28278 + Interview Questions in Maths in Class 12

1.	Solve 24x lt100 , when x is a natural number.
Answer» ANSWER :{1,2,3,4}

Discussion

2.	Integrate the function (4x+1)/(sqrt(2x^(2)+x-3))
Answer» ANSWER :`2sqrt(2X^(2)+x-3)+C`

Discussion

3.	SetA,B,C, A cap B, A cap B, Acap C, B cap C and A cap B cap Chave 35, 40, 45, 13, 12, 14 and 5 elements respectively. An element is selected at random from the set a cup V cup C . The probability thatthe selected elementbelongs to only set A is
Answer» `(13)/(86)` `(35)/(86)` `(5)/(86)` `(15)/(86)` ANSWER :D

Discussion

4.	Let f : [1/2, 1] to R (the set of all real numbers) be a positive, non -constant and differentiable function such that the f'(x) < 2 f(x) and f(1/2) = 1. Then the value of int_(1//2)^(1) f(x) dx lies in the interval :
Answer» `(2e - 1, 2e)` `(E - 1, 2e - 1)` `((e - 1)/(2), e - 1)` `(0,(e - 1)/(2))` ANSWER :D

Discussion

5.	1.5 ml of the gaseous hydrocarbonrequired 375 ml of air (containing 20% O_(2) by volume) for complete combustion. The resultantgaseous mixture occupied 345 ml. The formula of the hyrocarbonis
Answer» `C_(4)H_(8)` `C_(3)H_(8)` `C_(3)H_(4)` `C_(2)H_(4)` ANSWER :B

Discussion

6.	If the normal at (1,2) on the parabola y^(2)=4x meets the parabola again at the point (t^(2),2t) then the value of t is
Answer» 1 3 `-3` 1 Answer :C

Discussion

7.	Evaluate (ii) int_(a)^(b) sqrt((x-a)/(b-x))dx (a lt x lt b)
Answer» ANSWER :`pi/2 (a-b)`

Discussion

8.	A function f: R rarr R satisfies the equation f(x+ y)= f(x).f(y) "for all" x, y in R, f(x) ne 0. Suppose that the function is differentiable at x=0 and f'(0)=2, then prove that f'(x)= 2f(x)
Answer» ANSWER :`F'(X)= 2 f(x)`

Discussion

9.	Two gases N_(2)and H_(2) are allowed to react from mixture of N_(2)H_(2)(1) and N_(2)H_(4)(g) leaving none of the reactants. Formation of N_(2)H_(2) (1) does not create any energy change whereas formation of 1 ml N_(2)H_(4)(g) absorbs 2 Joule energy. Ratio of volume contraction to energy change (in ml/Joule) during reaction when 30 ml N_(2)and 40 ml H_(2) react under similar conditions of temperature and pressure.
Answer» Solution :`N_(2)+H_(2)toN_(2)H_(2)(1)+N_(2)H_(4)(g)` `POAC on H ""a ML""bml` `30xx2=2a+2bimpliesa+b=30` `POAC on H40xx2=2a+4bimpliesa+2b=30` `b=10,a=20` `V.C.=(30+40)-10=60ml` Energy change `=10xx2=20` `(V.C.)/("Energy change")=(60)/(20)=3`

Discussion

10.	Solve the following systems of linear inequalities graphically : x lt y, x gt 0 , y lt 1.
Answer» Solution :`x LT y` `x gt 0` `y lt 1` Step - Let US CONSIDER the POINT (1,0) that does not lie on these lines. Putting x = 0 , y = 0 in the inequations we get clearly (1,0) satisfies x`gt`0, y `lt` 1 but does not satisfy x `lt` y. `therefore` The shaded region is the solution region.

Discussion

11.	The solution vectors vecr of the equation vecr xx hati=hatj+hatk and vecr xx hatj=hatk+hatj represent two straight lines which are :
Answer» INTERSECTING NON COPLANAR Coplanar Non intersecting ANSWER :B::D

Discussion

12.	If P(A)= (2)/(5), P(B)= (3)/(10) and P(A cap B)= (1)/(5) , then P(A'//B') * P(B'//A') is equal to ……….
Answer» `(5)/(6)` `(5)/(7)` `(25)/(42)` 1 Answer :C

Discussion

13.	If (0,-3) is one limiting point of a coaxal system of circlesx^(2) + y^(2) + 4y + 7 = 0is a member , then the other limiting point is
Answer» (-2,-2) (2,1) (6,5) (5,3) ANSWER :A

Discussion

14.	Find (dy)/(dx) of the functions given in Exercises 12 to 15. xy= e^((x-y)).
Answer» ANSWER :`(y(X-1))/(x(y+ 1))`

Discussion

15.	Let vec(a)=hati+hatj+hatk,vec(b)=hati and vec( c )=c_(1)hati+c_(2)hatj+c_(3)hatk. Then If c_(1)=1 and c_(2)=2 find c_(3) which makes vec(a),vec(b) and vec( c ) coplanar.
Answer» ANSWER :`:.-c_(3)+2=0=>c_(3)=2`

Discussion

16.	int_(0)^(pi)(x dx)/(1+sin x)
Answer» Solution :`"Let I"= int_(0)^(pi) (x)/(1+sinx)DX` `RARR ""I=int_(0)^(pi) (pi-x)/(1+sin (pi-x))dx` `=int_(0)^(pi)(pi-x)/(1+sin x)dx` Adding equations (1) and (2) `2I =int_(0)^(pi)(x+pi-x)/(1+sin x)dx` `=piint_(0)^(pi)(1)/(1+sinx).(1-sin x)/(1-sin x)dx` `=piint_(0)^(pi)(1-sinx)/(1-sin^(2)x)dx` `=pi int_(0)^(pi)(1-sinx)/(COS^(2)x)dx` `=pi int_(0)^(pi)(sec^(2)x-secx tan x) dx` `=pi [tan x-sec x]_(0)^(pi)` `=pi [(tan pi-sec pi)-(tan 0-sec 0)]` ` =pi (1+1) =2pi` `rArr ""I=pi`

Discussion

17.	int(logx+(1)/(x^(2)))e^(x)dx=..........+c
Answer» `e^(x)(logx+(1)/(x^(2)))` `e^(x)(logx+(1)/(x))` `e^(x)(logx-(1)/(x^(2)))` `e^(x)(logx-(1)/(x))` ANSWER :D

Discussion

18.	Match thefollowing .
Answer» a,B,C,d b,c,a,d c,d,b,a d,c,b,a Answer :D

Discussion

19.	The slopes of the lines given by 12x^(2)+bxy-y^(2)=0 differ by 6, Then value of b is
Answer» `2` `PM2` `pm1` `1` ANSWER :C

Discussion

20.	We know that , ifa_(1),a_(2),….a_(n) are in A.P and vice versa . If a_(1),a_(2),…a_(n)are in A.P and viceversa . If a_(1),a_(2)….a_(n) are in A.Pwith common difference d, then for nay b ( gt 0) the numbersb^(a_(1)),b^(a_(2)),b^(a_(3)),....,b^(a_(n)) are in G.Pwith commonratio b^(d) If a_(1),a_(2),.....a_(n) are positive and in G.P with common ratio r , then for any base b(b gt 0), log_(b) a_(1) , log _(b) a_(2) , ..., log_(b) a_(n) are in A.P with common differencelog_(b)r If p,q,r are in A.P , then the pth , the qth , therth terms of any G.P are in
Answer» A.P G.P H.P A.G.P Answer :B

Discussion

21.	Two events E and F are independent. If P(E ) = 0.3and P(E cup F)= 0.5 ,then P(E//F)- P(F//E) equal ………
Answer» `(2)/(7)` `(3)/(35)` `(1)/(70)` `(1)/(7)` Answer :C

Discussion

22.	Consider a triangle ABC with sides AB and AC having the equations L_1 = 0 and L_2 = 0 . Let the centroid, orthocentre and circumcentre of the Delta ABCare G, H and S respectively. L = 0 denotes the equation of side BC. If L_1 : x+y – 1=0 and L_2 : 2x – y + 4=0and S(2, 1) then find the x-intercept of the line L = 0.
Answer» ANSWER :`3/2`

Discussion

23.	We know that , ifa_(1),a_(2),….a_(n) are in A.P and vice versa . If a_(1),a_(2),…a_(n)are in A.P and viceversa . If a_(1),a_(2)….a_(n) are in A.Pwith common difference d, then for nay(b gt 0) the numbersb^(a_(1)),b^(a_(2)),b^(a_(3)),....,b^(a_(n)) are in G.Pwith commonratio b^(d) If a_(1),a_(2),.....a_(n) are positive and in G.P with common ratio r , then for any base b(b gt 0), log_(b) a_(1) , log _(b) a_(2) , ..., log_(b) a_(n) are in A.P with common differencelog_(b)r If a,b,c,d are in G.P and a^(x) = b^(y) = c^(z) = d^(v) , then x, y , z , v are in
Answer» A.P G.P H.P None of these ANSWER :C

Discussion

24.	int_(0)^(1) (x-1) e^(-x) dx=
Answer» `- 1/e` `1/e` e 2e Answer :A

Discussion

25.	We know that , ifa_(1),a_(2),….a_(n) are in A.P and vice versa . If a_(1),a_(2),…a_(n)are in A.P and viceversa . If a_(1),a_(2)….a_(n) are in A.Pwith common difference d, then for nay b ( gt 0) the numbersb^(a_(1)),b^(a_(2)),b^(a_(3)),....,b^(a_(n)) are in G.Pwith commonratio b^(d) If a_(1),a_(2),.....a_(n) are positive and in G.P with common ratio r , then for any base b(b gt 0), log_(b) a_(1) , log _(b) a_(2) , ..., log_(b) a_(n) are in A.P with common differencelog_(b)r Ifx, y , zare respectively the pth , qth and the rthtermsof an A.P ..., A.P.., as well as of a G.P , then x^(y-z),y^(z-x).z^(x-y) is equal to
Answer» p q r 1 Answer :D

Discussion

26.	Find the condition that x^3-px^2+qx-r=0 may have the roots in G.P .
Answer» ANSWER :`p^3 r=q^3`

Discussion

27.	Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that (i) both balls are red. (ii) first ball is black and second is red. (iii) one of them is black and other is red.
Answer» ANSWER :(i) `(16)/(81)`, (II) `(20)/(81)`, (iii) `(40)/(81)`

Discussion

28.	If f: R to R, g: R to R and h: R to R is such that f(x)=x^(2), g(x)= tan x and h (x)= logx then the value of [ho (gof)]x , if x=(sqrt(pi))/(2) will be
Answer» 0 1 `-1` 10 Answer :A

Discussion

29.	Consider a triangle ABC with sides AB and AC having the equations L_1 = 0 and L_2 = 0 . Let the centroid, orthocentre and circumcentre of the Delta ABCare G, H and S respectively. L = 0 denotes the equation of side BC. If L_1 : 2x + y = 0 and L_2 : x – y + 2 = 0and H(2, 3) then find the y-intercept of L = 0.
Answer» ANSWER :2

Discussion

30.	If the position vectors of the points A,B,C are -2bar(i)+bar(j)-bar(k), -4bar(i)+2bar(j)+2bar(k), 6bar(i)-3bar(j)-13bar(k) respectively and bar(AB) = lambda bar(AC) then find the value of lambda.
Answer» ANSWER :`-(1)/(4)`

Discussion

31.	Evaluation of definite integrals by subsitiution and properties of its : f(x)=\|(sinx+sin2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,sinx,1)\| then int_(0)^(pi/2)f(x)dx=……….
Answer» 3 `(2)/(3)` `(1)/(3)` 0 Answer :C

Discussion

32.	Show that the vectors bar(a) = 2 hat(i) - 3 hat(j) + 4 hat(k) and bar(b) = -4 hat(i) + 6 hat(j) - 8k are collinear.
Answer» ANSWER :`BAR(B) = -2 HAT(a)`

Discussion

33.	The straight line x + y + 1 = 0 bisects an angle between a pair of lines, of which one is 2x - 3y + 4 = 0 . Then the equation of the other line in that pair is
Answer» 2x + 3Y + 4 = 0 X - y + 1 = 0 5x - 5y + 9 =0 3X - 2Y + 5 = 0 Answer :D

Discussion

34.	Consider the integral int_(-2)^(2) (dx)/(4 + x^(2)) . Itis easy to conclude that it is equal to (pi)/(4) .Indeed int_(-2)^(2) (dx)/(4 + x^(2)) = (1)/(2) "arc tan "(x)/(2) \|_(-2)^(2)= (1)/(2) [(pi)/(4) - (-(pi)/(4))]= (pi)/(4)On the other hand, making the substitution x = (1)/(t) we havedx = - (dt)/(t^(2))\|{:(x," "t),(-2,-1//2),(2,1//2):}\| int_(-2)^(2) (dx)/( 4 + x^(2)) = - int_(-1//2)^(1//2) (dt)/(t^(2)(4 + (1)/(t^(2))))= - int _(-1//2)^(+1//2) (dt)/(4t^(2) + 1)=(1)/(2) "arc tan 2t \|_((1)/(2))^((1)/(2)) = - (pi)/(4) This result is obviously wrong, since the integrand (1)/(4 + x^(2)) gt0 , andconsequently, thedefinite integral of this function cannot be equal to a negative number -(pi)/(4) . Find the mistake .
Answer» Answer :The SUBSTITUTION`X = (1)/(t)` will not do, since THISFUNCTION is descontinuous at t = 0

Discussion

35.	Let g be the inverse function of f and f '(x) = (x^(10))/(1+x^(2)) if g(2) = a then g'(2) is equal to:
Answer» `(a)/(2^(10))` `(1+a^(2))/(a^(10))` `(a^(10))/(1+a^(2))` `(1+a^(10))/(a^(2))` SOLUTION :`f(g(x))=x` `RARR f'(g(x)).g'(x)=1` `rArr g'(x)=(1)/(f'(g(x)))=(1+(g(x))^(2))/((g(x))^(10))` `rArr g'(2)=(1+(g(2))^(2))/((g(2))^(10))`

Discussion

36.	Area of the triangle is calculated by the formula A=(1)/(2)ab sin C. If C = (pi)/(6) and error in the measure of C is x%, find the approximate change in the area of the triangle. Where a and b are constant.
Answer» ANSWER :`(sqrt(3)PI X)/(6)%`

Discussion

37.	If the equation x^(2)-cx+d=0 has roots equal to the fourth powers of the roots of x^(2)+ax+b=0, where a^(2)gt4b, then the roots of x^(2)-4bx+2b^(2)-c=0 will be
Answer» both REAL both negative both POSITIVE ONE positive and one negative Answer :A::D

Discussion

38.	Integrate the following rational functions : int(dx)/(x(x+2))
Answer» Answer :`(1)/(2)LOG\|(X)/(x+2)\|+C`

Discussion

39.	Find the mean deviation about mean of first 2n+1 natural numbers from mean.
Answer» ANSWER :`(N(n+1))/(2n+1)`

Discussion

40.	Find the equation of the circle with centre (-3, 4)and touching y-axis.
Answer» Answer :`X^(2) + y^(2)+6x -8Y +16 =0`

Discussion

41.	Sho that 3/6 + (3.5)/(6.9) + (3.5.7)/(6.9.12)+ ……..oo 3 sqrt3 - 4
Answer» ANSWER :`3 SQRT3 - 4`

Discussion

42.	Prove that if (a + b+ c)(b + c - a) = 3bc then A = 60^@
Answer» SOLUTION :(a + B + c)(b + c + a) =3bc or, ab + ca - a^2 + b^2 + BC - ab + bc + c^2 - ca = 3bc` or, `b^2 + c^2 -a^2 = bc` or, `(b^2 + c^2 - a^2)/(2bc) = 1/2` or, COSA = 1/2 or , A = `60^@`

Discussion

43.	If the lines L_1 and L_2in space are defined by L_1 = {x=sqrt lambda y+ (lambda-1) z= (sqrtlamda -1) y+sqrtlambda ) and L_2 ={ x=sqrtmu y + (1-sqrtmu ), z =(1-sqrtmu )y +sqrtmu )thenL_ 1is perpendicular to L_2 for all non- negative realslambda and musuch that
Answer» ` sqrtlambda +SQRT mu =1` ` lambda NE mu ` ` lambda +mu =0 ` `lambda = mu` ANSWER :D

Discussion

44.	For any positive integers m, n (with n ge m) If ({:(n),(m):}) = .^(n)C_(m) Prove that ({:(n),(m):}) + ({:(n - 1),(m):}) + ({:(n - 2),(m):}) + … + ({:(m),(m):}) = ({:(n + 1),(m + 1):}) Prove that ({:(n),(m):}) + 2 ({:(n + 1),(m):}) + 3 ({:(n - 2),(m):}) + .... + (n - m + 1) ({:(m),(m):}) = ({:(n + 2),(m + 2):})
Answer» Solution : Let `S = ((n)/(m))+((n-1)/(m)) + ((n-2)/(m))+ ((n-2)/(m)) +.....+((m)/(m)) =((n+1)/(m+1)).....(i)` It is obvious that, `n ge m` Note : Thisquestion is based UPON additive loop. Now ,`S =((m)/(m)) + ((m+1)/(m)) + ((m+2)/(m)) +.......+((n)/(m))` ` ={((m+1)/(m+1))+((m+1)/(m))}[because ((m)/(m)) = 1= ((m+1)/(m+1))]` `= ((m+2)/(m+1)) + ((m+2))/(m)) + ......+ ((n)/(m))""[because""^(n)C_(R)+ ""^(n)C_(r+1) = ""^(n+1)C_(r+1)]` `=((m+2)/(m+1)) +......+((n)/(m))` `=.............` ` =((n)/(m+1))+((n)/(m)) = ((n+1)/(m+1))` whichis ture....(ii) Again, we haveto prove that `((n)/(m))+2((n-1)/(m)) + 3((n-2)/(m)) +......+ (n-m+1)((m)/(m)) = ((m+2)/(m+2))` Let`S_(1) = ((n)/(m))+2((n-1)/(m)) +3((n-2)/(m)) +......+(n-m+1)((mm)/(m))` `{:(= ((n)/(m)) + ((n-1)/(m)) + ((n-2)/(m)) +...+ ((m)/(m))), ( ""+ ((n-1)/(m)) + ((n-2)/(m)) +...+ ((m)/(m))), (""+ ((n-2)/(m)) +...+((m)/(m)) ),(""...) , (""+ ((m)/(m))):}}n-m + 1` rows Now, SUM of the first row is `((n+1)/(m+1))` Sum of the second row is `((n)/(m+1))` Sumof thethird row is `((n+1)/(m+1))`, .................... Sum of the last row is `((m)/(m)) = ((m+1)/(m+1))` THUS `S = ((n+1)/(m+1))+((n)/(m+1)) + ((n +1)/(m+1))+.......+ ((m+1)/(m+1)) = ((n+1+1)/(m+2)) = ((n+2)/(m+2))` [from Eq. (i) replacing nbyn +1 and m by m + 1]

Discussion

45.	Leta ne 0and p(x )be apolynomialof degreegreaterthan2.If P(x )leavesremaindera and-awhendividedrespectivelybyx+aand x-athentheremainderwhenp(X )isdividedbyx^2 -a^2 is
Answer» 2X `-2x` `X` `-x` ANSWER :D

Discussion

46.	Evaluate int x^(2) tan^(-1) x dx
Answer» Answer :`(X^(3))/(3) tan^(-1) x - (x^(2) )/(6) + (1)/(6) LOG"" \| 1 + x^(2)\| + C`

Discussion

47.	Find Order and Degree of given differential equation ((ds)/(dt))^(4) + 3s(d^(2)s)/(dt^(2)) = 0
Answer» ANSWER :ORDER 2; DEGREE 1

Discussion

48.	What are the coordinates of the point P in the xy-plane that divides the line segment whose endpoints are A(-2, 9) and B(7, 3) into two segments such that the ratio of AP to PB is 1 to 2?
Answer» <P>`P(1, 5)` `P(4, 1)` `P(1, 7)` `P(2, 6)` Answer :C

Discussion

49.	If lim_(x rarr 0) (1+px)^(q//x) = e^(4), where p, q, in N, then :
Answer» <P>p = 4, q = 2 p = 8, q = 4 p = 16, q = 8 None of these Answer :D

Discussion

50.	Evalute the following integrals int (x + 1)/(x^(2) + 3x + 12) dx
Answer» Answer :`(1)/(2) log \|x^(2) + 3x + 12 \| - (1)/(SQRT(39)) tan^(-1) ((2x+ 3)/(sqrt(39)))+ x `

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Solve 24x lt100 , when x is a natural number.

Integrate the function (4x+1)/(sqrt(2x^(2)+x-3))

SetA,B,C, A cap B, A cap B, Acap C, B cap C and A cap B cap Chave 35, 40, 45, 13, 12, 14 and 5 elements respectively. An element is selected at random from the set a cup V cup C . The probability thatthe selected elementbelongs to only set A is

Let f : [1/2, 1] to R (the set of all real numbers) be a positive, non -constant and differentiable function such that the f'(x) < 2 f(x) and f(1/2) = 1. Then the value of int_(1//2)^(1) f(x) dx lies in the interval :

1.5 ml of the gaseous hydrocarbonrequired 375 ml of air (containing 20% O_(2) by volume) for complete combustion. The resultantgaseous mixture occupied 345 ml. The formula of the hyrocarbonis

If the normal at (1,2) on the parabola y^(2)=4x meets the parabola again at the point (t^(2),2t) then the value of t is

Evaluate (ii) int_(a)^(b) sqrt((x-a)/(b-x))dx (a lt x lt b)

A function f: R rarr R satisfies the equation f(x+ y)= f(x).f(y) "for all" x, y in R, f(x) ne 0. Suppose that the function is differentiable at x=0 and f'(0)=2, then prove that f'(x)= 2f(x)

Solve the following systems of linear inequalities graphically : x lt y, x gt 0 , y lt 1.

The solution vectors vecr of the equation vecr xx hati=hatj+hatk and vecr xx hatj=hatk+hatj represent two straight lines which are :

If P(A)= (2)/(5), P(B)= (3)/(10) and P(A cap B)= (1)/(5) , then P(A'//B') * P(B'//A') is equal to ……….

If (0,-3) is one limiting point of a coaxal system of circlesx^(2) + y^(2) + 4y + 7 = 0is a member , then the other limiting point is

Find (dy)/(dx) of the functions given in Exercises 12 to 15. xy= e^((x-y)).

Let vec(a)=hati+hatj+hatk,vec(b)=hati and vec( c )=c_(1)hati+c_(2)hatj+c_(3)hatk. Then If c_(1)=1 and c_(2)=2 find c_(3) which makes vec(a),vec(b) and vec( c ) coplanar.

int_(0)^(pi)(x dx)/(1+sin x)

int(logx+(1)/(x^(2)))e^(x)dx=..........+c

Match thefollowing .

The slopes of the lines given by 12x^(2)+bxy-y^(2)=0 differ by 6, Then value of b is

Two events E and F are independent. If P(E ) = 0.3and P(E cup F)= 0.5 ,then P(E//F)- P(F//E) equal ………

int_(0)^(1) (x-1) e^(-x) dx=

Find the condition that x^3-px^2+qx-r=0 may have the roots in G.P .

Two balls are drawn at random with replacement from a box containing 10 black﻿ and 8 red balls. Find the probability that﻿ (i) both balls are red.﻿ (ii) first ball is black and second is red.﻿ (iii) one of them is black and other is red.﻿

If f: R to R, g: R to R and h: R to R is such that f(x)=x^(2), g(x)= tan x and h (x)= logx then the value of [ho (gof)]x , if x=(sqrt(pi))/(2) will be

If the position vectors of the points A,B,C are -2bar(i)+bar(j)-bar(k), -4bar(i)+2bar(j)+2bar(k), 6bar(i)-3bar(j)-13bar(k) respectively and bar(AB) = lambda bar(AC) then find the value of lambda.

Evaluation of definite integrals by subsitiution and properties of its : f(x)=|(sinx+sin2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,sinx,1)| then int_(0)^(pi/2)f(x)dx=……….

Show that the vectors bar(a) = 2 hat(i) - 3 hat(j) + 4 hat(k) and bar(b) = -4 hat(i) + 6 hat(j) - 8k are collinear.

The straight line x + y + 1 = 0 bisects an angle between a pair of lines, of which one is 2x - 3y + 4 = 0 . Then the equation of the other line in that pair is

Let g be the inverse function of f and f '(x) = (x^(10))/(1+x^(2)) if g(2) = a then g'(2) is equal to:

Area of the triangle is calculated by the formula A=(1)/(2)ab sin C. If C = (pi)/(6) and error in the measure of C is x%, find the approximate change in the area of the triangle. Where a and b are constant.

If the equation x^(2)-cx+d=0 has roots equal to the fourth powers of the roots of x^(2)+ax+b=0, where a^(2)gt4b, then the roots of x^(2)-4bx+2b^(2)-c=0 will be

Integrate the following rational functions : int(dx)/(x(x+2))

Find the mean deviation about mean of first 2n+1 natural numbers from mean.

Find the equation of the circle with centre (-3, 4)and touching y-axis.

Sho that 3/6 + (3.5)/(6.9) + (3.5.7)/(6.9.12)+ ……..oo 3 sqrt3 - 4

Prove that if (a + b+ c)(b + c - a) = 3bc then A = 60^@

If the lines L_1 and L_2in space are defined by L_1 = {x=sqrt lambda y+ (lambda-1) z= (sqrtlamda -1) y+sqrtlambda ) and L_2 ={ x=sqrtmu y + (1-sqrtmu ), z =(1-sqrtmu )y +sqrtmu )thenL_ 1is perpendicular to L_2 for all non- negative realslambda and musuch that

Leta ne 0and p(x )be apolynomialof degreegreaterthan2.If P(x )leavesremaindera and-awhendividedrespectivelybyx+aand x-athentheremainderwhenp(X )isdividedbyx^2 -a^2 is

Evaluate int x^(2) tan^(-1) x dx

Find Order and Degree of given differential equation ((ds)/(dt))^(4) + 3s(d^(2)s)/(dt^(2)) = 0

What are the coordinates of the point P in the xy-plane that divides the line segment whose endpoints are A(-2, 9) and B(7, 3) into two segments such that the ratio of AP to PB is 1 to 2?

If lim_(x rarr 0) (1+px)^(q//x) = e^(4), where p, q, in N, then :

Evalute the following integrals int (x + 1)/(x^(2) + 3x + 12) dx

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that (i) both balls are red. (ii) first ball is black and second is red. (iii) one of them is black and other is red.