28278 + Interview Questions in Maths in Class 12

1.	The tangents and normal at a point on (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 cut the y-axis A and B. Then the circle on AB as diameter passes through
Answer» ONE of the vertex of the HYPERBOLA one of the foot of directrix on X-axis of the hyperbola foci of the hyperbola none of these Solution :Equation of tangent at point `P(theta)` is `(sec theta)/(a) x -(tan theta)/(b) y =1` `:. A (0,-b cot theta)` Equation of NORMAL at point `P(theta)` is `a cos theta x + b cot theta y = a^(2) +b^(2)` `:. B(0,(a^(2)+b^(2))/(b cot theta))` Equation of circle as AB as a diameter is `(x-0) (x-0) + (y+b cot theta) (y-(a^(2)+b^(2))/(b cot theta)) =0` or `x^(2)+ (y+b cot theta) (y-(a^(2)e^(2))/(b cot theta)) =0` Clearly this passes through foci (ae,0)

Discussion

2.	If abs(z_(1))=abs(z_(2))=abs(z_(3))=abs(1/(z_(1))+1/(z_(2))+1/(z_(3)))=1 and z_(1),z_(2),z_(3) are imaginary numbers, then abs(z_(1)+z_(2)+z_(3)) is
Answer» EQUAL to 1 less than 1 greater than 1 equal to 3 Answer :A

Discussion

3.	Locus of midpoint of the portion between the axes of x cos alpha + y sin alpha=p where pis constant is
Answer» `x^(2)+y^(2)=(4)/(p^(2))` `x^(2)+y^(2)=4P^(2)` `(1)/(x^(2))+(1)/(y^(2))=(2)/(p^(2))` `(1)/(x^(2))+(1)/(y^(2))=(4)/(p^(2))` ANSWER :D

Discussion

4.	If Arg ((2 - z)/(2 + z)) = (pi)/(6) and z = x + iy , then the locus of z is
Answer» a STRAIGHT line a CIRCLE a parabola an ELLIPSE ANSWER :B

Discussion

5.	Solve graphically x - y gt 0
Answer» SOLUTION :

Discussion

6.	Find the area of the region bounded by y = ln x between the ordinates x = 1 and x = e
Answer» ANSWER :1

Discussion

7.	The ratio of apples to oranges in a fruit basket is 3:5. If there are 15 apples, how many oranges are there?
Answer» ANSWER :25

Discussion

8.	Find the number of 4 letter words that can be formed using the letters of the word MIXTURE which (1) Contain the letter X
Answer» ANSWER :480

Discussion

9.	If z is a complex number satisfying z^(4) + z^(3) + 2z^(2) + z + 1 = 0 then \|z\| is equal to
Answer» `(1)/(2)` 2 1 3 Answer :C

Discussion

10.	If a, b, c are three non-coplanar vectors and d is any unit vector, then \|(a.d)(bxx c) + (b.d) (c xx a) + (c .d) (a xx b)\|=
Answer» `2\|[ABC]\|` `(1)/(2) \|[abc]\|` `\|[abc]\|` `(1)/(6) \|[abc]\|` ANSWER :C

Discussion

11.	If A = [{:(costheta, sin theta),(-sin theta, cos theta):}] and A(adj A) = [{:(k,0),(0,k):}], then k=……………
Answer» 0 `SIN THETA` `COS theta` 1 Answer :D

Discussion

12.	Express the following matrices as the sum of a symmetric and a skew symmetric matrix: (i) [(3,5),(1,-1)](ii) [(6,-2,2),(-2,3,-1),(2,-1,3)] (iii) [(3,3,-1),(-2,-2,1),(-4,-5,2)] (iv) [(1,5),(-1,2)]
Answer» Answer :(i) `A=[(3,3),(3,-1)]+[(0,2),(-2,0)]` (II) `A=[(6,-2,2),(-2,3,-1),(2,-1,3)]+[(0,0,0),(0,0,0),(0,0,0)]` (III) `A=[(3,(1)/(2),(-5)/(2)),((1)/(2),-2,-2),((-5)/(2),-2,2)]+[(0,(5)/(2),(3)/(2)),((-5)/(2),0,3),((-3)/(2),-3,0)] (iv)A=[(1,2),(2,2)]+[(0,3),(-3,0)]`

Discussion

13.	The order of differential equation of all circles of given radius 'a' is _______
Answer» a.3 b.1 C.2 d.4 Answer :C

Discussion

14.	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)]
Answer» `X=(-1)/(3), y=7` Not POSSIBLE to find `y=7, x=(-2)/(3)` `x=(-1)/(3), y=(-2)/(3)` Answer :B

Discussion

15.	Lt_(ntooo)sum_(r=1)^(n)(1)/(sqrt(4n^(2)-r^(2)))=
Answer» `PI` `pi/2` `pi/3` `pi/6` ANSWER :D

Discussion

16.	int((sinx-cosx))/((sinx+cosx)sqrt(sinxcosx+sin^(2)xcos^(2)x))dx
Answer» Answer :`-TAN^(-1)(SQRT((sinx+cosx)^(4)-1))+c`

Discussion

17.	Choose the correct answer If A and B are events such that P(A\|B) = P(B\|A), then
Answer» `A SUBSET B` but `A != B` A = B `A CAP B = phi` P(A) = P(B) Answer :D

Discussion

18.	The value of Delta=\|(1,sin 3theta, sin^(3)theta),(2cos theta, sin 6 theta, sin^(3)2 theta),(4cos^(2)theta-1,sin 9 theta, sin^(3)3theta)\| equal to
Answer» `-2` `-1` 1 0 Answer :D

Discussion

19.	Solve the following equations : sin(tan^(-1)x),\|x\|lt1 equal to
Answer» `X/(SQRT(1-x^(2)))` `1/(sqrt(1-x^(2)))` `1/(sqrt(1+x^(2)))` `x/(sqrt(1+x^(2)))` ANSWER :D

Discussion

20.	Solve the following equations . x^4-10x^3+26x^2-10x+1=0
Answer» ANSWER :`2+-SQRT(3) . 3 +- 2 sqrt(2)`

Discussion

21.	If (1 + x) (1 + x + x^(2)) (1 + x + x^(2) + x^(3)) .... (1 + x + x^(2) + . . . + x^(n)) = a_(0) + a_(1) x + a_(2) x^(2) + . . . + a_(m)x^(m) , then the value of a_(1) is
Answer» m+1 (N+1) n m Answer :C

Discussion

22.	48:2x is equivalent of 144:600. What is x?
Answer» ANSWER :100

Discussion

23.	No. of term in (1 + 3x + 3x^2 + x^3)^6 is
Answer» 17 19 21 16 Answer :B

Discussion

24.	Find the equation of circles determined by the following conditions. The centre at (-1, 4) and circle tangent to y-axis.
Answer» Solution : `therefore` RADIUS = 2 `(x-h)^2 + (y-k)^2 = a^2` or, `(x+1)^2 + (y-4)^2 = 1` or, `x^2 + 1 + 2x + y^2 + 16 - 8y =1` `x^2 + y^2 + 2x -8y +16 = 0`

Discussion

25.	Evaluate the following determinants: [[1,2,3],[3,5,7],[8,14,20]]
Answer» SOLUTION :`[[1,2,3],[3,5,7],[8,14,20]]=2[[1,2,3],[3,5,7],[4,7,10]]` `2[[1,2,3],[3,5,7],[3,5,7]] (R_3=R_3-R_1)` =0 `(because R_2=R_3)`

Discussion

26.	The standard deviation of a variable x is sigma. The standard deviation of the variable (ax + b)/(c ) where a, b, c are constants is
Answer» `((a)/(C )) SIGMA` `\|(a)/(c )\|sigma` `\|(a^(2))/(c^(2))\|sigma` `sigma` ANSWER :B

Discussion

27.	Which of the following sentences are propositions and which are not ? Write with reason : Oh ! What a schubert ?
Answer» SOLUTION :OH ! What a SCENERY ? It is not a statement as it is neither TRUE nor FALSE.

Discussion

28.	If three dice are rolled. Find the probability of getting sum 16 or getting 6 on first die.
Answer» ANSWER :`(13)/(72)`

Discussion

29.	Ify= y(x)( 2 _ cosx ) /( y+1)(( dy )/(dx)) =- sinx, y(0) =1 theny((pi)/(2)) equal ____.
Answer» ANSWER :`0.33`

Discussion

30.	int e^(3 sqrt(x))dx =
Answer» `3 e^(3 SQRT(x)) [ (3 sqrt(x))^(2) + 2." "3 sqrt(x) + 2 ] + c ` `3 e^(3 sqrt(x)) [ (3 sqrt(x))^(2) - 2." "3 sqrt(x) + 2 ] + c ` `3 e^(3 sqrt(x)) [ (3 sqrt(x))^(2) + 4." "3 sqrt(x) - 3 ] + c ` `3 e^(3 sqrt(x)) [ (3 sqrt(x))^(2) - 6." "3 sqrt(x) + 4 ] + c ` Answer :B

Discussion

31.	What was the cause of Maharaja's death?
Answer» A WOODEN tiger A mosquito Both a and b None of the above Answer :A

Discussion

32.	Draw graph of the following expression. Also findexetrmeum value if it exists. (i) y = \|x-2\|+\|x-1\|+\|x+1\|+\|x+2\| (ii) y = \|2x-5\|-2\|2x+5\| (iii) y = \|2x-1\|+\|x-1\| (iv) y = \|x-1\|-\|x-6\|
Answer»

Discussion

33.	Column-1 gives pair of curves and column-II gives the angle theta between the curves at their intersection point.
Answer» ANSWER :ATO T; BtoR; C TOQ; DtoQ`

Discussion

34.	The slope of normal to (3t^(2)+1, t^(3)-1) at t = 1 is ………….
Answer» `(1)/(2)` `-2` 2 `-(1)/(2)` ANSWER :B

Discussion

35.	int_(2)^(5) ([x^(2)+49-14x])/([x^(2)-14x+49]+[x^(2)])dx=
Answer» `1/2` `3/2` `5/2` `7/2` ANSWER :B

Discussion

36.	Find the area of the region bounded by y=x^(2) and y = 4
Answer» ANSWER :(32)/(3)`

Discussion

37.	A die is thrown. If E is the event the number appearing is a multiple of 3' and F be the event 'the number appearing is even' then find whether E and F are independent ?
Answer» ANSWER :E and F are INDEPENDENT EVENTS.

Discussion

38.	The vectors (a,a+1, a+2)(a+3, a+4, a+5)(a+6, a+7, a+8) are coplanar for
Answer» `AA a in R` `AA a cancel in R` `a = sqrt(-3)` None of these Solution :VECTORS `(a, a+1, a+2), (a+3, a+4,a+5) and (a+6, a+7,a+8) ` are coplanar. `therefore \|(a, a+1,a+2),(a+3, a+4, a+5), (a+6, a+7, a+8)\|=0` On applying `C_(2) to C_(2) - C_(1) and C_(3) to C_(1)`, we get `\|(a,1,2),(a+3,1,2),(a+6,1,2)\|=0` HENCE, vectors are coplanar, `AA a in R`.

Discussion

39.	if cos 2theta = (sqrt(2)+1) ( costheta -1/sqrt(2)), then general value of theta is …………….
Answer» SOLUTION :`2NPI +- pi/4` or `2npi+- pi/3`

Discussion

40.	If z_1, z_2 are two complex numbers representing consecutive vertices of a regular hexagon then thecomplex number z_3 representing the vertex adjacent to z_2. is __________________.
Answer» ANSWER :`-(1)/(2) (1+i SQRT3)z_1 + (1)/(2) (3 PM sqrt3) z_2`

Discussion

41.	Find the area of the region enclosed by y^(2)= 4(4-x) and y^(2)= 4x
Answer» ANSWER :`(32 sqrt2)/(3)` SQ units

Discussion

42.	If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma, then match the following.{:("I) "cos3alpha+cos3beta+cos3gamma=,"a) "0),("II) "sin2alpha+sin2beta+sin2gamma=,"b) "3),("III) "cos^2alpha+cos^2beta+cos^2gamma=,"c) "3//2),("IV) "cos(2alpha-beta-gamma)+cos(2beta-gamma-alpha)+cos(2gamma-alpha-beta)=,"d) "3cos(alpha+beta+gamma)):}
Answer» A) d,a,C,b B) b,c,a,d C) d,a,b,c D) d,c,b,a Answer :A

Discussion

43.	Solve (1)/(x)(dy)/(dx)+y.e^(x)=e^((1-x)e^(x))
Answer» ANSWER :`(X^(2))/(2)+C`

Discussion

44.	If the objective function for an L.P.P. is Z=3x-4y and the corner points for the bounded feasible region are (0, 0), (5, 0), (6, 5), (6, 8), (4, 10)and (0, 8), then the maximum value of Z occurs at
Answer» (5, 0) (6, 5) (6, 8) (4, 10) Answer :A

Discussion

45.	The solution of (ydx - xdy)/(y^(2)) = 0 represents a family of
Answer» STRAIGHT LINES PASSING THOUGH the origin circles parabola hyperbola Answer :A

Discussion

46.	Show that the number of ways to select 'r' objects from n distinct objects which are arranged along a row so that no two of the selected objects are consecutive is ""^(n-r+1)C_(r). Where nge2r-1.
Answer» ANSWER :`""^(n-R+1)C_(r)`. Where `nge2r-1`.

Discussion

47.	Two groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.
Answer» ANSWER :`(2)/(9)`

Discussion

48.	Ifalpha , beta , gammaare therootsofx^3+ 2x^2 + 3x +8=0then( alpha+ beta ) ( beta + gamma)( gamma + alpha )=
Answer» `-4` `4` `-2` `2` ANSWER :D

Discussion

49.	A bracelet contains rubies, emeralds, and sapphires, such that there are 2 rubies for every 1 emerald and 5 sapphires for every 3 rubies. {:("Quantity A","Quantity B"),("The minimum possible number",20),("of gamstones on the bracelet",):}
Answer» ANSWER :QUANTITY B is GREATER.

Discussion

50.	To save on helium costs, a balllon is inflated with both helium and nitrogen gas. Between the two gases, the ballon can be inflated up to 8 liters in volume. The density of helium is 0.20 gram per liter, and the density of nitrogen is 1.30 grams per liter. The ballon must be filled so that the volumetric average density of the ballon is lower than that of air, which has a density of 1.20 grams per liter. Which if the following system of inequalities best describes how the ballon will be filled, if x represent the number in liters of helium and y represents the number of liters of nitrogen?
Answer» `{(x+ygt8), (20x+130ygt120):}` `{(x+y=8), ((0.2x+1.30y)/(2)lt1.20):}` `{(x+y=47), (0.78x+1.07y=45.94):}` `[(x+yle8), (0.20x+1.30ylt1.20):}` ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The tangents and normal at a point on (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 cut the y-axis A and B. Then the circle on AB as diameter passes through

If abs(z_(1))=abs(z_(2))=abs(z_(3))=abs(1/(z_(1))+1/(z_(2))+1/(z_(3)))=1 and z_(1),z_(2),z_(3) are imaginary numbers, then abs(z_(1)+z_(2)+z_(3)) is

Locus of midpoint of the portion between﻿ the axes of x cos alpha + y sin alpha=p where pis﻿ constant is

If Arg ((2 - z)/(2 + z)) = (pi)/(6) and z = x + iy , then the locus of z is

Solve graphically x - y gt 0

Find the area of the region bounded by y = ln x between the ordinates x = 1 and x = e

The ratio of apples to oranges in a fruit basket is 3:5. If there are 15 apples, how many oranges are there?

Find the number of 4 letter words that can be formed using the letters of the word MIXTURE which (1) Contain the letter X

If z is a complex number satisfying z^(4) + z^(3) + 2z^(2) + z + 1 = 0 then |z| is equal to

If a, b, c are three non-coplanar vectors and d is any unit vector, then |(a.d)(bxx c) + (b.d) (c xx a) + (c .d) (a xx b)|=

If A = [{:(costheta, sin theta),(-sin theta, cos theta):}] and A(adj A) = [{:(k,0),(0,k):}], then k=……………

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: (i) [(3,5),(1,-1)](ii) [(6,-2,2),(-2,3,-1),(2,-1,3)] (iii) [(3,3,-1),(-2,-2,1),(-4,-5,2)] (iv) [(1,5),(-1,2)]

The order of differential equation of all circles of given radius 'a' is _______

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)]

Lt_(ntooo)sum_(r=1)^(n)(1)/(sqrt(4n^(2)-r^(2)))=

int((sinx-cosx))/((sinx+cosx)sqrt(sinxcosx+sin^(2)xcos^(2)x))dx

Choose the correct answer If A and B are events such that P(A|B) = P(B|A), then

The value of Delta=|(1,sin 3theta, sin^(3)theta),(2cos theta, sin 6 theta, sin^(3)2 theta),(4cos^(2)theta-1,sin 9 theta, sin^(3)3theta)| equal to

Solve the following equations : sin(tan^(-1)x),|x|lt1 equal to

Solve the following equations . x^4-10x^3+26x^2-10x+1=0

If (1 + x) (1 + x + x^(2)) (1 + x + x^(2) + x^(3)) .... (1 + x + x^(2) + . . . + x^(n)) = a_(0) + a_(1) x + a_(2) x^(2) + . . . + a_(m)x^(m) , then the value of a_(1) is

48:2x is equivalent of 144:600. What is x?

No. of term in (1 + 3x + 3x^2 + x^3)^6 is

Find the equation of circles determined by the following conditions. The centre at (-1, 4) and circle tangent to y-axis.

Evaluate the following determinants: [[1,2,3],[3,5,7],[8,14,20]]

The standard deviation of a variable x is sigma. The standard deviation of the variable (ax + b)/(c ) where a, b, c are constants is

Which of the following sentences are propositions and which are not ? Write with reason : Oh ! What a schubert ?

If three dice are rolled. Find the probability of getting sum 16 or getting 6 on first die.

Ify= y(x)( 2 _ cosx ) /( y+1)(( dy )/(dx)) =- sinx, y(0) =1 theny((pi)/(2)) equal ____.

int e^(3 sqrt(x))dx =

What was the cause of Maharaja's death?

Draw graph of the following expression. Also findexetrmeum value if it exists. (i) y = |x-2|+|x-1|+|x+1|+|x+2| (ii) y = |2x-5|-2|2x+5| (iii) y = |2x-1|+|x-1| (iv) y = |x-1|-|x-6|

Column-1 gives pair of curves and column-II gives the angle theta between the curves at their intersection point.

The slope of normal to (3t^(2)+1, t^(3)-1) at t = 1 is ………….

int_(2)^(5) ([x^(2)+49-14x])/([x^(2)-14x+49]+[x^(2)])dx=

Find the area of the region bounded by y=x^(2) and y = 4

A die is thrown. If E is the event the number appearing is a multiple of﻿ 3' and F be the event 'the number appearing is even' then find whether E and F are﻿ independent ?

The vectors (a,a+1, a+2)(a+3, a+4, a+5)(a+6, a+7, a+8) are coplanar for

if cos 2theta = (sqrt(2)+1) ( costheta -1/sqrt(2)), then general value of theta is …………….

If z_1, z_2 are two complex numbers representing consecutive vertices of a regular hexagon then thecomplex number z_3 representing the vertex adjacent to z_2. is __________________.

Find the area of the region enclosed by y^(2)= 4(4-x) and y^(2)= 4x

Solve (1)/(x)(dy)/(dx)+y.e^(x)=e^((1-x)e^(x))

If the objective function for an L.P.P. is Z=3x-4y and the corner points for the bounded feasible region are (0, 0), (5, 0), (6, 5), (6, 8), (4, 10)and (0, 8), then the maximum value of Z occurs at

The solution of (ydx - xdy)/(y^(2)) = 0 represents a family of

Show that the number of ways to select 'r' objects from n distinct objects which are arranged along a row so that no two of the selected objects are consecutive is ""^(n-r+1)C_(r). Where nge2r-1.

Ifalpha , beta , gammaare therootsofx^3+ 2x^2 + 3x +8=0then( alpha+ beta ) ( beta + gamma)( gamma + alpha )=

A bracelet contains rubies, emeralds, and sapphires, such that there are 2 rubies for every 1 emerald and 5 sapphires for every 3 rubies. {:("Quantity A","Quantity B"),("The minimum possible number",20),("of gamstones on the bracelet",):}

Locus of midpoint of the portion between the axes of x cos alpha + y sin alpha=p where pis constant is

A die is thrown. If E is the event the number appearing is a multiple of 3' and F be the event 'the number appearing is even' then find whether E and F are independent ?