28278 + Interview Questions in Maths in Class 12

1.	X is nearly normally distributed, with a mean of 6 and a standard deviation of 2. Approximately what percent of the observations in X will be greater than 12 ?
Answer» ANSWER :APPROXIMATELY `0.1%`

Discussion

2.	Show that the coefficient of x^(k) (0 le k le n) in the expansion of 1+(1+x)+(1+x)^(2)+…+(1+x)^(n) is ""^(n+1)C_(K+1).
Answer» SOLUTION :N/A

Discussion

3.	X is nearly normally distributed, with a mean of 6 and a standard deviation of 2. Approximately what percent of the observations in X will be smaller than 4 ?
Answer» ANSWER :`17%`

Discussion

4.	Find the vector joining the points P(2,3,0) and Q(-1,-2,-4)directed from P to Q.
Answer» ANSWER :`VEC(PQ)=-3hati-5hatj-4hatk`

Discussion

5.	Assertion (A): The roots of ax^(2) + bx + c = 0, where a != 0, b, c in R are non-real complex and a + c lt b. Then 4a + c lt 2b Reason (R): If the quadratic equation ax^(2) + bx + c = 0 has imaginary roots then AAx in R ax^(2) + bx + c have same sign
Answer» Both A, R are TRUE and R explain Assertion Both A, R are true but R does't explain A A is true R is FALSE A is false R is true Answer :A

Discussion

6.	If y= tan^(-1)x, then find (d^(2)y)/(dx^(2)) in terms of y alone.
Answer» ANSWER :`-SIN (2Y) COS^(2)y`

Discussion

7.	A function y = f(x) has a second-order derivative f''(x) =6(x-1). If its graph passed through the point (2,1) and at that point tangent to the graph is y=3x-5, then the value of f(0) is
Answer» 1 `-1` 2 0 Answer :B

Discussion

8.	A radioactive substance with decay constant of 0.5s^(-1) is being produced at a constant rate of 50 nuclei per second . If there are no nuclei present initially, the time (in second) after which 25 nuclei will be present is :
Answer» 1 LN 2 ln(4/3) 2 ln (4/3) Solution :`(dN)/(dt)=50-(N)/(0.5)` `underset(0)OVERSET(N)int (dN)/(50-2N)=underset(0)overset(t)int dt` `RARR N= (100(1-e^(-t//2)))` N=25 `rArr t=2ln ((4)/(3))`

Discussion

9.	Prove by vector method that the medians of a triangle are concurrent.
Answer» Solution : Let ABC be a triangle and D,E,F be the mid POINTS of the sides of `triangleABC` Let `veca,vecb` and `vecc` be the position vectors of the points A, B, C. Then the position vectors of D< E, F are `(vecb+vecc)/2, (vecc+veca)/2` and `(veca+vecb)/2` respectively. Let G be the point which divides the median into the RATIO 2:1. Then the position vector of G is `2((veca+vecb)/2+1veca)/(2+1)` i.e. `(veca+vecb+vecc)/3` The summetry of the result shows that the point G also lies on the other TWO medians. HENCE the medians are concurrent. (Proved)

Discussion

10.	If the angles between the vectors veca and vecb, vecb and vecc, vecc and veca be (pi)/(4),(pi)/(3),(pi)/(3) respectively, then the angle which veca makes with the plane containing vecb and vecc is
Answer» `sin^(-1)SQRT((SQRT2)/(3))` `sin^(-1).(2)/(3)` `sin^(-1).(1)/(4)` `sin^(-1)sqrt((2)/(3))` Answer :A

Discussion

11.	Using differentials, find the approximate value of each of the up to 3 places of decimal. sqrt(25.3)
Answer» ANSWER :5.03

Discussion

12.	Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are kings and the third card drawn is an ace?
Answer» ANSWER :`(2)/(5525)`

Discussion

13.	The value of sum_(r=0)^(10) (r)""^(20)C_(r) is equal to
Answer» `20(2^(18)+.^(19)C_(10))` `10(2^(18)+.^(18)C_(10))` `20(2^(16)+.^(19)C_(11))` `10(2^(18)+.^(19)C_(11))` SOLUTION :`UNDERSET(R=0)overset(10)sum(r).^(20)C_(r) = underset(r=1)overset(10)sum20 xx .^(19)C_(r-1)` `= 20(.^(19)C_(0) + .^(19)C_(1) + "......"+ .^(19)C_(10))` `= 20 (.^(19)C_(0) +.^(19)C_(1) + "......" + .^(19)C_(10))` `= 20(1/2 xx 2^(10) + .^(19)C_(10))` `= 20(2^(18)+.^(19)C_(10))`

Discussion

14.	A die of six faces marked with the integers 1,2,3,4,5,6 one on each face is thrown twice in succession, what is the total number of outcomes thus obtained?
Answer» Solution :A die of six faces marked with the integers 1,2,3,4,5,6 one on each FACE , is THROWN twice in succession. `:.`The TOTAL NUMBER of OUTCOMES are `6^2=36`.

Discussion

15.	2xy + y^(2) - 2x^(2)(dy)/(dx) = 0, y = 2 when x = 1
Answer» ANSWER :`y = (2X)/(1 - log\|X\|)(x ne 0, x ne e)`

Discussion

16.	y= sin^(-1) [(5x + 12 sqrt(1-x^(2)))/(13)] then find (dy)/(dx)
Answer» ANSWER :`(1)/(SQRT(1-x^(2)))`

Discussion

17.	If (2+sqrt3)^(x^(2)-2x+1)+ (2-sqrt3)^(x^(2)-2x-1) = 2/(2-sqrt3) then x =
Answer» 0, 2 0, 1 0, 3 `0,sqrt3` Answer :A

Discussion

18.	If f(x)=((1-tanx)/(1+sinx))^(cosec x) is to be made continuous at x=0, then f(0) must be equal to
Answer» `e^(2)` `e` `(I)/(e)` `(I)/(e^(2))` SOLUTION :If f (X) is CONTINUOUS at x=0,` then underset(xrarr0)lim f (x) -f(0)` `impliesf (0) =underset(xrarr0)lim f (x) = e^(underset(srarr0)lim((-tanx-sin x)/((1-sin x).sin x)))` `= e^(underset(xrarr0)(lim)).((1+COS x))/((1-sin x),cos x)=e^(-2)`

Discussion

19.	If lim_(x to 0) ((sin 2x)/x^3 +a+ b/x^2)=0 then then value of 3a +b is
Answer» 2 `-2` `-1` 0 Answer :A

Discussion

20.	Let f(x)=[x][sinx]+[-x][-sinx]+x+[-x][sinx]+[x][-sinx], where [.] dentoes largest integer function. Then.
Answer» The number of POINTS of DISCONTINUITY in `(0,pi)` is 3. the number of points of discontinuity in `(0,pi)` is `4` `f(x)` is discontinuous at `x=1,2,3` `f(x)` is discontinuous at all integers. Solution :`f(x)=([x]+[-x]([SINX]+[-sinx])+x` `{{:(x," , " x in I),(x," , "x in (npi)/2" , " n in I),(x+1," , " "OTHERWISE"):}` POINT of `D.C.x=1,2,3,(pi)/(2)`

Discussion

21.	Ifalpha, beta are the roots of the equationx^(2) - 2x + 4 = 0then for anyn in N show thatalpha^(n) + beta^(n) = 2^(n+1) cos ((n pi)/3).
Answer»

Discussion

22.	Find (dy)/(dx) if ax+by^2=cosy
Answer» SOLUTION :Differentiating both sides w.r.t.x, we have `a+2by(DY)/(DX)=-siny(dy)/(dx)(2by+siny)(dy)/(dx)=-a(dy)/(dx)=2/(2by+siny)`

Discussion

23.	f: [0,1] to Ris defined as f(x) {{:( x^(3) (1-x) sin ((1)/(x^(2))), 0 ltx le 1),( 0, x=0):}
Answer» F iscontinuous but not DERIVABLE in [0,1] f is ontinuousin [0,1] f isbounded in [0,1] f' isbounded in [0,1] ANSWER :B::C::D

Discussion

24.	Integrate the follwing functions: (3x-1)/(x+2)^2
Answer» SOLUTION :`(3x-1)/(x+2)^2 = (3(x+2)-7)/(x+2)^2` = `3/(x+2) - 7/(x+2)^2` THEREFORE` int (3x-1)/(x+2)^2 DX` =`3log \|x+2\|+7/(x+2) +c`

Discussion

25.	Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} g(f(x)) is not defined if
Answer» `a in (10,oo), b in (5,oo)` `a in (4,10), b in (5,oo)` `a in (10,oo), b in (0,1)` `a in (4,10), b in (1, 5)` SOLUTION :`g(f(x))` is not defined if (i) `-2+a gt 8 and " (II) "b+3 gt 8` `or a gt 10 and b gt 5`

Discussion

26.	int_(0)^(1)(dx)/(e^(x)+e^(-x)) is equal to
Answer» `pi/4-TAN^(-1)(E)` `tan^(-1)(e)-pi/4` `tan^(-1)(e)+pi/4` `tan^(-1)(e)` ANSWER :B

Discussion

27.	f(x)= (1)/((x-1) (x-2)) and g(x)= (1)/(x^(2)). Find the points of discontinuity of the composite function f(g(x))?
Answer» ANSWER :`X= +- 1, 0, +- (1)/(SQRT2)`

Discussion

28.	If statements t and f represent a tautology and a contradiction (fallacy) respectively, thenp^^~equiv
Answer» t f p 1 Answer :B

Discussion

29.	For each of the differential equations in Exercises from 11 to 15, find the particular solution satisfying the given condition : 11.( x + y) dy + ( x - y) dx = 0, y = 1 when x = 1
Answer» Answer :`LOG (X^(2) + y^(2)) + 2 TAN^(-1) (y)/(x) = (PI)/(2) + log 2`

Discussion

30.	If the coefficient of (2r + 4)^(th) term and (r - 2)^(th) term in the expansion of (1 + x)^18 are equal then find r.
Answer» 9 4 6 3 Answer :C

Discussion

31.	Find the equation of a circle which is concentirc with x^(2) = y^(2) - 6x - 4y - 12 = 0 and passing through (-2,14).
Answer» ANSWER :`X^(2) + y ^(2) - 6x -4y -156 =0 `

Discussion

32.	Match the following :
Answer» ANSWER :1-D, 2-A, 3-B, 4-C

Discussion

33.	[bar(a)xx bar(b)" "bar(a)xx bar( c )" "bar(d)] = …………….
Answer» `(BAR(a)bar(d))[bar(a)bar(B)bar( C )]` `(bar(a)bar( c ))[bar(a)bar(b)bar( c )]` `(bar(a)*bar(b))[bar(a)bar(b)bar( c )]` NONE of these ANSWER :A

Discussion

34.	If n(U)=60,n(A)=35,n(B)=24 and n(A uu B)'=10 then n(A nn B) is
Answer» 9 8 6 7 Answer :A

Discussion

35.	Compute the integralI = int_(0)^(pi//h) e^(ux)sin bx dx
Answer» ANSWER :In PARTICULAR , at a = B = 1 we GET

Discussion

36.	A purse contains 2 silver and 4 copper coins. Another purse contains 4 silver and 3 copper coins. If a coin is pulled at random from one of the two purses, what is the probability that it is a silver coin?
Answer» ANSWER :`(19)/(42)`

Discussion

37.	Differentiate the following w.r.t. x : cos (log x +e^(x)), x gt 0.
Answer» Answer :`-(1)/(x)+E^(x) SIN (LOG x+ e^(x)), x gt 0`.

Discussion

38.	overline(a),overline(b),overline( c) are three vectors such that \|overline(a)\|=1, \|overline(b)\|=2, \|overline ( c) \|=3 and overline(b), overline( c) are perpendicular . If projection of overline(b) on overline(a) is the same as the projection of overline( c) on overline(a), then \|overline(a)-overline(b)+overline( c) \|=
Answer» `sqrt(2)` `sqrt(7)` `sqrt(14)` `sqrt(21)` Answer :C

Discussion

39.	Compute the length of the loop of the curve x= sqrt3 t^(2), y= t-t^(3)
Answer» ANSWER :4

Discussion

40.	A focal chord for parabola y^(2)=8(x+2) is inclined at an angle of 60^(@) with positive x-axis and intersects the parabola at P and Q. Let perpendicularbisector of the chord PQ intersectsthe x-axis at R, then the distance of R from focus is :
Answer» `(8)/(3)` `(16sqrt(3))/(3)` `(16)/(3)` `8sqrt(3)` ANSWER :C

Discussion

41.	If the coefficient of x^7 in (ax^2+(1)/(bx))^11 equals the coefficient of x^-7 in (ax-(1)/(bx^2))^11, then a and b satisfy the relation
Answer» AB= 1 a/B = 1 a + b = 1 a - b = 1 ANSWER :A

Discussion

42.	Examine the following functions for continuity. f(x)= (x^(2)-25)/(x+ 5), x ne -5
Answer» ANSWER :`X= -5`

Discussion

43.	Let A=[[1,2,3,4,1], [4,5,6,1,2], [3,9,1,1,6]]What is the order ofA^t?
Answer» SOLUTION :ORDER of `A^T " is " (5xx3).`

Discussion

44.	Using integration find the area of region bounded by the triangle whose vertices are (1, 0), (2, 2), and (3, 1).
Answer» ANSWER :`3/2`

Discussion

45.	Assertion (A) : Area enclosed by the curve y=e^(x^(3)) between the lines x = a, x = b and x - axis is int_(a)^(b) e^(x^(3)) dx. Reason (R ): e^(x^(3)) is an increasing functions.
Answer» Both A and R are INDIVIDUALLY TRUE and R is the correct explanation of A Both A and R are individually true and R is not the correct explanation of A A is true R is false A is false but R is true. Answer :2

Discussion

46.	Let X{a,b,c} , Y = {1,2,3,4} Find Out which of the following relations are functions and which are not and why ? {(a,2),(b,1),(c,1)}
Answer» SOLUTION :{(a,2),(b,1),(c,1)} is a FUNCTION from X to Y.

Discussion

47.	Let X{a,b,c} , Y = {1,2,3,4} Find Out which of the following relations are functions and which are not and why ? {(a,1),(b,1),(c,1)}
Answer» SOLUTION :{(a,1),(b,1),(c,1)} is a FUNCTION from X to Y.

Discussion

48.	Let X{a,b,c} , Y = {1,2,3,4} Find Out which of the following relations are functions and which are not and why ? {(a,3),(b,1),(a,4),(c,2)}
Answer» Solution :{(a,3),(B,1),(a,4),(c,2)} is no a function as .a. and .b. have TWO iamges ALSO DOMAIN of the function`ne` X.

Discussion

49.	Let X{a,b,c} , Y = {1,2,3,4} Find Out which of the following relations are functions and which are not and why ? {(a,2),(b,3),(c,4)}
Answer» Solution :{(a,2),(b,3),(c,4)} is a function from XTO Y as the ELEMENTS of X has UNIQUE IMAGES of Y.

Discussion

50.	The mean deviation from mean of the data 90,100,125,115,110 is
Answer» 10 10.4 10.6 10.8 Answer :B

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

X is nearly normally distributed, with a mean of 6 and a standard deviation of 2. Approximately what percent of the observations in X will be greater than 12 ?

Show that the coefficient of x^(k) (0 le k le n) in the expansion of 1+(1+x)+(1+x)^(2)+…+(1+x)^(n) is ""^(n+1)C_(K+1).

X is nearly normally distributed, with a mean of 6 and a standard deviation of 2. Approximately what percent of the observations in X will be smaller than 4 ?

Find the vector joining the points P(2,3,0) and Q(-1,-2,-4)directed from P to Q.

Assertion (A): The roots of ax^(2) + bx + c = 0, where a != 0, b, c in R are non-real complex and a + c lt b. Then 4a + c lt 2b Reason (R): If the quadratic equation ax^(2) + bx + c = 0 has imaginary roots then AAx in R ax^(2) + bx + c have same sign

If y= tan^(-1)x, then find (d^(2)y)/(dx^(2)) in terms of y alone.

A function y = f(x) has a second-order derivative f''(x) =6(x-1). If its graph passed through the point (2,1) and at that point tangent to the graph is y=3x-5, then the value of f(0) is

A radioactive substance with decay constant of 0.5s^(-1) is being produced at a constant rate of 50 nuclei per second . If there are no nuclei present initially, the time (in second) after which 25 nuclei will be present is :

Prove by vector method that the medians of a triangle are concurrent.

If the angles between the vectors veca and vecb, vecb and vecc, vecc and veca be (pi)/(4),(pi)/(3),(pi)/(3) respectively, then the angle which veca makes with the plane containing vecb and vecc is

Using differentials, find the approximate value of each of the up to 3 places of decimal. sqrt(25.3)

Three cards are drawn successively, without replacement from a pack of﻿ 52 well shuffled cards. What is the probability that first two cards are kings and the﻿ third card drawn is an ace?﻿

The value of sum_(r=0)^(10) (r)""^(20)C_(r) is equal to

A die of six faces marked with the integers 1,2,3,4,5,6 one on each face is thrown twice in succession, what is the total number of outcomes thus obtained?

2xy + y^(2) - 2x^(2)(dy)/(dx) = 0, y = 2 when x = 1

y= sin^(-1) [(5x + 12 sqrt(1-x^(2)))/(13)] then find (dy)/(dx)

If (2+sqrt3)^(x^(2)-2x+1)+ (2-sqrt3)^(x^(2)-2x-1) = 2/(2-sqrt3) then x =

If f(x)=((1-tanx)/(1+sinx))^(cosec x) is to be made continuous at x=0, then f(0) must be equal to

If lim_(x to 0) ((sin 2x)/x^3 +a+ b/x^2)=0 then then value of 3a +b is

Let f(x)=[x][sinx]+[-x][-sinx]+x+[-x][sinx]+[x][-sinx], where [.] dentoes largest integer function. Then.

Ifalpha, beta are the roots of the equationx^(2) - 2x + 4 = 0then for anyn in N show thatalpha^(n) + beta^(n) = 2^(n+1) cos ((n pi)/3).

Find (dy)/(dx) if ax+by^2=cosy

f: [0,1] to Ris defined as f(x) {{:( x^(3) (1-x) sin ((1)/(x^(2))), 0 ltx le 1),( 0, x=0):}

Integrate the follwing functions: (3x-1)/(x+2)^2

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} g(f(x)) is not defined if

int_(0)^(1)(dx)/(e^(x)+e^(-x)) is equal to

f(x)= (1)/((x-1) (x-2)) and g(x)= (1)/(x^(2)). Find the points of discontinuity of the composite function f(g(x))?

If statements t and f represent a tautology and a contradiction (fallacy) respectively, thenp^^~equiv

For each of the differential equations in Exercises from 11 to 15, find the particular solution satisfying the given condition : 11.( x + y) dy + ( x - y) dx = 0, y = 1 when x = 1

If the coefficient of (2r + 4)^(th) term and (r - 2)^(th) term in the expansion of (1 + x)^18 are equal then find r.

Find the equation of a circle which is concentirc with x^(2) = y^(2) - 6x - 4y - 12 = 0 and passing through (-2,14).

Match the following :

[bar(a)xx bar(b)" "bar(a)xx bar( c )" "bar(d)] = …………….

If n(U)=60,n(A)=35,n(B)=24 and n(A uu B)'=10 then n(A nn B) is

Compute the integralI = int_(0)^(pi//h) e^(ux)sin bx dx

A purse contains 2 silver and 4 copper coins. Another purse contains 4 silver and 3 copper coins. If a coin is pulled at random from one of the two purses, what is the probability that it is a silver coin?

Differentiate the following w.r.t. x : cos (log x +e^(x)), x gt 0.

Compute the length of the loop of the curve x= sqrt3 t^(2), y= t-t^(3)

A focal chord for parabola y^(2)=8(x+2) is inclined at an angle of 60^(@) with positive x-axis and intersects the parabola at P and Q. Let perpendicularbisector of the chord PQ intersectsthe x-axis at R, then the distance of R from focus is :

If the coefficient of x^7 in (ax^2+(1)/(bx))^11 equals the coefficient of x^-7 in (ax-(1)/(bx^2))^11, then a and b satisfy the relation

Examine the following functions for continuity. f(x)= (x^(2)-25)/(x+ 5), x ne -5

Let A=[[1,2,3,4,1], [4,5,6,1,2], [3,9,1,1,6]]What is the order ofA^t?

Using integration find the area of region bounded by the triangle whose vertices are (1, 0), (2, 2), and (3, 1).

Assertion (A) : Area enclosed by the curve y=e^(x^(3)) between the lines x = a, x = b and x - axis is int_(a)^(b) e^(x^(3)) dx. Reason (R ): e^(x^(3)) is an increasing functions.

Let X{a,b,c} , Y = {1,2,3,4} Find Out which of the following relations are functions and which are not and why ? {(a,2),(b,1),(c,1)}

Let X{a,b,c} , Y = {1,2,3,4} Find Out which of the following relations are functions and which are not and why ? {(a,1),(b,1),(c,1)}

Let X{a,b,c} , Y = {1,2,3,4} Find Out which of the following relations are functions and which are not and why ? {(a,3),(b,1),(a,4),(c,2)}

Let X{a,b,c} , Y = {1,2,3,4} Find Out which of the following relations are functions and which are not and why ? {(a,2),(b,3),(c,4)}

The mean deviation from mean of the data 90,100,125,115,110 is

Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are kings and the third card drawn is an ace?