28278 + Interview Questions in Maths in Class 12

1.	Solution set of sqrt(3 - x) = - x^(2) - x - 1 , x in R is
Answer» `(- 1 , INFTY)` (0,1) `(-1,3//4)` `PHI` ANSWER :D

Discussion

2.	Consider a plane prod:vecr(2hati+hatj-hatk)=5, a line L_(1): vecr=(3hati-hatj+2hatk)+lambda(2hati-3hatj-hatk)and a point a(3, -4, 1)L_(2)is a line passing through A intersecting L_(1) and parallel to plane prod. Q.Line L_(1) intersects plane prod at Q and xy-plane at R the volume of tetrahedron OAQR is : (where 'O' is origin)
Answer» 0 `(14)/(3)` `(3)/(7)` `(7)/(3)` ANSWER :D

Discussion

3.	Show that the area under the curve y = sin xandy = sin 2x between x = 0 and x = ( pi)/( 3)andx -axis are as 2:3
Answer» ANSWER :`:. A _(1) : A_(2) = 2:3`

Discussion

4.	Consider a plane prod:vecr(2hati+hatj-hatk)=5, a line L_(1): vecr=(3hati-hatj+2hatk)+lambda(2hati-3hatj-hatk)and a point a(3, -4, 1)L_(2)is a line passing through A intersecting L_(1) and parallel to plane prod. Q.Plane containing L_(1) and L_(2) is :
Answer» PARALLEL to yz-plane parallel to x-axis parallel to y-axis PASSING through ORIGIN ANSWER :B

Discussion

5.	Consider a plane prod:vecr(2hati+hatj-hatk)=5, a line L_(1): vecr=(3hati-hatj+2hatk)+lambda(2hati-3hatj-hatk)and a point a(3, -4, 1)L_(2)is a line passing through A intersecting L_(1) and parallel to plane prod. Q.Equation of L_(2) is :
Answer» `vecr=(1+LAMBDA)hati+(2-3lambda)hatj+(1-lambda)hatk:lambda in R` `vecr=(3+lambda)hati-(4-2lambda)hatj+(1+3lambda)hatk, lambda in R` `vecr=(3+lambda)hati-(4+3lambda)hatj+(1-lambda)hatk, lambda in R` None of the above ANSWER :C

Discussion

6.	A box contains N coins, m of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is 1/2, while it is 2/3 when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows heads and the second time it shows tails. The probability that the coin drawn is fair is
Answer» `(9M)/(8N+m)` `(9m)/(N+8m)` `(4M)/(8N+m)` `(4m)/(N+8m)` ANSWER :A

Discussion

7.	The solution of 2y cos y^(2) (dy)/(dx) - (2)/(x +1) sin y^(2) = (x + 1)^(3) is
Answer» `SIN y^(2) = (x + 1)^(2) [(x + 1)^(2) + c]` `sin y^(2) = (x +1)^(2) [(x + 1)^(2)//2 + c]` `sin y^(2) = (x + 1)^(2) [(x + 1)^(3)//3+ c]` `sin y^(2) = (x + 1)^(2) [(x + 1)^(4)//4+ c]` Answer :B

Discussion

8.	int(dx)/(1-sinx+cosx)=
Answer» `LOG\|(TAN((X)/(2))+1)\|+C` `-log\|(tan((x)/(2))+1)\|+c` `log\|(tan((x)/(2))-1)\|+c` `-log\|(tan((x)/(2))-1)\|+c` Answer :D

Discussion

9.	The locus of the points of intersection of tangents to the hyperbolax^(2) - y^(2) =a^(2) which include an angle of45^(@)is
Answer» ` (X^(2) + y^(2) )^(2) =4A^(2) (x^(2) + y^(2) +a^(2))` ` (x^(2) +y^(2) )^(2) = 4a^(2) (x^(2) -y^(2) +a^(2))` ` (x^(2) +y^(2)) ^(2) =4a^(2) (y^(2) -x^(2) +a^(2))` ` (x^(2) +y^(2) )^(2) =4a^(2) (x^(2) +y^(2) -a^(2))` ANSWER :C

Discussion

10.	Prove that the function f: N to Y defined by f(x) = x^(2), where y = {y : y = x^(2) , x in N} is invertible. Also write the inverse of f(x).
Answer» ANSWER :`F^(-1) (X) = SQRT(x)` OR `f^(-1) = sqrt(x)`.

Discussion

11.	Let (2x^(2)+3x+4)^(10)=sum_(r=0)^(20)a_(r )x^(r ), then the value of (a_(7))/(a_(13)) is
Answer» `6` `8` `12` `16` Solution :`(b)` Given `(2x^(2)+3x=4)^(10)=sum_(R=0)^(20)a_(r )x^(r )` Replacing `x` by `(2)/(x)`, we get `((8)/(x^(2))+(6)/(x)+4)^(10)=sum_(r=0)^(20)a_(r )((2)/(x))^(r )` `implies2^(10)(2x^(2)+3x+4)^(10)=sum_(r=0)^(20)a_(r )2^(r )x^(20-r)` `impliessum_(r=0)^(20)a_(r )x^(r )=sum_(r=0)^(20)a_(r )2^(r-10)x^(20-r)` Comparing coefficient `x^(7)` both SIDES , we get `a_(7)=a_(13)xx2^(3)`.

Discussion

12.	If x_(1) and x_(2) are the roots of the equation sqrt(2010)x^(log_(2010^(x))) = x^(2), then find the cyphers at the end of the product (x_(1)x_(2)).
Answer» ANSWER :`017`

Discussion

13.	Show that the tangent to the curve x^(2)(x^(2)-1)=cy^(2)c, c is a constant, P(x, y) cuts the y - axis at (0, y^(3)).
Answer» ANSWER :`CY^(2)`.

Discussion

14.	If z=(x+iy) and if the point P in the Argarand plane represent z, then desrcibe geo-metrically the locus of P satispfying the equation. \|z\|^(2) 4 Re (z+2)
Answer» a straight LINE an ELLIPSE a parabola a CIRCLE ANSWER :D

Discussion

15.	The point of intersection of the tangents at t_(1) and t_(2) to the parabola y^(2)=12x is
Answer» `[2t_(1)t_(2),2(t_(1)-t_(2))]` `[3t_(1)t_(2),3(t_(1)-t_(2))]` `[3t_(1)t_(2),3(t_(1)+t_(2))]` `[2t_(1)t_(2),2(t_(1)+t_(2))]` ANSWER :C

Discussion

16.	Find the values of x, y, z if the matrixA=[(0, 2y,z),(x,y,-z),(x,-y,z)] satisfy the equation A'A=I.
Answer» ANSWER :`x= PM (1)/(sqrt(2)), y=pm (1)/(sqrt(6)), z=pm (1)/(sqrt(3))`

Discussion

17.	Using the letters of the word 'RAM' 5 letter words are formed in such a way R, A, M each appears atleast once in each word. If a word is selected from these words find the probability that A appears exactly once in the selected word.
Answer» ANSWER :`(7)/(15)`

Discussion

18.	lim_(xto oo)(sqrt(x))/(sqrt(x+sqrt(x+sqrt(x))))
Answer» 1 0 `1/3` `1/sqrt(3)` ANSWER :A

Discussion

19.	If maximum value of int _(0)^(1) (f (x ))^(2) dx under the condition -1 le f (x) le 1, int _(0)^(1) f (x) dx -0 is (p)/(q) (where p and q are relatively prime positive integers). Find p+q.
Answer» ANSWER :5

Discussion

20.	Which of the given values of x and y make the following pair of matrices equal [(3x+7,5),(y+1,2-3x)],[(0,y-2),(8,4)]a) x= -(1)/(3), y=7b) Not possible to find c) y=7, x= -(2)/(3)d) x= -(1)/(3), y= -(2)/(3)
Answer» `x= -(1)/(3), y=7` Not POSSIBLE to FIND `y=7, x= -(2)/(3)` `x= -(1)/(3), y= -(2)/(3)` SOLUTION :N/A

Discussion

21.	There are 10 intermediate stations on a railway line between two particular stations. The number of ways that a train can be made to stop at 3 of these intermediate stations so that no twoof these halting stations are consecutive is
Answer» 56 20 126 120 Answer :A

Discussion

22.	Find the unit vectors perpendicular to the vectors. 2hati+3hatk, hati-2hatj
Answer» SOLUTION : `\|VECAXXVECB\| = SQRT(36+9+16) = sqrt(61)` therefore `HATN = +-(vecaxxvecb)/\|vecaxxvecb\| = +-(6hati+3hatj-4hatk)/sqrt(61)`.

Discussion

23.	Integrate the following functions (logx)^2/x
Answer» SOLUTION :PUT logx = t Then DT = 1/x dx THEREFORE` int (logx)^2/x dx = int t^2 dt = t^3/3 +c` =`(logx)^3/3 +c`

Discussion

24.	If z_(1), z_(2), z_(3) are affixes of the vertices A, B and C respectively of a triangle ABC having centroid at G such that z = 0 is the mid point of AG, then
Answer» `z_(1)+z_(2)+z_(3)=0` `z_(1)+4z_(2)+z_(3)=0` `z_(1)+z_(2)+4z_(3)=0` `4z_(1)+z_(2)+z_(3)=0` ANSWER :D

Discussion

25.	If (1+x -2x^2)^8 =1 -a_1x + a_2x^2+……+a_16x^16,then a_2+a_4+a_6+……+a_16=
Answer» 120 123 127 231 Answer :C

Discussion

26.	If p is the length of the perpendicular from the origin to the line whose intercepts will the coordinate axes are (1)/(3) and (1)/(4) then the value of p is
Answer» `(3)/(4)` `(1)/(12)` 5 `(1)/(5)` Answer :D

Discussion

27.	If the probability distribution of a random variable X is given by
Answer» `3` `9/4` `3/2` `3/4` ANSWER :D

Discussion

28.	If x is real and k = (x^2 - x+1)/(x^2 + x +1) then
Answer» `1/3 LE `K `le 3` `k GE 5` `k le 0` none Answer :A

Discussion

29.	All of the following has the same set of unique prime factors EXCEPT:
Answer» 420 490 560 700 Answer :A

Discussion

30.	Differentiate w.r.t.x the function (5x)^( 3 cos 2x)
Answer» ANSWER :`(5x)^(3 cos 2x)[(3 cos 2x)/(X)-6 SIN 2x log 5x]`

Discussion

31.	Integrate the following functions ((x+1)(x+logx)^2)/x
Answer» Solution :`((x+1)(x+logx)^2)/x` `(1+1/x)(x+logx)^2` LET t = x+logx. Then DT = (1+1/x)DX therefore `int ((x+1)(x+logx)^2)/x dx = int t^2 dt` `t^3/3 +C = (x+logx)^3/3 +c`

Discussion

32.	Evaluate: int(dx)/((x-1)xsqrt(x^(2)-1)
Answer» Solution :`INT(dx)/((x-1)xsqrt(x^(2)-1)) ("put" x-1=1/t rArr dx=-1/t^(2)DT)` `rArr I=int(-1/t^(2)dt)/(1/2sqrt(1/t+1)^(2)-(1/t+1)-1) = int(-dt)/SQRT(-t^(2)+t+1) = int(-dt)/sqrt(sqrt(5)/(2))^(2)-(t-1/2)^(2)` `=-sin^(-1)(t-1/2)/(sqrt(5)/2) + C=-sin^(-1)(2t-1)/(sqrt(5))+C`, where `t=1/(x-1)`

Discussion

33.	A bag contains 3 white and black balls. A person draws 3 balls at random from it. He then drops 3 red balls in the bag and again draws out 3 balls at random. What is the chance that the later 3 balls will be of different colours.
Answer» ANSWER :`(27)/(100)`

Discussion

34.	Which of the following is/are redox reaction.
Answer» `KCl + K_(2) Cr_(2)O_(7) to con.H_(2)SO_(4) to CrO_(2)Cl_(2) +K_(2)SO_(4) +H_(2)O` `K_(2) cr_(2)O_(7) + H_(2) O_(2) + dil.H_(2)SO_(4)+Cr_(2)(SO_(4))_(3) + 7H_(2)O + 3O_(2)` `K_(2) Cr_(2)O_(7) + H_(2)O_(2)+ dil.H_(2)SO_(4) to K_(2)SO_(4)+CR(SO_(4))_(3) + 7H_(2)O+3O_(2)` `K_(2)Cr_(2)O_(7) +2KOH to 2K_(2)CrO_(4) +H_(2)O` Answer :A::B::C

Discussion

35.	Evalute: int_(0)^(pi//2)(x sinx cosx)/(sin^(4)x+cos^(4)x)dx. Or, Eventuate: int_(0)^(4)(x+e^(2x))dx as the limit of a sum.
Answer» ANSWER :`(pi^(2))/(16)` Or, `8+1/2(e^(8)-1)`

Discussion

36.	If a, b, c are real numbers in A.P., then the roots of ax^(2) +bx +c=0 are real for
Answer» all a and C no a and c `\|( c)/(a)-7\| GE 4sqrt(7)` `\|(a)/(c ) +7\| ge 2sqrt(3)` ANSWER :c

Discussion

37.	Which of the following is a null set
Answer» {0} `{x//x gt 0" or "x LT 0}` `{x//x^(2)=4" or "x=3}` `{x//x^(2)+1=0,x in R}` Answer :D

Discussion

38.	Compute the following: [[a,b],[-b,a]][[a,-b],[b,a]]
Answer» SOLUTION :`[[a,B],[-b,a]], [[a,-b],[b,a]]=[[a^2+b^2, -ab+ab],[-ab+ab, b^2+a^2]]=[[a^2+b^2, 0],[0, a^2+b^2]]`

Discussion

39.	Solve the following differential equations. (dy)/(dx)+(3x^(2))/(1+x^(3)) y=(1+x^(2))/(1+x^(3))
Answer» ANSWER :`y(1+X^(3)) = x + (x^(3))/(3) + C`

Discussion

40.	20 persons A_1,A_2….A_(20), are sitting around a circle. In how many ways 7 persons out of them can be selected such that no two of the selected 7 are consecutive and A_1 must always be one among the selected 7.
Answer» ANSWER :924

Discussion

41.	Let z(x,y) =x^(3) - 3x^(2)y^(3), where x = se^(t), y =se^(-t), s, t in R. Find (del z)/(del s) and (del z)/(del t)
Answer» ANSWER :`= 3X ^(2) (E ^(3T) + s^(2) e ^(-t))`

Discussion

42.	If a, b, c in N, the probability that a^(2)+b^(2)+c^(2) is divisible by 7 is (m)/(n) where m, n are relatively prime naturalnumbers, then m + n is equal to :
Answer» ANSWER :8

Discussion

43.	Evaluate: int_(0)^(pi//2) sqrtsinthetacos^(5)theta d theta
Answer» ANSWER :`(64)/(231)` .

Discussion

44.	If (a-b)sin (theta+phi)=(a+b)sin(theta-phi) and a tan. (theta)/(2)-b tan.(phi)/(2)=c, then
Answer» `b tan PHI = a tan theta` `a tan phi = b tan theta` `sin phi=(2bc)/(a^(2)-b^(2)-c^(2))` `sin theta=(2ac)/(a^(2)-b^(2)+c^(2))` Solution :`(a-b)sin(theta+phi)=(a+b)sin(theta-phi)` `rArr (sin(theta+phi))/(sin(theta-phi))=(a+b)/(a-b)` `rArr (sin(theta + phi)+sin(theta-phi))/(sin(theta+phi)-sin(theta-phi))=(2A)/(2b)` `rArr (2sin theta cos phi)/(2 cos theta sin phi)=(a)/(b)=(tan theta)/(tan phi)=(a)/(b)` `rArr b tan theta = a tan phi` `therefore` (b) is TRUE `rArr (2a tan.(phi)/(2))/(1-"tan"^(2)(phi)/(2))=(2b tan.(theta)/(2))/(1-"tan"^(2)(theta)/(2))` `rArr (a((a tan.(theta)/(2)-c)/(b)))/(1-((a tan.(theta)/(2)-c)/(b))^(2))=(b tan.(theta)/(2))/(1-"tan"^(2)(theta)/(2))` `rArr ((a^(2)tan.(theta)/(2)-AC))/(b^(2)-(a^(2)"tan"^(2)(theta)/(2)+c^(2)-2ac tan.(theta)/(2)))` `=(tan.(tehta)/(2))/(1-"tan"^(2)(theta)/(2))` `rArr (a^(2)tan.(theta)/(2)-ac)(1-"tan"^(2)(theta)/(2))` `= b^(2) tan.(theta)/(2)-a^(2)"tan"^(3)(theta)/(2)-c^(2)tan.(theta)/(2)+2 ac "tan"^(2)(theta)/(2)` `= a^(2) tan.(theta)/(2)-ac - a^(2)"tan"^(3)(theta)/(2)+ac "tan"^(2)(theta)/(2)` `rArr b^(2) tan.(theta)/(2)-a^(2)"tan"^(3)(theta)/(2)-c^(2)tan.(thetA)/(2)+2 ac "tan"^(2)(thetA)/(2)` `rArr (a^(2)+c^(2)-b^(2))tan.(theta)/(2)=ac[1+ "tan"^(2)(thetA)/(2)]` `rArr (2 tan.(theta)/(2))/(1+ "Tan"^(2)(thetA)/(2))=(2ac)/(c^(2)+a^(2)-b^(2))` `rArr sin theta = (2ac)/(c^(2)+a^(2)-b^(2))` `rArr sin theta = (2ac)/(c^(2)+a^(2)-b^(2))` Similarly, `sin phi=(2bc)/(a^(2)-b^(2)-c^(2))`

Discussion

45.	Intergrate the following: intsin4x cos3xdx
Answer» SOLUTION :`intsin4x cos3xdx` =`1/2 int2sin4x .cos3xdx` =`1/2int(sin7x+sinx)DX` =`1/2{-(COS7X)/7-cosx}+C` =-1/14cos7x-1/2 cosx+C

Discussion

46.	If the quadratic equation 4^("sec"^(2)alpha).X^(2)+2x+(beta^(2)-beta+(1)/(2))=0 has real roots , then the value of cos^(2)alpha + cos^(-1)beta is
Answer» `(pi)/(3)` `(pi)/(3)+1` `(pi)/(2)` `(pi)/(2)-1` ANSWER :B

Discussion

47.	D.c.s of a line segment AB are (-2)/(sqrt(17)),(3)/(sqrt(17)),(-2)/(sqrt(17)). If AB=sqrt(17)andA-=(3,-6,10), then co-ordinates of B will be
Answer» `(2,5,8)` `(1,-2,4)` `(1,-3,8)` `(-1,3,-8)` ANSWER :C

Discussion

48.	The sum of 10 terms of the series sqrt(2) + sqrt(6) + sqrt(18) + .... is
Answer» `121(SQRT(6) + sqrt(2)` `243(sqrt(3) + sqrt(1)` `121/(sqrt(3) - 1` `243(sqrt(3) - 1)` Answer :A

Discussion

49.	(""^(m)C_(0) +""^(m) C_(1) -^(m) C_(2)-^(m)C_(3)) + (""^(m) C_(4) + ^(m) C_(5) -^(m)C_(6)-^(m) C_(7))+... = 0 if and only if for some positive integer k, m is equal to
Answer» 4k `4k+1` `4k-1` `4k+2` Solution :If `theta in R and i = SQRT(-1), "then " (cos theta + i sin theta )^(n)` `=^(m)C_(0) (cos theta)^(m) +^(m)C_(1)(costheta)^(m-1) (isin theta)` `+ C_(2)(costheta)^(m-1) (isin theta)^(2)+...+""^(m)C_(m)(isintheta)^(m)` `(cos m theta + isin m theta) = [""^(m)C_(0)(cos theta)^(m)-^(m)C_(2)(cos theta)^(m-2)CDOT sin ^(2) theta +""^(m)C_(4)(costheta)^(m-4)sin^(4) theta - ...] + i [""^(m)C_(1)(cos theta)^(m-1) sin theta -^(m) C_(3) (cos theta)^(m-3)sin^(3) theta +..]` [ using Demovire' s theromem] Comparing real and imaginary parts, we geta `cos mtheta = ^(m)(cos theta)^(m) -^(m) C_(2) (cos theta)^(m-2)sin^(2)theta+^(m)C_(4) (cos theta )^(m-4) sin ^(4) theta - ......(i)` `sin mtheta= ^(m) C_(1) (cos theta)^(m-1) cdot sintheta -^(m) C_(3)(cos theta)^(m-3 )cdot sin^(3) theta + ......(ii) ` On adding Eqs. (i) and (ii), we get `cos m theta + sin m theta = ^(m)C_(0)(costheta)^(m) + C_(1) (costheta)^(m-1)cdot sin theta -^(m) C_(2) (cos theta)^(m-2)sin ^(2) theta-^(m) C_(3)(cos)^(m-3)sin ^(3) theta` `+^(m)C_(4)(costheta)^(m-4)sin^(4)theta + ...sin (mtheta + pi/4)` `=(costheta)^(m){{:(""^(m)C_(0)+^(m)C_(1)tan theta-^(m)C_(2)tan^(2)theta -^(m)C_(3)tan^(3)),(+^(m)C_(4)tan^(4)theta + ^(m) C_(5)tan^(5) theta-...):}} ` Putting `theta=pi/4, sqrt(2)sin (((m+1)pi)/4)=1/2^(m//2)` `{{:((""^(m)C_(0) +^(m) C_(1)-^(m) C_(2)-^(m) C_(3))+(""^(m)C_(4)+^(m) C_(5)-^(m) C_(6)-^(m) C_(7))),(+...+(""^(m)C_(m-3)+^(m) C_(m-2)-^(m) C_(m-1)-^(m) C_(m)) ):}}` `because((""^(m)C_(0) +^(m) C_(1)-^(m) C_(2)-^(m) C_(3))+(""^(m)C_(4)+^(m) C_(5)-^(m) C_(6)-^(m) C_(7))` `therefore sin frac((m+1)pi)(4)=0 rArr ((m+1)pi)/4 = k pi` or `m=4k-1,AAkinI`

Discussion

50.	Find the area enclosed by the circle the ellpise x^(2)/a^(2) + y^(2)/b^(2) = 1
Answer» ANSWER :`piab`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Solution set of sqrt(3 - x) = - x^(2) - x - 1 , x in R is

Show that the area under the curve y = sin xandy = sin 2x between x = 0 and x = ( pi)/( 3)andx -axis are as 2:3

Consider a plane prod:vecr*(2hati+hatj-hatk)=5, a line L_(1): vecr=(3hati-hatj+2hatk)+lambda(2hati-3hatj-hatk)and a point a(3, -4, 1)*L_(2)is a line passing through A intersecting L_(1) and parallel to plane prod. Q.Plane containing L_(1) and L_(2) is :

Consider a plane prod:vecr*(2hati+hatj-hatk)=5, a line L_(1): vecr=(3hati-hatj+2hatk)+lambda(2hati-3hatj-hatk)and a point a(3, -4, 1)*L_(2)is a line passing through A intersecting L_(1) and parallel to plane prod. Q.Equation of L_(2) is :

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The locus of the points of intersection of tangents to the hyperbolax^(2) - y^(2) =a^(2) which include an angle of45^(@)is

Prove that the function f: N to Y defined by f(x) = x^(2), where y = {y : y = x^(2) , x in N} is invertible. Also write the inverse of f(x).

Let (2x^(2)+3x+4)^(10)=sum_(r=0)^(20)a_(r )x^(r ), then the value of (a_(7))/(a_(13)) is

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Show that the tangent to the curve x^(2)(x^(2)-1)=cy^(2)c, c is a constant, P(x, y) cuts the y - axis at (0, y^(3)).

If z=(x+iy) and if the point P in the Argarand plane represent z, then desrcibe geo-metrically the locus of P satispfying the equation. |z|^(2) 4 Re (z+2)

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Find the values of x, y, z if the matrixA=[(0, 2y,z),(x,y,-z),(x,-y,z)] satisfy the equation A'A=I.

Using the letters of the word 'RAM' 5 letter words are formed in such a way R, A, M each appears atleast once in each word. If a word is selected from these words find the probability that A appears exactly once in the selected word.

lim_(xto oo)(sqrt(x))/(sqrt(x+sqrt(x+sqrt(x))))

If maximum value of int _(0)^(1) (f (x ))^(2) dx under the condition -1 le f (x) le 1, int _(0)^(1) f (x) dx -0 is (p)/(q) (where p and q are relatively prime positive integers). Find p+q.

Which of the given values of x and y make the following pair of matrices equal [(3x+7,5),(y+1,2-3x)],[(0,y-2),(8,4)]a) x= -(1)/(3), y=7b) Not possible to find c) y=7, x= -(2)/(3)d) x= -(1)/(3), y= -(2)/(3)

There are 10 intermediate stations on a railway line between two particular stations. The number of ways that a train can be made to stop at 3 of these intermediate stations so that no twoof these halting stations are consecutive is

Find the unit vectors perpendicular to the vectors. 2hati+3hatk, hati-2hatj

Integrate the following functions (logx)^2/x

If z_(1), z_(2), z_(3) are affixes of the vertices A, B and C respectively of a triangle ABC having centroid at G such that z = 0 is the mid point of AG, then

If (1+x -2x^2)^8 =1 -a_1x + a_2x^2+……+a_16x^16,then a_2+a_4+a_6+……+a_16=

If p is the length of the perpendicular from﻿ the origin to the line whose intercepts will﻿ the coordinate axes are (1)/(3) and (1)/(4) then the﻿ value of p is

If the probability distribution of a random variable X is given by

If x is real and k = (x^2 - x+1)/(x^2 + x +1) then

All of the following has the same set of unique prime factors EXCEPT:

Differentiate w.r.t.x the function (5x)^( 3 cos 2x)

Integrate the following functions ((x+1)(x+logx)^2)/x

Evaluate: int(dx)/((x-1)xsqrt(x^(2)-1)

A bag contains 3 white and black balls. A person draws 3 balls at random from it. He then drops 3 red balls in the bag and again draws out 3 balls at random. What is the chance that the later 3 balls will be of different colours.

Which of the following is/are redox reaction.

Evalute: int_(0)^(pi//2)(x sinx cosx)/(sin^(4)x+cos^(4)x)dx. Or, Eventuate: int_(0)^(4)(x+e^(2x))dx as the limit of a sum.

If a, b, c are real numbers in A.P., then the roots of ax^(2) +bx +c=0 are real for

Which of the following is a null set

Compute the following: [[a,b],[-b,a]][[a,-b],[b,a]]

Solve the following differential equations. (dy)/(dx)+(3x^(2))/(1+x^(3)) y=(1+x^(2))/(1+x^(3))

20 persons A_1,A_2….A_(20), are sitting around a circle. In how many ways 7 persons out of them can be selected such that no two of the selected 7 are consecutive and A_1 must always be one among the selected 7.

Let z(x,y) =x^(3) - 3x^(2)y^(3), where x = se^(t), y =se^(-t), s, t in R. Find (del z)/(del s) and (del z)/(del t)

If a, b, c in N, the probability that a^(2)+b^(2)+c^(2) is divisible by 7 is (m)/(n) where m, n are relatively prime naturalnumbers, then m + n is equal to :

Evaluate: int_(0)^(pi//2) sqrtsinthetacos^(5)theta d theta

If (a-b)sin (theta+phi)=(a+b)sin(theta-phi) and a tan. (theta)/(2)-b tan.(phi)/(2)=c, then

Intergrate the following: intsin4x cos3xdx

If the quadratic equation 4^("sec"^(2)alpha).X^(2)+2x+(beta^(2)-beta+(1)/(2))=0 has real roots , then the value of cos^(2)alpha + cos^(-1)beta is

D.c.s of a line segment AB are (-2)/(sqrt(17)),(3)/(sqrt(17)),(-2)/(sqrt(17)). If AB=sqrt(17)andA-=(3,-6,10), then co-ordinates of B will be

The sum of 10 terms of the series sqrt(2) + sqrt(6) + sqrt(18) + .... is

(""^(m)C_(0) +""^(m) C_(1) -^(m) C_(2)-^(m)C_(3)) + (""^(m) C_(4) + ^(m) C_(5) -^(m)C_(6)-^(m) C_(7))+... = 0 if and only if for some positive integer k, m is equal to

Find the area enclosed by the circle the ellpise x^(2)/a^(2) + y^(2)/b^(2) = 1

Consider a plane prod:vecr(2hati+hatj-hatk)=5, a line L_(1): vecr=(3hati-hatj+2hatk)+lambda(2hati-3hatj-hatk)and a point a(3, -4, 1)L_(2)is a line passing through A intersecting L_(1) and parallel to plane prod. Q.Plane containing L_(1) and L_(2) is :

Consider a plane prod:vecr(2hati+hatj-hatk)=5, a line L_(1): vecr=(3hati-hatj+2hatk)+lambda(2hati-3hatj-hatk)and a point a(3, -4, 1)L_(2)is a line passing through A intersecting L_(1) and parallel to plane prod. Q.Equation of L_(2) is :

If p is the length of the perpendicular from the origin to the line whose intercepts will the coordinate axes are (1)/(3) and (1)/(4) then the value of p is