28278 + Interview Questions in Maths in Class 12

1.	Ife^x+ e^y = e^(x+y)then(dy )/( dx)=……..
Answer» `E^(x-y)` `e^(y-x)` `-e^(y-x)` `-e^(x-y)` ANSWER :D

Discussion

2.	If l_(n)=int_(0)^(pi//4)tan^(n)xdx, n in N then l_(n+2)+l_(n) equals
Answer» `(1)/(N)` `(1)/(n-1)` `(1)/(n+1)` `(1)/(n+4)` Solution :`I_(n+1)+I_(n)=int_(0)^(pi//4)tan^(n+2)XDX+int_(0)^(pi//4)tan^(n)xdx` `rArr I_(n+2)+I_(n)=int_(0)^(pi//4)tan^(n)x(1+tan^(2)x)dx=int_(0)^(pi//4)tan^(n)x.sec^(2)xdx` `rArr I_(n+2)+I_(n)=int_(0)^(1)t^(n)DT,` where `t=tanx` `rArr I_(n+2)+I_(n)=(1)/(n+1)`

Discussion

3.	If ax^(2) + 2 hxy+ by^(2) + 2 g x + 2 fy + c = 0 represents a pair of parallel lines , then sqrt((g^(2) - ac)/(f^(2) - bc)) , is equal to
Answer» `(a)/(B)` `SQRT((a)/(b))` `sqrt((b)/(a))` `(b)/(a)` ANSWER :B

Discussion

4.	If the normal to the parabola y^(2)=4x at P(1,2) meets the parabola again at Q, then coordinates of Q are
Answer» (-6,9) (9,-6) (-9,-6) (-6,-9) ANSWER :B

Discussion

5.	Determine whether or not each of the defination of given below gives a binary opertion. In the even that is not a binary opertion, give justification for this. (i) On Z ^(+), define by a b =a -b (ii) On Z ^(+), define by a b =ab (iii) On R, define by a b =ab ^(2) (iv) On Z ^(+), define by a b = \|a-b\| (v) On Z ^(+), define by a b =a
Answer» Answer :(i) NO (ii) YES (iii) es (IV) Yes (V) Yes

Discussion

6.	The odds infavour of drawing a king or a diamond from a well shuffled pack are
Answer» `9 : 4` `4 : 9` `5 : 9` `9 : 5` ANSWER :B

Discussion

7.	Resolve into Partial Fractions (ii) (x^(3))/((2x-1)(x+2)(x-3))
Answer» ANSWER :`1/2 - (1)/(50(2x-1))-(8)/(25(x+2))+(27)/(25(x-3))`

Discussion

8.	If x+y=3 is the equation of the chord AB of the circle x^2+y^2-2x+4y-8=0, find the equation of the circle having as diameter.
Answer» ANSWER :`x^2+y^2-6x+4=0`

Discussion

9.	(i) y=((x-a)(x-b))/(sqrt(x-c)) (ii) y=sqrt(((x-a)(x-b))/((x-c)(x-d)))
Answer» ANSWER :(i) `((x-a)(x-b))/(sqrt(x-c)){1/(x-a)+1/(x-b)-1/(2(x-c))}` (II) `1/2sqrt(((x-a)(x-b))/((x-c)(x-d)))CDOT[1/(x-a)+1/(x-b)-1/(x-c)-1/(x-d)]`

Discussion

10.	Maximum value of sin ^(8) x+cos ^(16) x is
Answer» 1 `3/2` `3/4` NONE of these. Answer :A

Discussion

11.	A pair of dice is rolled. What is the probability that they sum to 7 given that neither die shows a 2.
Answer» ANSWER :`(4)/(25)`

Discussion

12.	Find the equation of the circle for which the point given below are the end points of a diameter. (-4,3),( 3,-4)
Answer» ANSWER :` X^(2) + y^(2) + x + y -24 =0 `

Discussion

13.	Show that the common chord of the circles x^2+y^2-6x-4y+9=0 and x^2+y^2-8x-6y+23=0is the diameter of the second circle and also find its length.
Answer» ANSWER :`2sqrt(2)`

Discussion

14.	Evaluate the following integrals as the limits of sums int_(1)^(2) ( 4x^(2)-1)dx
Answer» ANSWER :`(25)/(3)`

Discussion

15.	The probability distribution of X is Then P("X is positive") =
Answer» `0.50` `0.70` `0.55` `0.45` ANSWER :A

Discussion

16.	Let u=2i-j+3k" and "a=4i-j+2k. The vector component of u orthogonal to a is
Answer» `-1/7(6i+2j-11k)` `1/7(-6i+2j-11k)` `-1/7(6i-2j+11k)` `-1/7(-6i+2j+11k)` ANSWER :A

Discussion

17.	Simplify the following (sqrt(2)+1)^(5) +(sqrt(2)-1)^(5)
Answer» SOLUTION :N/A

Discussion

18.	Show that 2tan^(-1)(1/2) + tan^(-1)(1/7) = tan^(-1)(31/17)
Answer» ANSWER :`TAN^(-1)(31/17)`

Discussion

19.	underset( x rarr - 1) ( "lim")( sqrt(pi ) - sqrt((cos^(-1) x)))/( sqrt( (x+1)))is given by :
Answer» `1//sqrt( PI )` `1//sqrt((2PI))` 1 0 Answer :B

Discussion

20.	If cos^(-1)(5/13)+cos^(-1)(3/5)=cos^(-1)x, then x is equal to
Answer» `3/65` `(-36)/65` `(-33)/65` `-1` Answer :C

Discussion

21.	Let x,y,z be the vector, such that \|x\|=\|y\|=\|z\| =sqrt(2) and x,y,z make angles of 60^(@) with each other also. The value of z is:
Answer» `1/2[(B-a) XX C + (a +b)]` `1/2[(b-a)+(a+b) xx c]` `(c-a) xx c +(a+b)` NONE of these ANSWER :B

Discussion

22.	Iftan (pi/4+ y/2)= tan^3 (pi/4 + x/2) then (3 sin x + sin^3 x)/(1+3 sin^2 x)=
Answer» 0 1 sin2y sin Y Answer :D

Discussion

23.	Let x,y,z be the vector, such that \|x\|=\|y\|=\|z\| =sqrt(2) and x,y,z make angles of 60^(@) with each other also. The value of x is:
Answer» `(a+ B) XX C-(a+b)` `(a+b)-(a+b) xx c` `1/2{(a + b) xx c -(a xx b)}` NONE of these ANSWER :C

Discussion

24.	Integrate the following functions : int(dx)/(xcos^(2)(1+logx))
Answer» ANSWER :`TAN(1+logx)+C`

Discussion

25.	Evaluate the following integrals inte^(x)((1+sinx)/(1+cosx))dx
Answer» ANSWER :`E^(X)tan(x)/(2)+C`

Discussion

26.	Which of the following statements is/are incorrect -
Answer» Number of atoms present in 80 amu CA are `2 N_A` Volume occupied by 2g-atom OXYGEN at 1 atm pressure and 273 K temperature is 44.8 L 9.8 g of `H_2SO_4` has 3.2 g of S-atom `H_2`(g) is an elemental form as well as a MOLECULE of hydrogen. Answer :A,B

Discussion

27.	A sample of 90 values has mean 55 and standard deviation 3. A second sample of 110 values has mean 60 and standard deviations 2. The combined variance is equal to (upto two decimal)
Answer» `12.43` ` 11.24` ` 10.43` `13.25` ANSWER :A

Discussion

28.	If theareaof theregionboundedby thecurvey= f(x) ,X - axisandx=1andx=bis (b-1) sin(3b+4)f(x) ……
Answer» `3 (X -1)cos( 3x +4) + SIN(3x +4)` `(b-1) sin (3x +4) + 3 cos (3 x+4)` `(b-1) cos( 3x+4) +3SIN( 3x +4)` None of these Answer :A

Discussion

29.	If f(x)= sin x, then f is
Answer» DISCONTINUOUS for all `X in R` CONTINUOUS for all `x in R^(+)` continuous for all ` x in R^(-)` continuous for all `x in R` ANSWER :D

Discussion

30.	If the distance between two latus rectum of a ellipse is 4sqrt3 unit and length of minor axis is 4unit then find its eccentricity.
Answer»

Discussion

31.	If int (4e^(x) + 6e^(-x))/(9e^(x) -4e^(-x)) " dx = Ax + B log" (9e^(2x) - 4) + c then (A,B) =
Answer» `(- (3)/(2),(35)/(36)) ` `((3)/(2),(35)/(36))` `(-(3)/(2),(35)/(36))` `((3)/(2), -(35)/(36))` ANSWER :A

Discussion

32.	Integration by partial fraction : int(dx)/(2x^(2)+x+1)=.....
Answer» `(1)/(SQRT(7))TAN^(-1)((4x+1)/(sqrt(7)))+c` `(1)/(2sqrt(7))tan^(-1)((4x+1)/(sqrt(7)))+c` `(1)/(2)tan^(-1)((4x+1)/(sqrt(7)))+c` None of these Answer :D

Discussion

33.	Integrate the following functions e^(2x) sinx
Answer» Solution :Let I = `int E^(2X) sinx dx,` Then I = `e^(2x)(-cosx)- int e^(2x) xx 2 xx -cosx dx` =`-e^(2x) cosx+2 int e^(2x) cosx dx` =`-e^(2x) cosx+2[e^(2x) sinx- int e^(2x) 2 sinx dx]` =`-e^(2x) cosx+2 e^(2x) sinx - 4I` `gt 5I = -e^(2x) cosx+2 e^(2x) sinx` = `e^(2x)[2sinx-cosx]` `gt I = e^(2x)/5[2 sinx-cosx]+C`

Discussion

34.	Let the lines L_1 = sqrt3 x - y (2+ sqrt3) = 0 and L_2 = sqrt3 x + y (2+ sqrt3)=0 intersect at A. Let C_1 From C_1 , draw a line perpendicular to L_2 meeting the line L_1 " at " B_2 . Continue in this way obtaining points C_2 B_2 O_3 and so on. If area of traingle AB_1C_1 = 1 and area (DeltaAB_2C_2)+ area (DeltaAB_3C_3) + area (DeltaAB_4C_4) = T , then \| T - 4360 \| = ..............
Answer» ANSWER :8

Discussion

35.	A coplanar beam of ligth emerging from a point source has the equation lambdax-y+2(1+alambda)-0, lambda in R.The rays of the beam strike an elliptical surface and get reflected. The reflected rays form another convergent beam having eqution mux-y+2(1-mu)=0, mu in R. Further, it is found that the foot of the perpendicular from the point (2,2) upon any tangent to the ellipse lies on the circle x^(2)+y^(2)-4y-5=0 The total distance travelled by an incident ray starting at one focus and the correcponding reflected ray terminating at another focus is
Answer» 9 8 7 6 Solution :REQUIRED area `=(1)/(2)(2ae)(b)=3XX(2)/(3)xxsqrt(5)=2sqrt(5)`

Discussion

36.	A coplanar beam of ligth emerging from a point source has the equation lambdax-y+2(1+alambda)-0, lambda in R.The rays of the beam strike an elliptical surface and get reflected. The reflected rays form another convergent beam having eqution mux-y+2(1-mu)=0, mu in R. Further, it is found that the foot of the perpendicular from the point (2,2) upon any tangent to the ellipse lies on the circle x^(2)+y^(2)-4y-5=0 The area of the largest triangle that na incident ray and the corresponding reflected rat can enclose with the axis of the ellipse is equal to
Answer» `4sqrt(5)` `2sqrt(5)~ `SQRT(5)` NONE of these Solution :Required AREA `=(1)/(2)(2ae)(b)=3xx(2)/(3)xxsqrt(5)=2sqrt(5)`

Discussion

37.	Evalute the following integrals int sqrt((1 + x)/(1 - x))dx on (-1,1)
Answer» ANSWER :`SIN^(-1) x -sqrt(1 -x^(2)) + C `

Discussion

38.	Two cards are drawn from pack and given that they are of different colours. The probability of getting one king and one Queen is
Answer» `(1)/(169)` `(2)/(169)` `(4)/(169)` `(5)/(169)` ANSWER :B

Discussion

39.	If f(x) = sqrt((1 + x^2)/(1-x^2)) (\|x \| < 1), then find f'(x)
Answer» ANSWER :A::B::D

Discussion

40.	The population of a village increases continuously at the rate proportional to the number of its Inhabitants present at any time. It the population of the village was 20,000 in 1999 and 25,000 in the year 2004, what will be the population of the village in 2009 ?
Answer» ANSWER :31250

Discussion

41.	The point where the line 4x-3y+7=0 touches the circule x^2+y^2-6x+4y-12=0 is
Answer» `(1,1)` `(1,-1)` `(-1,1)` `(-1,-1)` ANSWER :C

Discussion

42.	The order of the differential equation of all rectangular hyperbola is
Answer» two four ONE three ANSWER :C

Discussion

43.	Chords of an elipse are drawn through the positive end of minor axis . Then their midpoint lies on
Answer» a circle a parabola an ELIPSE a HYPERBOLA ANSWER :C

Discussion

44.	Let a, b and c be real numbers such that a - 7b + 8c = 4 and 8a + 4b - c = 7. What is the value of a^(2) - b^(2) + c^(2).
Answer» ANSWER :1

Discussion

45.	Match the items of column I to that of column II {:(,"Column I",,"Column II"),((A),"If a and b are noncollinear and xa + yb = (y + 1)",(p),6),(,"a + (2 - x)b Then x - y equals",,),((B),"If a, b are non-collinear and (2 - x)a + b and",(q),-1),(,"ya + (x - 3) b are equal, then \|x - y\| =",,),((C),"If a, b are non-collinear and (x - 1)a + 2b and 3a + xb",(s),1),(,"are collinear, then the sum of the values of x is",,),((D),"If a, b are non-collinear and 3a + xb and",(t),2),(,(1-x) a - (2)/(3)"b are like vectors, then x is",,):} The correct match is :
Answer» `A RARR s, B rarr p, C rarr t, D rarr q` `A rarr s, B rarr q, C rarr s, D rarr q` `A rarr p, B rarr q, C rarr R, D rarr s` `A rarr q, B rarr p, C rarr s, D rarr r` ANSWER :A

Discussion

46.	Find the value of (sqrt4, 4sqrt4 . 8sqrt4. 16sqrt4…oo)is-
Answer» 2 8 4 1 Answer :C

Discussion

47.	If a,b,c,dgt0,x epsilonR and (a^(2)+b^(2)+c^(2))x^(2)-2(ab+bc+cd)x+(b^(2)+c^(2)+d^(2))le0 then \|(33,14,loga),(65,17,logb),(97,40,logc)\|=
Answer» Solution :`F(1)lt0` `(-1)lt0` `f(0)gt0` `ALPHA epsilon(-1,0)` `BETA epsilon(0,1)` `[alpha]+[beta]` `-1+0=-1`

Discussion

48.	The order of the differential equation 2x^(2) (d^(2)y)/(dx^(2))-3(dy)/(dx) + y = 0 is
Answer» 2 1 0 not defined Answer :A

Discussion

49.	int_(0)^(pi//2) max (sin x cos x) dx is equal to
Answer» `1` `2` `2 - SQRT2` `sqrt2` ANSWER :D

Discussion

50.	The marginal cost of a product is given by MC = 2x + 30 and the fixed cost is Rs. 120. Find (i) the total cost of producing 100 units. (ii) the cost of increasing output from 100 to 200 units.
Answer» ANSWER :33000

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Ife^x+ e^y = e^(x+y)then(dy )/( dx)=……..

If l_(n)=int_(0)^(pi//4)tan^(n)xdx, n in N then l_(n+2)+l_(n) equals

If ax^(2) + 2 hxy+ by^(2) + 2 g x + 2 fy + c = 0 represents a pair of parallel lines , then sqrt((g^(2) - ac)/(f^(2) - bc)) , is equal to

If the normal to the parabola y^(2)=4x at P(1,2) meets the parabola again at Q, then coordinates of Q are

The odds infavour of drawing a king or a diamond from a well shuffled pack are

Resolve into Partial Fractions (ii) (x^(3))/((2x-1)(x+2)(x-3))

If x+y=3 is the equation of the chord AB of the circle x^2+y^2-2x+4y-8=0, find the equation of the circle having as diameter.

(i) y=((x-a)(x-b))/(sqrt(x-c)) (ii) y=sqrt(((x-a)(x-b))/((x-c)(x-d)))

Maximum value of sin ^(8) x+cos ^(16) x is

A pair of dice is rolled. What is the probability that they sum to 7 given that neither die shows a 2.

Find the equation of the circle for which the point given below are the end points of a diameter. (-4,3),( 3,-4)

Show that the common chord of the circles x^2+y^2-6x-4y+9=0 and x^2+y^2-8x-6y+23=0is the diameter of the second circle and also find its length.

Evaluate the following integrals as the limits of sums int_(1)^(2) ( 4x^(2)-1)dx

The probability distribution of X is Then P("X is positive") =

Let u=2i-j+3k" and "a=4i-j+2k. The vector component of u orthogonal to a is

Simplify the following (sqrt(2)+1)^(5) +(sqrt(2)-1)^(5)

Show that 2tan^(-1)(1/2) + tan^(-1)(1/7) = tan^(-1)(31/17)

underset( x rarr - 1) ( "lim")( sqrt(pi ) - sqrt((cos^(-1) x)))/( sqrt( (x+1)))is given by :

If cos^(-1)(5/13)+cos^(-1)(3/5)=cos^(-1)x, then x is equal to

Let x,y,z be the vector, such that |x|=|y|=|z| =sqrt(2) and x,y,z make angles of 60^(@) with each other also. The value of z is:

Iftan (pi/4+ y/2)= tan^3 (pi/4 + x/2) then (3 sin x + sin^3 x)/(1+3 sin^2 x)=

Let x,y,z be the vector, such that |x|=|y|=|z| =sqrt(2) and x,y,z make angles of 60^(@) with each other also. The value of x is:

Integrate the following functions : int(dx)/(xcos^(2)(1+logx))

Evaluate the following integrals inte^(x)((1+sinx)/(1+cosx))dx

Which of the following statements is/are incorrect -

A sample of 90 values has mean 55 and standard deviation 3. A second sample of 110 values has mean 60 and standard deviations 2. The combined variance is equal to (upto two decimal)

If theareaof theregionboundedby thecurvey= f(x) ,X - axisandx=1andx=bis (b-1) sin(3b+4)f(x) ……

If f(x)= sin x, then f is

If the distance between two latus rectum of a ellipse is 4sqrt3 unit and length of minor axis is 4unit then find its eccentricity.

If int (4e^(x) + 6e^(-x))/(9e^(x) -4e^(-x)) " dx = Ax + B log" (9e^(2x) - 4) + c then (A,B) =

Integration by partial fraction : int(dx)/(2x^(2)+x+1)=.....

Integrate the following functions e^(2x) sinx

Evalute the following integrals int sqrt((1 + x)/(1 - x))dx on (-1,1)

Two cards are drawn from pack and given that they are of different colours. The probability of getting one king and one Queen is

If f(x) = sqrt((1 + x^2)/(1-x^2)) (|x | < 1), then find f'(x)

The population of a village increases continuously at the rate proportional to the number of its Inhabitants present at any time. It the population of the village was 20,000 in 1999 and 25,000 in the year 2004, what will be the population of the village in 2009 ?

The point where the line 4x-3y+7=0 touches the circule x^2+y^2-6x+4y-12=0 is

The order of the differential equation of all rectangular hyperbola is

Chords of an elipse are drawn through the positive end of minor axis . Then their midpoint lies on

Let a, b and c be real numbers such that a - 7b + 8c = 4 and 8a + 4b - c = 7. What is the value of a^(2) - b^(2) + c^(2).

Find the value of (sqrt4, 4sqrt4 . 8sqrt4. 16sqrt4…oo)is-

If a,b,c,dgt0,x epsilonR and (a^(2)+b^(2)+c^(2))x^(2)-2(ab+bc+cd)x+(b^(2)+c^(2)+d^(2))le0 then |(33,14,loga),(65,17,logb),(97,40,logc)|=

The order of the differential equation 2x^(2) (d^(2)y)/(dx^(2))-3(dy)/(dx) + y = 0 is

int_(0)^(pi//2) max (sin x cos x) dx is equal to

The marginal cost of a product is given by MC = 2x + 30 and the fixed cost is Rs. 120. Find (i) the total cost of producing 100 units. (ii) the cost of increasing output from 100 to 200 units.