28278 + Interview Questions in Maths in Class 12

1.	Method of integration by parts : inte^(x)[tanx-log(cosx)]dx=.....
Answer» `E^(x)LOG(secx)+c` `e^(x)log("cosec"x)+c` `e^(x)log(secx)+c` `e^(x)log(SINX)+c` ANSWER :A

Discussion

2.	If roots of the equation x^(2)+alpha^(2)=8x +6alpha are real, then which one is correct?
Answer» `-2 LE alpha le 8` `2 le alpha le 8` `-2 LT alpha le 8` `-2 le alpha lt 8` ANSWER :a

Discussion

3.	The solution of the differential equation (dy)/(dx) = (x-2y +1)/(2x-4y)
Answer» `(x-2Y)^(2) + 2X = C` `(x-2y)^(2) + x = C` `(x- 2y) + x^(2) = C` `(x-2y) + x^(2) = C` Answer :A

Discussion

4.	Letngt 1bean interger. Whichof thefollowingsetsof numbersnecessarily containsmultipleof 3?
Answer» `N^(19)-1,n^(19)+1` `n^(19),n^(38)-1` `n^(38),n^(38)+1` `n^(38),n^(19)-1` SOLUTION :

Discussion

5.	Find the mean deviation and the standard deviation of thefirst 2n+1 natural numbers .
Answer» ANSWER :`=SQRT((N(n+1))/(3))`

Discussion

6.	n aritmetic means are inserted between 7 and 49 and their sum is found to be 364, then n is :
Answer» 11 12 12 14 Answer :C

Discussion

7.	Method of integration by parts : int tan^(-1)x dx=....
Answer» `x TAN^(-1)x+(1)/(2)log(1+x^(2))` `x tan^(-1)x-(1)/(2)log(1+x^(2))` `(x-1)tan^(-1)x` `XTAN^(-1) x-log(1+x^(2))` ANSWER :B

Discussion

8.	Stacy has 30 meters of fencing that she wishes to use to enclose a rectangular garden. If all of the fencing is used, what is the maximum area of the garden, in square meters, that can be enclosed?
Answer» `48.75` `56.25` `60.50` `168.75` ANSWER :B

Discussion

9.	Which one is not a requirement of a binomial distribution ?
Answer» There are 2 OUTCOMES for each trial There is a fixed NUMBER of trials The out come must be DEPENDENT on each other The probability of SUCCESS must be the same for all the trials Answer :C

Discussion

10.	Evalute the following integrals int e^(x) ((x + 2)/((x + 3)^(2)) )dx
Answer» ANSWER :`(E^(X))/(x + 3) + C `

Discussion

11.	Let f _(a)(x) =In x andfor n ge 0 and x gt 0 Let f _(a)(x) = int _(0) ^(x)f _(a) (t) dt then: f _(a) (x ) equals :
Answer» ` (x ^(3))/(3 ) (LN x - (5)/(6))` ` (x ^(3))/( 3) (ln x - (11)/(6))` `(x ^(3))/(lfloor3) (ln x -(11)/(6 )) ` `(x ^(3))/(lfloor3)(lnx -(5)/(6))` Answer :C

Discussion

12.	Find: int sin^-1 (2x) dx
Answer» ANSWER :`1/2sqrt(1-4x^2)+C`

Discussion

13.	int (1)/(1 - sin x )dx =
Answer» tan X + secx +c SEC x - tan x + c tan x - sec x + c x +sec x + c Answer :A

Discussion

14.	int " cosec"^(m) x cot x dx=
Answer» `("cosec"^(m)X)/(m) +C ` `(-1)/(m - 1) "cosec"^(m) ` x + c `- (1)/(m sin^(m) x) + c` `(1)/(m) sin^(m) ` x +c Answer :C

Discussion

15.	Consider f(x)=Lim_(nto oo)((a^(n)+b^(n))^((1)/(n))sinx+{e^(x)}^(n))([(1)/(ncot^(-1)n)]+1),AAx inR where agtbgt0. [Note : {k} and [k] denotes fractinal part of k and greatest interger less than or equal to k respectively.] If H(x)=sgn (f(x)-3) has exactly one point of discontinuity AA x in[0,2pi], then number of integral value of a, is
Answer» 1 2 0 infinite Solution :`F(x)=underset(ntooo)Lim((a(1+((b)/(a))^(n))^((1)/(n)))sinx+{e^(x)}^(n))([((1)/(n))/("tan"^(-1)(1)/(n))]+1)` `:.""f(x)=(asinx+0)(1+1)` `:.""f(x)=2asinx` (i) `H(x)=SGN (2asinx-3)` has exactly one POINT of discontinuty in `[0,2pi]`, then `2A sinx-3=0` must have one real root in `[0,2pi],sin(3)/(2a)` `:." "a=(3)/(2)` only `:.""` Number integral value of a is ZERO. `G(x)=\|2asinx\|+2asin\|x\|` (ii) Number of non-differential point of G(x) is `x=-2pi,-pi,0,pi,2pi` separately we can prove that G(x) is non-differentiable at x=0.

Discussion

16.	Prove that the function f : R to Rdefined byf(x)= 2x+ 7, is invertible. Hence findf^(-1)
Answer» ANSWER :` F^(-1): R to R , ` such that ` f^(-1) (y)=(1)/(2)(y-7)`

Discussion

17.	If \|x\| is so small that x^4 and higher powers of x many be neglected , then find an approximate value of root(4)(x^2 + 81) - root(4)(x^2 + 16)
Answer» SOLUTION :N/A

Discussion

18.	4+(9)/(2!)+27/(3!)+....=
Answer» `e^2` `e^3` `e^4` `1/(e^2)` ANSWER :B

Discussion

19.	A: f(x)=x-[x] is discontinuous at x=2 R: underset(x to a)"Lt" f(x)=f(a)
Answer» Both A and R are true and R is the correct explanation of A Both A and R are true and R ISNOT the correct explanation of A A is true but R is false A is false but R is true Answer :B

Discussion

20.	What is the total number of functions that can be defined from the set{1,2}" to the set" {1,2,3}?
Answer» SOLUTION :The TOTAL number of FUNCTIONS that can be defined from the set {1,2} to the set {1,2,3} is `3^2=9`.

Discussion

21.	If A and B are events such that P(A)=p_(1), P(B)=p_(2) and P(AnnB)=p_(3) then P(barAuuB)=
Answer» `1-p_(1)+p_(2)` `1-p_(1)+p_(3)` `1-p_(1)-p_(2)` `p_(1)+p_(2)-1` ANSWER :B

Discussion

22.	A : x^ 2 +x+1gt 0forallx in R R :if therootsof ax ^2+ bx+ c=0are imaginarythen forx inR , ax^2 + bx+ canda havethe samesign .
Answer» BothA are RARE tureR ISTHE correctexplanationOf A BothA are Rare truebutR isnotcorrectexplanationof A A istruebutR is false A isfalsebutR ISTRUE ANSWER :A

Discussion

23.	Out of 100 bulbs in a box 10 bulbs are defective. Five bulbs are selected at random from it. Then find the probability of an event that selected bulb is of without defect.
Answer» `((9)/(10))^(10)` `((1)/(10))^(10)` `((9)/(10))^(5)` `((1)/(10))^(5)` Answer :C

Discussion

24.	Focii of the curve xy = -4 are
Answer» ` (SQRT2, -sqrt2 ) (-sqrt2, - sqrt2) ` ` (2SQRT2 , -2sqrt2) , ( -2sqrt2, -2sqrt2) ` ` (-2sqrt2, 2sqrt2) , ( 2sqrt2,-2sqrt2) ` ` (-SQRT3, sqrt3)(sqrt3,-sqrt3) ` ANSWER :C

Discussion

25.	Let f: X rarrYbe a function. Define a relation R in X given by R = {(a, b): f(a) = f(b)}. Examine whether R is an equivalence relation or not.
Answer» SOLUTION :N/A

Discussion

26.	Show that number of equivalence relation in the set {1,2,3} containing (1,2) and (2,1) is two.
Answer» ANSWER :`R _(1)`

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27.	Evaluate the following:""^(20)C_(4)=
Answer»

Discussion

28.	Evaluate : Lim_(x to 0)lim_(0)^(x^(2))(sinsqrt(t)tansqrt(t)dt)/(x^(4))
Answer» Solution :Applying L' hospital rule `UNDERSET(xrarr0')("LIM")'(2xsinxtanx)/(4x^(3))rArr underset(xrarr0)("Lim")'(1)/(2)((sinx)/(X))(tanx/x) = 1/2`

Discussion

29.	Let f(x)={(0 , x "is irrational"),(2/(2q^(3)-q^(2)+q+sin^(2)q+5) , if x=p/q ("rational")):}(where HCF (p,q)=1,p,q,gt0) and f(x) is defined AAxgt0 then which of the following is/are incorrect?
Answer» `f(x)` is continuous at each irrational in `(0,oo)` `f(x)` is continuous at each rational in `(0,oo)` `f(x)` is discontinuous at each rational in `(0,oo)` `f(x)` is discontinuous for all `x` in `(0,oo)` Solution :LET `x=SQRT(3)` `f(sqrt(3))=0` `because sqrt(3)=1.732050807`………. As the decimal PART increase then in the expression `p/q, q` becomes very large So, `2/(2q^(3)-q^(2)+q+sin^(2)q+t)to0` Hence `lim_(xtosqrt(3))f(x)=0` THUS, `f(x)` is continuous at each irrational

Discussion

30.	The circle on SS^' as diameter intersects the ellipse in real points then its eccentricity
Answer» ANSWER :`1/sqrt2`

Discussion

31.	Let f(x)=x^(4)-4x^(3)+4x^(2)+c, c in R. Then
Answer» f(x) has infinitely MANY zeros in (1, 2) for all C f(x) has exactly one ZERO in (1, 2) if `-1 lt c lt 0` f(x) has double zeros in (1, 2) if `-1 lt c lt 0` whatever be the value of c,f(x) has no zero in (1,2) Answer :B

Discussion

32.	If intx.e^(2x)dx=e^(2x)f(x)+c where c is arbitary constant then f(x)=…….
Answer» `(x-4)/(6)` `(2x-1)/(4)` `(2x+1)/(2)` `(3x-1)/(4)` ANSWER :B

Discussion

33.	If E and F are independent events such that 0 lt P(E) lt 1 and 0 lt P(F) lt 1, then
Answer» E and `F^(C)` (the complement of the EVENT F) are INDEPENDENT `E^(C) and F^(C)` are independent____ `P(E/F)+P(E^(C)/F^(C))=1` All of these Answer :D

Discussion

34.	If x_(1) and x_(2) are the real roots of the equation x^(2)-kx+c=0, then the distance between the points A(x_(1),0) and B(x_(2),0) is
Answer» `SQRT(K^(2)+4c)` `sqrt(k^(2)-c)` `sqrt(c-k^(2))` `sqrt(k^(2)-4c)` ANSWER :D

Discussion

35.	If three dice are rolled, the probability of getting sum 12 is
Answer» `(15)/(216)` `(25)/(216)` `(5)/(216)` `(7)/(216)` ANSWER :B

Discussion

36.	Let f : N to R be a function defined as f(x) = 4x ^(2) + 12x + 15. Show that f: N to S. where, S is the range of f, is invertible. Find the inverse of f.
Answer» ANSWER :`6 =y`

Discussion

37.	The value of sum_(n=1)^(13)(i^(n)+i^(n-1)),i=sqrt(-1), is
Answer» i i-1 1 0

Discussion

38.	Prove that ""^(10)C_(3)+""^(10)C_(4)=""^(11)C_(4).
Answer» ANSWER :`=""^(11)C_(4)`

Discussion

39.	A function f(x) having the followingproperties, (i) f(x) iscontinuous except at x=3 (ii) f(x) isdifferentiable except at x=-2 and x=3 (iii) f(0) =0 lim_( x to 3) f(x) to - oo lim_( x to -oo) f(x) =3 , lim_(x to oo) f(x)=0 (iv) f'(x) gt 0 AA in (-oo, -2) uu (3,oo) " and " f'(x) le 0 AA x in (-2,3) (v) f''(x) gt 0 AA x in (-oo,-2)uu (-2,0)" and "f''(x) lt 0 AA x in (0,3) uu(3,oo) Then answer the followingquestions show that graph of fucntion y=f (-\|x\|) iscontinuous but notdifferentiable at two points if f(0)=0
Answer»

Discussion

40.	Let x, y, z be three positive real numbers such that x+y+z=1 then the maximum value of the expression (1-x)(2-y)(3-z) is __________
Answer» ANSWER :1

Discussion

41.	If A+B+C=180^(@)C then (sin 2A+sin 2B+sin 2C)/(cos A +cos B +cos C-1)=
Answer» `4cos A//2 COS B//2 cos C//2` `4 SIN A//2 sin B//2 sin C//2` `8 cos A//2 cos B//2 cos C//2` `1+4sin A//2 sin B//2 sin C//2` Answer :C

Discussion

42.	A function f(x) having the followingproperties, (i) f(x) iscontinuous except at x=3 (ii) f(x) isdifferentiable except at x=-2 and x=3 (iii) f(0) =0 lim_( x to 3) f(x) to - oo lim_( x to -oo) f(x) =3 , lim_(x to oo ) f(x)=0 (iv) f'(x) gt 0 AA in (-oo, -2) uu (3,oo) " and " f'(x) le 0 AA x in (-2,3) (v) f''(x) gt 0 AA x in (-oo,-2)uu (-2,0)" and "f''(x) lt 0 AA x in (0,3) uu(3,oo) Then answer the followingquestions Show that f'(x) +3x=0 has five solutions if f'(0) gt -3 " and " f(-2) gt6
Answer»

Discussion

43.	Consider the identity function I_(N):N to N defined as I _(N) (x)=x AA x in N. Show that although I _(N) is onto but I _(N) + I _(N) : N to Ndefined as (I _(N) + I _(N)) (x) = I _(N) (x) + I _(N) (x) x +x = 2xis not onto.
Answer» ANSWER :`2X =3`

Discussion

44.	Method of integration by parts : int(cos^(-1)x+cos^(-1)sqrt(1-x^(2)))dx=Ax+f(x)sin^(-1)x-2sqrt(1+x^(2))+c,AAx""in[-1,0) then ..........
Answer» ANSWER :A

Discussion

45.	Find the coefficient of x^(10) in the expansion of (1+2x)/((1-2x)^(2)).
Answer» ANSWER :`21 XX 2^10`

Discussion

46.	Let A = Q xxQand be a binary operation on A defined by (a, b) (c,d) = (ad + b, ac). Prove that is closed on A = QxxQ . Find (i) Identity element of (A, ) , (ii) The invertible element of (A,**).
Answer» ANSWER :IDENTITY ELEMENT of `(A,**) = (B/a,(a-b)/(a))` ; INVERSE of (a,b) `= ((a-b)/a^2,(b-ab)/a^2)`

Discussion

47.	int_((pi)/(5))^((3pi)/(10))(f(sin x))/(f(sin x) + f(cos x)) dx
Answer» ANSWER :`(PI)/(20)`

Discussion

48.	Find the direction cosines of the vector hati+2hatj+3hatk.
Answer» ANSWER :`(1)/(SQRT(2)),(2)/(sqrt(14)),(3)/(sqrt(14))`

Discussion

49.	Statement-1, For any two complex numbers z_(1) and z_(2) \|z_(1)+sqrt(z_(1)^(2)-z_(2)^(2))\|+\|z_(1)-sqrt(z_(1)^(2)-z_(2)^(2))\|=\|z_(1)+z_(2)\|+\|z_(1)-z_(2)\| Statement-2: For any two complex numbers z_(1) and z_(2) \|z_(1)+z_(2)\|^(2)+\|z_(1)-z_(2)\|^(2)=2(\|z_(1)\|^(2)+\|z_(2)\|^(2))
Answer» STATEMENT-1 is True, Statement-2 is True: Statement-2 is a correct EXP,anation for statement-1. Statement-1 is true, statement -2 is true, Statement-2 is not a correct explanation for statement-1. Statement-1 is True, statement-2 is FALSE, statement-1 is False, Statement-2 is true. ANSWER :a

Discussion

50.	What is the value of(sin34^(@)cos236^(@)-sin56^(@)sin124^(@))/(cos28^(@)cos88^(@)+cos178^(@)sin208^(@))?
Answer» `-2` `-1` 2 1 Solution :`(sin34^(@)cos236^(@)-sin56^(@)sin124^@)/(cos28^(@)cos88^(@)+cos178^(@)sin208^(@))` `=(sin34^(@)(-cos56^(@))-sin56^(@)cos34^(@))/(cos28^(@)SIN2^(@)+COS2^(@)sin28^(@))` `(-sin34^(@)cos56^(@)-sin56^(@)cos34^(@))/(SIN(28^(@)+2))` `=-(sin(34^(@)+56^(@)))/(sin30^(@))=(-SIN90^(@))/(sin30^(@))=(-1)/(1/(2))=-2`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Method of integration by parts : inte^(x)[tanx-log(cosx)]dx=.....

If roots of the equation x^(2)+alpha^(2)=8x +6alpha are real, then which one is correct?

The solution of the differential equation (dy)/(dx) = (x-2y +1)/(2x-4y)

Letngt 1bean interger. Whichof thefollowingsetsof numbersnecessarily containsmultipleof 3?

Find the mean deviation and the standard deviation of thefirst 2n+1 natural numbers .

n aritmetic means are inserted between 7 and 49 and their sum is found to be 364, then n is :

Method of integration by parts : int tan^(-1)x dx=....

Stacy has 30 meters of fencing that she wishes to use to enclose a rectangular garden. If all of the fencing is used, what is the maximum area of the garden, in square meters, that can be enclosed?

Which one is not a requirement of a binomial distribution ?

Evalute the following integrals int e^(x) ((x + 2)/((x + 3)^(2)) )dx

Let f _(a)(x) =In x andfor n ge 0 and x gt 0 Let f _(a)(x) = int _(0) ^(x)f _(a) (t) dt then: f _(a) (x ) equals :

Find: int sin^-1 (2x) dx

int (1)/(1 - sin x )dx =

int " cosec"^(m) x cot x dx=

Prove that the function f : R to Rdefined byf(x)= 2x+ 7, is invertible. Hence findf^(-1)

If |x| is so small that x^4 and higher powers of x many be neglected , then find an approximate value of root(4)(x^2 + 81) - root(4)(x^2 + 16)

4+(9)/(2!)+27/(3!)+....=

A: f(x)=x-[x] is discontinuous at x=2 R: underset(x to a)"Lt" f(x)=f(a)

What is the total number of functions that can be defined from the set{1,2}" to the set" {1,2,3}?

If A and B are events such that P(A)=p_(1), P(B)=p_(2) and P(AnnB)=p_(3) then P(barAuuB)=

A : x^ 2 +x+1gt 0forallx in R R :if therootsof ax ^2+ bx+ c=0are imaginarythen forx inR , ax^2 + bx+ canda havethe samesign .

Out of 100 bulbs in a box 10 bulbs are defective. Five bulbs are selected at random from it. Then find the probability of an event that selected bulb is of without defect.

Focii of the curve xy = -4 are

Let f: X rarrYbe a function. Define a relation R in X given by R = {(a, b): f(a) = f(b)}. Examine whether R is an equivalence relation or not.

Show that number of equivalence relation in the set {1,2,3} containing (1,2) and (2,1) is two.

Evaluate the following:""^(20)C_(4)=

Evaluate : Lim_(x to 0)lim_(0)^(x^(2))(sinsqrt(t)tansqrt(t)dt)/(x^(4))

Let f(x)={(0 , x "is irrational"),(2/(2q^(3)-q^(2)+q+sin^(2)q+5) , if x=p/q ("rational")):}(where HCF (p,q)=1,p,q,gt0) and f(x) is defined AAxgt0 then which of the following is/are incorrect?

The circle on SS^' as diameter intersects the ellipse in real points then its eccentricity

Let f(x)=x^(4)-4x^(3)+4x^(2)+c, c in R. Then

If intx.e^(2x)dx=e^(2x)f(x)+c where c is arbitary constant then f(x)=…….

If E and F are independent events such that 0 lt P(E) lt 1 and 0 lt P(F) lt 1, then

If x_(1) and x_(2) are the real roots of the equation x^(2)-kx+c=0, then the distance between the points A(x_(1),0) and B(x_(2),0) is

If three dice are rolled, the probability of getting sum 12 is

Let f : N to R be a function defined as f(x) = 4x ^(2) + 12x + 15. Show that f: N to S. where, S is the range of f, is invertible. Find the inverse of f.

The value of sum_(n=1)^(13)(i^(n)+i^(n-1)),i=sqrt(-1), is

Prove that ""^(10)C_(3)+""^(10)C_(4)=""^(11)C_(4).

Let x, y, z be three positive real numbers such that x+y+z=1 then the maximum value of the expression (1-x)(2-y)(3-z) is __________

If A+B+C=180^(@)C then (sin 2A+sin 2B+sin 2C)/(cos A +cos B +cos C-1)=

Consider the identity function I_(N):N to N defined as I _(N) (x)=x AA x in N. Show that although I _(N) is onto but I _(N) + I _(N) : N to Ndefined as (I _(N) + I _(N)) (x) = I _(N) (x) + I _(N) (x) x +x = 2xis not onto.

Method of integration by parts : int(cos^(-1)x+cos^(-1)sqrt(1-x^(2)))dx=Ax+f(x)sin^(-1)x-2sqrt(1+x^(2))+c,AAx""in[-1,0) then ..........

Find the coefficient of x^(10) in the expansion of (1+2x)/((1-2x)^(2)).

Let A = Q xxQand **be a binary operation on A defined by (a, b) **(c,d) = (ad + b, ac). Prove that **is closed on A = QxxQ . Find (i) Identity element of (A, **) , (ii) The invertible element of (A,**).

int_((pi)/(5))^((3pi)/(10))(f(sin x))/(f(sin x) + f(cos x)) dx

Find the direction cosines of the vector hati+2hatj+3hatk.

Statement-1, For any two complex numbers z_(1) and z_(2) |z_(1)+sqrt(z_(1)^(2)-z_(2)^(2))|+|z_(1)-sqrt(z_(1)^(2)-z_(2)^(2))|=|z_(1)+z_(2)|+|z_(1)-z_(2)| Statement-2: For any two complex numbers z_(1) and z_(2) |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2)=2(|z_(1)|^(2)+|z_(2)|^(2))

What is the value of(sin34^(@)cos236^(@)-sin56^(@)sin124^(@))/(cos28^(@)cos88^(@)+cos178^(@)sin208^(@))?

Let A = Q xxQand be a binary operation on A defined by (a, b) (c,d) = (ad + b, ac). Prove that is closed on A = QxxQ . Find (i) Identity element of (A, ) , (ii) The invertible element of (A,**).