28278 + Interview Questions in Maths in Class 12 Page 225 InterviewSolution

11201.	int_(-1)^( sqrt3) (dx)/( 1+x^2) = …...... .
Answer» `(7pi)/( 12)` `( PI)/(6)` `(pi)/(12)` `(5PI)/( 12)` ANSWER :A

Discussion

11202.	The sum of the fifth powers of the roots of the equation x^(4) - 3x^(3) + 5x^(2) - 12x + 4= 0is
Answer» 123 36 149 795 Answer :1

Discussion

11203.	Let f : R to R be defined by f(x)=x^(4), then
Answer» 1.f is ONE - one and ONTO 2.f MAY be one - one and onto 3.f is one - one but not onto 4.f is NEITHER one - one nor onto ANSWER :D

Discussion

11204.	What would be the reduction potential of an electrode at298 K , which originally contained1K_(2)Cr_(2)O_(7) solution in acidic buffer solution ofpH = 1.0 and which was treated with 50% of the Sn necessary to reduce all Cr_(2)O_(7)^(2-)" to "Cr^(3+).Assume pH of solution remains constant. Given : E^(0)._(Cr_(2)O_(7)^(2-)//Cr^(3+), H^(+))= 1. 33 V , log 2 = 0.3 , (2.303RT)/F = 0.06
Answer» `1.285 V` `1.193 V` `1.187 V` NONE of these Answer :C

Discussion

11205.	Which of the following is not equivalent to the equation a/(bc)=d/(ef) ?
Answer» `(ae)/(DB)=c/f` `(af)/d =(BC)/E` `a/d=(bc)/(ef)` `(ae)/f=(db)/c` ANSWER :D

Discussion

11206.	Find the number of ways of arranging 10 persons A_(1),A_(2),……….A_(10) in a row if no two of A_(1),A_(2) and A_(3) come together.
Answer» <P> ANSWER :`=7!xx""^(8)P_(3)`

Discussion

11207.	A person has 21 tickets with numbered 1 to 21. Three tickets are selected from it at random. Find the probability of an event that numbers of selected three tickets are in A.P.
Answer» ANSWER :`(10)/(133)`

Discussion

11208.	If the lines kx^(2)+6xy+2y^(2)=0 and x+3y=9 form an isosceles triangle, then k=
Answer» `-8` `8` `6` `-6` ANSWER :D

Discussion

11209.	lim_(alpha to 0) (sin(alpha^n))/((sin alpha)^m) (m , n in I^+) is equal to
Answer» 1 if `m gt N` 0 if ` n gt m` 1 if ` gt m` 1 if m=n Answer :B

Discussion

11210.	Let K_(1)= Total number of ways of selecting of ball from a bag which contains n balls of first colour (n+1) balls of second colour, (n+2) balls of third colour ,…….,(2n-1) balls of n colour. K_(2)= number of n -digit numbers using the digit 1,2,3,n and K_(3)= number of ways of arranging (n+1) objects on a circle. The value of lim_(nto oo)((K_(1))/(K_(2)+K_(3))) is
Answer» `E` `1` `0` does not exist Answer :B

Discussion

11211.	If a lt 0 lt bthen int_(a)^(b)(\|x\|)/(x) dx=
Answer» `a-b` `b-a` `a+b` 0 Answer :C

Discussion

11212.	A line through the origin meets the circlex^(2) +y^(2) =a^(2)at P and the hyperbolax^(2) - y^(2) =a^(2)at. Q the locus of the point of intersection of the tangents at P to the circle and with the tangents at Q to the hyperbola is
Answer» ` ( X^(4) +y^(4) )=a^(6)` ` (a^(4) +4y^(4)) x^(2) =a^(6) ` ` (a^(4) +4x^(4) )y^(2) =a^(6) ` none ANSWER :B

Discussion

11213.	Let K_(1)= Total number of ways of selecting of ball from a bag which contains n balls of first colour (n+1) balls of second colour, (n+2) balls of third colour ,…….,(2n-1) balls of n colour. K_(2)= number of n -digit numbers using the digit 1,2,3,n and K_(3)= number of ways of arranging (n+1) objects on a circle. The value of lim_(nto oo)((K_(1))/(K_(2)))^(1//n), is
Answer» `E^(2)` `log4-1` `4/e` `1/e` ANSWER :C

Discussion

11214.	If A , B and A+B are non -singular matrices then (A^(-1)+B^(-1)) [(A-A(A+B)^(-1)A]equals
Answer» O I A B Answer :B

Discussion

11215.	Find the numerically greatest term of (3+7x)^(15), x=(4)/(5)
Answer» SOLUTION :N/A

Discussion

11216.	If f(x)=f'(x) and f(1) =2, then f(3) equals :
Answer» `e^2` `2e^2` `3e^2` `4e^2` ANSWER :B

Discussion

11217.	Out of 20 consecutive integers two are drawn at random. Then find the probability that the sum is odd.
Answer» ANSWER :`(10)/(19)`

Discussion

11218.	Evaluate the following integrals intx^(n)logxdx
Answer» ANSWER :`(X^(n+1))/(n+1)[LOGX-(1)/(n+1)]+C`

Discussion

11219.	Let P(x) = (x - 3)(x - 4)(x - 5). For how many polynomials Q(x). does there exist a polynomial R(x) of degree 0 such that P(Q(x)) = P(x)R(x)?
Answer» ANSWER :22

Discussion

11220.	Differentiate (x^3+1)(3x^2+2x-7)
Answer» SOLUTION :`y=(x^3+1)(3x^2+2x-7)` dy/dx=d/dx(x^3+1)CDOT(3x^2+2x-7)+(x^3+1)xxd/dx(3x^2+2x-7)` `=3x^2(3x^2+2x-7)+(x^3+1)(6x+2)`

Discussion

11221.	The slope of the tangent to the curve x=t^(2)+3t-8, y=2t^(2)-2t-5 at the point (2,-1) is …………
Answer» `(22)/(7)` `(6)/(7)` `(7)/(6)` `(-6)/(7)` ANSWER :B

Discussion

11222.	If S is the area in the figure below then S is equal to
Answer» ANSWER :2.13

Discussion

11223.	Find the area of the region enclosed by the curves x^(2)=4y, x=2y and y=0
Answer» ANSWER :`((1)/(3))`

Discussion

11224.	Equation of the plane perpendicular to the line (x)/(1)=(y)/(2)=(z)/(3) and passing through the point (2,3,4) is
Answer» 2x+3y+z=17 x+2y+3z=9 3x+2y+z=16 x+2y+3z=20 Answer :D

Discussion

11225.	An ellipse has semi-major axis of length 2 and semi-minor axis of length 1. It sides between the co-ordinate axes in the first quadrant, while maintaining contactwith both x-axis and y-axis. Q. The locus of the foci of the ellipse is :
Answer» `X^(2)+y^(2)+(1)/(x^(2))+(1)/(y^(2))=16` `x^(2)+y^(2)+(1)/(x^(2))-(1)/(y^(2))=2sqrt(3)+4` `x^(2)+y^(2)-(1)/(x^(2))-(1)/(y^(2))=2sqrt(3)+4` `x^(2)-y^(2)+(1)/(x^(2))-(1)/(y^(2))=2sqrt(3)+4` Answer :A

Discussion

11226.	An ellipse has semi-major axis of length 2 and semi-minor axis of length 1. It sides between the co-ordinate axes in the first quadrant, while maintaining contactwith both x-axis and y-axis. Q. The locus of the centre of ellipse is :
Answer» `x^(2)+y^(2)=3` `x^(2)+y^(2)=5` `(x-2)^(2)+(y-1)^(2)=5` `(x-2)^(2)+(y-1)^(2)=3` ANSWER :B

Discussion

11227.	Consider a system of linear equation in three variablesx,y,z a_1x+b_1y+ c_1z = d_1 , a_2x+ b_2y+c_2z=d_2 ,a_3x + b_3y + c_3z=d_3 The systemscan be expressed by matrix equation [(a_1,b_1,c_1),(a_2,b_2,c_2),(c_1,c_2,c_3)][(x),(y),(z)]=[(d_1),(d_2),(d_3)] if A is non-singular matrix then the solution of above system can be found by X =A^(-1)B, the solution in this case is unique. if A is a singular matrix i.e.then the system will have no unique solution ifno solution (i.e. it is inconsistent) ifWhereAdjA is the adjoint of the matrix A, which is obtained by taking transpose of the matrix obtained by replacing each element of matrix A with corresponding cofactors. Now consider the following matrix. A=[(a,1,0),(1,b,d),(1,b,c)], B=[(a,1,1),(0,d,c),(f,g,h)], U=[(f),(g),(h)], V=[(a^2),(0),(0)], X=[(x),(y),(z)] IfAX=Uhas infinitely many solutions then the equation BX=Uis consistent if
Answer» a=0 d=0 f=0 adf `NE` 0 Answer :A::B::C

Discussion

11228.	Consider a system of linear equation in three variablesx,y,z a_1x+b_1y+ c_1z = d_1 , a_2x+ b_2y+c_2z=d_2 ,a_3x + b_3y + c_3z=d_3 The systemscan be expressed by matrix equation [(a_1,b_1,c_1),(a_2,b_2,c_2),(c_1,c_2,c_3)][(x),(y),(z)]=[(d_1),(d_2),(d_3)] if A is non-singular matrix then the solution of above system can be found by X =A^(-1)B, the solution in this case is unique. if A is a singular matrix i.e.then the system will have no unique solution ifno solution (i.e. it is inconsistent) ifWhereAdjA is the adjoint of the matrix A, which is obtained by taking transpose of the matrix obtained by replacing each element of matrix A with corresponding cofactors. Now consider the following matrix. A=[(a,1,0),(1,b,d),(1,b,c)], B=[(a,1,1),(0,d,c),(f,g,h)], U=[(f),(g),(h)], V=[(a^2),(0),(0)], X=[(x),(y),(z)] If AX=Uhas infinitely many solutions then the equationhas:
Answer» UNIQUE solution INFINITELY MANY solution no solution either infinitely many SOLUTIONS or no solution Answer :D

Discussion

11229.	Consider a system of linear equation in three variablesx,y,z a_1x+b_1y+ c_1z = d_1 , a_2x+ b_2y+c_2z=d_2 ,a_3x + b_3y + c_3z=d_3 The systemscan be expressed by matrix equation [(a_1,b_1,c_1),(a_2,b_2,c_2),(c_1,c_2,c_3)][(x),(y),(z)]=[(d_1),(d_2),(d_3)] if A is non-singular matrix then the solution of above system can be found by X =A^(-1)B, the solution in this case is unique. if A is a singular matrix i.e.then the system will have no unique solution if no solution (i.e. it is inconsistent) ifWhereAdjA is the adjoint of the matrix A, which is obtained by taking transpose of the matrix obtained by replacing each element of matrix A with corresponding cofactors. Now consider the following matrix. A=[(a,1,0),(1,b,d),(1,b,c)], B=[(a,1,1),(0,d,c),(f,g,h)], U=[(f),(g),(h)], V=[(a^2),(0),(0)], X=[(x),(y),(z)] A: if AX=U ,has infinitesolutions and cf ne0, then one solutionof BX=V is (0,0,0). R: If a systemhas infinitesolutionsthen onesolution must be trivial . Then
Answer» A and R are both CORRECT and R is correct EXPLANATION of A A and R both are correct but R is not correct explanation of A A is correct R is wrong A and R are both wrong Answer :A::B::C

Discussion

11230.	Consider a system of linear equation in three variablesx,y,z a_1x+b_1y+ c_1z = d_1 , a_2x+ b_2y+c_2z=d_2 ,a_3x + b_3y + c_3z=d_3 The systemscan be expressed by matrix equation [(a_1,b_1,c_1),(a_2,b_2,c_2),(c_1,c_2,c_3)][(x),(y),(z)]=[(d_1),(d_2),(d_3)] if A is non-singular matrix then the solution of above system can be found by X =A^(-1)B, the solution in this case is unique. if A is a singular matrix i.e.then the system will have no solution (i.e. it is inconsistent) ifWhereAdjA is the adjoint of the matrix A, which is obtained by taking transpose of the matrix obtained by replacing each element of matrix A with corresponding cofactors. Now consider the following matrix. A=[(a,1,0),(1,b,d),(1,b,c)], B=[(a,1,1),(0,d,c),(f,g,h)], U=[(f),(g),(h)], V=[(a^2),(0),(0)], X=[(x),(y),(z)] The systemAX=U has infinitelymany solutions if :
Answer» c=d, ab=1 c=d,h=g ab=1,h=g c=d,h=g,ab=1 Answer :D

Discussion

11231.	Which of the following defined on Z is not an equivalence relation ?
Answer» `(X,y) in S hArr x GE y` `(x,y) in S hArr x = y ` `(x,y) inS harr x - y ` is a multiple of 3 `(x,y) in S ` if \|x-y\| is EVEN Solution :N/A

Discussion

11232.	Determine order and degree (if defined) of the following differential equations y' +y =e^x
Answer» Solution :The highest order DERIVATIVE in the differential equation is y. and its degree is 1. `therefore` The order and the degree of the differential equation are 1 and 1 RESPECTIVELY.

Discussion

11233.	Evalute the following integrals intcos mx cos nx dx
Answer» ANSWER :`(1)/(2) [ (SIN(m + n)X)/(m + n) + (sin (m - n)x)/(m-n) ] +` C

Discussion

11234.	The negation of the proposition q vv ~(p ^^ r) is
Answer» <P>`~q vv (p ^^ R)` `~q ^^ (p ^^ r)` `~p vv ~q vv ~r` `q ^^ (~p vv ~r)` ANSWER :B

Discussion

11235.	Let A,B and C be three distinct points on y^(2) = 8x such that normals at these points are concurrent at P. The slope of AB is 2 and abscissa of centroid of Delta ABC is (4)/(3). Which of the following is (are) correct?
Answer» AREA of `DeltaABC` is 8 sq. units Coordinates of `P -= (6,0)` Angle between normals are `45^(@),45^(@),90^(@)` Angle between normals are `30^(@),30^(@),60^(@)` Solution :Let `A = (2t_(1)^(2),4t_(1)), B = (2t_(2)^(2), 4t_(2))` and `C = (2t_(3)^(2),4t_(3))` Slope of `AB = 2 RARR t_(1) + t_(2) =1` and `t_(1) + t_(2) + t_(3) =0` So, `t_(3) =-1` Also, `(2(t_(1)^(2)+t_(2)^(2)+t_(3)^(2)))/(3) =(4)/(3) rArr t_(1)^(2)+t_(2)^(2) =1` `rArr t_(1) =1, t_(2) =0` `A = (2,4), B =(0,0)` and `C = (2,-4)` HENCE `P = (6,0)`

Discussion

11236.	Let X, Y be non-empty sets such that abs(X)=m and abs(Y)=n. If mltn, then how many one-to-one can be defined from X to Y?
Answer» ANEMOPHILY ENTOMOPHILY Ornithophily hydrophily ANSWER :B

Discussion

11237.	Equation of the line through (-1,2,3) and parallel to (x-4)/(2) =(y+1)/(-3) =(z+10)/(8) is
Answer» `(x-1)/(2)=(y-3)/(-3)=(z-3)/(8)` `(x+1)/(2)=(y-2)/(-3)=(z-3)/(8)` `(x-4)/(-1)=(y+1)/(2)=(z+10)/(3)` none Answer :B

Discussion

11238.	If \|z_(1) \| = \|z_(2)\| = 1 , then \|z_(1) + z_(2)\| =
Answer» `\|(1)/(z_(1)) + (1)/(z_(2))\|` `\| (1)/(z_(1)) - (1)/(z_(2))\|` `\| (1)/(z_(1)) * (1)/(z_(2))\|` `\| (1)/(z_(1)^(2)) + (1)/(z_(2)^(2)))\|` ANSWER :A

Discussion

11239.	Integrate the rational functions (3x+5)/(x^(3)-x^(2)-x+1)
Answer» Answer :`(1)/(2)LOG\|(x+1)/(x-1)\|=(-4)/((x-1))+c`

Discussion

11240.	Find the approximate value of each of the following :sqrt(399)
Answer» ANSWER :`19.975`

Discussion

11241.	The vectors bar(a)=3bar(i)-2bar(j)+2bar(k) and bar(b)=-bar(i)-2bar(k) are the adjacent sides of a parallelogram. The angle between its diagonals is …………….
Answer» ANSWER :`:.THETA=(PI)/(4)` OR `45^(@)`.

Discussion

11242.	The two lines bar (r )= (1,1,-1) + lambda (3,-1,0) and bar (r ) = ( 4 , -1 , 0 ) + mu (2,0,3)are
Answer» parallel intersecting non-coplanar none of these Answer :C

Discussion

11243.	Let A_(1) be the area of the parabola y^(2)=4ax lying between vertex and latus rectum and A_(2) be the area between latus rectum and double ordinate x=2a. Then A_(1)//A_(2)=
Answer» `(2sqrt(2)-1)/(7)` `(2sqrt(2)+1)/(7)` `(2sqrt(2)+1)/(3)` `(2sqrt(2)-1)/(9)` Answer :B

Discussion

11244.	Is the function defined by f(x)= x^(2)-sin x+5 continuous at x= pi?
Answer» ANSWER :F is CONTINUOUS at `X= PI`.

Discussion

11245.	int_(0)^(pi//4)(sinx+cosx)/(7+9sin2x)dx=
Answer» `(LOG3)/(4)` `(log3)/(36)` `(log7)/(12)` `(log7)/(24)` Answer :D

Discussion

11246.	If f(x) and g(x) are continuous functions satisfysing f(x)=f(a-x)andg(x)+g(a-x)=2 then int_(0)^(a)f(x)g(x)dx=
Answer» `2 int_(0)^(a) f(x)DX` `int_(0)^(a) f(x)dx` `2 int_(0)^(a) g(x)dx` `int_(0)^(a)g(x)dx` Answer :B

Discussion

11247.	Let f(x)=lim_(ntooo)(cos sqrt(x/n))^(n),g(x)=lim_(nto oo)(1+x+x root(n)(e))^(n) Now consider the function y=h(x) where h(x)=tan^(-1)(g^(-1)f^(-1)(x)). lim_(xto0)(In(f(x)))/(In(g(x))) is equal to
Answer» `1/2` `-1/2` `0` `1` ANSWER :B

Discussion

11248.	A dice is tossed 100 times. If even number is obtained on dice is success then variance of success is ……….
Answer» 10 20 25 50 Answer :C

Discussion

11249.	Match the graph of y= f(x) in Column I with the corresponding graph of y = f'(x) in Column II.
Answer» <P> Solution :`(a) to(s)""(B)to(r)""(c) to(Q)""(d) to (p)`

Discussion

11250.	Solve in R and represent the solution on the number line. x/5 lt (2x + 1)/3 + (1-3x)/6
Answer» SOLUTION :`x/5 lt (2x + 1)/3 + (1-3x)/6` `rArr x/5 lt (4x +2+1-3x)/6` `rArr x/5 lt (x+3)/6` `rArr 6x lt 5x + 15` `rArr x lt 15` If x `in` R the solution SET is S = `(-infty,5)` We can REPRESENT the solution on number LINE as

Discussion

Explore topic-wise InterviewSolutions in .

int_(-1)^( sqrt3) (dx)/( 1+x^2) = …...... .

The sum of the fifth powers of the roots of the equation x^(4) - 3x^(3) + 5x^(2) - 12x + 4= 0is

Let f : R to R be defined by f(x)=x^(4), then

Which of the following is not equivalent to the equation a/(bc)=d/(ef) ?

Find the number of ways of arranging 10 persons A_(1),A_(2),……….A_(10) in a row if no two of A_(1),A_(2) and A_(3) come together.

A person has 21 tickets with numbered 1 to 21. Three tickets are selected from it at random. Find the probability of an event that numbers of selected three tickets are in A.P.

If the lines kx^(2)+6xy+2y^(2)=0 and x+3y=9 form an isosceles triangle, then k=

lim_(alpha to 0) (sin(alpha^n))/((sin alpha)^m) (m , n in I^+) is equal to

If a lt 0 lt bthen int_(a)^(b)(|x|)/(x) dx=

A line through the origin meets the circlex^(2) +y^(2) =a^(2)at P and the hyperbolax^(2) - y^(2) =a^(2)at. Q the locus of the point of intersection of the tangents at P to the circle and with the tangents at Q to the hyperbola is

If A , B and A+B are non -singular matrices then (A^(-1)+B^(-1)) [(A-A(A+B)^(-1)A]equals

Find the numerically greatest term of (3+7x)^(15), x=(4)/(5)

If f(x)=f'(x) and f(1) =2, then f(3) equals :

Out of 20 consecutive integers two are drawn at random. Then find the probability that the sum is odd.

Evaluate the following integrals intx^(n)logxdx

Let P(x) = (x - 3)(x - 4)(x - 5). For how many polynomials Q(x). does there exist a polynomial R(x) of degree 0 such that P(Q(x)) = P(x)R(x)?

Differentiate (x^3+1)(3x^2+2x-7)

The slope of the tangent to the curve x=t^(2)+3t-8, y=2t^(2)-2t-5 at the point (2,-1) is …………

If S is the area in the figure below then S is equal to

Find the area of the region enclosed by the curves x^(2)=4y, x=2y and y=0

Equation of the plane perpendicular to the line (x)/(1)=(y)/(2)=(z)/(3) and passing through the point (2,3,4) is

An ellipse has semi-major axis of length 2 and semi-minor axis of length 1. It sides between the co-ordinate axes in the first quadrant, while maintaining contactwith both x-axis and y-axis. Q. The locus of the foci of the ellipse is :

An ellipse has semi-major axis of length 2 and semi-minor axis of length 1. It sides between the co-ordinate axes in the first quadrant, while maintaining contactwith both x-axis and y-axis. Q. The locus of the centre of ellipse is :

Which of the following defined on Z is not an equivalence relation ?

Determine order and degree (if defined) of the following differential equations y' +y =e^x

Evalute the following integrals intcos mx cos nx dx

The negation of the proposition q vv ~(p ^^ r) is

Let A,B and C be three distinct points on y^(2) = 8x such that normals at these points are concurrent at P. The slope of AB is 2 and abscissa of centroid of Delta ABC is (4)/(3). Which of the following is (are) correct?

Let X, Y be non-empty sets such that abs(X)=m and abs(Y)=n. If mltn, then how many one-to-one can be defined from X to Y?

Equation of the line through (-1,2,3) and parallel to (x-4)/(2) =(y+1)/(-3) =(z+10)/(8) is

If |z_(1) | = |z_(2)| = 1 , then |z_(1) + z_(2)| =

Integrate the rational functions (3x+5)/(x^(3)-x^(2)-x+1)

Find the approximate value of each of the following :sqrt(399)

The vectors bar(a)=3bar(i)-2bar(j)+2bar(k) and bar(b)=-bar(i)-2bar(k) are the adjacent sides of a parallelogram. The angle between its diagonals is …………….

The two lines bar (r )= (1,1,-1) + lambda (3,-1,0) and bar (r ) = ( 4 , -1 , 0 ) + mu (2,0,3)are

Let A_(1) be the area of the parabola y^(2)=4ax lying between vertex and latus rectum and A_(2) be the area between latus rectum and double ordinate x=2a. Then A_(1)//A_(2)=

Is the function defined by f(x)= x^(2)-sin x+5 continuous at x= pi?

int_(0)^(pi//4)(sinx+cosx)/(7+9sin2x)dx=

If f(x) and g(x) are continuous functions satisfysing f(x)=f(a-x)andg(x)+g(a-x)=2 then int_(0)^(a)f(x)g(x)dx=

Let f(x)=lim_(ntooo)(cos sqrt(x/n))^(n),g(x)=lim_(nto oo)(1+x+x root(n)(e))^(n) Now consider the function y=h(x) where h(x)=tan^(-1)(g^(-1)f^(-1)(x)). lim_(xto0)(In(f(x)))/(In(g(x))) is equal to

A dice is tossed 100 times. If even number is obtained on dice is success then variance of success is ……….

Match the graph of y= f(x) in Column I with the corresponding graph of y = f'(x) in Column II.

Solve in R and represent the solution on the number line. x/5 lt (2x + 1)/3 + (1-3x)/6