)+x^(2)+1)^(1//2))dx

If y = cos x. Cos 2x . Cos 3x find (dy)/(dx)

Iff(x) isis a polynomialofdegreen withrationalcoefficients and 1 +2 I ,2 - sqrt(3)and 5arerootsoff(x)=0then theleastvalueof n is

A balanced dice is tossed (2n + 1) times. Find probability of an event that number 1 OR 3 OR 4 comes up at most n times.

Probability that A speaks truth is (4)/(5). A coin is tossed. A reports that a head appears. The probability that actually there was head is

If the two equations x^2 - cx + d = 0 and x^2- ax + b = 0 have one common root and the second equation has equal roots, then 2 (b + d) =

If the opposite vertices of a square are (-2, 3) and (8, 5), then the equations ofthe sides of that square are

If veca=2hati+hatj+4hatk and vecb=3hati-2hatj+hatk then veca.vecb=

If area bounded by y=logx, y = x and x^(2)+y^(2)+2xy-k^(2)=0 is sq. units, then area bounded by y=e^(x),y=log x and x^(2)+y^(2)+2xy-k^(2)=0 will be

If (sqrt3-i)^n=2^n,b epsilon 1,the set of integers,then n is a multiple of

If a=sqrt(2i), then which of the following is correct?

If y=(2)/(sqrt(a^(2)-b^(2)))tan^(-1) [sqrt((a-b)/(a+b))tan""(x)/(2)]

A and B are independent events P(A cap B)= 0.5 and P(A)= 0.2 then P(B)= ……….

{:(,"List-I",,"List-II"),((A),~(p^^q)" equals",(i),~p^^~q),((B),~(pvvq)" equals",(ii),p^^(~q)),((C),pimpliesq=,(iii),~pvv~q),((D),~(pimpliesq)=,(iv),(~p)vvq):}

If bar(a)=(1,1,1),bar(b)=(4,-2,3) and bar( c )=(1,-2,1)then the vector of magnitude 6 in the direction of 2bar(a)-bar(b)+3bar( c ) is ……………..

Let the tangents drawn from the origin to the circle, x^(2)+y^(2)-8x-4y+16=0 touch it at the points A and B. Then (AB)^(2) is equal to :

sin{pi/3-sin^(-1)(-1/2)} is _____

Some standard forms of integration : intx^(2)sqrt(x^(6)-1)dx=.......+c

Express the following differential equations in the form (dx)/(dy) = F((x)/(y)) (i) (1+e^((x)/(y)))dx + e^((x)/(y))(1-(x)/(y))dy = 0 (ii) xdy - ydx + y e^(-(2x)/(y)) dy = 0

Find the derivatives w.r.t. x : (5x)/(root(3)(1-x^(2)))+sin^(2)(2x+3)

If f(x)={(([x]-1)/(x-1)",",xne1),(0",",x=1):} then f(x) is

Write the value of intxsec^2xdx.

If f(x)=(sin^(-1)([x]+x))/"[x]" , [x] ne 0 =0, [x] = 0where [x] denotes the greatest integer less than or equal to x, then lim_(x to 0) f(x) is

Let S denote the sum of the infinite series 1+(8)/(2!)+(21)/(3!)+(40)/(4!)+(65)/(5!) + ….. Then

C_3//4+C_5//6+C_7//8+….=