28278 + Interview Questions in Maths in Class 12 Page 111 InterviewSolution

5501.	Let A_(1), A_(2) and A_(3) be subsets of a set X. Which one of the following is correct ?
Answer» `A_(1)uuA_(2)uuA_(3)` is the SMALLEST SUBSET of `X` containing elements of each of `A_(1)`, `A_(2)` and `A_(3)` `A_(1)uuA_(2)uuA_(3)` is the smallest subset of `X` containing elements EITHER `A_(1)` or `A_(2)uuA_(3)` but not both The smallest subset of `X` containing `A_(1)uuA_(2)` and `A_(3)` equals the smallest subset of `X` containing both `A_(1)` and `A_(2)uuA_(3)` only if `A_(2)=A_(3)` None of these Answer :A

Discussion

5502.	Let f : R rarr R be defined as f(x) = 10 x +7. Find the function g:R rarrR such that gof= fog = I_(g)
Answer» SOLUTION :N/A

Discussion

5503.	underset(0)overset(2)int \|1-x\| dx
Answer» 0 1 `1/2` `- 1/2` ANSWER :B

Discussion

5504.	If m is chosen in the quadratic equation (m^(2)+1)x^(2)-3x+(m^(2)+1)^(2)=0such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is
Answer» `4sqrt(3)` `10sqrt(5)` `8sqrt(5)` `8sqrt(3)` ANSWER :C

Discussion

5505.	At what points, f(x)=1+2 sin x + 3 cos^(2)x, 0 lt x lt (2pi)/(3) has maximum or minimum ? Find the maximum and minimum value of the function.
Answer» ANSWER :For `x=sin^(-1)((1)/(3))`, Maximum VALUE `(13)/(3)` and `x = 90^(@)`, Minimum value = 3.

Discussion

5506.	If y=log(x+sqrt(x^(2)+a^(2))), then prove that y=log(x+sqrt(x^(2)+a^(2))),
Answer»

Discussion

5507.	In triangleABC, with usual notation, ovserve the two statement given below, Statement I : rr_1r_2r_3= triangle^2 Statement II r_1r_2+r_2r_3+r_3r_1=S^2 which of the following is correct ?
Answer» Both I and II are TRUE I is true, II is FALSE I is false, II is true Both I and II are false Answer :A

Discussion

5508.	Find the number of onto functions that can be defined from a set A={a_(1),a_(2),......,a_(n)} onto another set B={x,y} such that a_(1) is always mapped to x.
Answer» ANSWER :`=2^(n-1)-1`

Discussion

5509.	int(3x+1)/((x+1)^(2)(x+3))dx
Answer» ANSWER :`(1)/(2)LOG\|(x-1)/(x+2)\|-(1)/(x-1)+C`

Discussion

5510.	A comet moves in a parabolic orbit with the sun as focus . When the comet is 2 xx 10^(7) K. M. from the sun, the line from the sun to it makes an angle (pi)/(2) with the axis of the orbit. Find how near the comet come to the sun.
Answer» ANSWER :`10^(7)` k.m.

Discussion

5511.	How many factors does 1155 have that are divisible by 3?
Answer» Solution : `:.`In order to be a factor of 1155 divisible by 3, we have to choose one or TWO of 5,7,11 along with 3 or 3 ALONE. `:." The NUMBER of ways." = ""^3C_1+ ""^3C_2 + ""^3C_0 =2^3-1 =7` ` :.' The number of FACTORS is 7 excluding 1155 itself.

Discussion

5512.	Find thearea of the regionboundedby thecurvey= 2 x -x^2and X- axis.
Answer» ANSWER :`4/3` spunits

Discussion

5513.	Two flagstaffs stand on a horizontal plane. A and B are two points on the line joining their feet and between them. The angles of elevation of the tops of the flagstatts as seen from A are 30^(@) and 60^(@) and as seen from B are 60^(@) and 45^(@). If AB=30 , then the distance between the flagstaffs in motres is:
Answer» `30 + 15 SQRT3` `30 - 15 sqrt3` `60 + 15 sqrt3` `60-15 sqrt3.` Answer :C

Discussion

5514.	The position of the points O(0, 0) and P(2, -1) is ………, in the region of the inequality 2y-3xlt5.
Answer» <P>O is inside the REGION and P is outside the region O and P both are inside the region O and P both are outside the region O is outside the region and P is inside the region Answer :B

Discussion

5515.	Find the centre and radius of each of the circles whose equations are given below. sqrt(1+m^(3) ) (x^(2)+y^(2))-2cx - 2mcy = 0
Answer» ANSWER :` ((C)/(SQRT(1+m^(2))).(MC)/(sqrt(1+m^(2)))) . \|C\| `

Discussion

5516.	Find the points of localmaximaor minima for f(x) =" sin "2x -x, x in (0,pi)
Answer» Solution :`f(X) =" sin "2x -x` `f'(x) =2 COS 2x -1` `f'(x) =0 ""rArr ""cos 2x=(1)/(2) ""rArr ""x=(pi)/(6),(5pi)/(6)` `f''(x) =-4 sin 2x` `f''((pi)/6) LT0 ""rArr "" "Maxima at " x=(pi)/(6)` `f''((5pi)/(6)) gt 0 ""rArr """MINIMA at " x=((5pi)/(6))`

Discussion

5517.	Determine P(E\|F) Two coins are tossed once, where E : tail appears on one coin, F : one coin shows head
Answer» ANSWER :1

Discussion

5518.	The value of lambda such that lambda x^(2) - 10 xy + 12 y^(2) + 5x - 16 y-3 = 0 represents a pair of straight lines , is
Answer» 1 `-1` 2 `-2` ANSWER :C

Discussion

5519.	Let S=(2n)/(1)C_(0)+(2^(2)n)/(2)C_(1)+(2^(3)n)/(3)C_(2)+.....+(2^(n+1)n)/(n+1)C_(n). . Then S equals-
Answer» `(2^(N+1)-1)/(1)` `(3^(n+1)-1)/(1)` `(3^(n)-1)/(1)` `(2^(n)-1)/(1)` Answer :B

Discussion

5520.	Let f(x)={{:((log(1+ax)-log(1-bx))/x, x ne 0), (k,x=0):}. Find 'k' so that f(x) is continuous at x = 0.
Answer» ANSWER :k=a+b

Discussion

5521.	Area bounded by the curve v=x, the x-axis and the ordinates x = -2 and x = 1 is
Answer» -9 `-15/4` `15/4` `17/4` ANSWER :D

Discussion

5522.	Solve system of linear equations , using matrix method if exists x-y+2z=1 2y-3z=1 3x-2y+4z=7
Answer» ANSWER :x=0,y=5,z=3

Discussion

5523.	Calculate number of electrons present in 3.5 g of PO :-
Answer» 6 `5 N_(A)` `0.1 N_(A)` `4.7 N_(A)` ANSWER :A

Discussion

5524.	The valueof 'lambda' if ax^4 +bx^3 + cx^2 + 50x+d =\|(x^3-14x^2, -x , 3x+lambda),(4x+1,3x,x-4),(-3,0,0)\| , is :
Answer» 0 1 2 3 Answer :C

Discussion

5525.	If f(x) = x^(a) log x and f(0) = 0then the value of alpha for which Rolle's theorem can be applied in [0,1] is
Answer» `-1/2` `-1/3` `-1/4` `-1` ANSWER :B::C

Discussion

5526.	ABCD is a rhombus IF M,N,P are points taken on sides AB,BC,CD respectively such that centroid of DeltaMNP is G, IF AM=1/12 units, BN=1/5 units then
Answer» If G LIES on AC, `PD=7/60` units If G lies on BD `PD=31/60`units IF G lies on AC, `PC=13/20` units IF G lies on BD, `PC=17/60` units Answer :A::D

Discussion

5527.	Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(pi/2)(tanx)/(1+tanx)dx=...........
Answer» `(pi)/(2)` `(pi)/(3)` `(pi)/(4)` `-pi` ANSWER :C

Discussion

5528.	The van dar Waals parameters for gases W, X, Y and Z are {:(Gas,a(atm L^2 mol^(-2)),b(L mol^(-1))),(W,4.0,0.027),(X,8.0,0.030),(Y,6.0,0.032),(Z,12.0,0.027):} Which one of these gases has the highest critical temperature?
Answer» W<BR>X Y Z Solution :`T_(C) = (8A)/(27 bR)` For high critical temperature VALUE of a should be maximum and value of B should be MINIMUM.

Discussion

5529.	The pole of 3x+4y-45=0 w.r.t. circle x^(2)+y^(2)-6x-8y+5=0 is
Answer» (6,8) (3,4) (3/5,4/5) (-6,8) ANSWER :A

Discussion

5530.	Evaluate int_(0)^(100pi) sqrt(1-cos 2 x) dx
Answer» ANSWER :`200(SQRT(2))`

Discussion

5531.	Determine whether (t_n) is an arithmetic sequence if: t_n=an^2+b
Answer» SOLUTION :`t_nan^2+brArrt_(N+1)=a(n+1)^2+b` `thereforet_(n+1)-t_n=a[n+1)^2-n^2]+b-b=a(2n+1)` (does not independent of n) `THEREFORE(t_n)` is not an ARITHMETIC SEQUENCE.

Discussion

5532.	Write the derivative of sec^-1x with respect to x at x=-1/3.
Answer» SOLUTION :DOM `sec^-1s=R-[-1,1] I,E, sec^-1x` is not DEFINED at `1/3`.

Discussion

5533.	If f(x)={{:(Kx^(2),"if x" le 2),(3,"if x" gt 2):}} is continuous at x = 2, then the value of K is
Answer» 1)3 2)4 3)`3//4` 4)`4//3` ANSWER :C

Discussion

5534.	If z_(1) =2 -3i and z_(2) = -1 + i, then the locus of a point P represented by z = x +iy in the argand plane satisfying the equation arg ((z-z_(1))/(z-z_(2))) = (pi)/(2) is
Answer» `x^(2) + y^(2) -x + 2y -5 = 0` `x^(2) + y^(2) -x + 2y -5 = 0 and 4X + 3y + 1 lt 0` `4x + 3y + 1 = 0 and x^(2) + y^(2) -x + 2y -5 GT 0` `x^(2) + y^(2) -x + 2y -5 = 0 and 4x + 3y + 1 gt 0` Answer :D

Discussion

5535.	findthe areaof theregionincludedbetweeny^2 = 9xand y = x.
Answer» ANSWER :`27/2` SEQ . UNIT

Discussion

5536.	For a**b = a +b + 10on Z , the identity element is ........
Answer» 0 `-5` `-10` 1 Solution :N/A

Discussion

5537.	Differentiate the following w.r.t.x. tan^(-1) ((sin x)/(1+cos x))
Answer» ANSWER :`F'(X)= (1)/(2)`.

Discussion

5538.	Find local maximum and local minimum values of the function f given by f(x)=3x^(4)+4x^(3)-12x^(2)+12.
Answer» Answer :Function f has local maximum VALUE 12 at x = 0 and local minimum value 7 and - 20 at x = 1 and x = -2 respectively.

Discussion

5539.	Letf'(sin x)lt0 and f''(sin x) gt0 forall x in (0,(pi)/(2)) and g(x) =f(sinx)+f(cosx) If x=3 is a point of minima and x=4ios a popint of maximan then which of the followingis true?
Answer» `a lt0, B gt0` `a GT 0, b lt 0` `a gt 0, b gt 0` not possible Solution :If f(X) is continous then `f(3^(-))=f(3^(+))` or `-9+12+a=3a+b or 2a+b=3` Also `f(4^(+)) or 4a+b=-b+6 r 2a+b=3` Thus f(x) is contnous for infinite values of a and b also `f(x)={{:(-2x+4,xlt3),(a,3ltxlt4),((-b)/(4),xgt4):}` For f(x) to be diffentiable `f(3^(-))=f(3^(+))` or `a=-2 and -(bb)/(4) =a=-2 or b=8` But these values do not SATISFY equation (1) Hence f(x) cannot be DIFFERENTIABLE

Discussion

5540.	Integrate the following int(sectheta tantheta)/(sec^2theta+4) d theta
Answer» Solution :`INT(sectheta TANTHETA)/(sec^2theta+4) d theta` [put `sectheta=t` then `sectheta CDOT tantheta d theta =dt` `int(dt)/(4+t^2)`=`int(dt)/(2^2+t^2)=(1/2)tan^(-1)(t/2)+C` `(1/2)tan^(-1)(sectheta/2)+C`

Discussion

5541.	If y= log ((1-x^(2))/(1+ x^(2))), then (dy)/(dx) is equal to _______
Answer» 1)`(-4x^(3))/(1-x^(4))` 2)`(1)/(4-x^(4))` 3)`(4x^(3))/(1-x^(4))` 4)`(-4x)/(1-x^(4))` Answer :D

Discussion

5542.	If a, b, c,d are 4 vector such that a.b =0, \|a xx c\| = \|a\|\|c\|, \|a xx d\| = \|a\|\|d\|, " then " [bcd]=
Answer» `\|a\|\|b\|\|c\|` `\|b\|\|c\|\|d\|` `(1)/(6)` 0 Answer :D

Discussion

5543.	int_0^(pi) (x tanx dx)/(sec x+ cosx) =
Answer» `pi^2//4` `pi^2//2` `3pi^2//2` `pi^2//3` ANSWER :A

Discussion

5544.	The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x)=0.007 x^(3)-0.003 x^(2)+15x+4000. Find the marginal cost when 17 units are produced.
Answer» ANSWER :RS. 20.967

Discussion

5545.	If bar(x)=(a,4,2a) and bar(y)=(2a,-1,a) are perpendicualr to each other then a = …………..
Answer» 2 1 4 Any REAL NUMBER ANSWER :B

Discussion

5546.	In the followinggraph, state the absolute and local maximum and minimum values of the function. (##CEN_GRA_C01_S01_022_Q01.png" width="80%">
Answer» Solution :x = 2 is the POINT of local MINIMA, and the local minimum value isf(2) = 1. x = 4 is thepoint of absolute MAXIMA, and the absolute maximum value is f(4) = 4. x = 5 is the point of local minima, and the local minimum value is f(5) = 2. x = 6 is the point of local maxima, and the local maximum value isf(6) = 3. x = 7is the point of absolute minima, and the local minimum value is f (7) = 0.

Discussion

5547.	If x^(2)-3x+2 is a factor of x^(2)-ax^(2)+b=0 then equation whose roots are a and b is
Answer» `X^(2)+9x+20=0` `x^(2)-9x-20=0` `x^(2)-9x+20=0` `x^(2)+9x-20=0` ANSWER :C

Discussion

5548.	Find P^(-1) , if it exists given P=[{:(10,-2),(-5,1):}].
Answer» <P> ANSWER :`P^(-1)` Does not EXIST.)

Discussion

5549.	The volume of a cube is increasing at a rate of 9cc/sec. How fast is the surface area increasing when the length of an edge is 10 cm.
Answer» ANSWER :`18/5cm^(2)//SEC`

Discussion

5550.	int (sum_(r = 0)^(infty) (x^(r) 3^(r))/(r!) )dx =
Answer» `e^(x) + c ` `(e^(3X))/(3) + c ` `(-3)/(1 - 3x)` + c `3E^(3x)+c` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Let A_(1), A_(2) and A_(3) be subsets of a set X. Which one of the following is correct ?

Let f : R rarr R be defined as f(x) = 10 x +7. Find the function g:R rarrR such that gof= fog = I_(g)

underset(0)overset(2)int |1-x| dx

If m is chosen in the quadratic equation (m^(2)+1)x^(2)-3x+(m^(2)+1)^(2)=0such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is

At what points, f(x)=1+2 sin x + 3 cos^(2)x, 0 lt x lt (2pi)/(3) has maximum or minimum ? Find the maximum and minimum value of the function.

If y=log(x+sqrt(x^(2)+a^(2))), then prove that y=log(x+sqrt(x^(2)+a^(2))),

In triangleABC, with usual notation, ovserve the two statement given below, Statement I : rr_1r_2r_3= triangle^2 Statement II r_1r_2+r_2r_3+r_3r_1=S^2 which of the following is correct ?

Find the number of onto functions that can be defined from a set A={a_(1),a_(2),......,a_(n)} onto another set B={x,y} such that a_(1) is always mapped to x.

int(3x+1)/((x+1)^(2)(x+3))dx

A comet moves in a parabolic orbit with the sun as focus . When the comet is 2 xx 10^(7) K. M. from the sun, the line from the sun to it makes an angle (pi)/(2) with the axis of the orbit. Find how near the comet come to the sun.

How many factors does 1155 have that are divisible by 3?

Find thearea of the regionboundedby thecurvey= 2 x -x^2and X- axis.

The position of the points O(0, 0) and P(2, -1) is ………, in the region of the inequality 2y-3xlt5.

Find the centre and radius of each of the circles whose equations are given below. sqrt(1+m^(3) ) (x^(2)+y^(2))-2cx - 2mcy = 0

Find the points of localmaximaor minima for f(x) =" sin "2x -x, x in (0,pi)

Determine P(E|F) Two coins are tossed once, where E : tail appears on one coin, F : one coin shows head

The value of lambda such that lambda x^(2) - 10 xy + 12 y^(2) + 5x - 16 y-3 = 0 represents a pair of straight lines , is

Let S=(2n)/(1)C_(0)+(2^(2)n)/(2)C_(1)+(2^(3)n)/(3)C_(2)+.....+(2^(n+1)n)/(n+1)C_(n). . Then S equals-

Let f(x)={{:((log(1+ax)-log(1-bx))/x, x ne 0), (k,x=0):}. Find 'k' so that f(x) is continuous at x = 0.

Area bounded by the curve v=x, the x-axis and the ordinates x = -2 and x = 1 is

Solve system of linear equations , using matrix method if exists x-y+2z=1 2y-3z=1 3x-2y+4z=7

Calculate number of electrons present in 3.5 g of PO :-

The valueof 'lambda' if ax^4 +bx^3 + cx^2 + 50x+d =|(x^3-14x^2, -x , 3x+lambda),(4x+1,3x,x-4),(-3,0,0)| , is :

If f(x) = x^(a) log x and f(0) = 0then the value of alpha for which Rolle's theorem can be applied in [0,1] is

ABCD is a rhombus IF M,N,P are points taken on sides AB,BC,CD respectively such that centroid of DeltaMNP is G, IF AM=1/12 units, BN=1/5 units then

Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(pi/2)(tanx)/(1+tanx)dx=...........

The van dar Waals parameters for gases W, X, Y and Z are {:(Gas,a(atm L^2 mol^(-2)),b(L mol^(-1))),(W,4.0,0.027),(X,8.0,0.030),(Y,6.0,0.032),(Z,12.0,0.027):} Which one of these gases has the highest critical temperature?

The pole of 3x+4y-45=0 w.r.t. circle x^(2)+y^(2)-6x-8y+5=0 is

Evaluate int_(0)^(100pi) sqrt(1-cos 2 x) dx

Determine whether (t_n) is an arithmetic sequence if: t_n=an^2+b

Write the derivative of sec^-1x with respect to x at x=-1/3.

If f(x)={{:(Kx^(2),"if x" le 2),(3,"if x" gt 2):}} is continuous at x = 2, then the value of K is

If z_(1) =2 -3i and z_(2) = -1 + i, then the locus of a point P represented by z = x +iy in the argand plane satisfying the equation arg ((z-z_(1))/(z-z_(2))) = (pi)/(2) is

findthe areaof theregionincludedbetweeny^2 = 9xand y = x.

For a**b = a +b + 10on Z , the identity element is ........

Differentiate the following w.r.t.x. tan^(-1) ((sin x)/(1+cos x))

Find local maximum and local minimum values of the function f given by f(x)=3x^(4)+4x^(3)-12x^(2)+12.

Letf'(sin x)lt0 and f''(sin x) gt0 forall x in (0,(pi)/(2)) and g(x) =f(sinx)+f(cosx) If x=3 is a point of minima and x=4ios a popint of maximan then which of the followingis true?

Integrate the following int(sectheta tantheta)/(sec^2theta+4) d theta

If y= log ((1-x^(2))/(1+ x^(2))), then (dy)/(dx) is equal to _______

If a, b, c,d are 4 vector such that a.b =0, |a xx c| = |a||c|, |a xx d| = |a||d|, " then " [bcd]=

int_0^(pi) (x tanx dx)/(sec x+ cosx) =

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x)=0.007 x^(3)-0.003 x^(2)+15x+4000. Find the marginal cost when 17 units are produced.

If bar(x)=(a,4,2a) and bar(y)=(2a,-1,a) are perpendicualr to each other then a = …………..

In the followinggraph, state the absolute and local maximum and minimum values of the function. (##CEN_GRA_C01_S01_022_Q01.png" width="80%">

If x^(2)-3x+2 is a factor of x^(2)-ax^(2)+b=0 then equation whose roots are a and b is

Find P^(-1) , if it exists given P=[{:(10,-2),(-5,1):}].

The volume of a cube is increasing at a rate of 9cc/sec. How fast is the surface area increasing when the length of an edge is 10 cm.

int (sum_(r = 0)^(infty) (x^(r) 3^(r))/(r!) )dx =