28278 + Interview Questions in Maths in Class 12

1.	To determine the age of stone it was analysed for the nuclei of 'B' & 'D' and were found to 10^(18)and3xx10^(18) respectively. Assuming that all the 'D' was produced by the disintegration of 'A' only, the age of the stone is [(Given : ln2=0.3,ln3=0.45]
Answer» 6930 days 10395 days 13860 days 3465 days Solution :`t=(6930)/("In 2")"In"([B]_("INITIAL"))/([B]_("final"))=(6930)/("In 2")"In"(4xx10^(18))/(1XX10^(18))=13860" days"]`

Discussion

2.	Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are (2veca+vecb)and(veca-3vecb) externally in the ratio 1:2 Also , show that P is the mid point of the line segment RQ.
Answer» ANSWER :`3veca+5vecb`

Discussion

3.	Find the value of the following cos^(-1)(cos frac(13pi)6)
Answer» SOLUTION :`TAN^(-1)(tan FRAC(7pi)6)=tan^(-1)tan(pi+pi/6)` `tan^(-1)tan(pi/6=pi/6)`

Discussion

4.	Find the point on the straight line 3x+y+4=0 which is equidistant from the points (-5,6) and (3,2).
Answer» SOLUTION :NA

Discussion

5.	The value of the expression ""^(23)C_(6)underset(j=1)overset(5)Sigma ^(28-j)C_(5)+underset(k=1)overset(5)Sigma^(33-k)C_(28)-k is
Answer» `""^(33)C_(6)` `""^(23)C_(16)` `""^(33)C_(7)` NONE of these Answer :A

Discussion

6.	int_(0)^(x) (dx)/(1-2a cos x+a^(2)) is equal to
Answer» `(pi)/(2(1-a^(2)))` `pi(1-a^(2))` `(pi)/(1-a^(2))` None of these Solution :Let ` l = INT _(0)^(pi) (DX)/(1-2A cos x+a^(2))` `int _(0)^(pi) (dx)/((1+a^(2)) (cos^(2).x/2 +SIN^(2). x/2 ) - 2a (cos^(2). x/2 - sin^(2) .x/2 ) )` `= int _(0)^(pi) (dx)/((1-a^(2))cos^(2) . x/2 + (1+ a^(2)) sin^(2). x/2 ) ` ` = 2/ ((1+a^(2)) )int _(0)^(oo)(dt)/({((1-a))/((1+a))}^(2)+t^(2))` ` [ t = tan .x/2 rArr dt = 1/2 sec^(2) . x/2 dx] ` ` l = 2/(1+a)^(2).((1+a))/((1-a)) [ tan^(-1)((1+a)/(1-a).t ) ] _(0)^(oo) ` ` l = 2/((1-a^(2))) [ tan ^(-1) oo - tan ^(-1) 0 ] = pi/(1-a^(2))`

Discussion

7.	Find the equation of parabola whose focus is (-2,3) and the directrix is 2x+3y=4
Answer» Answer :Required PARABOLA is `9X^(2) -12xy+ 4Y^(2) + 68x - 54Y + 153=0`

Discussion

8.	(overset(-)a+2overset(-)b-overset(-)c) (overset(-)a-overset(-)b) xx (overset(-)a -overset(-)b-overset(-)c) is equal to
Answer» `-[OVERSET(-)a overset(-)B overset(-)C]` `2 [overset(-)a overset(-)b overset(-)c]` `3 [overset(-)a overset(-)b overset(-)c]` `overset(-)0` Answer :C

Discussion

9.	Find (dy)/(dx) of each of the functions expressed in parametric form:x=3 cos theta-2 cos^(3) theta, y= 3 sin theta- 2 sin^(3) theta
Answer» ANSWER :`COT THETA`

Discussion

10.	Probability that A is telling the truth is given as 0.6 and probability that B is telling the truth is 0.7 while narrating on same question. Find the probability that both of them will give contradict options narrating on same scene
Answer»

Discussion

11.	Let a = a_(1) I + a_(2) + a_(3) k. Assertion (A) : The identity \|a xx i\|^(2) + \|a xx j\|^(2) + \|a xx k\|^(2) = 2 \|a\|^(2) hold for a, Reason (R ) : a xx I = a_(3) j = a_(2) k, a xx j = a_(1) k - a_(3) I, a xx k = a_(2) I = a_(1) j Which of the following is correct?
Answer» both A and R are TRUE and R is the correct EXPLANATION of A Both A and R are true but R is not correct explanation of A A is true but R is false A is false but R is true Answer :A

Discussion

12.	Find the mean deviation about the mean for the following data38,70,48,40,42,55,63,46,54,44
Answer» ANSWER :8.4

Discussion

13.	Using properties evaluate the following definite integrals, evaluate the following: int_(-pi/2)^(pi/2) sin^2x dx
Answer» SOLUTION :`sin^2(-x) = (-SINX)^2 = sin^2x` THEREFORE `sin^2x` is an even FUNCTION therefore `int_(-pi/2)^(pi/2) sin^2 x dx = 2int_0^(pi/2) sin^2x dx` =`2 int_0^(pi/2) (1-cos 2x)/2 dx` =`[x-(sin2x)/2]_0^(pi/2)` `(pi/2 -sinpi/2) -(0-sin0/2) = pi/2`

Discussion

14.	If area bounded by the curves y^(2)=4axandy=mx is a^(2)//3 then the value of m is
Answer» 1 2 3 `(1)/(2)` ANSWER :B

Discussion

15.	A circle cuts therectangular hyperbola xy=1 in the points (x_(1),y_(1)), r=1,2,3,4. Prove that x_(1)x_(2)x_(3)x_(4)=y_(1)y_(2)y_(3)y_(4)=1
Answer» ANSWER :`-1`

Discussion

16.	If a, b, c are in AP then ax + by + c = 0 will always pass through a fixed point whose coordinates are
Answer» (1,-2) (-1,2) (1,2) (-1, -2) ANSWER :A

Discussion

17.	Find the graph of linear inequation in xy plane 2y+7 le 0
Answer»

Discussion

18.	Integrate the following functions: sin^3(2x+1)
Answer» Solution :`sin^3(2x+1) = (3 sin(2x+1) -sin3(2x+1))/4` =1/4[3sin(2x+1)-sin(6x+3)] therefore` int sin^3(2x+1) dx` `=1/4[(-3cos(2x+1)/2 + COS(6x+3)/6]+c`

Discussion

19.	The value of c in Rolle's theorem for the function f(x)= x^(3) in the interval x in [0, sqrt3]
Answer» 1 `-1` `(3)/(2)` `(1)/(3)` ANSWER :A

Discussion

20.	Find the most general solution of the following (i) sin 6x=sin 4x-sin 2x (ii)sec 4x-sec 2x=2 (iii)3-2 cos theta - 4 sin theta - cos 2 theta + sin 2theta =0 (iv)2(cos theta + cos 2 theta )+ sin 2 theta (1+cos theta)=2 sin theta
Answer» ANSWER :(i) `mpipm(PI)/(6),(n pi)/(4)` (ii)`(2n+1)(pi)/(10),(2m+1)(pi)/(2) ` (iii)`2npi,2npi+(pi)/(2)` (IV)`2npi(pi)/(2),2npui+(pi)/(3),(2n+1)pi`

Discussion

21.	Let alpha and beta be the roots of the quadratic equation ax^(2) + bx + c = 0, observe the lists given below : The correct match is
Answer» `{:(A,B,C,D),(5,2,4,6):}` `{:(A,B,C,D),(5,2,1,4):}` `{:(A,B,C,D),(5,4,2,6):}` `{:(A,B,C,D),(5,2,4,1):}` ANSWER :D

Discussion

22.	Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, - 1), (4, 3, - 1).
Answer» Answer :`THEREFORE` Line OA `bot` Line BC

Discussion

23.	Find \|vec(a)-vec(b)\|, if two vectors vec(a) and vec(b) are such that \|vec(a)\|=2,\|vec(b)\|=3 and vec(a).vec(b)=4.
Answer» ANSWER :`\|VEC(a)-vec(B)\|=SQRT(5)`

Discussion

24.	Find the probability of getting a prime number in a single roll of the die
Answer» <P> ANSWER :Probability of getting an prime NUMBER `=P(3)+P(5)+P(2)` `3/21+ 5/21+2/21=10/21`

Discussion

25.	a' xx b' + b' xx c' + c' xx a' =
Answer» `(a + B+ C)/([a BC])` `(a - b - c)/([a b c])` `(a + b + c)/([b a c])` `(a + b + c)/(2[a b c])` ANSWER :A

Discussion

26.	If e is the eccentricity, l is the semi latus-rectum and S. S^(1) are foci of the hyperbola 9x^(2)-16y^(2)+72x-32y=16 then ascending order of l, e SS^(1) is
Answer» `1,e,SS^(1)` `e,1,SS^(1)` `e,SS^(1),L` `SS^(1),l,e` ANSWER :B

Discussion

27.	If I_(n)=int_(0)^(pi//4) tan^(n) x dx then {:(" " Lt),(n rarr oo):}n(I_(n)+I_(n+2))=
Answer» `1//2` 1 `OO` 0 Answer :B

Discussion

28.	The slope of tangents drawn from a point (4,10) to the parabola y^(2)=9x are
Answer» `(1)/(4),(3)/(4)` `(1)/(4),(9)/(4)` `(1)/(3),(1)/(4)` `(1)/(2),(1)/(4)` Answer :B

Discussion

29.	Find the points of local mixima and local minima, if any, of the following function : f(x)=sinx+(1)/(2)cos2x:0lexle(pi)/(2).
Answer» ANSWER :`(PI)/(6).`

Discussion

30.	Select correct set of quantum numbers ?
Answer» `{:(N,L,m,s),(2,2,0,-1/2):}` `{:(n,l,m,s),(6,3,+4,+1/2):}` `{:(n,l,m,s),(4,1,-1,+1/2):}` `{:(n,l,m,s),(3,2,-3,-1/2):}`

Discussion

31.	Find the eccentricity of the ellipse (i) whose latus rectum is equal to half of its minor axis (ii) whose latus rectum is equal to half of its major axis (iii) if the major axis is three times the minor axis
Answer» ANSWER :`sqrt3/2``1/sqrt2`

Discussion

32.	Let f(x)={(lim_(nto oo) ((px)/n sum_(r=1)^(n) ([r^(2)-e^(-x)+r-1])/(r(r+1)))+lamda,xgt0),(q, x=0),(lim_(nto oo) sum_(r=1)^(n) ({r^(2)+r+e^(x)-1})/(r(r+1)), xlt0):} Is differentiable is R: ([.] is G.I.f and {.} is F.P. of x) Then,
Answer» `p=1` `q=1` `p+q+lamda=3` if `g` is inverse of `F` then `g^(')(1//2)=2` Solution :abcd `f(x)={(px+lamda, XGT0),(q,x=0),(E^(x),XLT0):}`

Discussion

33.	State with reason,"All sincere students of Ravenshaw college during the academic year 1998-99 " is set or not ?
Answer» Solution :It is not a set, as the WORD SINCERE. is not PROPERLY defined.

Discussion

34.	If a=(1-isqrt(3))/(2)then the correct matching of List - I from List - II is {:("List - I","List - II"),("i)"abara,"A)"2pi//3),("ii)"arg(1//bara),"B)"-i//sqrt3),("iii)"a-bara,"D)"1),("iv)"Im (4//3a),"E)"pi//3),(,"F)"2sqrt(3)):} Correct match is
Answer» `{:("(i)",(II),(iii),(iv)),(D,E,C,B):}` `{:("(i)",(ii),(iii),(iv)),(D,A,B,F):}` `{:("(i)",(ii),(iii),(iv)),(F,E,B,C):}` `{:("(i)",(ii),(iii),(iv)),(D,A,B,C):}` ANSWER :B

Discussion

35.	A lottery sells n^(2) tickets and declares n prizes. If a man purchases n tickets, the probability of his winning exactly one prize is ……
Answer» `1-(.^(N^(2)-n)C_(n))/(.^(n^(2))C_(n))` `(C_(1).^(n^(2)-n)C_(n-1))/(.^(n^(2))C_(n))` `(.^(n)C_(n).^(n^(2)-n)C_(0))/(.^(n^(2))C_(n))` `1-(1)/(.^(n^(2))C_(n))` SOLUTION :`f(x)=pi((x)/(2pi))^(2)+((L-x)/(4))^(2)` `f'(x)=0" at "x=(piL)/(pi+4)."Check "f(0),f(L),f((piL)/(pi+4))`

Discussion

36.	Find the number of words that can be formed by taking all the letters of the word "QUESTION' such that Q, N are separated exactly by 2 letters
Answer» ANSWER :7200

Discussion

37.	Find the number of words that can be formed by taking all the letters of the word "QUESTION' such that Q, N are separated by atmost 4 letters
Answer» ANSWER :36000

Discussion

38.	If AB =3hati-2hatj+2hatk and BC=-hatj-2hatk are adjacent sides of a parallelogram, then angle its diagonals can be
Answer» `cos^(-1)((2)/(SQRT(13)))` `(pi)/(3)` `(4pi)/(3)` `(2PI)/(3)` SOLUTION :Here , `AC=AB+BC` `=(3hat(i)-2hat(j)2hat(k))+(-hat(j)-2hat(k))` `=3hat(i)-3hat(j)` Also `BC=AD` and `AB=AD+DB` `DB=AB=AD` `=(3hat(i)-2hat(j)+2hat(k))-(-hat(j)-2hat(k))` `=3hat(i)-hat(j)+4hat(k)` `THEREFORE` Angle between AC and BD is `theta = cos^(-1)(AC.BD)/(\|AC\|.AD\|)` `=cos^(-1).((3hat(i)-3hat(j)).(3hat(i)-hat(j)+4hat(k)))/(sqrt(3^2+(-3)^2)sqrt(3^2+1^2+4^2))` `=cos^(-1).((9+3)/(sqrt(18)sqrt(20)))=cos^(-1).((12)/(3sqrt(2)sqrt(2)sqrt(3)))` `=cos^(-1)((2)/(sqrt(13)))` .

Discussion

39.	bar(a)=2hati+hatj-2hatk and bar(b)=hati+hatj. The vector bar( c ) is such that bar(a)*bar( c )=\|bar( c )\|,\|bar( c )-bar(a)\|=2sqrt(2) and the angle between bar(a)xx bar(b) and bar( c ) is 30^(@) then \|(bar(a)xx bar(b))xx bar( c )\| = …………
Answer» `(2)/(3)` `(3)/(2)` 2 3 Answer :B

Discussion

40.	Evaluation of definite integrals by subsitiution and properties of its : int(dx)/(sqrt(2x-x^(2)))=..........+C
Answer» `2SIN^(-2)(x-1)` `(1)/(2)sin^(-1)(x-1)` `sin^(-1)(x-1)` `log\|(x-1)+sqrt(2x-x^(2))\|` ANSWER :C

Discussion

41.	Let f(x) = {{:((cos x-e^(x^(2)//2))/(x^(3))",",x ne 0),(0",",x = 0):}, then Statement I f(x) is continuous at x = 0. Statement II lim_(x to 0 )(cos x-e^(-x^(2)//2))/(x^(3)) = - (1)/(12)
Answer» STATEMENT I is CORRECT, Statement II is also correct, Statement II is the correct EXPLANATION of Statement I Statement I is correct, Statement II is also correct, Statement II is not the correct explanation of Statement I Statement I is correct, Statement II is incorrect Statement I is incorrect, Statement II is correct. ANSWER :A

Discussion

42.	if Sigma_(i=1)^(4)(x_(i)^(2)+y_(i)^(2))le 2x_1x_3+2x_2x_4+2y_2y_3+2y_1y_4, the points (x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4) are
Answer» the vertices of a rectangle collinear the vertices of a trapezium none of these Solution :LET `A-=(x_1,y_1),B-=(x_2,y_2), C-=(x_3,y_3), D-=(x_4,y_4)` Given `x_1^2+x_2^(2)+x_4^(2)+y_1^(2)+y_2^(2)+y_3^(2) +y_4^2-2x_1x_3-2x_(2)x_4-2y_(2)y_(3)-2y_(1)y_4le0` or `(x_1-x_3)^2+(x_2-x_4)^2+(y_2-y_3)^2+(y_2-y_3)^2+(y_1-y_4)^2le0` or `(x_1+x_2)/(2)=(x_3+x_4)/(2) and (y_1+y_2)/(2)=(y_4+y_3)/(2)` Hence AB and CD bisect each other. therefore, ACBD is a PARALLELOGRAM. Also, `AB^2=(x_1-x_2)^2+(y_1-y_2)^2` `=(x_3-x_4)^2+(y_4-y_3)^2` `=CD^2`

Discussion

43.	int_(-1)^(1)(x+1)dx.
Answer» ANSWER :2

Discussion

44.	Let f (x) = x \|x\| and g (x) = sin x Statement -1 g^(@) f is differentiable at x =0 and its derivative is continous at that point Statement -2 g ^(@)f is twice differentiable at x =0.
Answer» STATEMENT -1 is true, Statement-2 is true, Statement-2 is not a CORRECT explanatin for Statement-1 Statement-1 is true , Statement-2 is FALSE Statement-1 is false, Statement-2 is true Statement-1 is true, Statement-2 is true, Statement-2 is a correct EXPLANATION for Statement-1 Answer :B

Discussion

45.	Determine if A sub B or A cancel sub B where A=\|a,b,c\|,B ={\|a\|,\|b\|,\|c\|}
Answer» SOLUTION :`A cancelsub B`

Discussion

46.	(2+5omega +2 omega^2)^6=(2+2omega+5 omega^2)^6=729
Answer» Solution :`L.H.S.=(2+5OMEGA+2omega^2)^6` `=(2+2omega^2+5omega)^6={2(1+omega^2)+5omega}^6` `=(-2omega+5omega)^6=(3omega)^6=729omega^6=729` `"Again", (2+2omega+5omega^2)^6` `={2(1+omega)+5omega^2}^6` `=(-2omega^2+5omega^2)^6=(3omega^2)^6` `=729omega^(12)=729` `:.(2+5omega+2omega^2)^6=(2+2omega+5omega^2)^6=729`

Discussion

47.	If the coefficient of the 2^(nd),3^(rd) and 4^(th) terms in the expansion of (1 + x)^(n) are in A.P, then n=
Answer» 7 8 9 4 Answer :C

Discussion

48.	int_(0)^(1)(x^(3))/((1+x^(2))^(3))dx=
Answer» `1/8` `1/4` `1/12` `1/16` ANSWER :D

Discussion

49.	Obtain the following integrals : int (x^((1)/(2)))/(1+x^((3)/(4)))dx
Answer» ANSWER :`:. I=(4)/(3)(X^((3)/(4)))-(4)/(3)log\|1+x^((3)/(4))\|+C`

Discussion

50.	Differentiate the functions given in Exercises 1 to 11 w.r.t. x. x^(cos x)+(x^(2)+1)/(x^(2)-1).
Answer» ANSWER :`x^(x cos x)[cos x. (1+ LOG x)-x sin xlog x]-(4X)/((x^(2)-1)^2)`.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

To determine the age of stone it was analysed for the nuclei of 'B' & 'D' and were found to 10^(18)and3xx10^(18) respectively. Assuming that all the 'D' was produced by the disintegration of 'A' only, the age of the stone is [(Given : ln2=0.3,ln3=0.45]

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are (2veca+vecb)and(veca-3vecb) externally in the ratio 1:2 Also , show that P is the mid point of the line segment RQ.

Find the value of the following cos^(-1)(cos frac(13pi)6)

Find the point on the straight line 3x+y+4=0 which is equidistant from the points (-5,6) and (3,2).

The value of the expression ""^(23)C_(6)underset(j=1)overset(5)Sigma ^(28-j)C_(5)+underset(k=1)overset(5)Sigma^(33-k)C_(28)-k is

int_(0)^(x) (dx)/(1-2a cos x+a^(2)) is equal to

Find the equation of parabola whose focus is (-2,3) and the directrix is 2x+3y=4

(overset(-)a+2overset(-)b-overset(-)c) (overset(-)a-overset(-)b) xx (overset(-)a -overset(-)b-overset(-)c) is equal to

Find (dy)/(dx) of each of the functions expressed in parametric form:x=3 cos theta-2 cos^(3) theta, y= 3 sin theta- 2 sin^(3) theta

Probability that A is telling the truth is given as 0.6 and probability that B is telling the truth is 0.7 while narrating on same question. Find the probability that both of them will give contradict options narrating on same scene

Let a = a_(1) I + a_(2) + a_(3) k. Assertion (A) : The identity |a xx i|^(2) + |a xx j|^(2) + |a xx k|^(2) = 2 |a|^(2) hold for a, Reason (R ) : a xx I = a_(3) j = a_(2) k, a xx j = a_(1) k - a_(3) I, a xx k = a_(2) I = a_(1) j Which of the following is correct?

Find the mean deviation about the mean for the following data38,70,48,40,42,55,63,46,54,44

Using properties evaluate the following definite integrals, evaluate the following: int_(-pi/2)^(pi/2) sin^2x dx

If area bounded by the curves y^(2)=4axandy=mx is a^(2)//3 then the value of m is

A circle cuts therectangular hyperbola xy=1 in the points (x_(1),y_(1)), r=1,2,3,4. Prove that x_(1)x_(2)x_(3)x_(4)=y_(1)y_(2)y_(3)y_(4)=1

If a, b, c are in AP then ax + by + c = 0﻿ will always pass through a fixed point﻿ whose coordinates are﻿

Find the graph of linear inequation in xy plane 2y+7 le 0

Integrate the following functions: sin^3(2x+1)

The value of c in Rolle's theorem for the function f(x)= x^(3) in the interval x in [0, sqrt3]

Find the most general solution of the following (i) sin 6x=sin 4x-sin 2x (ii)sec 4x-sec 2x=2 (iii)3-2 cos theta - 4 sin theta - cos 2 theta + sin 2theta =0 (iv)2(cos theta + cos 2 theta )+ sin 2 theta (1+cos theta)=2 sin theta

Let alpha and beta be the roots of the quadratic equation ax^(2) + bx + c = 0, observe the lists given below : The correct match is

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, - 1), (4, 3, - 1).

Find |vec(a)-vec(b)|, if two vectors vec(a) and vec(b) are such that |vec(a)|=2,|vec(b)|=3 and vec(a).vec(b)=4.

Find the probability of getting a prime number in a single roll of the die

a' xx b' + b' xx c' + c' xx a' =

If e is the eccentricity, l is the semi latus-rectum and S. S^(1) are foci of the hyperbola 9x^(2)-16y^(2)+72x-32y=16 then ascending order of l, e SS^(1) is

If I_(n)=int_(0)^(pi//4) tan^(n) x dx then {:(" " Lt),(n rarr oo):}n(I_(n)+I_(n+2))=

The slope of tangents drawn from a point (4,10) to the parabola y^(2)=9x are

Find the points of local mixima and local minima, if any, of the following function : f(x)=sinx+(1)/(2)cos2x:0lexle(pi)/(2).

Select correct set of quantum numbers ?

Find the eccentricity of the ellipse (i) whose latus rectum is equal to half of its minor axis (ii) whose latus rectum is equal to half of its major axis (iii) if the major axis is three times the minor axis

Let f(x)={(lim_(nto oo) ((px)/n sum_(r=1)^(n) ([r^(2)-e^(-x)+r-1])/(r(r+1)))+lamda,xgt0),(q, x=0),(lim_(nto oo) sum_(r=1)^(n) ({r^(2)+r+e^(x)-1})/(r(r+1)), xlt0):} Is differentiable is R: ([.] is G.I.f and {.} is F.P. of x) Then,

State with reason,"All sincere students of Ravenshaw college during the academic year 1998-99 " is set or not ?

If a=(1-isqrt(3))/(2)then the correct matching of List - I from List - II is {:("List - I","List - II"),("i)"abara,"A)"2pi//3),("ii)"arg(1//bara),"B)"-i//sqrt3),("iii)"a-bara,"D)"1),("iv)"Im (4//3a),"E)"pi//3),(,"F)"2sqrt(3)):} Correct match is

A lottery sells n^(2) tickets and declares n prizes. If a man purchases n tickets, the probability of his winning exactly one prize is ……

Find the number of words that can be formed by taking all the letters of the word "QUESTION' such that Q, N are separated exactly by 2 letters

Find the number of words that can be formed by taking all the letters of the word "QUESTION' such that Q, N are separated by atmost 4 letters

If AB =3hati-2hatj+2hatk and BC=-hatj-2hatk are adjacent sides of a parallelogram, then angle its diagonals can be

bar(a)=2hati+hatj-2hatk and bar(b)=hati+hatj. The vector bar( c ) is such that bar(a)*bar( c )=|bar( c )|,|bar( c )-bar(a)|=2sqrt(2) and the angle between bar(a)xx bar(b) and bar( c ) is 30^(@) then |(bar(a)xx bar(b))xx bar( c )| = …………

Evaluation of definite integrals by subsitiution and properties of its : int(dx)/(sqrt(2x-x^(2)))=..........+C

Let f(x) = {{:((cos x-e^(x^(2)//2))/(x^(3))",",x ne 0),(0",",x = 0):}, then Statement I f(x) is continuous at x = 0. Statement II lim_(x to 0 )(cos x-e^(-x^(2)//2))/(x^(3)) = - (1)/(12)

if Sigma_(i=1)^(4)(x_(i)^(2)+y_(i)^(2))le 2x_1x_3+2x_2x_4+2y_2y_3+2y_1y_4, the points (x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4) are

int_(-1)^(1)(x+1)dx.

Let f (x) = x |x| and g (x) = sin x Statement -1 g^(@) f is differentiable at x =0 and its derivative is continous at that point Statement -2 g ^(@)f is twice differentiable at x =0.

Determine if A sub B or A cancel sub B where A=|a,b,c|,B ={|a|,|b|,|c|}

(2+5omega +2 omega^2)^6=(2+2omega+5 omega^2)^6=729

If the coefficient of the 2^(nd),3^(rd) and 4^(th) terms in the expansion of (1 + x)^(n) are in A.P, then n=

int_(0)^(1)(x^(3))/((1+x^(2))^(3))dx=

Obtain the following integrals : int (x^((1)/(2)))/(1+x^((3)/(4)))dx

Differentiate the functions given in Exercises 1 to 11 w.r.t. x. x^(cos x)+(x^(2)+1)/(x^(2)-1).

If a, b, c are in AP then ax + by + c = 0 will always pass through a fixed point whose coordinates are