28278 + Interview Questions in Maths in Class 12

1.	The system of equations lambdax + (lambda+ 1) y+ (lambda- 1)z=0,(lambda+1)x+lambday+(lambda+z)z=0,(lambda-1)x+(lambda+2)y+lambdaz=bas a non-trivial solutions for
Answer» exactly three REAL value of `lambda` exactly two real valuesof `lambda` exactly three real value of `lambda` INFINITELY MANY real value of `lambda` Answer :C

Discussion

2.	Consider the function f (x)={{:(max (x, (1)/(x))",", If x ne0),(min (x, (1)/(x)),),(1"," , if x=0):}, then lim _(xto 0^(-)) {f(x)} + lim _(xto 1 ^(-)) {f (x)}+ lim _(x to 1 ^(-)) [f (x)]= (where {.} denotes fraction part function and [.] denotes greatest integer function)
Answer» 0 1 2 3 Answer :A

Discussion

3.	Let a_(n)=3^(n)+5^(n), ninN and let A=((a_(n),a_(n+1),a_(n+2)),(a_(n+1),a_(n+2),a_(n+3)),(a_(n+2),a_(n+3),a_(n+4)))Then
Answer» 0 is a root of the EQUATION DET (A-xl) =0 det (A) =`a_(N)a_(n+2) a_(n+4)` det (A) `lt0` det (A) `= a_(n)+a_(n+2)+a_(n+4)` ANSWER :A

Discussion

4.	If int(x^((1)/(3))+(tanx)^((1)/(3)))dx=(3)/(4)x^((4)/(3))-lambdalog(l+t^(2))+(1)/(sqrt(3))tan^(-1)(2t^(2)-1)/(sqrt(3))+C,t=tan^((1)/(3))x then lambda is equal to
Answer» ANSWER :`1.50`

Discussion

5.	Coefficient of x^3y^4z^2 in (2x-3y+4z)^9 is
Answer» `(9!)/(4!4!)2^(3)3^(4)4^2` `(-9!)/(3!2!4!)2^(3)3^(4)4^2` `(9!)/(4!4!) 2^(3)3^(4)4^2` `(9!)/(3!4!2!)2^(3)3^(4)4^2` ANSWER :D

Discussion

6.	Integrate the following functions. int(cosx)/(cos(x-2))dx
Answer» ANSWER :`xcosalpha+(SINALPHA)log\|cos(x-alpha)\|+C`

Discussion

7.	The vertex or the parabola y = ax^(2)+bx+c is
Answer» `((b)/(2A),(b^(2)-4ac)/(4A))` `((-b)/(2a),(b^(2)-4ac)/(4a))` `((b)/(2a),(4ac-b^(2))/(4a))` `((-b)/(2a),(4ac-b^(2))/(4a))` Answer :D

Discussion

8.	Principal value of cos^-1 (-frac{1}{2}) is :
Answer» `-2π/3` `-π/3` `π/3` `2π/3` ANSWER :D

Discussion

9.	The solution of the differential equation (dy)/(dx)= (x)/(1 + x^(2)) is
Answer» `y=(1)/(2) LOG \|2+X^(2)\| +c` `y= (1)/(2) log \|1 +x^(2)\| +c` `y= log \|SQRT(1+x^(2))\|+c` None of these Answer :B::C

Discussion

10.	Solve the following linear programming problem graphically: Maximize : z=x+9y Subject to: x+3yle60 x+yge10 xley xge0 yge0
Answer» SOLUTION :NA

Discussion

11.	If the coefficients of x^2 and x^4 in the expansion of (x^(1/3) + (2)/(x^(1/3)) )^18 , (x lt 0) are m and n respectively then m/n is equal to
Answer» 27 182 `5/4` `4/5` ANSWER :B

Discussion

12.	Find (dy)/(dx) ofy=e^xlogx
Answer» SOLUTION :`d/dx(e^xlogx)=e^xxx1/X+logxxxe^x=e^x[1/x+logx]=(e^x(1+xlogx))/x`

Discussion

13.	If matrix AB=O ,then A=O or B=O or both A and B are null matrices .
Answer» ANSWER :FALSE

Discussion

14.	Evaluate Lt_(x to 0)(log(1 + 5x))/(x)
Answer»

Discussion

15.	Find the number of solution to the equation sin x = x^(2) + 2x + 1.
Answer» Solution :Let F(x) = sin x and `g(x) = x^(2) + 2x + 1 = (x + 1)^(2)` Graphs of y = sin x and `y = (x + 1)^(2)` are as shown in the following figure. Since the curvey `y = (x + 1)^(2)` MEETS the y - axis at (0, 1), it never INTERSECTS y = sin x. HENCE no solution.

Discussion

16.	Let L_(1) -= ax+by+a root3 (b) = 0 and L_(2) -= bx - ay + broot3 (a) = 0be two straightlines . The equatins of the bisectors of the angle formed by the foci whose equations are lambda_(1)L_(1)-lambda_(2)L_(2)=0 and lambda _(1) l_(1) + lambda_(2) = 0 , lambda_(1) and lambda_(2) being non - zero real numbers,are given by
Answer» `L_(1)=0` `L_(2)=0` `lambda_(1)L_(1)+lambda_(2)L_(2)=0` `lambda_(2)L_(1)-lambda_(1)L_(2)=0` Answer :A::B

Discussion

17.	If \|{:(a,a+x^(2),a+x^(2)+x^(4)),(2a,3a+2x^(2),4a+3x^(3)+2x^(4)),(3a,6a+3x^(2),10a+6x^(2)+3x^(4)):}\| =a_(0)+a_(1)x+a_(2)x^(2)+a_(3)x^(3)+a_(4)x^(4)+a_(5)x^(5)+a_(6)x^(6)+a_(7)x^(7) and f(x) =+a_(0)x^(2)+a_(3)x+a_(6) then
Answer» `f(X)gt=0,forallin R if algt0` f(x)=0, only ifa=0 f(x)=0, has of a=0 f(x) =0 has equal ROOTS f(x)=0, hasmore than TWO ROOT if a=0 Answer :A::B::C::D

Discussion

18.	The value of the \|(log_a(x/y),log_a(y/z),log_a(z/x)),(log_a^2(y/z),log_a^2(z/x),log_a^2(x/y)),(log_a^3(z/x),log_a^3(x/y),log_a^3(y/z))\|
Answer» 1 `-1` 0 `1/6log_axyz`. ANSWER :C

Discussion

19.	If a,b,c are non-coplanar vector and lambda is a real number then [lambda (a + b) lambda^(2) b lambda c] - [a b + c b] for
Answer» EXACTLY ONE value of `lambda` no value of `lambda` exactly three values of `lambda` exactly two value of `lambda` ANSWER :B

Discussion

20.	For positive l, m and n, if the points x=ny+mz, y=lz+nx, z=mx+ly intersect in a straight line, when Q. The equation of the straight line is (x)/(a)=(y)/(b)=(z)/(c) , where the ordered traid (a, b, c) is
Answer» `SQRT(1-L^2), sqrt(1-m^2), sqrt(1-N^2)` `l, m and n` `(1)/(sqrt(1-l^2)), (1)/(sqrt(1-m^2)) and (1)/(sqrt(1-n^2))` NONE of these Answer :(a)

Discussion

21.	Evaluate int (x^(2))/(sqrt(1+x^(2)) ( sqrt(1 + x^(2)) - 1) )" dx " ( x ne 0 )
Answer» ANSWER :X + `SINH^(-1)` x + C

Discussion

22.	Find the derivative of the function given by f(x)= sin (x^2).
Answer» ANSWER :`= 2X COS X^(2)`

Discussion

23.	Evaluate the following determinates \|{:(1+2hati,1-hati),(1+hati,1-2hati):}\|
Answer» ANSWER :3

Discussion

24.	There are two vectors vecA and vecB then component of vecA in the direction of vecB is :
Answer» `(vecA.HATB)hatB` `(VECB.hatA)hatB` `(vecA.vecB)hatB` `(vecA.hatB)vecB`

Discussion

25.	Find the number of divisors of lfloor20
Answer» ANSWER :41040

Discussion

26.	Sum to n terms of the series (1)/(1.2.3)+(3)/(2.3.4)+(5)/(3.4.5)+(7)/(4.5.6)+…. is
Answer» `(n(n+1))/(2(n+2)(n+3))` `(n(3n+1))/(4(n+1)(n+2))` `(1)/(6)-(5)/((n+1)(n+4))` none of these Answer :B

Discussion

27.	For x in R, tanx+1/2tan""(1)/(2^(2))tan""(x)/(2^(2))+...+(1)/(2^(n-1))tan""((x)/(2^(n-1))) is equal to
Answer» `2cot2x-(1)/(2^(n-1))COS""((X)/(2^(n-1)))` `(1)/(2^(n-1))COT""((x)/(2^(n-1)))-2cot2x` `cot""((x)/(2^(n-1)))-cot2x` none of these Answer :B

Discussion

28.	If A=[[1,2],[-2,3]]B=[[3,2],[1,4]],C=[[2,2],[1,3]]Calculate CB.
Answer» SOLUTION :`CB=[[2,2],[1,3]][[3,2],[1,4]]` `=[[2.3+2.1""2.2+2.4],[1.3+3.1" "1.2+3.4]]=[[8,12],[6,14]]`

Discussion

29.	(i) int sin mx dx (ii) int 2x sin (x^2+1) dx (iii) int x sqrt(1+2x^2) dx.
Answer» ANSWER :`tan^-1 a/b`

Discussion

30.	A circle of radius r is concentric with theellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 Prove that slope of the common tangent of the above curves is sqrt((r^(2)-b^(2))/(a^(2)-r^(2)))
Answer» ANSWER :`SQRT(R^(2)-B^(2))/(a^(2)-r^(2))`

Discussion

31.	Are the following sets relation ? phi x C from A to B .Determinethe domain range and inverse of each of the relations mentioned above.
Answer» Solution :`phi` XX C` from A to B is a RELATION.

Discussion

32.	Let Q be the set of rational numbers and R be a relation on Q defined by R{":"x,y inQ,x^2+y^2=5} is
Answer» An EQUIVALENCE RELATION Only symmetric Only reflexive Reflexive, TRANSITIVE but nor symmetric Answer :B

Discussion

33.	A model for the number of questions on an assignment when the assignment is worth p points, is q=p^2/50. According to this model , what is the number of questions, q for an assignment worth 80 points ?
Answer» 128 80 26 13 Answer :A

Discussion

34.	If truth value of p is T, q is F, then truth values of ( p rarr q ) and ( q rarr p ) vee (~ p )are respectively
Answer» F, F F, T T, F T, T ANSWER :B

Discussion

35.	If a fair coin is tossed 6 times. Find the probability of (i) at least five heads and (ii) exactly 5 heads.
Answer» ANSWER :(i) `7/24` (II) `63/64` (III) `3/32`

Discussion

36.	If the two regression coefficients are - 0.4 and -1.6, then the coefficient of correlations is
Answer» 0 `-0.9` 0.8 1 Answer :B

Discussion

37.	Find the points on the curve x^(2)y^(2)+xy=2 at which the slope of the tangent is -1.
Answer» ANSWER :(1, 1) and `(-1,-1)`

Discussion

38.	If f(x) =X^(3) + ax^(2) +bx +c has extreme values at x=-1 and x=3 . Finda,b,c.
Answer» Solution :Extreme values basically mean maximum or minimum values SINCE F(x) isdifferentiable function so `f(-1) =0 =f'(3)` `f'(x) =3x^(2) +2ax +b` ` f'(3) =27 +6a +b=0` `f'(-1) =3 -2A +b =0` `rArr "" a=-3 ,b =- 9, c in R`

Discussion

39.	20 persons are sitting along a round circle. In how many ways 4 persons can be selected such that exactly 3 of them are consecutive
Answer» ANSWER :300

Discussion

40.	20 persons are sitting along a round circle. In how many ways 4 persons can be selected such that exactly 2 of them are consecutive.
Answer» ANSWER :2100

Discussion

41.	Find the maximum and minimum values in the following functions :x^(5)-5x^(4)+5x^(3)-10
Answer» Answer :MAXIMUM VALUE `-9` at x = 1 Minimum value `-37` at x = 3

Discussion

42.	Solve the following linear programming problem graphically: Maximize : z=3x+5y Subject to: x+yge2 x+3yge3 xge0 yge0
Answer» SOLUTION :NA

Discussion

43.	A conical tent of given capacity will require the least amount of canvas when the height is …… times the radius of the tent
Answer» 1 2 `SQRT3` `SQRT2` ANSWER :D

Discussion

44.	Method of integration by parts : int log(x+1)dx=....
Answer» `(x+1)LOG(x+1)-x+c` `(x+1)log(x+1)+x+c` `(x-1)log(x+1)-x+c` `(x-1)log(x+1)+x+c` ANSWER :A

Discussion

45.	Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5).
Answer» Answer :Area of `DeltaABC=(1)/(2)\|vec(AB)xx vec(AC)\|=(1)/(2)sqrt(61)` SQ. UNITS

Discussion

46.	Let f(x) be a differentiable non-decreasing function such that int_(0)^(x)(f(t))^(3)dt=(1)/(x^(2))(int_(0)^(x)f(x)dt)^(3)AAx inR-{0} andf(1)="1. If "int_(0)^(x)f(t)dt=g(x)" then "(xg'(x))/(g(x)) is
Answer» always equal to 1 always equal to `-2` may be 1 or `-2` not independent of x Solution :`int_(0)^(x)(F(t))^(3)dt=(1)/(x^(2))(int_(0)^(x)f(t)dt)^(3)` `THEREFORE""int_(0)^(x)(f(t))^(3)dt=(1)/(x^(3))(g(x))^(3)` Differentiating w.r.t. x, `therefore""(f(x))^(3)=(1)/(x^(2))3(g(x))^(2)g'(x)-(2)/(x^(3))(g(x))^(3)` `rArr""((xg'(x))/(g(x)))^(3)-3((x.g'(x))/(g(x)))+2=0` `rArr""(xg'(x))/(g(x))=1or -2` If `(xg'(x))/(g(x))=1` `rArr""XF(x)=int_(0)^(x)f(t)dt` `rArr""xf'(x)+f(x)=f(x)` `rArr""f(x)=1` `"or"xf'(x)+f(x)=-2f(x)` `""(f'(x))/(f(x))=(-3)/(x)` `logf(x)=-3LOG x+logc` `rArr""f(x)=c//x^(3)` `rArr""f(1)=1 rArr f(x)=1//x^(3)" (decreasing function)"`

Discussion

47.	squareABCD is a parallelogram. The position vectors of the points A, B and Care respectively 4hati+5hatj-10hatk,2hati-3hatj+4hatk and -hati+2hatj+hatk. Find the vector equation of the line BD.
Answer» ANSWER :`vecr=2hati-3hatj+4hatk+lambda(hati-13hatj+17hatk)`

Discussion

48.	The set of points (x,y) in the plnae satisfying x ^(2//5)+ \|y\| =1 form a curve enclosing a region of area p/q square units, when p and q are relatively prime positive intergers. Find p-q.
Answer» ANSWER :1

Discussion

49.	Show that 3C_0-8C_1 + 13C_2 - 18C_3 + ..... + (n+1)^(th) term = 0
Answer» Solution :`3C_0-8C_1 + 13C_2 - 18C_3 + ..... + (N+1)^TH` term = `3C_0 - (5+3)C_1 + (10+3)C_2 - (15+3)C_3` + .... = `3(C_0 - C_1 + C_2 ....) + 5(-C_1 + 2C_2 - 3C_3 ....) But `(1+X)^n` = `C_0 - C_1x + C_2x^2 - C_3x^3 + ... + (-1)^n x^nC_n ....(1) putting x = 1 we get `C_0 - C_1 + C_2 .... + (-1) "^nC_n` = 0 and differentiating (1) we get `n(1-x)^(n-1) (-1) = `-C_1 + 2C_2 x - 3C_3x^2 + .... putting x = 1 we get `-C_1 + 2C_2 - 3C_3 + .... = 0 THEREFORE `3C_0 - 8C_1 + 13C_2 ..... (n+1)` terms = 0

Discussion

50.	Find all points of discontinuityof f, where f is defined by f(x)={{:((x)/(\|x\|)," if "x lt0),(-1," if "x ge 0):}
Answer» ANSWER :No POINT of DISCONTINUITY

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The system of equations lambdax + (lambda+ 1) y+ (lambda- 1)z=0,(lambda+1)x+lambday+(lambda+z)z=0,(lambda-1)x+(lambda+2)y+lambdaz=bas a non-trivial solutions for

Consider the function f (x)={{:(max (x, (1)/(x))",", If x ne0),(min (x, (1)/(x)),),(1"," , if x=0):}, then lim _(xto 0^(-)) {f(x)} + lim _(xto 1 ^(-)) {f (x)}+ lim _(x to 1 ^(-)) [f (x)]= (where {.} denotes fraction part function and [.] denotes greatest integer function)

Let a_(n)=3^(n)+5^(n), ninN and let A=((a_(n),a_(n+1),a_(n+2)),(a_(n+1),a_(n+2),a_(n+3)),(a_(n+2),a_(n+3),a_(n+4)))Then

If int(x^((1)/(3))+(tanx)^((1)/(3)))dx=(3)/(4)x^((4)/(3))-lambdalog(l+t^(2))+(1)/(sqrt(3))tan^(-1)(2t^(2)-1)/(sqrt(3))+C,t=tan^((1)/(3))x then lambda is equal to

Coefficient of x^3y^4z^2 in (2x-3y+4z)^9 is

Integrate the following functions. int(cosx)/(cos(x-2))dx

The vertex or the parabola y = ax^(2)+bx+c is

Principal value of cos^-1 (-frac{1}{2}) is :

The solution of the differential equation (dy)/(dx)= (x)/(1 + x^(2)) is

Solve the following linear programming problem graphically: Maximize : z=x+9y Subject to: x+3yle60 x+yge10 xley xge0 yge0

If the coefficients of x^2 and x^4 in the expansion of (x^(1/3) + (2)/(x^(1/3)) )^18 , (x lt 0) are m and n respectively then m/n is equal to

Find (dy)/(dx) ofy=e^xlogx

If matrix AB=O ,then A=O or B=O or both A and B are null matrices .

Evaluate Lt_(x to 0)(log(1 + 5x))/(x)

Find the number of solution to the equation sin x = x^(2) + 2x + 1.

If |{:(a,a+x^(2),a+x^(2)+x^(4)),(2a,3a+2x^(2),4a+3x^(3)+2x^(4)),(3a,6a+3x^(2),10a+6x^(2)+3x^(4)):}| =a_(0)+a_(1)x+a_(2)x^(2)+a_(3)x^(3)+a_(4)x^(4)+a_(5)x^(5)+a_(6)x^(6)+a_(7)x^(7) and f(x) =+a_(0)x^(2)+a_(3)x+a_(6) then

The value of the |(log_a(x/y),log_a(y/z),log_a(z/x)),(log_a^2(y/z),log_a^2(z/x),log_a^2(x/y)),(log_a^3(z/x),log_a^3(x/y),log_a^3(y/z))|

If a,b,c are non-coplanar vector and lambda is a real number then [lambda (a + b) lambda^(2) b lambda c] - [a b + c b] for

For positive l, m and n, if the points x=ny+mz, y=lz+nx, z=mx+ly intersect in a straight line, when Q. The equation of the straight line is (x)/(a)=(y)/(b)=(z)/(c) , where the ordered traid (a, b, c) is

Evaluate int (x^(2))/(sqrt(1+x^(2)) ( sqrt(1 + x^(2)) - 1) )" dx " ( x ne 0 )

Find the derivative of the function given by f(x)= sin (x^2).

Evaluate the following determinates |{:(1+2hati,1-hati),(1+hati,1-2hati):}|

There are two vectors vecA and vecB then component of vecA in the direction of vecB is :

Find the number of divisors of lfloor20

Sum to n terms of the series (1)/(1.2.3)+(3)/(2.3.4)+(5)/(3.4.5)+(7)/(4.5.6)+…. is

For x in R, tanx+1/2tan""(1)/(2^(2))tan""(x)/(2^(2))+...+(1)/(2^(n-1))tan""((x)/(2^(n-1))) is equal to

If A=[[1,2],[-2,3]]B=[[3,2],[1,4]],C=[[2,2],[1,3]]Calculate CB.

(i) int sin mx dx (ii) int 2x sin (x^2+1) dx (iii) int x sqrt(1+2x^2) dx.

A circle of radius r is concentric with theellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 Prove that slope of the common tangent of the above curves is sqrt((r^(2)-b^(2))/(a^(2)-r^(2)))

Are the following sets relation ? phi x C from A to B .Determinethe domain range and inverse of each of the relations mentioned above.

Let Q be the set of rational numbers and R be a relation on Q defined by R{":"x,y inQ,x^2+y^2=5} is

A model for the number of questions on an assignment when the assignment is worth p points, is q=p^2/50. According to this model , what is the number of questions, q for an assignment worth 80 points ?

If truth value of p is T, q is F, then truth values of ( p rarr q ) and ( q rarr p ) vee (~ p )are respectively

If a fair coin is tossed 6 times. Find the probability of (i) at least five heads and (ii) exactly 5 heads.

If the two regression coefficients are - 0.4 and -1.6, then the coefficient of correlations is

Find the points on the curve x^(2)y^(2)+xy=2 at which the slope of the tangent is -1.

If f(x) =X^(3) + ax^(2) +bx +c has extreme values at x=-1 and x=3 . Finda,b,c.

20 persons are sitting along a round circle. In how many ways 4 persons can be selected such that exactly 3 of them are consecutive

20 persons are sitting along a round circle. In how many ways 4 persons can be selected such that exactly 2 of them are consecutive.

Find the maximum and minimum values in the following functions :x^(5)-5x^(4)+5x^(3)-10

Solve the following linear programming problem graphically: Maximize : z=3x+5y Subject to: x+yge2 x+3yge3 xge0 yge0

A conical tent of given capacity will require the least amount of canvas when the height is …… times the radius of the tent

Method of integration by parts : int log(x+1)dx=....

Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5).

Let f(x) be a differentiable non-decreasing function such that int_(0)^(x)(f(t))^(3)dt=(1)/(x^(2))(int_(0)^(x)f(x)dt)^(3)AAx inR-{0} andf(1)="1. If "int_(0)^(x)f(t)dt=g(x)" then "(xg'(x))/(g(x)) is

squareABCD is a parallelogram. The position vectors of the points A, B and Care respectively 4hati+5hatj-10hatk,2hati-3hatj+4hatk and -hati+2hatj+hatk. Find the vector equation of the line BD.

The set of points (x,y) in the plnae satisfying x ^(2//5)+ |y| =1 form a curve enclosing a region of area p/q square units, when p and q are relatively prime positive intergers. Find p-q.

Show that 3C_0-8C_1 + 13C_2 - 18C_3 + ..... + (n+1)^(th) term = 0

Find all points of discontinuityof f, where f is defined by f(x)={{:((x)/(|x|)," if "x lt0),(-1," if "x ge 0):}