28278 + Interview Questions in Maths in Class 12

1.	Evaluate int x^(3) sin x dx
Answer» `- (x^(3) COS3X)/(3 ) + (3 x^(2)sin 3x)/(9) + (6x cos 3x)/(27) - (2)/(27)`SIN3X + C `- (x^(3) cos3x)/(3 ) - (3 x^(2)sin 3x)/(9) + (6x cos 3x)/(27) + (2)/(27)`sin3x + c `- (x^(3) cos3x)/(3 ) - (3 x^(2)sin 3x)/(9) - (6x cos 3x)/(27) - (2)/(27)`sin3x + c `- (x^(3) cos3x)/(3 ) - (3 x^(2)sin 3x)/(9) - (6x cos 3x)/(27)` + c Answer :A

Discussion

2.	Find the number of 4-digited numbes of the form xyzt withx,z, tlty and x ne0
Answer» ANSWER :1740

Discussion

3.	The orthocentre of the triangle formed by the lines y=0, (1+t)x-ty+t(1+t)=0 and (1+u)x-uy+u(1+u)=0(t ne u) for all values of t and u lies on the line.
Answer» `x-y=0` `x+y=0` `x-y+1=0` `x+y+1=0` ANSWER :B

Discussion

4.	Correct rectivity order of molecular hydrogen, Nascent hydrogen and atomic hydrogen is : {:(H_(2),, to,, "Molecular hydrogen"),(H,, to,, "Atomic hydrogen"),([H],, to,, "Nascent hydrogen"):}
Answer» `[H]gtHgtH_(2)` `HGT[H]gtH_(2)` `[H]=HgtH_(2)` `[H]gtH_(2)gtH` SOLUTION :Atomic HYDROGEN is more reactive than NASCENT hydrogen.

Discussion

5.	Integrate the functions (xe^(x))/((1+x)^(2))
Answer» ANSWER :`(E^(X))/(1+x)+C`

Discussion

6.	intx^(2)logxdx
Answer» ANSWER :`(X^(3))/(3)[LOGX-(1)/(3)]+C`

Discussion

7.	If therangeof thefunctionf(x)=- 3x -3 is{ 3,-6,-9,-18} , thenwhichof the followingelementsis notin thedomainof f ?
Answer» `-1` `-2` `1` `2` ANSWER :A

Discussion

8.	If A and B are two events such that P(A cup B)=(5)/(6), P(A cap B)=(1)/(3), then whichone of the followingis not correct ?
Answer» A and B are independent A and `barB` are independent `BARA` and B are independent A and B are DEPENDENT ANSWER :D

Discussion

9.	If standard deviation of 1,2,3,4,….,10 is sigma then standard deviation of 11, 12, …20 is
Answer» `SIGMA + 10` `10 sigma` `sigma` `5 sigma` ANSWER :C

Discussion

10.	The common roots of the equationx^(12)-1=0,x^4+x^2+1=0 are
Answer» ANSWER :`cis pi/3,cis(2pi)/(3),cis(4PI)/(3),cis(5PI)/(3)`

Discussion

11.	Evaluate the following define integrals as limit of sums : lim_(n rarroo) [(1+1/n) (1+2/n)......(1+n/n)]^(1//n)
Answer» ANSWER :`4/e`

Discussion

12.	Iff (x) =[((1-cos kx)/(x^2) : x ne 0),(8 , x=0)] iscontinuesatx=0 , thenK=……
Answer» `+-1` `+-2` ` +-3 ` `+-4` ANSWER :D

Discussion

13.	Find (dy)/(dx) if y= sec^(-1)((1)/(2x^(2)-1)), 0 lt x lt (1)/(sqrt(2))
Answer» ANSWER :` (DY)/( DX) = (-2)/( SQRT( 1-x^(2) ) )`

Discussion

14.	If {:(f(x)=x^(2)",if "0 le x le 1),(""=sqrt(x)",if " x ge 1","):} then area above X-axis, bounded by the line x = 4 and the curve y = f(x) is
Answer» 1 2 5 None of these Answer :C

Discussion

15.	How many 5 digit telephonenumbers can be constructedusing the digits 0 to 9, if starts with 67 and no digit appears more than once ?
Answer» 335 336 338 337 Answer :B

Discussion

16.	Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below have inverses. Find f^(-1) if it exist f={(1,3)(2,1),(3,1),(4,2)}
Answer» SOLUTION :F(2)=f(3) =1 `implies` f is not injective `:.` f is not invertible.

Discussion

17.	The sum of the coefficient of x^32 and x^-17 in (x^4-(1)/(x^3))^15 is
Answer» 1 `-1` 2 0 Answer :D

Discussion

18.	Match the following : {:("LIST - I","LIST - II"),("I)" int_(0)^(2)\|1-x\|dx=,"a) " 1),("II)" int_(0)^(2)\|x-2\|dx=,"b) "2),("III)" int_(0)^(2)(\|x\|+\|x-1\|)dx=,"c) "3):}
Answer» a,B,C b,c,a b,a,c a,c,b Answer :A

Discussion

19.	If x, y, z are in G.P. and (x + 3), (y + 3), (z + 3) are in H.P., then the value of y is -
Answer» ANSWER :3

Discussion

20.	The value of (18^(3) + 7^(3) + 3.18.7.25)/(3^(6) + 6(243)2 + 15(81)4 + 20.27.8 + 15(9).16 + 6(3)(32) + 64) is
Answer» 15 25 5 100 Answer :A

Discussion

21.	If a variable line of slope 4 intersects the hyperbolaxy =1 at two points. Then the locus of the point which divides the line segment between these points in the ratio 1 : 2 is
Answer» `16X^(2) +10 xy + y^(2) -2=0` ` 16x^(2) -10 xy +2Y^(2) -2=0` ` 16x^(2) +20 xy +10 y ^(2) -2=0` ` 16x^(2) + 15XY +10 y^(2) -2=0 ` Answer :A

Discussion

22.	IfA= cos^(2) 76^(@) + cos^2 16^(@) - cos 76^(@) cos 16^(@) , B= cos^(2)( 45^(@) - alpha ) + cos^(2)(15^(@) + alpha ) - cos^(2)(15^(@)- alpha ) , C= ( cos ( 45^(@)+ A) cos (45^(@) - A))/( sin (120^(@) + A)-sin(120^(@) - A)) then the ascending order is
Answer» C,A,B B,A,C A,C,B A,B,C Answer :B

Discussion

23.	Let a and b be real numbers such that sina + sinb =1/sqrt(2), cosa + cosb =sqrt(3)/2, then
Answer» `COS(a-b)=1` cos(a-b)=0 SIN(a+b) =`SQRT(3)/2` `sin(a-b)=1` ANSWER :B::D

Discussion

24.	xy(dy)/(dx)-y^(2)=(x+y)2_(e)^(-(y)/(x))
Answer» ANSWER :`(X+y)log\|xc\|=xe^((y)/(x))`

Discussion

25.	Resolve (3x^(2)+5)/((x^(2)+2)^(2)(x^(2)+1)) into partial fractions
Answer» ANSWER :`(2)/(X^(2)+1)+(1)/(x^(2)+2)-(2)/((x^(2)+2)^(2))`

Discussion

26.	(dy)/(dx) - (y)/(x) + cosec ((y)/(x)) = 0, y = 0 when x = 1.
Answer» ANSWER :`COS ((y)/(X)) = LOG \|EX\|`

Discussion

27.	If bar(a),bar( c ) and bar(d) are not coplanar vectors and bar(d).(bar(a)xx(bar(b)xx(bar( c )xx bar(d))))=K[bar(a),bar( c ),bar(d)] then K = ….
Answer» `BAR(B)bar(d)` `bar(a)bar(d)` `bar(b)bar(a)` `bar(a)bar( C )` ANSWER :A

Discussion

28.	If 25^(log_5cos x)=a and e^(ln(-sinx))=b then the correct option is (where , a,b in R) :-
Answer» `a^2+b^2=1` `a^2+b=1` X LIES in FIRST QUADRANT x lies in FOURTH quadrant

Discussion

29.	If intsqrt(2+tan^(2)x)dx-ln tanx+sqrt(2+tan^(2)x)+f(x)+c, then f(x)=
Answer» `SIN^(-1)((SINX)/(SQRT2))` `cos^(-1)((sinx)/(sqrt2))` `cos^(-1)((cosx)/(sqrt2))` `sin^(-1)((cosx)/(sqrt2))` Answer :A

Discussion

30.	A is a set containing n_(1) elements and B is another set containing n_(2) elements, The number of non -decreasing functions from A rightarrow B is
Answer» `(n_(1)+n_(2-1))C_(n_(1))` `(n_(1)+n_(2-1))C_(n_(2))` `N^(1)C_(n_(2))` `n^(2)C_(n_(1))` ANSWER :A

Discussion

31.	The number of ways in which 6 things canbe divided Statement-I: into 2 equal groups is 10. Statement-II: among 2 persons equally is 20. Which of the above statements is true.
Answer» only I is TRUE only II is true both I and II are true neither I nor II true Answer :C

Discussion

32.	Obtain the equation of straight lines : Passing through (-1,2) and making intercept 2 on the y-axis.
Answer» Solution :LET the equation of the line be y = mx + C or, y = mx + 2 As the line passes through (-1,2) we have 2 = m = 2 or m = 0 `THEREFORE` Equation of the lineis y = 2.

Discussion

33.	If veca=hati+hatj+hatk,vecb=2hati-hatj+3hatkandvecc=hati-2hatj+hatk,find a unit vector parallel to the vector 2veca-vecb+3vecc.
Answer» Answer :`(3)/(sqrt(22))hati-(3)/(sqrt(22))HATJ+(2)/(sqrt(22))HATK`

Discussion

34.	If x =alpha, y=beta, z = gamma is a solution of the system of equations x+y+z=4 2x-y+3z=9
Answer» ANSWER :22.6

Discussion

35.	If a^3+b^3+c^3=3abc, where a,b,c are positive integers then the value of (a^2+2b^2+3c^2)/((a+b+c)^2) is :-
Answer» 3 1 `3/2` `2/3`

Discussion

36.	Find derivatives of the following functions.tan^(-1)(cossqrtx)
Answer» SOLUTION :`y=tan^(-1)(cossqrtx)` `dy/dx=1/(1+cos^2sqrtx).d/dx(cossqrtx)` `1/(1+cos^2sqrtx).d/dx(cossqrtx)` 1/(1+cos^2sqrtx).(-sinsqrtx).d/dx(SQRTX)` `=-sinsqrtx/(1+cos^2sqrtx).1/(2sqrtx)`

Discussion

37.	Integrate the following intcosec^2(x/2)dx
Answer» Solution :`intcosec^2(x/3)dx` `put(x/3)= theta` then dx=`3D theta` `intcosec^2theta CDOT 3theta` `-3COT theta+C=-3cot(x/3)+C`

Discussion

38.	If the domain of the function f (x) =[log _(10) ((5x - x ^(2))/( 4 )) ]^(1//2) is a le x le b, then a,b is
Answer» ANSWER :4

Discussion

39.	Let y =f (x) be a twice differentiable, non- negative function defined on [a.b]. The area int _(a) ^(b) f(x) dx, b gt a bounded by y = f(x), the x-axis and the ordinates at x = a and x = b can be approximated as int _(a ) ^(b) f (x) dx ~~((b-a))/( 2) {f(a) + f (b)}. Since int _(a)^(b) f (x) dx = int _(a) ^(c ) f (x) dx + int _(c ) ^(b) f (x) dx, x hatI (a,b) , abetter approximation to int _(a) ^(b) f(x) dx can be written as int _(a) ^(b)f (x) dx "@" ((c-a))/(2) {f(a)+f(c )}_ ((b-c))/(2) {f(c )+ f (b)} ""^(@)F(c ), If c = (b-a)/(2), then this gives: int _(a) ^(b )f (x) dx "@" (b-a)/(4) {f(a) + 2f (a) + 2f (c )+ f(b) },.......(1) If f ''(x) lt 0, x in (a,b), then at the point C(c, f (c))on y = f (x)for which F(c ) is a maximum, f '(c )is given by
Answer» `F'(c ) (f (B) -f (a))/(b-a)` `f ' (c ) (f (b) - f(a))/(a-b) ` ` f ' (c ) = (2 (f (b) -f (a)))/(b-a)` `f ' (c ) =0` Answer :A

Discussion

40.	The numberof fiveletterwordscan beformedusing3 consonentsand 2vowelsfromthe lettersof thewordMIXTUREis
Answer» ANSWER :1440

Discussion

41.	Let y =f (x) be a twice differentiable, non- negative function defined on [a.b]. The area int _(a) ^(b) f(x) dx, b gt a bounded by y = f(x), the x-axis and the ordinates at x = a and x = b can be approximated as int _(a ) ^(b) f (x) dx ~~((b-a))/( 2) {f(a) + f (b)}. Since int _(a)^(b) f (x) dx = int _(a) ^(c ) f (x) dx + int _(c ) ^(b) f (x) dx, x hatI (a,b) , abetter approximation to int _(a) ^(b) f(x) dx can be written as int _(a) ^(b)f (x) dx "@" ((c-a))/(2) {f(a)+f(c )}_ ((b-c))/(2) {f(c )+ f (b)} ""^(@)F(c ), If c = (b-a)/(2), then this gives: int _(a) ^(b )f (x) dx "@" (b-a)/(4) {f(a) + 2f (a) + 2f (c )+ f(b) },.......(1) If Lim _(t to a ) {(int _(0)^(t) f (x)dx -((t-a))/(2)(f(t)+ f(a)))/((t-a )^(3))}=0, for each fixed a, then f(x) is a polynomial of degree utmost
Answer» 4 3 2 1 Answer :D

Discussion

42.	Find the number of ways of arranging 15 students A_(1),A_(2),………A_(15) in a row such that A_(1),A_(2) and A_(3) sit together in specified order
Answer» ANSWER :`lfloor13`

Discussion

43.	Let y =f (x) be a twice differentiable, non- negative function defined on [a.b]. The area int _(a) ^(b) f(x) dx, b gt a bounded by y = f(x), the x-axis and the ordinates at x = a and x = b can be approximated as int _(a ) ^(b) f (x) dx ~~((b-a))/( 2) {f(a) + f (b)}. Since int _(a)^(b) f (x) dx = int _(a) ^(c ) f (x) dx + int _(c ) ^(b) f (x) dx, x hatI (a,b) , abetter approximation to int _(a) ^(b) f(x) dx can be written as int _(a) ^(b)f (x) dx "@" ((c-a))/(2) {f(a)+f(c )}_ ((b-c))/(2) {f(c )+ f (b)} ""^(@)F(c ), If c = (b-a)/(2), then this gives: int _(a) ^(b )f (x) dx "@" (b-a)/(4) {f(a) + 2f (a) + 2f (c )+ f(b) },.......(1) The approximate value of int _(0) ^(pi//2) sin x dx using rule (1) given above is
Answer» `(pi)/(8 SQRT2)(1+ sqrt2)` `(pi)/(4 sqrt2) (1+ sqrt2)` `pi/8 (1+ sqrt2)` `pi/4 (1+ sqrt2)` Answer :C

Discussion

44.	Find the chord of contact of (0,5) with respect to the circle x(2) + y^(2) - 5 x +4y - 2 =0
Answer» ANSWER :` - 5X+ 14Y +16 =0`

Discussion

45.	An ellipse has its centre C(1,3) focus at S( 6, 3) and passing throughthe point P(4, 7) then The point of the lines joining each focus to the foot of the perpendicular from the other focus upon the tangent at point P is
Answer» `((5)/(3), 5)` `((4)/(3), 3)` `((8)/(3), 3)` `((10)/(3), 5)` Answer :D

Discussion

46.	findthe multiplerootsof8x^3 + 20 x^2 + 6 x-9 =0
Answer» ANSWER :`3/2,3/2,(-1)/(2)`

Discussion

47.	int_(0)^(1) (ax^3 + bx)=0 for
Answer» Any VALUE of a and b `a gt 0, b gt 0` only `a gt 0, b LT 0` only `a lt 0, b GT0` only Answer :A

Discussion

48.	C. (b + c) xx (a + b + c) =
Answer» `C. B XX a` 0 `c. a xx b` `-a c xx b` ANSWER :A

Discussion

49.	int_(0)^(2/3)(dx)/(4+9x^(2))
Answer»

Discussion

50.	If D_(1)=\|(a,b,c),(d,e,f),(g,h,k)\|,D_(2)=\|(a,g,x),(b,h,y),(c,k,z)\| and d=tx,e=ty,f=tz then
Answer» `D_(1)=tD_(2)` `tD_(1)=D_(2)` `D_(1)=-tD_(2)` `D_(2)=-tD_(1)` ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Evaluate int x^(3) sin x dx

Find the number of 4-digited numbes of the form xyzt withx,z, tlty and x ne0

The orthocentre of the triangle formed by the lines y=0, (1+t)x-ty+t(1+t)=0 and (1+u)x-uy+u(1+u)=0(t ne u) for all values of t and u lies on the line.

Correct rectivity order of molecular hydrogen, Nascent hydrogen and atomic hydrogen is : {:(H_(2),, to,, "Molecular hydrogen"),(H,, to,, "Atomic hydrogen"),([H],, to,, "Nascent hydrogen"):}

Integrate the functions (xe^(x))/((1+x)^(2))

intx^(2)logxdx

If therangeof thefunctionf(x)=- 3x -3 is{ 3,-6,-9,-18} , thenwhichof the followingelementsis notin thedomainof f ?

If A and B are two events such that P(A cup B)=(5)/(6), P(A cap B)=(1)/(3), then whichone of the followingis not correct ?

If standard deviation of 1,2,3,4,….,10 is sigma then standard deviation of 11, 12, …20 is

The common roots of the equationx^(12)-1=0,x^4+x^2+1=0 are

Evaluate the following define integrals as limit of sums : lim_(n rarroo) [(1+1/n) (1+2/n)......(1+n/n)]^(1//n)

Iff (x) =[((1-cos kx)/(x^2) : x ne 0),(8 , x=0)] iscontinuesatx=0 , thenK=……

Find (dy)/(dx) if y= sec^(-1)((1)/(2x^(2)-1)), 0 lt x lt (1)/(sqrt(2))

If {:(f(x)=x^(2)",if "0 le x le 1),(""=sqrt(x)",if " x ge 1","):} then area above X-axis, bounded by the line x = 4 and the curve y = f(x) is

How many 5 digit telephonenumbers can be constructedusing the digits 0 to 9, if starts with 67 and no digit appears more than once ?

Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below have inverses. Find f^(-1) if it exist f={(1,3)(2,1),(3,1),(4,2)}

The sum of the coefficient of x^32 and x^-17 in (x^4-(1)/(x^3))^15 is

Match the following : {:("LIST - I","LIST - II"),("I)" int_(0)^(2)|1-x|dx=,"a) " 1),("II)" int_(0)^(2)|x-2|dx=,"b) "2),("III)" int_(0)^(2)(|x|+|x-1|)dx=,"c) "3):}

If x, y, z are in G.P. and (x + 3), (y + 3), (z + 3) are in H.P., then the value of y is -

The value of (18^(3) + 7^(3) + 3.18.7.25)/(3^(6) + 6(243)2 + 15(81)4 + 20.27.8 + 15(9).16 + 6(3)(32) + 64) is

If a variable line of slope 4 intersects the hyperbolaxy =1 at two points. Then the locus of the point which divides the line segment between these points in the ratio 1 : 2 is

IfA= cos^(2) 76^(@) + cos^2 16^(@) - cos 76^(@) cos 16^(@) , B= cos^(2)( 45^(@) - alpha ) + cos^(2)(15^(@) + alpha ) - cos^(2)(15^(@)- alpha ) , C= ( cos ( 45^(@)+ A) cos (45^(@) - A))/( sin (120^(@) + A)-sin(120^(@) - A)) then the ascending order is

Let a and b be real numbers such that sina + sinb =1/sqrt(2), cosa + cosb =sqrt(3)/2, then

xy(dy)/(dx)-y^(2)=(x+y)2_(e)^(-(y)/(x))

Resolve (3x^(2)+5)/((x^(2)+2)^(2)(x^(2)+1)) into partial fractions

(dy)/(dx) - (y)/(x) + cosec ((y)/(x)) = 0, y = 0 when x = 1.

If bar(a),bar( c ) and bar(d) are not coplanar vectors and bar(d).(bar(a)xx(bar(b)xx(bar( c )xx bar(d))))=K[bar(a),bar( c ),bar(d)] then K = ….

If 25^(log_5cos x)=a and e^(ln(-sinx))=b then the correct option is (where , a,b in R) :-

If intsqrt(2+tan^(2)x)dx-ln tanx+sqrt(2+tan^(2)x)+f(x)+c, then f(x)=

A is a set containing n_(1) elements and B is another set containing n_(2) elements, The number of non -decreasing functions from A rightarrow B is

The number of ways in which 6 things canbe divided Statement-I: into 2 equal groups is 10. Statement-II: among 2 persons equally is 20. Which of the above statements is true.

Obtain the equation of straight lines : Passing through (-1,2) and making intercept 2 on the y-axis.

If veca=hati+hatj+hatk,vecb=2hati-hatj+3hatkandvecc=hati-2hatj+hatk,find a unit vector parallel to the vector 2veca-vecb+3vecc.

If x =alpha, y=beta, z = gamma is a solution of the system of equations x+y+z=4 2x-y+3z=9

If a^3+b^3+c^3=3abc, where a,b,c are positive integers then the value of (a^2+2b^2+3c^2)/((a+b+c)^2) is :-

Find derivatives of the following functions.tan^(-1)(cossqrtx)

Integrate the following intcosec^2(x/2)dx

If the domain of the function f (x) =[log _(10) ((5x - x ^(2))/( 4 )) ]^(1//2) is a le x le b, then a,b is

The numberof fiveletterwordscan beformedusing3 consonentsand 2vowelsfromthe lettersof thewordMIXTUREis

Find the number of ways of arranging 15 students A_(1),A_(2),………A_(15) in a row such that A_(1),A_(2) and A_(3) sit together in specified order

Find the chord of contact of (0,5) with respect to the circle x(2) + y^(2) - 5 x +4y - 2 =0

An ellipse has its centre C(1,3) focus at S( 6, 3) and passing throughthe point P(4, 7) then The point of the lines joining each focus to the foot of the perpendicular from the other focus upon the tangent at point P is

findthe multiplerootsof8x^3 + 20 x^2 + 6 x-9 =0

int_(0)^(1) (ax^3 + bx)=0 for

C. (b + c) xx (a + b + c) =

int_(0)^(2/3)(dx)/(4+9x^(2))

If D_(1)=|(a,b,c),(d,e,f),(g,h,k)|,D_(2)=|(a,g,x),(b,h,y),(c,k,z)| and d=tx,e=ty,f=tz then