28278 + Interview Questions in Maths in Class 12

1.	Solve the following differential equations.dy+(y^2+1)dx=0
Answer» SOLUTION :`DY+(y^2+1)dx=0` `rArrdy/(1+y^2)+dx=0` `RARR intdy/(1+y^2)+intdx=C` `rArr TAN^(-1)y+x=C`

Discussion

2.	The point of intersection of two tangents to hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 the product of whose slopes is c^2?, lies on the curve
Answer» `y^(2)-B^(2)=C^(2) (X^(2)+a^(2))` `x^(2)+a^(2)=c^(2) (x^(2)-b^(2))` `y^(2)-a^(2)=c^(2) (x^(2)+b^(2))` `y^(2)+b^(2)=c^(2) (x^(2)-a^(2))` ANSWER :D

Discussion

3.	The solution of (dy)/(dx) = (1+y^(2))(1+x^(2))^(-1) is
Answer» `y - X = C(1+xy)` `y + x = c(1+xy)` `y + x = c(1-xy)` `y - x = c(1-xy)` ANSWER :A

Discussion

4.	Using elementary row transformations , find the inverse of [{:(2,-3),(-1,2):}]
Answer» ANSWER :`thereforeA^(-1)=[{:(2,3),(1,2):}]`

Discussion

5.	If lim_(x to 0) (axe^x -b log (1+x))/x^2=5/2 then the value of 2a+b is
Answer» ANSWER :5

Discussion

6.	Find the order and degree (if defined) of the following differential equations. ((ds)/(dt))^4 + 3s (d^2s)/(dt^2) = 0
Answer» Solution :The HIGHEST order DERIVATE in the differential equation is `(d^2s)/(dt^2)`. its order is 2 and its DEGREE is 1 . `therefore` The order of the dimential equation = 2 and its degree = 1.

Discussion

7.	Find the projection of the point (7,-5,3) on x-axis,
Answer» SOLUTION :(7,0,0),

Discussion

8.	The value of the sin 1^(@) + sin2^(@) + … + sin359^(@) is equal to
Answer» a.0 b.1 c.`-1` d.180 Answer :A

Discussion

9.	If (2, 1) is limiting point of coaxial system of which x^(2) + y^(2) - 6x - 4y - 3 = 0 is a member, then the other limiting point is
Answer» (-5,-6) (-2,-3) (3,2) (5,6) ANSWER :A

Discussion

10.	Calculate the variance and standard deviation of the following continuous frequency distribution . (##VIK_MAT_IIA_QB_C08_SLV_010_Q01.png" width="80%">
Answer» ANSWER :`14.18`

Discussion

11.	Find the derivative of tan (2x + 3)
Answer» ANSWER :`2 SEC^(2) (2X + 3)`

Discussion

12.	IF y=e^(tan^(-1)x) then prove that : (1-x^(2))(d^2y)/(dx^2)+(2x-1)(dy)/(dx)=0.
Answer»

Discussion

13.	If 2a + 3b - 5c = 0, then ratio in which c divides AB is
Answer» 3 : 2 INTERNALLY 3 : 2 externally 2 : 3 internally 2 : 3 externally Solution :Given, 2a + 3b - 5c = 0 `implies (2a+3b)/(5)=c` `implies (2a+3b)/(2+3)=c` `implies (a+(3)/(2)b)/(1+(3)/(2))=c"...(i)"` Let c divides AB in the ratio `LAMBDA : 1`. Then, `c=(a+lambdab)/(1+lambda)"... (ii)"` On comparing Eqs. (i) and (ii), we get `lambda = (3)/(2)` So, required ratio is 3 : 2 internally.

Discussion

14.	If AP, BQ and CR are the altitudes of acute triangleABC and 9AP+4BQ+7CR=0 Q. angleABC is equal to
Answer» `cos^(-1)(2)/(SQRT(7))` `(pi)/(2)` `"cos"^(-1)((sqrt(7))/(3))` `(pi)/(3)` ANSWER :A

Discussion

15.	Let triangleABC be a given triangle. If \|vec(BA)-tvec(BC)\|ge\|vec(AC)\| for any t in R,then triangleABC is
Answer» Equilateral Right angled Isosceles None of these Solution :`\|vec(BA)\|^(2)+t^(2)\|vec(BC)\|^(2)-2vec(BA).vec(BC).t-\|vec(AC)\|^(2)ge0 AA t in R` Discrimiant of the quadratic equation `le0` `rArr 4(vec(BA).vec(BC))^(2)-4\|vec(BC)\|^(2)\|vec(BA)\|^(2)+4\|vec(BC)\|^(2)\|vec(AC)\|^(2)le0` USING `(vec(BA).vec(BC))^(2)-\|vec(BC)\|^(2)\|vec(BA)\|^(2)` `=-\|vec(BA) xx vec(BC)\|^(2)` `rArr =-\|vec(CA) xx vec(BC)\|^(2)` But `\|vec(AC) xx vec(BC)\|=\|vec(AC)\|\|vec(BC)\|SINC` `rArr sin^(2) Cge1` `rArr sinC=+1 rArr angleC=pi//2`

Discussion

16.	There are two cars of which one holds not more than 5 and the other not more than 4. The number of ways can a party of 8 people go for excursion in the two cars is
Answer» 8400 126 124 6400 Answer :B

Discussion

17.	For what value of x the tangent of the curve y=x^(3)-3x^(2)+x-2 is parallel to the line y=x
Answer» ANSWER :x=0 and x=2

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18.	Consider the function f(x)=(x^(3)-x)\|x^(2)-6x+5\|, AA x in R, then f(x) is
Answer» DISCONTINUOUS at X = 1 discontinuous at x = 5 non DIFFERENTIABLE at x = 1 non differentiable at x = 5 Answer :D

Discussion

19.	If sin^(-1)(x)-cos^(-1)(x)=pi/6,then x is equal to
Answer» `1/2` `sqrt3/2` `-1/2` `-sqrt3/2` ANSWER :B

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20.	Differentiate log(cos e^(x)) w.r." to "x.
Answer» ANSWER :`= -E^(X) TAN e^(x)`

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21.	The position vectors of the points A, B, C and D are 3hat(i)-2hat(j)-hat(k),2hat(i)-3hat(j)+2hat(k),5hat(i)-hat(j)+2hat(k)and4hat(i)-hat(j)+lamdahat(k) respectively. If the points A, B, C and D lie on a plane, the value of lamda is
Answer» 0 1 2 -4 Answer :D

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22.	Corner points of fealible region of inequalities gives
Answer» an optiomal SOLUTION of L.P.P. an OBJECTIVE function the constraints. the LINEAR assumption. Answer :A

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23.	If thetworootsof 4x^3 + 20 x^2 -23x + 6=0are equalthen findallthe roots .
Answer» ANSWER :`1/2,1/2-6`

Discussion

24.	The set of values that beta can assume so that the pont (0,beta) should lie on or inside the triangle having sides 3x+y+2=0,2x-3y+5=0 and x+4y-14=0 is
Answer» `[(5)/(3),(7)/(2)]` `[(2)/(3),(5)/(2)]` `[-(1)/(3),(2)/(3)]` `[(1)/(2),(5)/(2)]` ANSWER :A

Discussion

25.	Write down the set of letters forming that word Demonstration?
Answer» SOLUTION :{a,d,E,I,m,N,o,R,s,t}

Discussion

26.	All points lying inside the triangle formed by the points (1, 3), (5,0) and (-1, 2) satisfy
Answer» `3x+2y GE 0` `2x+y-13 ge 0` `2x-3y-12 ge 0` `-2x+y ge 0` ANSWER :A

Discussion

27.	If underset (nrarroo)" lim " underset(r=1) overset(n) (sum) (4r^(3))/(r^(4+n^(4)))= p, then e^(4)=
Answer» 4 3 2 1 Answer :C

Discussion

28.	Prove that the radical axis of the circles x^2+y^2+2gx +2fy+c=0 and x^2+y^2+2g'x + 2f'y+c'=0 is the diameter of the later circle (or the former bisects the circumference of the later ) if 2g'(g-g')+2f'(f-f')=c-c'
Answer» ANSWER :1

Discussion

29.	यदि A={1,2,3,4} तो AxA में अवयवों की संख्या है
Answer» 4 8 12 इनमें से कोई नहीं Answer :D

Discussion

30.	If \|3x-5\|le2 then
Answer» 1)`1lexle9/3` 2)`-1lexle7/3` 3)`-1lexle9/3` 4)`1lexle7/3` ANSWER :D

Discussion

31.	Let A ={a,a_(2),…….a_(n)}be a set containing a elements. The number of symmetric relations that can be denned on A is
Answer» `2^(N(n-1)//2)` `2^(n)` `2^(n(n+1)//2)` `2^(2N)` ANSWER :C

Discussion

32.	Examine the consistency of the system of equations 5x-y+4z =5 2x+ 3y + 5z =2 5x-2y + 6z =-1
Answer» ANSWER :CONSISTENT

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

Discussion

34.	A flagpolestandson abuildingand anobserver on alevelgroundis 300feetfromthe baseof thebuiling. Theangleofelevationof thebottionof theflagpoleis30^@and theheightof theflagpoleis 50feetifthetais theangleof elevationof htetop of the flagpole , thentan thetaisequalto
Answer» `(2 SQRT(3) +1)/( 6)` `(sqrt(3))/(2)` `1` `( 6 sqrt(3)+1)/(6)` Answer :A

Discussion

35.	Let f(x)={{:(x\|x\|",", x le -1),([x+1]+[1-x]",",-1ltxlt1),(-x\|x\|",",x ge 1):} where [.] denotes the greatest integer function, then the value of int_(-2)^(2)f(x)dx, is equal to
Answer» `-8//3` `-4//3` `8//3` `4//3` ANSWER :A

Discussion

36.	If the system of linear equations x+4y-3z=2 2x+7y-4z=alpha -x-5y+5z=beta has infinitely many solutions then the ordered pair (alpha, beta) cannot take value
Answer» (4,-2) (2,-4) (3,-3) (-3,3) ANSWER :D

Discussion

37.	The area of the quadrilateral formed by the tangents from the point (4,5) to the circle x^(2)+y^(2)-4x-2y-11=0 with a pair of the radii joining the points of contact of these tangents is
Answer» ANSWER :8 SQ. UNITS.

Discussion

38.	(23)^(-1//2)~~....
Answer» `5.0008` `5.8` `5.08` `5.008` ANSWER :D

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39.	If A any square matrix then
Answer» `A+A ` is SKEW symmetric A-A is symmetric AA is symmetric NONE of these ANSWER :C

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40.	The solution set contained in R of the inequation 3^(x)+3^(1-x)-4 lt0, is
Answer» (1, 3) (0, 1) (1, 2) (0, 2) ANSWER :B

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41.	If a circle cuts a parabola in four points then the sum of ordinates of four points is
Answer» 1 `-1` 0 2 Answer :C

Discussion

42.	Forthe functionf : (0,1) to R, ,f(x)= [ 2^(n)x] + { 2^(m)x}, (n ,m N, ngt m), , thenumberof points ofdiscontinuityof the functioncan bebe( where[.] {}representgreatestintegerfunctionandfractinoalpartof xrespectively )
Answer» 24 28 26 496 Answer :A::B::D

Discussion

43.	The mean of the data set comprisingof 16 observations is 16. If one of the observation valued 16 is deteted and three new observa- tions valued3,4 and 5 are added to the data, then the mean of the resultant data, is :
Answer» `16.8` `16.0` `15.8` `14.0` ANSWER :D

Discussion

44.	If \|a\|=3 and -1 le k le 2, then \|k a\|lies in the interval
Answer» [0, 6] [-3, 6] [3, 6] [1, 2] Solution :The smalest value of \|k \| will exist at NUMERICALLY SMALLEST value of k, i.e, at k =0, which gives `\|ka\|=\|k\|\|a\|=0xx3=0` The numerically greaterst value of k is 2 at which `\|k a\|=6`

Discussion

45.	If bara+barb+barc=bar0 then prove that bara xx barb= barb xx barc= barc xx bara.
Answer» ANSWER :We have, `BARA XX BARB= barb xx BARC= barc xx bara`

Discussion

46.	Which of the following is/are a contradiction ?
Answer» `(p^^q)^^~(PVVQ)` `(p^^~q)^^(~p^^q)` `p^^~p` `pvv~p` ANSWER :A,B,C

Discussion

47.	If there are only two linear functions f and g which map [1,2] on [4,6] and in a DeltaABC, c =f (1)+g (1) and a is the maximum valur of r^(2), where r is the distance of a variable point on the curve x^(2)+y^(2)-xy=10 from the origin, then sin A: sin C is
Answer» `1:2` `2:1` `1:1` NONE of these ANSWER :C

Discussion

48.	A man has 6 friends. In how many ways can he invite two or more to a dinner party ?
Answer» Solution :A MAN has 6 friends. He can INVITE 2 or more of his friends to a dinner party. `:.` He can invite 2,3,4,5 or 6 of his friends in ` ""^6C_2+ ""^6C_3+ ""^6C_4+ ""^6C_5 = ""^6C_6 =2^6- ""^6C_0- ""^6C_1` `=64-7=57"ways."`

Discussion

49.	bar(a)xx[bar(a)xx(bar(a)xx bar(b))] = …………….
Answer» `(VEC(a)XX vec(a))(vec(B)xx vec(a))` `vec(a)(vec(b)xx vec(a))-vec(b)(vec(a)xx vec(b))` `[vec(a)(vec(a)xx vec(b))]vec(a)` `(vec(a)*vec(a))(vec(b)xx vec(a))` ANSWER :D

Discussion

50.	Match the following Column I- with Column-II
Answer» SOLUTION :(A) `F(x)=x^(3)+ax^(2)+bx+c=(x^(2)+1)(x+a)+(B-)x+(c-a)` `:' f(x)` is DIVISIBLE by `x^(2)+1impliesb-1=0impliesc=a` (B) `(A+B)(A-B)=(A-B)(A+B)impliesAB=BA, A^(T)=A,B^(T)=-B` `(AB)^(T)-(-1)^(k-1)ABimpliesk` is an odd number (C) `10^(100)-43=999…..9957` Sum of digits `=98(9)+5+7=894` (D) `x=7costheta-sintheta, y=7sintheta+costheta, z=10` `(x^(2)+y^(2))/z=5`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Solve the following differential equations.dy+(y^2+1)dx=0

The point of intersection of two tangents to hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 the product of whose slopes is c^2?, lies on the curve

The solution of (dy)/(dx) = (1+y^(2))(1+x^(2))^(-1) is

Using elementary row transformations , find the inverse of [{:(2,-3),(-1,2):}]

If lim_(x to 0) (axe^x -b log (1+x))/x^2=5/2 then the value of 2a+b is

Find the order and degree (if defined) of the following differential equations. ((ds)/(dt))^4 + 3s (d^2s)/(dt^2) = 0

Find the projection of the point (7,-5,3) on x-axis,

The value of the sin 1^(@) + sin2^(@) + … + sin359^(@) is equal to

If (2, 1) is limiting point of coaxial system of which x^(2) + y^(2) - 6x - 4y - 3 = 0 is a member, then the other limiting point is

Calculate the variance and standard deviation of the following continuous frequency distribution . (##VIK_MAT_IIA_QB_C08_SLV_010_Q01.png" width="80%">

Find the derivative of tan (2x + 3)

IF y=e^(tan^(-1)x) then prove that : (1-x^(2))(d^2y)/(dx^2)+(2x-1)(dy)/(dx)=0.

If 2a + 3b - 5c = 0, then ratio in which c divides AB is

If AP, BQ and CR are the altitudes of acute triangleABC and 9AP+4BQ+7CR=0 Q. angleABC is equal to

Let triangleABC be a given triangle. If |vec(BA)-tvec(BC)|ge|vec(AC)| for any t in R,then triangleABC is

There are two cars of which one holds not more than 5 and the other not more than 4. The number of ways can a party of 8 people go for excursion in the two cars is

For what value of x the tangent of the curve y=x^(3)-3x^(2)+x-2 is parallel to the line y=x

Consider the function f(x)=(x^(3)-x)|x^(2)-6x+5|, AA x in R, then f(x) is

If sin^(-1)(x)-cos^(-1)(x)=pi/6,then x is equal to

Differentiate log(cos e^(x)) w.r." to "x.

The position vectors of the points A, B, C and D are 3hat(i)-2hat(j)-hat(k),2hat(i)-3hat(j)+2hat(k),5hat(i)-hat(j)+2hat(k)and4hat(i)-hat(j)+lamdahat(k) respectively. If the points A, B, C and D lie on a plane, the value of lamda is

Corner points of fealible region of inequalities gives

If thetworootsof 4x^3 + 20 x^2 -23x + 6=0are equalthen findallthe roots .

The set of values that beta can assume so that the pont (0,beta) should lie on or inside the triangle having sides 3x+y+2=0,2x-3y+5=0 and x+4y-14=0 is

Write down the set of letters forming that word Demonstration?

All points lying inside the triangle formed﻿ by the points (1, 3), (5,0) and (-1, 2)﻿ satisfy

If underset (nrarroo)" lim " underset(r=1) overset(n) (sum) (4r^(3))/(r^(4+n^(4)))= p, then e^(4)=

Prove that the radical axis of the circles x^2+y^2+2gx +2fy+c=0 and x^2+y^2+2g'x + 2f'y+c'=0 is the diameter of the later circle (or the former bisects the circumference of the later ) if 2g'(g-g')+2f'(f-f')=c-c'

यदि A={1,2,3,4} तो AxA में अवयवों की संख्या है

If |3x-5|le2 then

Let A ={a,a_(2),…….a_(n)}be a set containing a elements. The number of symmetric relations that can be denned on A is

Examine the consistency of the system of equations 5x-y+4z =5 2x+ 3y + 5z =2 5x-2y + 6z =-1

Integrate the functions x(e^(x^(2)))

A flagpolestandson abuildingand anobserver on alevelgroundis 300feetfromthe baseof thebuiling. Theangleofelevationof thebottionof theflagpoleis30^@and theheightof theflagpoleis 50feetifthetais theangleof elevationof htetop of the flagpole , thentan thetaisequalto

Let f(x)={{:(x|x|",", x le -1),([x+1]+[1-x]",",-1ltxlt1),(-x|x|",",x ge 1):} where [.] denotes the greatest integer function, then the value of int_(-2)^(2)f(x)dx, is equal to

If the system of linear equations x+4y-3z=2 2x+7y-4z=alpha -x-5y+5z=beta has infinitely many solutions then the ordered pair (alpha, beta) cannot take value

The area of the quadrilateral formed by the tangents from the point (4,5) to the circle x^(2)+y^(2)-4x-2y-11=0 with a pair of the radii joining the points of contact of these tangents is

(23)^(-1//2)~~....

If A any square matrix then

The solution set contained in R of the inequation 3^(x)+3^(1-x)-4 lt0, is

If a circle cuts a parabola in four points then the sum of ordinates of four points is

Forthe functionf : (0,1) to R, ,f(x)= [ 2^(n)x] + { 2^(m)x}, (n ,m N, ngt m), , thenumberof points ofdiscontinuityof the functioncan bebe( where[.] {}representgreatestintegerfunctionandfractinoalpartof xrespectively )

The mean of the data set comprisingof 16 observations is 16. If one of the observation valued 16 is deteted and three new observa- tions valued3,4 and 5 are added to the data, then the mean of the resultant data, is :

If |a|=3 and -1 le k le 2, then |k a|lies in the interval

If bara+barb+barc=bar0 then prove that bara xx barb= barb xx barc= barc xx bara.

Which of the following is/are a contradiction ?

If there are only two linear functions f and g which map [1,2] on [4,6] and in a DeltaABC, c =f (1)+g (1) and a is the maximum valur of r^(2), where r is the distance of a variable point on the curve x^(2)+y^(2)-xy=10 from the origin, then sin A: sin C is

A man has 6 friends. In how many ways can he invite two or more to a dinner party ?

bar(a)xx[bar(a)xx(bar(a)xx bar(b))] = …………….

Match the following Column I- with Column-II

All points lying inside the triangle formed by the points (1, 3), (5,0) and (-1, 2) satisfy