28278 + Interview Questions in Maths in Class 12

1.	For a bivariate date, you are given following information:sum x = 125 , sum x^(2) = 1650 , sum y = 100 , sum y^(2)= 1500 , sum xy= 50 , n= 25 Findline of regression.
Answer» ANSWER :REGRESSION EQUATION of y on X: y `=-0.44x +6.2` Regression equation of x on y : x `=- 0.41 y +6.64`

Discussion

2.	Find the derivative of e^(sin^(-1)x) w.r.t.x.
Answer» ANSWER :`(E^(sin-1)X)/(SQRT(1-x^(2))),x in(-1,1)`

Discussion

3.	How many three digit can be formed using the digits 1, 2, 3, 4, 5, without repetition of digits? How many of these are even?
Answer» ANSWER :24

Discussion

4.	Angle subtended by double ordinate of length 32 sqrt ( 3)of the parabola x^(2) -6x +16y +25 =0 at the vertex
Answer» A) `(pi)/(2) ` B) ` (pi )/(2) ` C) ` (pi )/(6) ` D) ` ( pi )/(3) ` Answer :D

Discussion

5.	Examine the consistency of the following system of equation x+2y=12 2x+3y =3
Answer» SOLUTION :Here A =[[1,2],[2,3]],\|A\|=\|[1,2][,2,3]\|`THEREFORE \|A\| =3-4 =-1 !=0` `rArr`A is non-singular. The given SYSTEM is CONSISTENT.

Discussion

6.	Evaluate the following define integrals as limit of sums : lim_(n rarroo) 1/n [tan. (pi)/(4n) + tan. (2pi)/(4n)+....+tan. (n pi)/(4n)]
Answer» `1/PI LOG 2` `2/pi log 2` `pi log 2` `pi/2 log 2` ANSWER :B

Discussion

7.	Find the locus of the point of intersections of the tangent drawn to the circles x ^(2) +y^(2)=a ^(2)which makes a constant angle alphato each other.
Answer» ANSWER :` (x^(2) +y^(2) -2A^(2))^(2)=4A^(2)(x^(2) +y^(2) -a^(2) ) cot ^(2) alpha `

Discussion

8.	The value of (P-R) is equal to
Answer» 1 -1 `2^(50)` `2^(100)` ANSWER :A

Discussion

9.	Evaluate the following determinants: [[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]]
Answer» SOLUTION :`[[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]]` =`[[0,b-c,c-a],[0,c-a,a-b],[0,a-b,b-c]] (C_1=C_1+C_2+C_3)` =0

Discussion

10.	Integrate the functions in exercise. (x+3)/(x^(2)-2x-5)
Answer» ANSWER :`(1)/(2)log\|x^(2)-2x-5\|+(2)/(SQRT(6))log\|(x-1-sqrt(6))/(x-1+sqrt(6))\|+c`

Discussion

11.	If sin^(2) x + cos xy = k find (dy)/(dx).
Answer» ANSWER :`(y SIN XY)/(sin 2y-x sin xy)`

Discussion

12.	Let f(x) = x (-1)^([1//x]), x ne 0, where [x] denotes the greatest integer le x, then lim_(x rarr 0) f(x) :
Answer» does not exist is `oo` is 0 is -1 ANSWER :C

Discussion

13.	If ""^((n+1))P_(5): ""^(n)P_(5)=3:2, find n
Answer» 8 14 10 6 Answer :B

Discussion

14.	Find (dy)/(dx), If x^(2)+ xy + y^(2)=100
Answer» ANSWER :`=(-(2x+y))/(x+2y)`

Discussion

15.	Integrate the functions tan^(-1)sqrt((1-x)/(1+x))
Answer» ANSWER :`1/2[XCOS^(-1)x-sqrt(1-x^(2))]+C`

Discussion

16.	int (1+sin^(2)x)/(1+cos 2x)dx=
Answer» ANSWER :`TANX-(X)/(2)+C`

Discussion

17.	A firm is engaged in breeding pigs. The pigs are fed on various products grown on the firm. They need certain nutrinets, named as X,Y,Z. The pigs are fed on two products, A and B One unit of product B contains 6 units of X, 12 units of Y and 10 units of Z, while one unit of product B contains 6 units of X, 12 units of Y and 10 units of Z. The minimum requirements of X,Y,Z are 108 units, 36 unis and 100 units respectively. Product A costs Rs.20 per unit and product B costs Rs.40 per unit. How many units of each peofuct must be taken to minimize the cost? Also, find the minimum cost.
Answer» SOLUTION :Let x UNITS of A and y units of B be taken. Then, minimize `C=20x+40y,` SUBJECT to `x GE0,yge0,36+6yge108,3x+12yge36,20x+10yge100.`

Discussion

18.	(dy)/(dx) = sqrt(4 - y^(2))(-2 lt y lt 2)
Answer» ANSWER :`y = 2 SIN (X + C)`

Discussion

19.	Consider the family of circles x^(2)+y^(2)-2x-2ay-8=0 passingthrough two fixed points A and B . Also, S=0 is a cricle of this family, the tangent to which at A and B intersect on the line x+2y+5=0. If the circle x^(2)+y^(2)-10x+2y=c=0 is orthogonal to S=0, then the value of c is
Answer» 8 9 10 12 Solution :CIRCLE `x^(2)+y^(2)-10x+2y+C=0` is orthogonal to `x^(2)+y^(2)-2x-6y-8=0`. So, by applying condition of orthogonal intersection, we get `2(-5)(-1)+2(1) (-3)= c-8` `:. C= 12`

Discussion

20.	Find the number of ways in which 5 boys and 4 girls can be arranged along a row such that atleast one of the first 3 places must be arranged with a girl,
Answer» ANSWER :319680

Discussion

21.	Let f(x)=\|x-1\|. Then,
Answer» `F(X^(2))=[f(x)]^(2)` `f(\|x\|)=\|f(x)\|` `f(x+y)=f(x)+f(y)` NONE of these ANSWER :D

Discussion

22.	prove that 3 cos^(-1) x = cos^(-1) (4x^3 - 3x), x in [1/2,1]
Answer» Solution :PUT `COS^(-1) x = y.` Then cos y = x `therefore 4x^3 - 3X = 4 cos^3 y - 3 cos y = cos 3y` `IMPLIES 3y = cos^(-1) (4x^3 - 3x)` `implies 3 cos^(-1) x = (4x^3 - 3x)`

Discussion

23.	A consignment of 15 record players contains 4 efective. The record players are selected at randoom one by one and examined. The ones examined are not placed back. What is the probability that the 9th one examined is the last defective.
Answer» ANSWER :`(.^(11)C_(5)xx.^(4)C_(3))/(.^(15)C_(8))xx(1)/(7)`

Discussion

24.	Find the odd one out Rangeof trigonometric functions (sin x , cos x , tan x, sec x , "cosec" x , cot x )can be :
Answer» `[-1,1]` R `R//(-1,1)` `R//[-1,1]` ANSWER :d

Discussion

25.	If I_(n) = int_(0)^(pi//4) tan^(n) x dx then (1)/(I_(3)+I_(5))=
Answer» `1/4` `1/2` `1/8` 4 Answer :D

Discussion

26.	Evaluate underset(0)overset(a)int (dx)/(x^(2)+a^(2))
Answer» ANSWER :`(PI)/(4A)`

Discussion

27.	For any two complex numbers z_1,z_2 and real numbers a and b , \|az_1 -bz_2\|^2+\|bz_1+az_2\|^2=
Answer» `(a^2-B^2)(\|z_1\|^2+\|z_2\|^2)` `(a^2+b^2)(\|z_1\|^2+\|z_2\|^2)` `(a^2+b^2)(\|z_1\|^2-\|z_2\|^2)` None Answer :B

Discussion

28.	int_(0)^((pi)/(4))(dx)/(9cos^2 x +sin^2x).
Answer» ANSWER :`(1)/(3)TAN^(-1)((1)/(3))`

Discussion

29.	Ifproductof tworootsof4x^3+ 16 x^2+kx- 36 =0is -6thenk=
Answer» 9 `-9` `8` `-8` ANSWER :B

Discussion

30.	ABisa verticalpolewithB atthegroundleveland Aat thetop. Amanfindsthatthe angleof elevationof thepointA froma certainpointC onthegroundis 60^@. Hemovesaway fromthe polealongthe lineBCto a pointD suchthatCD = 7 m. fromD theangleof elevationof thepointA is45then theheightof thepoleis
Answer» `(7sqrt(3))/(2)(1)/(sqrt(3) +1)m` `(7sqrt(3))/(2)(1)/(sqrt(3) -1)m` `(7sqrt(3))/(2) (sqrt(3) +1)m` `(7 sqrt(3))/(2) ( sqrt(3)-1) m` Answer :C

Discussion

31.	Solution of the differential equation(2+ 2x ^(2)sqrty) ydx+(x ^(21) sqrty+2) x dy =0 is/are:
Answer» `xy ( X ^(2) SQRTY +5 )=C` `xy (x ^(2) sqrty +3)=c` `xy (y ^(2) SQRTX+3)=c` `xy (y ^(2) sqrtx +5)=c` Answer :B

Discussion

32.	Find the changes of sign of the following expressions and find extreme values i) 15+4x-3x^(2) ii) 4x-5x^(2)+2
Answer» Answer :i) If `-(5)/(3) lt X lt 3`, the expression is positive. If `x lt -(5)/(3)` or `x GT 3`, the expression is NEGATIVE. The extreme value is `(49)/(3)`. ii) If `(2-sqrt(14))/(5) lt x lt (2+sqrt(14))/(5)` the expression is positive. `x lt (2-sqrt(14))/(5)` or `x gt (2+sqrt(14))/(5)` the expression is negative.

Discussion

33.	If the function f is defined by f(x) = {(3,,x,ne,0),(a+1,,x,=,0):} and f is continuous at x = 0, then value of a is :
Answer» 1 2 3 4 Answer :B

Discussion

34.	Evaluate: inte^(x)((1-x)/(a+x^(2)))^(2)dx.
Answer» `(E^(X))/((1+4x)^(2))+C` `(e^(x))/((1+3x)^(2))+C` `(e^(x))/((1+x)^(2))+C` `(e^(x))/((1+2x)^(2))+C` ANSWER :C

Discussion

35.	Find the sum of all the distinct prime divisors of underset(r=0)overset(2015)Sigma r^(2) ((2015),(r)) i.e., underset(r=0)overset(2015)Sigma r^(2). ""^(2015)C_(r)
Answer» ANSWER :61

Discussion

36.	Solve (x-y-1) dx = (1-x-4y)dy.
Answer» Answer :`LOG[4y^(2) + (x-1)^(2)] + "arc TAN " (2y)/(x-1) = c`

Discussion

37.	If A and B are square matrices of same order then (A^(-1)BA)^(n)=………… , n inN.
Answer» `A^(-N)B^(n)A^(n)` `A^(n)B^(n)A^(-n)` `A^(-1)B^(n)A` `n(A^(-1)BA)` ANSWER :C

Discussion

38.	Find the Principle values of the following : cos^(-1)((sqrt(3))/2)
Answer» ANSWER :`(PI)/6`

Discussion

39.	The tangent at 't' on the parabola y^(2) =4ax is parallel to a normal chord then distance between them is
Answer» a 2A 4a 8a Answer :C

Discussion

40.	Evaluate int_(0)^((pi)/(2)) sin x dx as the limit of a sum.
Answer» ANSWER :1

Discussion

41.	A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3cm longer than the shortest and the third length is to be twice as long as the shortest. What are the lengths of the shortest board if the third piece is to be at least 5 cm longer than the second ?
Answer» Answer :The value of X must be GREATER than or equal to 8 but less than or equal to 22 CM.

Discussion

42.	A box contains 10 mangoes out of which 4 are spoiled. 2 mangoes are taken together at random. If one of them is found to be good, then the probability that the other is also good, is
Answer» `(5)/(13)` `(8)/(13)` `(1)/(5)` `(2)/(3)` ANSWER :A

Discussion

43.	Let f:X rarr Y be a function defined by f(x)=2sin(x+pi/4)-sqrt(2)cosx+c. bb"Statement" For set X,x in [0,pi/2] cup [pi,(3pi)/2], f(x) is one-one function. bb"Statement II" f'(x) ge 0,x in [0,pi/2]
Answer» ANSWER :d

Discussion

44.	All three roots of az^3+bz^2+cz+d=0 , z being complex number. Further , assume that the origin, z_1 and z_2 form an equilateral triangle, then :
Answer» All a,B,C,d have the same SIGN a,b,c have same sign a,b,d have same sign b,c,d have same sign ANSWER :C

Discussion

45.	Find the area of the region bounded by the curve y=x^(2) and line y=4
Answer» ANSWER :`(33)/(4)` SQ. UNITS

Discussion

46.	If f(x)=int_(0)^(1)(dt)/(1+\|x-t\|),x epsilonR the value of f'(1//2) is equal to
Answer» `1//2` `0` `1` `2` Solution :`f(X)=int_(0)^(1)(dt)/(1+\|x-t\|)` `={(int_(0)^(1)(dt)/(1+\|x-t\|),xlt0),(int_(0)^(1)(dt)/(1+\|x-t+),0LEXLE1),(int_(0)^(1)(dt)/(1+\|x-t\|),xgt1):}` `={(int_(0)^(1)(dt)/(1+t-x),xlt0),(int_(0)^(x)(dt)/(1+x-t)+int_(x)^(1)(dt)/(1+t-x),0lexle1),(int_(0)^(1)(dt)/(1+x-t),xgt1):}` `={([log_(e)(1+t-x)]_(0)^(1),xlt0),([-log_(e)(1+x-t)]_(0)^(1)+[log_(e)(1+t-x)]_(x)^(1),0lexle1),([-log_(e)(1+x-t)]_(0)^(1),xgt1):}` `={("log"_(e)(2-x)/(1-x),xlt0),("log"_(e)(1+x)(2-x),0lexle1),("log"_(e)(1+x)/x,xgt1):}`

Discussion

47.	STATEMENT -1 : There are 12 points in a plane of which only 5 are collinear , then the number of straight lines obained by joining these points in pairs is ""^(12)C_(2) - ""^(5)C_(2) . STATEMENT-2: ""^(n +1)C_(r) - ""^(n-1)C_(r - 1) = ""^(n)C_(r) + ""^(n)C_(r - 2) STATEMENT -3 :2n persons may be seated at two round tables , n person seated at each , in ((2n)!)/(n^(2)) in differnet ways.
Answer» F T F T T F F F T F T T Answer :C

Discussion

48.	If A xx B = B xx A then what can you say about A and B ?
Answer» SOLUTION :If `A XX B = B xx A` then A = B

Discussion

49.	IF(a + x) ^(2//3)+ (a - x) ^(2//3)= 4( a^2- x ^2 )^(1//3)thenx=
Answer» `+-(3a )/( 4 sqrt(4))` `+- (4 a)/( 3 sqrt(3))` `+-(5A )/( 3 sqrt(3))` ` +-(5a ) /( 6sqrt(6))` ANSWER :C

Discussion

50.	If 2x+2y=22 and 3x -4y=12, what is the value of y/x ?
Answer» Solution :None of the coefficients in EITHER EQUATION is 1, so using combination is a BETTER strategy than substitution here. Examine the coefficients of x : they don't share any FACTORS, so multiply each equation by the coefficient from the other equation: `3 (2x + 2y =22) to 6x + 6y =66` ` 2 (3x -4y =12) to 6x -8y=24` Subtract the second equation from the first: `6x + 6y =66` `-((6x-8y=24))/(14y=42)` `y =3` Next, you need x so you can determine the value of `y /x.` Substitute 3 for y in one of the original equations: `2x + 2(3)=22` `2x +6 =22` ` 2x =16` ` x =8` Plug your x-axis and y-values into `c/x` to GET `3/8.` Grid in `3/8.`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

For a bivariate date, you are given following information:sum x = 125 , sum x^(2) = 1650 , sum y = 100 , sum y^(2)= 1500 , sum xy= 50 , n= 25 Findline of regression.

Find the derivative of e^(sin^(-1)x) w.r.t.x.

How many three digit can be formed using the digits 1, 2, 3, 4, 5, without repetition of digits? How many of these are even?

Angle subtended by double ordinate of length 32 sqrt ( 3)of the parabola x^(2) -6x +16y +25 =0 at the vertex

Examine the consistency of the following system of equation x+2y=12 2x+3y =3

Evaluate the following define integrals as limit of sums : lim_(n rarroo) 1/n [tan. (pi)/(4n) + tan. (2pi)/(4n)+....+tan. (n pi)/(4n)]

Find the locus of the point of intersections of the tangent drawn to the circles x ^(2) +y^(2)=a ^(2)which makes a constant angle alphato each other.

The value of (P-R) is equal to

Evaluate the following determinants: [[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]]

Integrate the functions in exercise. (x+3)/(x^(2)-2x-5)

If sin^(2) x + cos xy = k find (dy)/(dx).

Let f(x) = x (-1)^([1//x]), x ne 0, where [x] denotes the greatest integer le x, then lim_(x rarr 0) f(x) :

If ""^((n+1))P_(5): ""^(n)P_(5)=3:2, find n

Find (dy)/(dx), If x^(2)+ xy + y^(2)=100

Integrate the functions tan^(-1)sqrt((1-x)/(1+x))

int (1+sin^(2)x)/(1+cos 2x)dx=

(dy)/(dx) = sqrt(4 - y^(2))(-2 lt y lt 2)

Consider the family of circles x^(2)+y^(2)-2x-2ay-8=0 passingthrough two fixed points A and B . Also, S=0 is a cricle of this family, the tangent to which at A and B intersect on the line x+2y+5=0. If the circle x^(2)+y^(2)-10x+2y=c=0 is orthogonal to S=0, then the value of c is

Find the number of ways in which 5 boys and 4 girls can be arranged along a row such that atleast one of the first 3 places must be arranged with a girl,

Let f(x)=|x-1|. Then,

prove that 3 cos^(-1) x = cos^(-1) (4x^3 - 3x), x in [1/2,1]

A consignment of 15 record players contains 4 efective. The record players are selected at randoom one by one and examined. The ones examined are not placed back. What is the probability that the 9th one examined is the last defective.

Find the odd one out Rangeof trigonometric functions (sin x , cos x , tan x, sec x , "cosec" x , cot x )can be :

If I_(n) = int_(0)^(pi//4) tan^(n) x dx then (1)/(I_(3)+I_(5))=

Evaluate underset(0)overset(a)int (dx)/(x^(2)+a^(2))

For any two complex numbers z_1,z_2 and real numbers a and b , |az_1 -bz_2|^2+|bz_1+az_2|^2=

int_(0)^((pi)/(4))(dx)/(9cos^2 x +sin^2x).

Ifproductof tworootsof4x^3+ 16 x^2+kx- 36 =0is -6thenk=

ABisa verticalpolewithB atthegroundleveland Aat thetop. Amanfindsthatthe angleof elevationof thepointA froma certainpointC onthegroundis 60^@. Hemovesaway fromthe polealongthe lineBCto a pointD suchthatCD = 7 m. fromD theangleof elevationof thepointA is45then theheightof thepoleis

Solution of the differential equation(2+ 2x ^(2)sqrty) ydx+(x ^(21) sqrty+2) x dy =0 is/are:

Find the changes of sign of the following expressions and find extreme values i) 15+4x-3x^(2) ii) 4x-5x^(2)+2

If the function f is defined by f(x) = {(3,,x,ne,0),(a+1,,x,=,0):} and f is continuous at x = 0, then value of a is :

Evaluate: inte^(x)((1-x)/(a+x^(2)))^(2)dx.

Find the sum of all the distinct prime divisors of underset(r=0)overset(2015)Sigma r^(2) ((2015),(r)) i.e., underset(r=0)overset(2015)Sigma r^(2). ""^(2015)C_(r)

Solve (x-y-1) dx = (1-x-4y)dy.

If A and B are square matrices of same order then (A^(-1)BA)^(n)=………… , n inN.

Find the Principle values of the following : cos^(-1)((sqrt(3))/2)

The tangent at 't' on the parabola y^(2) =4ax is parallel to a normal chord then distance between them is

Evaluate int_(0)^((pi)/(2)) sin x dx as the limit of a sum.

A box contains 10 mangoes out of which 4 are spoiled. 2 mangoes are taken together at random. If one of them is found to be good, then the probability that the other is also good, is

Let f:X rarr Y be a function defined by f(x)=2sin(x+pi/4)-sqrt(2)cosx+c. bb"Statement" For set X,x in [0,pi/2] cup [pi,(3pi)/2], f(x) is one-one function. bb"Statement II" f'(x) ge 0,x in [0,pi/2]

All three roots of az^3+bz^2+cz+d=0 , z being complex number. Further , assume that the origin, z_1 and z_2 form an equilateral triangle, then :

Find the area of the region bounded by the curve y=x^(2) and line y=4

If f(x)=int_(0)^(1)(dt)/(1+|x-t|),x epsilonR the value of f'(1//2) is equal to

If A xx B = B xx A then what can you say about A and B ?

IF(a + x) ^(2//3)+ (a - x) ^(2//3)= 4( a^2- x ^2 )^(1//3)thenx=

If 2x+2y=22 and 3x -4y=12, what is the value of y/x ?