28278 + Interview Questions in Maths in Class 12

1.	Findangle between two lines, one of which has direction ratios lt2,2,1gtwhile theother one is obtained by joining the points (3, 1, 4) and (7,2, 12).
Answer» SOLUTION :N/A

Discussion

2.	Find X and Y, if (i) X+Y=[(7,0),(2,5)] and X-Y=[(3,0),(0,3)] (ii) 2X+3Y=[(2,3),(4,0)] and 3X+2Y=[(2,-2),(-1,5)]
Answer» ANSWER :`(i) X=[(5,0),(1,4)], Y=[(2,0),(1,1)] (ii) X=[((2)/(5), (-12)/(5)),((-11)/(5),3)],Y=[((2)/(5),(13)/(5)),((14)/(5), -2)]`

Discussion

3.	Find absolute maximum and minimum values of a function f given byf(x)=12x^((4)/(3))-6x^((1)/(3)), x in [-1, 1]
Answer» Answer :FUNCTION f has GLOBAL maximum value 18 at `x=-1` and global minimum value `-(9)/(4)` at `x=(1)/(8)`

Discussion

4.	A plane passing through a point (1, 2, 2) and is perpendicular to two planes 2x-2y+z=0 and x-y+2z=4. Square of the distance of the plane from the point (2, 5, 18) is_________
Answer» ANSWER :`8.00`

Discussion

5.	Given that the events A and B are such that P(A)= (1)/(2),P( A cap B)= (3)/(5). And P(B )= p. Find p if they are (i) mutually exclusive (ii) independent.
Answer» <P> Answer :(i) `p= (1)/(10)` (ii)` p= (1)/(5)`

Discussion

6.	Observe the following statements for the curve x=a( cos t + log tan 1/2), y=a sin t I : Slope of the tangent at any point is tant II : Length of the tangent at any point is constant III : Length of the sub-tangent at any point is \| a cos t\|
Answer» only I,II are true only II,III are true only I,III are true I,II,III are true Answer :D

Discussion

7.	x=a sin t and y= a (cos t + log "tan"(t)/(2)) then find (d^(2)y)/(dx^(2)).
Answer» ANSWER :`-(COSEC^(2) t)/(4 COS t)`

Discussion

8.	Without expanding the determinant, Prove that \|[a,a^2, bc],[b,b^2,ca],[c,c^2,ab]\|= \|[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]\|
Answer» SOLUTION :L.H.S.`=1/(ABC)\|[a^2,a^3,abc],[b^2,b^3,abc],[c^2,c^3,abc]\|=1/(abc)(abc)\|[a^2,a^3,1],[b^2,b^3,1],[c^2,c^3,1]\|=\|[a^2,a^3,1],[b^2,b^3,1],[c^2,c^3,1]\|` `=\|[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]\|` (by `C_2 harrC_3`and then by `C_1harrC_2`)=R.H.S.

Discussion

9.	If one root of 24x^(3) + 46x^(2) + 9x - 9 = 0 is the double the other then the roots are
Answer» `-1, 1//2, 1 ` 2, 2, - 1 3/4, 3/2 , -5/3 `-3//2, -3//4, 1//3` ANSWER :4

Discussion

10.	If a random variable X has the probability distrbution given by P(X = 0) = 2 C^(3), P(X= 2) = 5 C - 10C^(2) and P(X= 4) = 4 C - 1, then the variance of that distribution is
Answer» `68/9` `22/9` `612/81` `128/81` ANSWER :D

Discussion

11.	Evaluate: int(x^4\ dx)/((x-1)(x^2+1))
Answer» ANSWER :`1/2`

Discussion

12.	For all real values of m' the straight line y=mx + sqrt(9m^(2)-4) is a tangent to the curve
Answer» `9x^(2)+4y^(2)=36` `4x^(2)+9Y^(2)=36` `9x^(2)-4y^(2)=36` `4x^(2)-9y^(2)=36` ANSWER :D

Discussion

13.	If f(9x)=ax^(2)+bx+c, how must a and b be related so that the graph of f(x-3) will be symmetric about the y-axis?
Answer» a=B b=0, a is any real number b=3a b=6a Solution :The graph of the function is a PARABOLA, and the equation of its axis of symmetry is `x=-(b)/(2a)`. Since the graph of `y=f(x-3)` is the translation of `y=f(x)` 3 UNITS to the right, `f(x-3)` will be SYMMETRIC about the y-axis when f(x) is symmetric about -3. THEREFORE, `-(b)/(2a)=-3`, or `b=6a`.

Discussion

14.	Let the function f : [-4,4] to [-1, 1] be defined impicity by the equatin x +5y - y^(5)=0 If the area of triangle formed by tangent and normal to f (x) at x=0 and the line y =5 is A, find (A)/(13).
Answer» ANSWER :5

Discussion

15.	Find (dy)/(dx) in the following : sin^(2)x + cos^(2) y=1.
Answer» ANSWER :`(SIN 2X)/(sin 2Y)`.

Discussion

16.	lim_(ntooo)sum_(r=1)^(n)tan^(-1)((2r)/(r^(4)+r^(2)+2))=
Answer» `PI/4` `pi/2` `(-pi)/4` `(-pi)/2` ANSWER :A

Discussion

17.	16 cos^6 10^@-24cos^4 10^@ +9 cos^2 10^@ is equal to
Answer» `1/4` `3/4` `1/2` 1 Solution :Given expression =`(4 cos^3 10^@ - 3cos10^@)^2` `=(cos30^@)^2` `=3/4`

Discussion

18.	To remove the first degree terms in the following equation origin should be shifted to the another point then calculate the new origins is
Answer» d,B,a,C e,c,b,d c,b,d,a d,c,b,a Answer :C

Discussion

19.	The marks of some students were listed out of 75. The S.D. marks was found to be 9. Subsequently the marks were raised to a maximum of 100 and variance of new marks was calculated. The new variance is
Answer» 144 122 81 75 Answer :A

Discussion

20.	The feasible region for an LLP is shown in the Figure. Let z = 3x - 4y be the objective function. Minimum value of z is
Answer» 0 -16 12 does not exist Answer :B

Discussion

21.	If \|veca\|=2, \|vecb\|=7 and vecaxxvecb=3hati-2hatj+6hatk find the angle between veca and vecb.
Answer» `(i) (PI)/(6) ``(ii)(pi)/(4)`` (ii)(pi)/(3) `` (iv)(pi)/(2) ` ANSWER :a

Discussion

22.	Integrate the functions ((x-3))/((x-1)^(3))
Answer»

Discussion

23.	int(dx)/(sin^(2)xcos^(2)x) equals
Answer» `tanx+cotx+C` `tanx-cotx+C` `tanxcotx+C` `tanx-cot2x+C` ANSWER :B

Discussion

24.	Integrate the functions sin(ax+b)cos(ax+b)
Answer» ANSWER :`-1/(4A)COS2(ax+b)+C`

Discussion

25.	If p(q-r)x^(2) + q(r-p) x+ r(p-q) = 0 has equal roots, then (2)/(q)=
Answer» <P>`(1)/(p)+ (1)/(R)` `(1)/(p)- (1)/(r)` `(1)/(r)- (1)/(p)` `(1)/(PR)` ANSWER :A

Discussion

26.	Find the points at which the function f given by f (x) = (x-2)^(4)(x+1)^(3) has (i) local maxima (ii) local minima (iii) point of inflexion
Answer» Answer :local MAXIMA at `x=(2)/(7) ` (II) local MINIMA at x =2(iii) POINT of inflection at x = –1

Discussion

27.	Evaluate the following integrals: int (x^3 +3x +4)/sqrtx dx
Answer» SOLUTION :`int (X^3+3x+4)/sqrtx DX = int (x^3/sqrtx + (3x)/sqrtx + 4/sqrtx) dx` =`int(x^(3-1/2) +3sqrtx+4/sqrtx)dx = int(x^(5/2) + 3x^(1/2) +4/sqrtx) dx` =`x^(5/2+1)/(5/2+1) +3x^(1/2+1)/(1/2+1) + 4xx2sqrtx+C` =`x^(7/2)/(7/2) +(3x^3/2))/(3/20 + 8sqrtx +c = (2x^(7/2)/7 + 2x^93/2) + 8sqrtx+c`

Discussion

28.	Evaluate the following (ii) int_(-2)^(2)[x]dx
Answer» ANSWER :-2

Discussion

29.	If vertices are (2, -2), (2, 4) and e = 1/3 then equation of the ellipse is
Answer» `(x-2)^(2)/(8)+(y-1)^(2)/(18)=1` `(x-2)^(2)/(16)+(y-1)^(2)/(9)=1` `(x-2)^(2)/(8)+(y-1)^(2)/(9)=1` `(x-2)^(2)/(9)+(y-1)^(2)/(8)=1` Answer :D

Discussion

30.	Show that the general solution of the differential equation (dy)/(dx) + (y^(2) + y + 1)/(x^(2) + x + 1) = 0 isgiven by ( x + y + 1) = A(1 - x - y - 2xy), where A is parameter.
Answer»

Discussion

31.	Let A_(1) = int_(0)^(x)(int_(0)^(u)f(t)dt) dt and A_(2) = int_(0)^(x)f(u).(x-u) then (A_(1))/(A_(2)) is equal to :
Answer» `1/2` 1 2 `-1` SOLUTION :N//A

Discussion

32.	Ifx + (1)/(x )=2sinalpha , y +(1)/(y) =2cosbeta,thenx^3y^3 + (1)/( x^3 y^3)is
Answer» A. `2 cos3( BETA= alpha )` B. ` 2 cos3( beta+ alpha )` C. ` 2 SIN3 ( beta- alpha )` D. `2 sin 3 ( beta+ alpha )` Answer :C

Discussion

33.	Consider f(x)=x^2-3x+2 The area bounded by \|y\|=\|f(\|x\|)\|,xge1 is A, then find the value of 3A+2.
Answer» ANSWER :7

Discussion

34.	hati(hatkxx hatj)+hatj(hati xx hatk)+hatk(hatj xx hati)+hati(hati xx hatj)+hatj*(hatj xx hatk) = ………..
Answer» `-1` 1 3 `-3` ANSWER :D

Discussion

35.	If \|(2+x,x,x^(2)),(x,2+x,x^(2)),(x^(2),x,2+x)\|=(1)/(6)(x-a)(x-b)(x-c)(x-d) an identity in x where a, b, c, d are independent of x, then the value of (13)/(25)abcd is
Answer» ANSWER :24.96

Discussion

36.	The value of a for which the system linear of equations x+ay+z=1 ax+y+z=1 x+y+az=3 has no solution is :
Answer» 1 `-1` 2 `-2` ANSWER :D

Discussion

37.	For any vector vec(a),(vec(a)xx vec(i))^(2)+(vec(a)xx hatj)^(2)+(vec(a)xx vec(k))^(2)= ……….. .
Answer» `4A^(2)` `2a^(2)` `a^(2)` `3A^(2)` Answer :B

Discussion

38.	If cos^(-1)2x+cos ^(-1)3x=(pi)/(3), " then "x=
Answer» `(SQRT(3))/(2sqrt(7))` `(sqrt(3))/(sqrt(7))` `(sqrt(2))/(sqrt(5))` `(sqrt(3))/(2sqrt(5))` Answer :A

Discussion

39.	There are two types of fertilizers F_(1) and F_(2).F_(1) consists of 10% nitrogen and 6% phosphoricacid and F_(2)contains 5% nitrogen and 10% phosphoric acid. After testing the soil condition a farmer finds that he needs at least 14 kg of nitrogen and 14 kg of phosphoric acid forhis crop. If F_(1)costs Rs. 6 per kg and F_(2) costsRs. 5 perkg, determine how muchofeach of fertilizers beused so that nutrient requirements are met at a minimum cost. What is the minimum cost?
Answer» SOLUTION :N/A

Discussion

40.	Find the angle between the lines whose direction ratios are proportional to a,b,c and b-c,c-a,a-b,.
Answer» Solution :The ANGLE `THETA` between the lines is GIVEN by `costheta=(a(b-C)+b(c-a)+c(a-b))/(sqrt(a^2+b^2+c^2)sqrt((b-c)^2+(c-a)^2+(a-c)^2))` =0 `ifftheta=pi/2`

Discussion

41.	The shadow of a tower standing on a level ground is x metres long when the sun's altitude is 30^(@), while it is y metres long when the altitude is 60^(@). If the height of the tower is 45. (sqrt3)/(3) meters, then x -y is :
Answer» 30 METERS `45sqrt3` meters `(45)/(SQRT3)` meters `45. (sqrt3)/(2)` meters. Answer :A

Discussion

42.	Integrate the functions x^(2)logx
Answer» ANSWER :`(X^(3))/3logx-(x^(3))/9+C`

Discussion

43.	Let vec r = (veca xx vecb) sin x + (vecb + vec c) cos y+ 2 (vec c xx vec a)where veca , vecb , vec care three non coplanar vectors . If vec r is perpendicular to veca + vecb + vec c , the minimum value of x^2 + y^2is
Answer» `pi^2` `(pi^2)/(4)` `(5pi^2)/(4)` NONE of these ANSWER :C

Discussion

44.	Find lambda if the vector hati-lambdahatj+2hatk and 2hati+4hatj are perpendicular to each other .
Answer» ANSWER :`lambda=1//2`

Discussion

45.	Show that the following four points in each jof the following are concyclic and find the equation of the circle on which they lie.(1,-6),(5,2),(7,0),(-1,-4)
Answer» ANSWER :` X^(2) + y ^(2)- 6X + 4Y -7=0 `

Discussion

46.	The value of sum_(0leiltjle5) sum(""^(5)C_(j))(""^(j)C_(i)) is equal to "_____"
Answer» SOLUTION :`UNDERSET(0leiltjle5)(sumsum)(.^(5)C_(j))(.^(j)C_(i))` `=.^(5)C_(1)..^(1)C_(0)+.^(5)C_(2)(.^(2)C_(0)+.^(2)C_(1))+"......"+.^(5)C_(5)(.^(5)C_(0)+.^(5)C_(1)+"...."+.^(5)C_(5))` `= .^(5)C_(1)(2^(1)-1)+.^(5)C_(2)(2^(2)-1)+"....."+.^(5)C_(5)(2^(5)-1)` `= (.^(5)C_(1).2^(1)+.^(5)C_(2).2^(2)+".....".+.^(5)C_(5).2^(5))-(.^(5)C_(1)+.^(5)C_(2)+"...."+.^(5)C_(5))` `= [(1+2)^(5)-1][2^(5)-1]` `= 3^(5)-2^(5)` `= 243-32=211`

Discussion

47.	Let f (x) be a polynomial satisfying lim _(x to oo) (x ^(4) f (x))/( x ^(8) +1)=3 f (2) =5, f(3) =10, f (-1)=2, f (-6)=37The value of lim _(x to -6) (f (x) -x ^(2) -1)/(3 (x+6)) equals to:
Answer» `-\|UNDERSET-(6)` `\|underset-(6)` `(\|underset-(6))/(2)` `(\|underset-(-6))/(2)` ANSWER :D

Discussion

48.	int_(-1)^(1) Sin^(-1) ((x)/(1+x^(2)))dx=
Answer» `pi/4` 0 4 `pi/2` ANSWER :B

Discussion

49.	A,B,C are three horses in a race. The probability of A to win the race is twice that of B and probability of B is twice that of C. What are the probability of A,B and C to win the race?
Answer» ANSWER :`(4)/(7),(2)/(7),(1)/(7)`

Discussion

50.	Show that the following four points in each of the following are concylic and find the equation of the circle on which they lie(9,1 ) ,(7,9 ),( -2,12),(6,10)
Answer» ANSWER :` X^(2) +y^(2) - 6Y -76 =0`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Findangle between two lines, one of which has direction ratios lt2,2,1gtwhile theother one is obtained by joining the points (3, 1, 4) and (7,2, 12).

Find X and Y, if (i) X+Y=[(7,0),(2,5)] and X-Y=[(3,0),(0,3)] (ii) 2X+3Y=[(2,3),(4,0)] and 3X+2Y=[(2,-2),(-1,5)]

Find absolute maximum and minimum values of a function f given byf(x)=12x^((4)/(3))-6x^((1)/(3)), x in [-1, 1]

A plane passing through a point (1, 2, 2) and is perpendicular to two planes 2x-2y+z=0 and x-y+2z=4. Square of the distance of the plane from the point (2, 5, 18) is_________

Given that the events A and B are such that P(A)= (1)/(2),P( A cap B)= (3)/(5). And P(B )= p. Find p if they are (i) mutually exclusive (ii) independent.

Observe the following statements for the curve x=a( cos t + log tan 1/2), y=a sin t I : Slope of the tangent at any point is tant II : Length of the tangent at any point is constant III : Length of the sub-tangent at any point is | a cos t|

x=a sin t and y= a (cos t + log "tan"(t)/(2)) then find (d^(2)y)/(dx^(2)).

Without expanding the determinant, Prove that |[a,a^2, bc],[b,b^2,ca],[c,c^2,ab]|= |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

If one root of 24x^(3) + 46x^(2) + 9x - 9 = 0 is the double the other then the roots are

If a random variable X has the probability distrbution given by P(X = 0) = 2 C^(3), P(X= 2) = 5 C - 10C^(2) and P(X= 4) = 4 C - 1, then the variance of that distribution is

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

For all real values of m' the straight line y=mx + sqrt(9m^(2)-4) is a tangent to the curve

If f(9x)=ax^(2)+bx+c, how must a and b be related so that the graph of f(x-3) will be symmetric about the y-axis?

Let the function f : [-4,4] to [-1, 1] be defined impicity by the equatin x +5y - y^(5)=0 If the area of triangle formed by tangent and normal to f (x) at x=0 and the line y =5 is A, find (A)/(13).

Find (dy)/(dx) in the following : sin^(2)x + cos^(2) y=1.

lim_(ntooo)sum_(r=1)^(n)tan^(-1)((2r)/(r^(4)+r^(2)+2))=

16 cos^6 10^@-24cos^4 10^@ +9 cos^2 10^@ is equal to

To remove the first degree terms in the following equation origin should be shifted to the another point then calculate the new origins is

The marks of some students were listed out of 75. The S.D. marks was found to be 9. Subsequently the marks were raised to a maximum of 100 and variance of new marks was calculated. The new variance is

The feasible region for an LLP is shown in the Figure. Let z = 3x - 4y be the objective function. Minimum value of z is

If |veca|=2, |vecb|=7 and vecaxxvecb=3hati-2hatj+6hatk find the angle between veca and vecb.

Integrate the functions ((x-3))/((x-1)^(3))

int(dx)/(sin^(2)xcos^(2)x) equals

Integrate the functions sin(ax+b)cos(ax+b)

If p(q-r)x^(2) + q(r-p) x+ r(p-q) = 0 has equal roots, then (2)/(q)=

Find the points at which the function f given by f (x) = (x-2)^(4)(x+1)^(3) has (i) local maxima (ii) local minima (iii) point of inflexion

Evaluate the following integrals: int (x^3 +3x +4)/sqrtx dx

Evaluate the following (ii) int_(-2)^(2)[x]dx

If vertices are (2, -2), (2, 4) and e = 1/3 then equation of the ellipse is

Show that the general solution of the differential equation (dy)/(dx) + (y^(2) + y + 1)/(x^(2) + x + 1) = 0 isgiven by ( x + y + 1) = A(1 - x - y - 2xy), where A is parameter.

Let A_(1) = int_(0)^(x)(int_(0)^(u)f(t)dt) dt and A_(2) = int_(0)^(x)f(u).(x-u) then (A_(1))/(A_(2)) is equal to :

Ifx + (1)/(x )=2sinalpha , y +(1)/(y) =2cosbeta,thenx^3y^3 + (1)/( x^3 y^3)is

Consider f(x)=x^2-3x+2 The area bounded by |y|=|f(|x|)|,xge1 is A, then find the value of 3A+2.

hati*(hatkxx hatj)+hatj*(hati xx hatk)+hatk*(hatj xx hati)+hati*(hati xx hatj)+hatj*(hatj xx hatk) = ………..

If |(2+x,x,x^(2)),(x,2+x,x^(2)),(x^(2),x,2+x)|=(1)/(6)(x-a)(x-b)(x-c)(x-d) an identity in x where a, b, c, d are independent of x, then the value of (13)/(25)abcd is

The value of a for which the system linear of equations x+ay+z=1 ax+y+z=1 x+y+az=3 has no solution is :

For any vector vec(a),(vec(a)xx vec(i))^(2)+(vec(a)xx hatj)^(2)+(vec(a)xx vec(k))^(2)= ……….. .

If cos^(-1)2x+cos ^(-1)3x=(pi)/(3), " then "x=

Find the angle between the lines whose direction ratios are proportional to a,b,c and b-c,c-a,a-b,.

The shadow of a tower standing on a level ground is x metres long when the sun's altitude is 30^(@), while it is y metres long when the altitude is 60^(@). If the height of the tower is 45. (sqrt3)/(3) meters, then x -y is :

Integrate the functions x^(2)logx

Let vec r = (veca xx vecb) sin x + (vecb + vec c) cos y+ 2 (vec c xx vec a)where veca , vecb , vec care three non coplanar vectors . If vec r is perpendicular to veca + vecb + vec c , the minimum value of x^2 + y^2is

Find lambda if the vector hati-lambdahatj+2hatk and 2hati+4hatj are perpendicular to each other .

Show that the following four points in each jof the following are concyclic and find the equation of the circle on which they lie.(1,-6),(5,2),(7,0),(-1,-4)

The value of sum_(0leiltjle5) sum(""^(5)C_(j))(""^(j)C_(i)) is equal to "_____"

Let f (x) be a polynomial satisfying lim _(x to oo) (x ^(4) f (x))/( x ^(8) +1)=3 f (2) =5, f(3) =10, f (-1)=2, f (-6)=37The value of lim _(x to -6) (f (x) -x ^(2) -1)/(3 (x+6)) equals to:

int_(-1)^(1) Sin^(-1) ((x)/(1+x^(2)))dx=

A,B,C are three horses in a race. The probability of A to win the race is twice that of B and probability of B is twice that of C. What are the probability of A,B and C to win the race?

Show that the following four points in each of the following are concylic and find the equation of the circle on which they lie(9,1 ) ,(7,9 ),( -2,12),(6,10)

hati(hatkxx hatj)+hatj(hati xx hatk)+hatk(hatj xx hati)+hati(hati xx hatj)+hatj*(hatj xx hatk) = ………..