28278 + Interview Questions in Maths in Class 12

1.	The point of intersection of the line (x-4)/(2) = (y+3)/(5) = (z-3)/(3) and the plane x + y + z + 2 = 0 is........
Answer» `(18/5, - 3, 18/5)` `(-18/5, -2, -8/5)` `(13/5, -2,18/5)` `(-18/5, -2,18/5)` ANSWER :D

Discussion

2.	Evaluate the following integrals int sin (log x) dx
Answer» ANSWER :`(X)/(2)[SIN(LOGX)-cos(logx)]+C`

Discussion

3.	Integrate the following functions: cos(2x)/(cosx+sinx)^2
Answer» SOLUTION :`(COS2X)/(cosx+sinx)^2 = (cos^2x-sin^2x)/(cosx+sinx)^2` `=(cosx-sinx)/(cosx+sinx)` PUT cosx+sinx = t Then dt = (-sinx+cosx) DX therefore` INT(cos2x)/(cosx+sinx)^2 dx` =`int dt/t = log\|t\|+c` =`log\|cos+sinx\|+c`

Discussion

4.	int (sec^2x)/((tanx+1)(tanx+2)) dx
Answer» ANSWER :`LOG \|(tanx+1)/(tanx+2)\|+C`

Discussion

5.	Differentiate (8^(x))/(x^(8))
Answer» ANSWER :`(8^(X))/(x^(8)) (LOG 8-(8)/(x))`

Discussion

6.	Three distinct vertices are chosen at random from the vertices of a gien regular polygon of (2n+1) sides. Let all such choices are equalty likely and the probability that the centre of the given polygon lies in the interior of the triangle determined by these three chosen random points is (5)/(14). The number of diagonals of the polygon is equal to
Answer» 14 18 20 27 Answer :D

Discussion

7.	Three distinct vertices are chosen at random from the vertices of a gien regular polygon of (2n+1) sides. Let all such choices are equalty likely and the probability that the centre of the given polygon lies in the interior of the triangle determined by these three chosen random points is (5)/(14). The number of points of intersection of the diagonals lying exactly inside the polygon is equal to
Answer» 70 35 126 96 Answer :C

Discussion

8.	If x = (13)/(36)+(135)/(369)+(1357)/(36912)+. . .to infinite terms, then9x^(2) + 24 x =
Answer» 11 21 31 41 Answer :A

Discussion

9.	To find the coefficient of x^(4) in the expansion of (3x)/((x-2)(x-1)), the interval in which the expansion is valid, is
Answer» `-2 LT x lt INFTY` `-1/2 lt x lt 1/2` `-1 lt x lt 1` `-infty lt x lt infty` Answer :C

Discussion

10.	Solve the following systems of linear inequalities graphically : x + y gt 1 , 3x - y lt 3, x- 3y + 3 gt 0.
Answer» Solution : `x + y GT 1 `3x-y lt 3` Step-2 : Let us CONSIDER the point (0,0) that does not lie on these Putting x=0,y=0 in the inequations we get, thus (0,0) satisfies 3x-y `lt`3 and x-3y + 3 `gt`0 but does satisfy x + y `gt` 1. `therefore` The shaded REGION is the solutions region.

Discussion

11.	If (6 sqrt6+14)^(2n+1)=R and F=[R], where [R] denotes the greatest integer less than or equal to R thwn RF=
Answer» `20^n` `20^(2N)` `20^(2n + 1)` 1 Answer :C

Discussion

12.	The set of all real values of alpha for which the equation, \|a+2\|\|x-2\|=alpha^(2)-2alpha has real solution for s, is :
Answer» `(OO,0)uu[2,oo)` `(-oo,0)uu[2,1+sqrt(5)]` `[-1-sqrt(5),1-sqrt(5)]uu[1+sqrt(5),oo)` `[1-sqrt(5),0)uu[2,1+sqrt(5)]` ANSWER :A

Discussion

13.	The number of ways in which 5 players be chosen from 12 players so as to include one particular player is
Answer» `""^(12)C_(4)` `""^(11)C_(5)` `""^(12)C_(5)` `""^(11)C_(4)` ANSWER :D

Discussion

14.	int ((x-1)dx)/((x+1)sqrt(x^(3)+x^(2)+x))=
Answer» `tan^(-1) ((sqrt(X^(2) + x + 1))/(x)) + c` `2. tan^(-1) ((x^(2) + x + 1)/(x)) + c` `tan^(-1) ((x^(2) + x + 1)/(x)) + c` `2. tan^(-1) (sqrt(x + (1)/(x) + 1)) + c` ANSWER :D

Discussion

15.	If the function f : R rarr R defined by f(x)= {((sin(a +1) x + sin x)/(x),x lt 0),((sqrt(x + x^(2)) - sqrtx)/(x^(1//2)),x gt 0):} continuous on R, then a + b=
Answer» `-1` 2 1 3 Answer :A

Discussion

16.	Match the following.{:(Column-I,""Column-II),(I" : "x=costheta+isintheta" then "x^n-(1)/(x^n),"a) "2isin(alpha-beta)),(II" : If "z=costheta+sintheta" then "(z^n-1)/(z^(2n)+1),"b) "2cos(alpha-beta)),(III" : "x=cisalpha","y=cisbeta" then "x/y+y/x=,"c) "itanntheta),(IV " : " x=cisalpha","y=cisbeta" then "x/y-y/x=,"d) "2iSinntheta):}
Answer» a,b,c,d b,c,a,d d,a,b,c d,c,b,a Answer :D

Discussion

17.	Evaluate the following integrals (v) int_(0)^(a)(sqrt(a)-sqrt(x))^(2)dx
Answer» ANSWER :`(a^(2))/(6)`

Discussion

18.	If 0 lt alphalt beta lt gamma lt pi//2, then the equation (x-sinbeta)(x-singamma)+(x-sinalpha)(x-singamma)+(x-sinalpha)(x-sinbeta)=0 has
Answer» real and unequal ROOTS non-real roots real and equal roots real and unequal roots greater than `2` Solution :`(a)` Let `F(x)=(x-sinbeta)(x-singamma)+(x-sinalpha)(x-singamma)+(x-sinalpha)(x-sinbeta)` Now, `f(sin ALPHA)=(sinalpha-sinbeta)(sinalpha-singamma)` `=(-)(-)=positive `f(sinbeta)=(sinbeta-sinalpha)(sinbeta-sinalpha)=(+)(-)=`negative `f(sin gamma)=(sin gamma-sinalpha)(singamma-sinbeta)=(+)(+)=`positive `IMPLIES "Roots of " f(x)=0` are real and distinct.

Discussion

19.	alpha,beta are the real roots of ax^(2) + bx + c = 0 observe the following lists then the correct matching is
Answer» `{:(A,B,C,D),(1,1,2,5):}` `{:(A,B,C,D),(1,3,4,5):}` `{:(A,B,C,D),(3,1,5,4):}` `{:(A,B,C,D),(3,1,5,2):}` ANSWER :D

Discussion

20.	For function f(x) = (alpha x)/(x+1) , x ne -1if fof(x) = x then alpha =..........
Answer» `SQRT2` `-1` `1/2` `-sqrt2` SOLUTION :N/A

Discussion

21.	The slope m of a tangent through the point (7,1) to the circle x^(2)+y^2=25 satisfies the equation.
Answer» `12M^(2)+7m+12=0` `12m^(2)-7m+12=0` `12m^(2)+7m-12=0` `12m^(2)-7m-12=0` ANSWER :D

Discussion

22.	The random variable X has a probability distribution P(X) of the following form, where k is some number : P(X)={{:(k, "if " x=0),(2k, "if " x=1),(3k, "if " x=2),(0, "otherwise"):} (a) Determine the value of k. (b) Find P (X lt 2), P (Xle 2), P(X ge 2).
Answer» <P> ANSWER :(a) `k=(1)/(6)` (b)`P(X lt 2)=(1)/(2), P(X le 2)=1, P(X ge 2)=(1)/(2)`

Discussion

23.	Let f(x)(xgt1) be a differentiable function satisfying f(x)=(In x)^(2)-int_(1)^(e) (f(t))/t dt. Then if area bounded by tangent line ofy=f(x) at (e,f(e)), then curve y=f(x) and x=1 is A then [A] is ([.] is G.I.F)
Answer» SOLUTION :0

Discussion

24.	Show that the function f(x) = log (sin x) (i) is strictly increasing in the interval]0,pi/2[. (ii) is strictly decreasing in the interval]pi/2,pi[.
Answer»

Discussion

25.	Lt_(n to oo)[1/(n+1) + 1/(n+1)+..." to n terms"] =
Answer» LOG 2 `log ""1/2` `log 3` `2 LOG2` ANSWER :A

Discussion

26.	Which of the following is (are) incorrect ?
Answer» If `f (X)= sin x and g(x) =` in x then range of `g (f (x))` is `[-1,1]`If `f (x)=(2011 -x ^(2012))^(1/2012)` then `f (f(2)) =1/2` The FUNCTION `f : R to R` DEFINED as `f (x) = (x^(2) + 4x+30)/( x ^(2) -8x+18)` is not surjective. ANSWER :A::B

Discussion

27.	If x = (2.5)/(3.6) - (2.5.8 )/(3.6.9) (2/5) + (2.5.8.11)/(3.6.12) (2/5)^2 - …… oo , then7^2 (12 x + 55)^3 =
Answer» `3^(8) 5^3` `3^(8) 5^5` `3^(3) 5^5` `3^(2) 5^8` ANSWER :D

Discussion

28.	If P is a point such that the ratio of the square of the lengths of the tangents from R to the circles x^(2) + y^(2) + 2x - 4y - 20 = 0 and x^(2) + y^(2) - 4x + 2y - 44 = 0 is 2 : 3, then the locus of P is a circle with centre
Answer» (7, -8) (-7, 8) (7, + 8) (-7, -8) ANSWER :B

Discussion

29.	Find the number of solutions of the equations (sin x - 1)^(3) + (cos x - 1)^(3) + ( sin x)^(3) = ( 2 sin x + cos x - 2)^(3)in [ 0, 2 pi] .
Answer» ANSWER :5

Discussion

30.	If vec(a)=2hat(i)+3hat(j)-5hat(k),vec(b)=mhat(i)+nhat(j)+12hat(k)andvec(a)xxvec(b)=vec(0), then (m,n) =
Answer» `((-24)/(5),(-36)/(5))` `((-24)/(5),(36)/(5))` `((24)/(5),(-36)/(5))` `((24)/(5),(36)/(5))` ANSWER :A

Discussion

31.	Find (dy)/(dx) in the following 2x+ 3y= sin y
Answer» ANSWER :`(2)/(COS y-3)`

Discussion

32.	The points in the argand plane represented by the complex conjugates of 1+2i, 2-3i, 3-4i
Answer» are collinear form an EQUILATERAL triangle form an OBTUSE ANGLED triangle form an ACUTE angled triangle Answer :C

Discussion

33.	(Diet Problem): A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain atleast 8 unitsof vitamin A and 10 units of vitamins C. Food I contains 2 units/ kg of vitamins A and 1 unit/kg of vitamin C. Food II contains 1 unit/kg of vitamin A and 2 units/kg of vitamine C. It costs Rs. 50 per kg to purchase Food I Rs. 70 per kg to purchase Food II. Formulate this problem as a linear programming problem to minimise the cost of such a mixture.
Answer» ANSWER :RS. 380

Discussion

34.	sin(tan^(-1)x),\|x\|lt1 is 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

35.	Differentiate (x+1)^(2) (x + 2)^(3) (x + 3)^(4)
Answer» ANSWER :`(x+1) (x+2)^(2) (x+3)^(3) (9x^(2) + 34x + 29)`

Discussion

36.	How many odd number of six significant digits can be formed with the digits 0,1,2,5,6,7 when no digit is repeated?
Answer» 120 96 360 288 Answer :D

Discussion

37.	The mean deviation about median for the following data is
Answer» 10.34 10.43 10.78 10.87 Answer :A

Discussion

38.	Evaluate int_(0)^(2)[x^(2)] dx where [ ] denotes the GIF
Answer» ANSWER :`5-SQRT(2) - sqrt(3)`

Discussion

39.	(iv) Find the coefficient of x^(2) in the powers of x specifying the interval in which the expansion is valid.
Answer» ANSWER :25

Discussion

40.	Discuss the continuityof the function f defined by {{:(x+2," if "x le 1),(x-2," if "x gt 1):}.
Answer» ANSWER :HENCE, x=1 is the only POINT of DISCONTINUITY of F.

Discussion

41.	Using matrix method, solve the system of equations: {:( x+2y+z=1 ),( x-y -z=2 ),( 2x+3y+z=1):}
Answer» ANSWER :` x=3, y=-3 , z=4`

Discussion

42.	Find (1)/(2)(A+A') and(1)/(2)(A-A'), when A=[(0, a, b),(-a,0,c),(-b,-c,0)]
Answer» ANSWER :`[(0,0,0),(0,0,0),(0,0,0)],[(0,a,B),(-a,0,C),(-b,-c,0)]`

Discussion

43.	Thequotientobtainedwhen 3x^4 -x^3 +2x^2 -2x -4isdivided byx^2 -4 is
Answer» `3X^2 -7X+16` ` 3x^2 +X +14` `3x^2 -x-14` `3x^2 -x+14` ANSWER :D

Discussion

44.	Over which of the following sequences of months did total sales decline the most?
Answer» FEB - Mar Mar - Apr Jun - Jul Aug - Sep Answer :D

Discussion

45.	""^(15)C_(8)+""^(15)C_(9)-""^(15)C_(6)-""^(15)C_(7)is equal to
Answer» 8 0 6 4 Answer :B

Discussion

46.	Evaluate the following integrals int(dx)/(xsqrt(x^(2)+x+1))
Answer» ANSWER :`-SINH^(-1)((2+x)/(xsqrt(3)))+C`

Discussion

47.	Evaluate the following integrals: int_2^3 (1/(x^2-1))dx
Answer» SOLUTION :`int_2^3 DX/(x^2-1) = [1/2 LOG\|(x-1)/(x+1)\|]_2^3` =`1/2[log\|(3-1)/(3+1)\| -log\|(2-1)/(2+1)\|]` =`1/2[log (2/4) -log(1/3)]` =`1/2 log[(2/4)/(1/3)] = 1/2 log[3/2]`

Discussion

48.	Find the area of the triangle whose vertices are (-2,3), (3,2) and (-1,-8) by using determinant method.
Answer» ANSWER :15 SQ. UNITS

Discussion

49.	(cos15^0+isin15^0)(cos45^0+isin45^0)=
Answer» `1/2(1+sqrt3i)` `1/sqrt2(1-sqrt3i)` `1/sqrt3(1+sqrti)` `1/sqrt3(1-sqrt3i)` ANSWER :A

Discussion

50.	If f:R^(+) rarr R , f(x) = x/(x+1) is .......
Answer» ONE - one and ONTO . one - one and not onto . not one - one and not onto. Onto but not one - one. SOLUTION :N/A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The point of intersection of the line (x-4)/(2) = (y+3)/(5) = (z-3)/(3) and the plane x + y + z + 2 = 0 is........

Evaluate the following integrals int sin (log x) dx

Integrate the following functions: cos(2x)/(cosx+sinx)^2

int (sec^2x)/((tanx+1)(tanx+2)) dx

Differentiate (8^(x))/(x^(8))

If x = (1*3)/(3*6)+(1*3*5)/(3*6*9)+(1*3*5*7)/(3*6*9*12)+. . .to infinite terms, then9x^(2) + 24 x =

To find the coefficient of x^(4) in the expansion of (3x)/((x-2)(x-1)), the interval in which the expansion is valid, is

Solve the following systems of linear inequalities graphically : x + y gt 1 , 3x - y lt 3, x- 3y + 3 gt 0.

If (6 sqrt6+14)^(2n+1)=R and F=[R], where [R] denotes the greatest integer less than or equal to R thwn RF=

The set of all real values of alpha for which the equation, |a+2||x-2|=alpha^(2)-2alpha has real solution for s, is :

The number of ways in which 5 players be chosen from 12 players so as to include one particular player is

int ((x-1)dx)/((x+1)sqrt(x^(3)+x^(2)+x))=

If the function f : R rarr R defined by f(x)= {((sin(a +1) x + sin x)/(x),x lt 0),((sqrt(x + x^(2)) - sqrtx)/(x^(1//2)),x gt 0):} continuous on R, then a + b=

Evaluate the following integrals (v) int_(0)^(a)(sqrt(a)-sqrt(x))^(2)dx

If 0 lt alphalt beta lt gamma lt pi//2, then the equation (x-sinbeta)(x-singamma)+(x-sinalpha)(x-singamma)+(x-sinalpha)(x-sinbeta)=0 has

alpha,beta are the real roots of ax^(2) + bx + c = 0 observe the following lists then the correct matching is

For function f(x) = (alpha x)/(x+1) , x ne -1if fof(x) = x then alpha =..........

The slope m of a tangent through the point (7,1) to the circle x^(2)+y^2=25 satisfies the equation.

The random variable X has a probability distribution P(X) of the following form,﻿ where k is some number :﻿ P(X)={{:(k, "if " x=0),(2k, "if " x=1),(3k, "if " x=2),(0, "otherwise"):} (a) Determine the value of k.﻿ (b) Find P (X lt 2), P (Xle 2), P(X ge 2).﻿

Let f(x)(xgt1) be a differentiable function satisfying f(x)=(In x)^(2)-int_(1)^(e) (f(t))/t dt. Then if area bounded by tangent line ofy=f(x) at (e,f(e)), then curve y=f(x) and x=1 is A then [A] is ([.] is G.I.F)

Show that the function f(x) = log (sin x) (i) is strictly increasing in the interval]0,pi/2[. (ii) is strictly decreasing in the interval]pi/2,pi[.

Lt_(n to oo)[1/(n+1) + 1/(n+1)+..." to n terms"] =

Which of the following is (are) incorrect ?

If x = (2.5)/(3.6) - (2.5.8 )/(3.6.9) (2/5) + (2.5.8.11)/(3.6.12) (2/5)^2 - …… oo , then7^2 (12 x + 55)^3 =

If P is a point such that the ratio of the square of the lengths of the tangents from R to the circles x^(2) + y^(2) + 2x - 4y - 20 = 0 and x^(2) + y^(2) - 4x + 2y - 44 = 0 is 2 : 3, then the locus of P is a circle with centre

Find the number of solutions of the equations (sin x - 1)^(3) + (cos x - 1)^(3) + ( sin x)^(3) = ( 2 sin x + cos x - 2)^(3)in [ 0, 2 pi] .

If vec(a)=2hat(i)+3hat(j)-5hat(k),vec(b)=mhat(i)+nhat(j)+12hat(k)andvec(a)xxvec(b)=vec(0), then (m,n) =

Find (dy)/(dx) in the following 2x+ 3y= sin y

The points in the argand plane represented by the complex conjugates of 1+2i, 2-3i, 3-4i

sin(tan^(-1)x),|x|lt1 is equal to

Differentiate (x+1)^(2) (x + 2)^(3) (x + 3)^(4)

How many odd number of six significant digits can be formed with the digits 0,1,2,5,6,7 when no digit is repeated?

The mean deviation about median for the following data is

Evaluate int_(0)^(2)[x^(2)] dx where [ ] denotes the GIF

(iv) Find the coefficient of x^(2) in the powers of x specifying the interval in which the expansion is valid.

Discuss the continuityof the function f defined by {{:(x+2," if "x le 1),(x-2," if "x gt 1):}.

Using matrix method, solve the system of equations: {:( x+2y+z=1 ),( x-y -z=2 ),( 2x+3y+z=1):}

Find (1)/(2)(A+A') and(1)/(2)(A-A'), when A=[(0, a, b),(-a,0,c),(-b,-c,0)]

Thequotientobtainedwhen 3x^4 -x^3 +2x^2 -2x -4isdivided byx^2 -4 is

Over which of the following sequences of months did total sales decline the most?

""^(15)C_(8)+""^(15)C_(9)-""^(15)C_(6)-""^(15)C_(7)is equal to

Evaluate the following integrals int(dx)/(xsqrt(x^(2)+x+1))

Evaluate the following integrals: int_2^3 (1/(x^2-1))dx

Find the area of the triangle whose vertices are (-2,3), (3,2) and (-1,-8) by using determinant method.

(cos15^0+isin15^0)(cos45^0+isin45^0)=

If f:R^(+) rarr R , f(x) = x/(x+1) is .......

If x = (13)/(36)+(135)/(369)+(1357)/(36912)+. . .to infinite terms, then9x^(2) + 24 x =

The random variable X has a probability distribution P(X) of the following form, where k is some number : P(X)={{:(k, "if " x=0),(2k, "if " x=1),(3k, "if " x=2),(0, "otherwise"):} (a) Determine the value of k. (b) Find P (X lt 2), P (Xle 2), P(X ge 2).