28278 + Interview Questions in Maths in Class 12

1.	If I_(1) = int_0^(1) 2^(x^(2)) dx, I_(2) = int_0^(1) 2^(x^(3)) dx, I_(3) = int_1^(2) 2^(x^(2)) dx, I_(4) = int_1^(2) 2^(x^(3)) dx then,
Answer» `I_1 GT I_2` `I_2 gt I_1` `I_3 gt I_4` `I_3 = I_4` ANSWER :A

Discussion

2.	Find the area between the curves y = x and y = x^(2).
Answer» ANSWER :AREA = `1/6` SQ. UNITS

Discussion

3.	Using elementary row transformations , find the inverse of each of the matrices , if it exists in example number . [{:(1,-1),(2,3):}]
Answer» ANSWER :`=[{:((3)/(5),(1)/(5)),(-(2)/(5),(1)/(5)):}]`

Discussion

4.	Evaluate : inte^x((1 + sin x)/(1+ cos x))dx
Answer» ANSWER :`LOG\|(tan""(x)/(2))/((tan""(x)/(2)-1)^(2))\|+c//(1)/(4) log\|(cos x - 1)/(cos x + 1)\|+(1)/(2)((1)/(1+cos x))+ tan""(x)/(2)+c`

Discussion

5.	Evaluate the following integrals (iv) int_(0)^(1)sqrt((1-x)/(1+x))dx
Answer» ANSWER :`pi/2 -1`

Discussion

6.	If A is square matrix such that A^(2) +I = O, then A equals:
Answer» `[(1,0),(0,1)]` `[(1,2),(-1,1)]` `[(-1,0),(0,-i)] ` `[(i,0),(0,i)]` ANSWER :D

Discussion

7.	Consider a right angled triangle ABC right angled at C with integer sides. List-I gives inradius. List-II gives the number of triangles.
Answer» <P> ANSWER :`A to P; B to P; C to T; D to S`

Discussion

8.	A random variable X has the following probability distribution Determine P(X
Answer» <P> SOLUTION :`P(Xlt3)`=P(X=0 or 1 or 2) =P(X=0)+P(X=1)+P(X=2) =P(0)+P(1)+P(2) (`because` X=0, X=1 and X=2 are THREE mutually EXCLUSIVE CASES) =0+k+2k=3k=3/13

Discussion

9.	Method of integration by parts : inte^(3x)cos 4xdx=e^(3x)(A sin 4x+B cos4x)+c then.....
Answer» `4A=3B` `2A=3B` `3A=4B` `4A+3B=1` ANSWER :D

Discussion

10.	Determine the inverse function and its domain of definition, if (a) y=tan hx, ""(b) y={{:(,x,"if "-oo lt x lt 1),(,x^(2),"if "1 le x le 4),(,2^(x), "if "4 lt x lt oo):}.
Answer» ANSWER :(a) `X=1/2 ln (1+y)/(1-y) (-1 lt y lt 1);` (B) `x={{:(,y,"for "-oo lt y lt 1),(,log_(2)" for "16 lt y lt oo):}`

Discussion

11.	Three boxes B_(1), B_(2), B_(3) contain with different colours as shown below. {:(,"White","black","red"),(B_(1),2,1,2),(B_(2),3,2,4),(B_(3),4,3,2):} A die is thrown. B_(1) is chosen if either 1 or 2 turns up. B_(2) is chosen if 3 or 4 turns up and B_(3) is chosen if 5 or 6 turns up. Having chosen a box in this way, a ball is chosen at random from this box. If the ball found to be red, find the probability that it is drawn from box B_(2).
Answer» ANSWER :`(5)/(12)`

Discussion

12.	If the area of the triangle formed by the points z, z+iz and iz is 50 square units, then \|z\| is equal to
Answer» `5` `8` `10` `12` ANSWER :C

Discussion

13.	The plane 3x+4y+6z+7=0 is rotated about the line r=(hati+2hatj-3hatk)+t(2hati-3hatj+hatk) until the plane passes through origin. The equation of the plane is the new position is
Answer» `x+y+z=0` `6x+3y-4z=0` `4x-5y-2z=0` `x+2y+4z=0` ANSWER :A

Discussion

14.	int Cos^(-1)(2x^(2)-1)dx=
Answer» `2(X SIN^(-1) x + SQRT(1 - x^(2))) + c ` `2 (x cos^(-1) x + sqrt(1 - x^(2))) + c ` `2 (x cos^(-1) x -sqrt(1 -x^(2)) )+ c` `2 (x sin^(-1) x - sqrt(1 -x^(2)) )+ c ` Answer :C

Discussion

15.	Energy levels A, B and C of a certain atoms correspond to increasingvalues of energy, i.e. E_(A)lt E_(B)ltE_(c). If lambda_(1),lambda_(2), lambda_(3) are the wavelengths ofradiation correspondingto the transitions C rarr B, B rarrA and C rarr A respectively, then :
Answer» `lambda_(1)=lambda_(2)=lambda_(3)` `lambda_(3)=(lambda_(1)lambda_(2))/(lambda_(1)+lambda_(2))` `lambda_(3)^(2)=lambda_(1)^(2)+lambda_(2)^(2)` NONE of these Solution :`E_(CB)+E_(BA)=E_(CA)RARR(1)/(lambda_(1))+(1)/(lambda_(2))=(1)/(lambda_(3))`

Discussion

16.	If the planes x = cy + bz, y =az+cx and z = bx + ay pass througha line then
Answer» `a^(2)+B^(2)+C^(2)+2ABC=0` `a^(2)+b^(2)+c^(2)+2abc=1` `a^(2)+b^(2)+c^(2)=2abc` a+b+c=abc Answer :B

Discussion

17.	If A is a 3xx3 matrix and absA=2, then which matrix is represented by Axx adjA?
Answer» SOLUTION :We have `AXX adjA=(Axx adjA)/(ABSA) XX absA` =`AxxA^-1xx2(because absA=2)` =`2I=2[[1,0,0],[0,1,0],[0,0,1]]=[[2,0,0],[0,2,0],[0,0,2]]` where `I=[[1,0,0],[0,1,0],[0,0,1]]`

Discussion

18.	If f(x)= {(ax+b,1le x lt 5),(7x-5,5 le x lt 10),(bx + 3a,x ge 10):} is continuous, (a,b)= ……...
Answer» (5, 10) (5,5) (10, 5) (0, 0) ANSWER :B

Discussion

19.	Let f(x) ={{:( xe^(x), xle0),( x+x^(2)-x^(3), xgt0):} thenthe correctstatement is
Answer» F iscontinuousand differentiablefor ALLX, f iscontinuousbut notdifferentiable ATA x=0 f iscontinuousand DIFFERENTIABLE for all x. f ' is continuousbutnot differentiableat x=0. Answer :A::C

Discussion

20.	Let P(x) =ax^(7) + bx^(3) +cx-5, where a,b,c are constants. Given P(-7) =7, find the value of P(7).
Answer» ANSWER :`-17`

Discussion

21.	Show that the points of intersection of the perpendicular tangets to an ellipse lie on a circle.
Answer» ANSWER :`x^2+y^2=a^2+b^2`

Discussion

22.	If lim_(xto)(f(x))/(x^(2))=k then lim_(xto1)f(x)=
Answer» 0 1 k not defined Answer :C

Discussion

23.	If A is 3 × 4 matrix and B is 4 × 3 matrix,then the order of AB is
Answer» `3 × 4` `4 × 3` `4 × 4` `3 × 3` ANSWER :D

Discussion

24.	Let a function f(x), x ne 0 be such that f(x)+f((1)/(x))=f(x)*f((1)/(x))" then " f(x) can be
Answer» `1-X^(2013)` `sqrt(\|x\|)+1` `(pi)/(2tan^(-1)\|x\|)` `(2)/(1+k" In "\|x\|)` SOLUTION :`(f((1)/(x))-1)=(1)/((f(x)-1))i.e., (f((1)/(x))-1)` is reciprocal of `(f(x)-1).` Now, for `f(x)=((pi)/(2))/(tan^(-1)\|x\|)` `f(x)-1=(cot^(-1)\|x\|)/(tan^(-1)\|x\|),f((1)/(x))-1=(tan^(-1)\|x\|)/(cot^(-1)\|x\|)` ALSO for `f(x)=(2)/(1+k" In " \|x\|)` `f(x)-1=(1-k" In " \|x\|)/(1+k" In " \|x\|),f((1)/(x))-1=(1+k" In "\|x\|)/(1-k " In "\|x\|)`

Discussion

25.	Write the component statement "Every parallelogram is a trapezium or a rhombus" compound statements and check whether the compound statement is true or false.
Answer» SOLUTION :The component STATEMENTS are p :Every PARALLELOGRAM is a trapezium q : Every parallelogram is a RHOMBUS . The truth value of the compound statement is "false"

Discussion

26.	Match the following {:(I.,"Centroid of the triangle formed by (2,3,-1),(5,6,3),(2,-3,1)" ,"a)(1,1,0)"),(II.,"Circumcentre of the triangle formed by (1,2,3),(2,3,1),(3,1,2)","b) (3,1,4)"),(III.,"Orthocentre of the triangle formed by (2,1,5),(3,2,3),(4,0,4)","c)(2,2,2)"),(IV.,"Incentre of the triangle formed by (0,0,0),(3,0,0),(0,4,0)","d)(3,2,1)"):}
Answer» d, a , B ,C a,b,c,d d,c,b,a a,c,d,b Answer :C

Discussion

27.	If barc=3bara-2barb, then prove that [bara barb barc]0
Answer» Solution :Given `""vecc=3veca-2vecb` `therefore""[vec a vec B vec c]=veca . (vecb xx vec)` `=veca . [vecb xx (3 veca xx2vecb)]` `=veca. (3 vecb xx veca - 2 vecb xx vecb)` `=veca.(3VECB xx vec a -0)` `(because vecb xx vec b=0)` `=3xx0=0"Hence PROVED"`

Discussion

28.	If x is so small, higher powers of x may be neglected then sqrt(x^2 + 25)-sqrt(x^2 +9)=
Answer» `2-(x^2)/(15)` `3+(x^2)/(15)` `3-(x^2)/(15)` `2+(x^2)/(15)` ANSWER :A

Discussion

29.	Evaluate : int_((pi)/(4))^((3pi)/(4))(x)/(1+sinx)dx
Answer» ANSWER :`PI (SQRT(2)-1)`

Discussion

30.	Find the particular solution of the following differential equaitonx(x^(2) - 1)(dy)/(dx) = 1, y = 0 when x = 2.
Answer» Answer :`y = 1/(2) LOG (x^(2) - 1)/(x^(2)) -(1)/(2) log(3)/(4)`

Discussion

31.	Examine the consistency of the system of linear equtions in 1 to 6 x+y+z=1 2x+3y+2z=2 ax+ay+2az=4
Answer» ANSWER :`ANE0`

Discussion

32.	A line makes equal angles with coordinate axes. Direction cosines of this line are :
Answer» `PM LT 1, 1,1 gt` `pm lt 1/SQRT3, 1/sqrt3 , 1/sqrt3 gt` `pm lt 1/3, 1/3, 1/3, gt` `pm lt 1/sqrt3 , -1/sqrt3, (-1)/sqrt3 gt ` Answer :B

Discussion

33.	Find \| veca\| , if ( veca - hatp ) . (veca +hatp ) = 15
Answer» ANSWER :` \|VEC a \| =4`

Discussion

34.	The plane containing the line (x-1)/(1) =(y-2)/( 2) =(z-3)/(3)and parallel to the line(x)/(1) =(y)/(1) =(z)/(4)passes through the point
Answer» `(1,-2,5) ` ` (1,0,5)` ` ( 0, 3,-5)` ` ( -1,-3,0)` Answer :B

Discussion

35.	Find an equation of the line of shortest distance between the lines r=lambda(i-j+k)andr=(i-j)+mu(-2j+k) In the vectorial notation and Cartesian notation. Also find the shortest distance between them.
Answer» ANSWER :`(2)/(SQRT(6))`

Discussion

36.	f(x)=\|x\| is increasing in
Answer» `(-OO,oo)` `(-oo,0)` `(0,oo)` `(-oo,-1)` ANSWER :C

Discussion

37.	The points representing the complex number z for which arg((z-2)/(z+2)=pi/3 lie on
Answer» A circle A STRAIGHT line An ellipse A parabola Answer :A

Discussion

38.	Co - ordinates of the foot of the perpendicular from the point (a,b,c) on the Z - axis are
Answer» `(a,B,0)` `(0,0,C)` `(a,0,0)` `(0,b,0)` ANSWER :b

Discussion

39.	Let bara, barb, barc be three non-coplanar vectors and barr be any vector in space such that barr.bara=1,barr.barb=2 and barr.barc=3 If [barabarb barc]=1, then : barr=
Answer» `bara+2barb+3barc` `(barbxxbarc)+2(barcxxbara)+3(BARAXXBARB)` `(barb.barc)bara+2(barc.bara)barb+3(bara.barb)barc` none of these Answer :B

Discussion

40.	If alpha is non real root of x^(6)=1, then (alpha^(5)+alpha^(3)+alpha+1)/(alpha^(2)+1) is equal to
Answer» `ALPHA^(2)` 0 `-alpha^(2)` `alpha` ANSWER :C

Discussion

41.	If f(1) = 1, f(n+1)= 2f (n) + 1, n ge 1then f(n) = .........
Answer» `2^(N)+1` `2^n` `2^(n)-1` `2^(n-1)-1` SOLUTION :N/A

Discussion

42.	(Allocation problem) A cooperative society of farmers has 50 hectare of land to grow two crops X and Y. The profit from crops X and Y per hectare are estimated as rs. 10,500 and Rs. 9,000 respectively. To control weeds, a liquid herbicide has to be used forcrops X and Y at rates of 20 litres and 10 litres pre hectare. Further, no more than 800 litres of herbicide should be used in order to protect fish and wild life using a pond which collects drainage from this land. How much land should be allocated to each crop so as to maximise the total profit of the society?
Answer» ANSWER :30 HECTARES for CROP X and 20 hectares for crop Y.

Discussion

43.	Show that number of equivalence relation in the set {1,2,2} containing (1,2) and (2,1) is two.
Answer» ANSWER :`R _(1)`

Discussion

44.	int_(0)^(2) [x^(2)-1]dx=
Answer» `4-SQRT(3)-sqrt(2)` `4+sqrt(3)+sqrt(2)` `sqrt(3)-1` `sqrt(2)+1` ANSWER :A

Discussion

45.	If 1 + (1 + 2)/2 + (1 + 2 + 3)/3 + ...... to n terms is s, then s is equal to
Answer» `(n(n + 3))/4` `(n(n + 2))/4` `(n(n + 1)(n + 2))/6` `n^(2)` ANSWER :A

Discussion

46.	Find two number whose sum 24 and whose product is as large as possible.
Answer» ANSWER :12 and 12

Discussion

47.	If f (x) = u//v then f '' (x) =
Answer» `(1)/(V^(3))` `(1)/(v ^(3)) \|{:(v ,0, U),(v _(1) , v , u _(1)),( v _(2) , 2 v _(1), u _(2)):}\|` `v ^(3)` none ANSWER :B

Discussion

48.	Sum of the series P=(1)/(2sqrt(1)+sqrt(2))+(1)/(3sqrt(2)+2sqrt(3))+.........+(1)/(100sqrt(99)+99sqrt(100)) is
Answer» `(1)/(10)` `(3)/(10)` `(9)/(10)` `(1)/(2)` Solution :Put `y=x+(3+5)/(2)=x+4` The EQUATION becomes `(y-1)^(4)+(y+1)^(4)=16` `implies2{y^(4)+6y^(2)+1}=16 ""implies""y^(4)+6y^(2)-7=0` `implies (y^(2)+7)(y^(2)-1)=0""implies " "y^(2)=-7" or "y^(2)=1` `implies y=pmsqrt(7i)" or "y= pm1 ""implies ""x=-4pmsqrt(7i) " or " x=-4pm1=-5" or"-3`. Thus, the given equation has TWO real roots.

Discussion

49.	The roots of the equation 8x^(2)+22x+5=0 are thetaandphi. Then
Answer» (a) `sin^(-1)thetaandsin^(-1)phi`, both the REAL (b) `SEC^(-1)thetaandsec^(-1)phi`, both the real (c) `tan^(-1)thetaandtan^(-1)phi`, both the real (d) NONE of these Answer :C

Discussion

50.	If A=[{:(2,lambda,-3),(0,2,5),(1,1,3):}], then A^(-1) exists if"............"
Answer» `LAMBDA=2` `lambda NE 2` `lambda ne -2` NONE of these ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If I_(1) = int_0^(1) 2^(x^(2)) dx, I_(2) = int_0^(1) 2^(x^(3)) dx, I_(3) = int_1^(2) 2^(x^(2)) dx, I_(4) = int_1^(2) 2^(x^(3)) dx then,

Find the area between the curves y = x and y = x^(2).

Using elementary row transformations , find the inverse of each of the matrices , if it exists in example number . [{:(1,-1),(2,3):}]

Evaluate : inte^x((1 + sin x)/(1+ cos x))dx

Evaluate the following integrals (iv) int_(0)^(1)sqrt((1-x)/(1+x))dx

If A is square matrix such that A^(2) +I = O, then A equals:

Consider a right angled triangle ABC right angled at C with integer sides. List-I gives inradius. List-II gives the number of triangles.

A random variable X has the following probability distribution Determine P(X

Method of integration by parts : inte^(3x)cos 4xdx=e^(3x)(A sin 4x+B cos4x)+c then.....

Determine the inverse function and its domain of definition, if (a) y=tan hx, ""(b) y={{:(,x,"if "-oo lt x lt 1),(,x^(2),"if "1 le x le 4),(,2^(x), "if "4 lt x lt oo):}.

If the area of the triangle formed by the points z, z+iz and iz is 50 square units, then |z| is equal to

The plane 3x+4y+6z+7=0 is rotated about the line r=(hati+2hatj-3hatk)+t(2hati-3hatj+hatk) until the plane passes through origin. The equation of the plane is the new position is

int Cos^(-1)(2x^(2)-1)dx=

Energy levels A, B and C of a certain atoms correspond to increasingvalues of energy, i.e. E_(A)lt E_(B)ltE_(c). If lambda_(1),lambda_(2), lambda_(3) are the wavelengths ofradiation correspondingto the transitions C rarr B, B rarrA and C rarr A respectively, then :

If the planes x = cy + bz, y =az+cx and z = bx + ay pass througha line then

If A is a 3xx3 matrix and absA=2, then which matrix is represented by Axx adjA?

If f(x)= {(ax+b,1le x lt 5),(7x-5,5 le x lt 10),(bx + 3a,x ge 10):} is continuous, (a,b)= ……...

Let f(x) ={{:( xe^(x), xle0),( x+x^(2)-x^(3), xgt0):} thenthe correctstatement is

Let P(x) =ax^(7) + bx^(3) +cx-5, where a,b,c are constants. Given P(-7) =7, find the value of P(7).

Show that the points of intersection of the perpendicular tangets to an ellipse lie on a circle.

If lim_(xto)(f(x))/(x^(2))=k then lim_(xto1)f(x)=

If A is 3 × 4 matrix and B is 4 × 3 matrix,then the order of AB is

Let a function f(x), x ne 0 be such that f(x)+f((1)/(x))=f(x)*f((1)/(x))" then " f(x) can be

Write the component statement "Every parallelogram is a trapezium or a rhombus" compound statements and check whether the compound statement is true or false.

If barc=3bara-2barb, then prove that [bara barb barc]0

If x is so small, higher powers of x may be neglected then sqrt(x^2 + 25)-sqrt(x^2 +9)=

Evaluate : int_((pi)/(4))^((3pi)/(4))(x)/(1+sinx)dx

Find the particular solution of the following differential equaitonx(x^(2) - 1)(dy)/(dx) = 1, y = 0 when x = 2.

Examine the consistency of the system of linear equtions in 1 to 6 x+y+z=1 2x+3y+2z=2 ax+ay+2az=4

A line makes equal angles with coordinate axes. Direction cosines of this line are :

Find | veca| , if ( veca - hatp ) . (veca +hatp ) = 15

The plane containing the line (x-1)/(1) =(y-2)/( 2) =(z-3)/(3)and parallel to the line(x)/(1) =(y)/(1) =(z)/(4)passes through the point

Find an equation of the line of shortest distance between the lines r=lambda(i-j+k)andr=(i-j)+mu(-2j+k) In the vectorial notation and Cartesian notation. Also find the shortest distance between them.

f(x)=|x| is increasing in

The points representing the complex number z for which arg((z-2)/(z+2)=pi/3 lie on

Co - ordinates of the foot of the perpendicular from the point (a,b,c) on the Z - axis are

Let bara, barb, barc be three non-coplanar vectors and barr be any vector in space such that barr.bara=1,barr.barb=2 and barr.barc=3 If [barabarb barc]=1, then : barr=

If alpha is non real root of x^(6)=1, then (alpha^(5)+alpha^(3)+alpha+1)/(alpha^(2)+1) is equal to

If f(1) = 1, f(n+1)= 2f (n) + 1, n ge 1then f(n) = .........

Show that number of equivalence relation in the set {1,2,2} containing (1,2) and (2,1) is two.

int_(0)^(2) [x^(2)-1]dx=

If 1 + (1 + 2)/2 + (1 + 2 + 3)/3 + ...... to n terms is s, then s is equal to

Find two number whose sum 24 and whose product is as large as possible.

If f (x) = u//v then f '' (x) =

Sum of the series P=(1)/(2sqrt(1)+sqrt(2))+(1)/(3sqrt(2)+2sqrt(3))+.........+(1)/(100sqrt(99)+99sqrt(100)) is

The roots of the equation 8x^(2)+22x+5=0 are thetaandphi. Then

If A=[{:(2,lambda,-3),(0,2,5),(1,1,3):}], then A^(-1) exists if"............"