28278 + Interview Questions in Maths in Class 12

1.	Show that the area enclosed by y^(2)=4ax and its latus rectum is (8a^(2))/(3) sq units.
Answer» ANSWER :`=(8)/(3)a^(2)` SQ units

Discussion

2.	Write the component statement "2 is an even number and a prime number"compound statements and check whether the compound statement is true or false.
Answer» <P> SOLUTION :The COMPONENT statements are p :2 is an even number q:2 is a prime number The truth VALUE of the COMPOUND statement is .True..

Discussion

3.	Find the number of ways in which 6 men can sit at a round table so that all shall not have the same neighbours in any two arrangements
Answer» ANSWER :60

Discussion

4.	{:(,"Vitamin C Content","Vitamin A Conent"),("Apples","low","low"),("Banans","medium","low"),("Oranges","high","medium"),("Lettuce","high","low"),("Potatoes","medium","low"),("Tomatoes","high","high"),("Carrots","low","high"):} Approximately what were the total April sales of produce itmes at Produce Stand P that were high in both vitamin A and vitamin C content?
Answer» 451 488 577 624 Answer :C

Discussion

5.	{:(,"Vitamin C Content","Vitamin A Conent"),("Apples","low","low"),("Banans","medium","low"),("Oranges","high","medium"),("Lettuce","high","low"),("Potatoes","medium","low"),("Tomatoes","high","high"),("Carrots","low","high"):} Approximately what dollar amount of the produce sold by Produce Stand P in April had medium or high amounts of either vitamin A or vitamin C?
Answer» `$3,120` `$3,600` `$4,000` `$4,600` ANSWER :B

Discussion

6.	Evaluate :\|{:( 0, sin alpha , - cos alpha ), ( - sin alpha , 0 ,sin beta) , (cos alpha , -sin beta ,0):}\|
Answer» `-1` ` SIN ALPHA- sin beta ` ` sin beta ` ` 0` Answer :D

Discussion

7.	Let f(x)=(2x)/(2x^(2)+5x+2) and g(x)=(1)/(x+1).
Answer» ANSWER :`X in (-2) cup (-(2)/(3),(1)/(2))`

Discussion

8.	If \|z + 1\| = sqrt2 \| z- 1\| and z is a complex number , then the locus of z is
Answer» straight LINE a CIRCLE an ellipse a parabola ANSWER :B

Discussion

9.	(dy)/(dx) + 3y = e^(-2x)
Answer» ANSWER :`y = E^(-2X) + CE^(-3X)`

Discussion

10.	Compute the volume of the solid generated by revolving about the x-axis the area bounded by the axes of coordinates and the parabola x^((1)/(2)) +y^((1)/(2)) = a^((1)/(2)).
Answer» ANSWER :`(1)/(15) PI a^(3)`

Discussion

11.	Find the number of ways of arranging all the letters of the word MATHEMATICS
Answer» ANSWER :`(lfloor11)/(lfloor2lfloor2lfloor2)`

Discussion

12.	Let Delta=\|{:(a,a+b,a+3d),(a+d,a+2d,a),(a+2d, a, a+d):}\| then :
Answer» `DELTA` DEPENDS on a `Delta` depends on d `Delta` is INDEPENDENT of a,d `Delta=0` ANSWER :A::B

Discussion

13.	State the converse, inverse and contrapositive of A parallelogram which is inscribed in a circle is a rectangle propositions. Stating it as a conditional, wherever necessary.
Answer» SOLUTION :If a PARALLELOGRAM is INSCRIBED in a CIRCLE, then it is a RECTANGLE. Con :If a parallelogram is a rectangle, then it is inscribed in a circle. Inv: If a parallelogram is not inscribed in a circle then it is not a rectangle. Cont :If a parallelogram is not a rectangle, then it is not inscribed in a circle.

Discussion

14.	Examine the following functions for continuity. f(x)= (1)/(x-5), x ne 5
Answer» ANSWER :x=5

Discussion

15.	If the relation f'(a+b) =f'( a)+ f '(b) and(d)/(dx)(f(x))=f'(x) ,then f(x) =
Answer» ` x^(4)` `x^(2) ` ` x^(3)` x Answer :C

Discussion

16.	A factory manufatures two types pf screws A and B, Each type of screw requires the use of two machines, an automatic and a hand operated.It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B.Each machine is available for at the most 4 hours on any day.The manufacturer can sell a package of screws A at a profit of ₹ 7 and screws B at a profit of ₹ 10.Assuming that he can sell all the screws he amnufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit?Determine the maximum profit.
Answer» Answer :30 PACKAGES of SCREWS A and 20 packages of screws B.Max.profit = ₹ 410.

Discussion

17.	(31)^((1)/(5)) has approximate value ………..
Answer» `2.1` `2.01` `2.0125` `1.9875` ANSWER :D

Discussion

18.	Bag A contains 2 white and 3 red balls, and bag B contains 4 white and 5 red balls. One ball is drawn at randow from one of the bags and it is found to be red. Find the probability that it was drawn from bag B.
Answer» SOLUTION :Let `E_1`= ENVENT of CHOOSING bag A, `E_2`= event of choosing bag B, and E= event of drawing a red ball. Then, `P(E-1)=1/2 and P(E-2)=1/2` Also, `P(E//E_1)`= event of drawing a red ball from bag `A=3/5`, and `P(E//E-2)` = event of drawing a red ball from bag `B=5/9`. Probability of drawing a ball from B, it being given that it is red `=P(E_2//E)` `=(P(E//E_2).P(E_2))/(P(E//E_1).P(E_1)+P(E//E_2).P(E_2))`[by Bayes's theorem] `=((5/9xx1/2))/((3/5xx1/2)+(5/9xx1/2))=25/52`. Hence, the REQUIRED probability is`25/52`.

Discussion

19.	The sum of odd integers from 1 to 2001 is
Answer» 100200 102001 202001 502001 Answer :A

Discussion

20.	Solve(x^(3)-3xy^(2))dx+(3x^(2)y-y^(3))dy=0
Answer» ANSWER :`C^(2)(y^(2)+X^(2))^(2)`

Discussion

21.	Two tangents are drawn from a point (-2, -1) to the curve y^(2)=4x. If alpha is the angle between them, then \|tan alpha\| is equal to :
Answer» `(1)/(3)` `(1)/(SQRT3)` `sqrt3` 3 Answer :D

Discussion

22.	Prove that 3lerlen ""^(n-3)C_(r)+3""^(n-3)C_(r-1)+3""^(n-3)C_(r-2)+""^(n-3)C_(r-3)=""^(n)C_(r)
Answer» ANSWER :`=""^(N)C_(R)`

Discussion

23.	If(1+ sin^(@))/( cos 6^(@))=tan A =sqrt((1+ sinB)/(1- sin B)), where A and B in (0.90^(@)), then
Answer» A=8B 8A=B A=7B=`6^(@)` `A+B=54^(@)` ANSWER :A::C::D

Discussion

24.	Evaluate the following integrals intx logx dx
Answer» Answer :`(x^(2))/(2) LOG x - (x^(2))/(4) + c`

Discussion

25.	If (2x+3)/(5) lt (4x-1)/(2) , then x lies in the interval
Answer» `[0,(11)/(16)]` `[(11)/(16),OO)` `(o,(11)/(16))` `((11)/(16),oo)` ANSWER :D

Discussion

26.	solvethe differentialequation(dy)/(dx) +ysec x= tanx,0 lex lepi/2
Answer» ANSWER :`= SEC X+ TAN x -x +C`

Discussion

27.	which of the following statement is//are correct?
Answer» MAXIMUM NUMBER pof atom present in same plane in `BrF_(5)` are 5 In `O(SiH_(3))_(2) p_(n)-d_(n)` BACK bonding is present while in `BF_(3) P_(n) -P_(n)` back bonding is present Pyroxene chain silicateand 5 memebered cyclic SILICATE both have 2 number of corner shared PER tetrahedron. Number o flone pair on central atom of `ICI_(4)^(ominus)` is 2 Answer :B::C::D

Discussion

28.	A vanadium ...............
Answer» Solution :SINCE magnetic moment `=1.73` B.M. `=sqrt(3)` `IMPLIES` no. of unpaired electron in vanadium will be 1, so it confirms that V will exist as `V^(4+)` in its compound. According to Faraday's first LAW `W=(Axxixxt)/(nxx96500)` `102xx10^(-3)=(51xxixx8)/(4xx96500)` `i=96.5` amp

Discussion

29.	The periodofthefunctionf(x)= a^({ tan( pix) } +x -[x] ),whereagt0 ,[x]denotesthe greatest integer functionandx is realnumber, is
Answer» `PI` `pi/2` `pi/4` 1 Answer :D

Discussion

30.	Integrate the function 1/(sqrt((2-x)^(2)+1))
Answer» ANSWER :`logabs(1/(2-X+sqrt(x^(2)-4x+5)))+C`

Discussion

31.	Area of a rectangle having vertices A, B, C and D with position vectors -hati+(1)/(2)hatj+4hatk,hati+(1)/(2)hatj+4hatk, hati-(1)/(2)hatj+4hatk and -hati-(1)/(2)hatj+4hatk, respectively is ………..
Answer» `(1)/(2)` 1 2 4 Answer :C

Discussion

32.	int(x+sqrt(x+1))/(x+2) dx is equal to:
Answer» `(x+1)-2sqrt(x+1)+2"LN"\|x+2\|=2tan^(-1)sqrt(x+1)+C` `(x+1)+2sqrt(x+2)-2"ln"\|x+2\|-2tan^(-1)sqrt(x+2)+C` `(x+1)+2sqrt(x+1)-2"ln"\|x+2\|-2tan^(-1)sqrt(x+1)+C` `(x=1)+2sqrt(x+2)-2"ln"\|x+1\|+2tan^(-1)sqrt(x+2)+C` Answer :c

Discussion

33.	If line (x-3)/(2)=(y-4)/(3)=(z-5)/(4)lines in the plane 4x+4y-cz-d=0, then values of c,d are
Answer» 5,3 4,8 `-4,-8` `-5,-3` ANSWER :A

Discussion

34.	If the coefficient of variation and standard deviation are 60 and 21 respectively, the arithmetic mean of distribution is
Answer» 40 `7//20` `20//7` `1//40` ANSWER :A

Discussion

35.	Number n is selected from the set {1,2, ….200}. and the number 2^(n)+3^(n)+5^(n) is formed. Find the total number of ways of selecting n so that the formed number is divisible by 4
Answer» ANSWER :99

Discussion

36.	lim _(y to1) ((1)/(y^2-1)-(2)/(y^4-1))=
Answer» `1/2` `1/3` `1/4` `0` ANSWER :A

Discussion

37.	[vec(a)-vec(b).vec(b)-vec(c).vec(a)+vec(c)]" equals"
Answer» `2[VEC(a).vec(B).vec(C)]` `3[vec(a).vec(b).vec(c)]` `[vec(a).vec(b).vec(c)]` 0 Answer :A

Discussion

38.	Integrate the following functions 1/(x+xlogx)
Answer» Solution :Put 1+logx = t. Then DT = 1/X dx THEREFORE `INT 1/(x+xlogx) dx = int 1/(1+logx)x) dx` `int 1/t dt = log\|t\| +c` =`log\|1+logx\| +c`

Discussion

39.	Identify correct pair from the following. (i) veca xx (vecb xx vecc)=(vecavecb)vecc-(vecavecc)vecb (ii) Projection of veca on vecb is (veca*vecb)/(\|veca\|) (iii) [hati +2hatj, hatj+2hatk, hatk +2hatj]=9 (iv) If vecr=veca+t vecb and vecr=vecc+s vecd are two skew lines then shortest distance between the lines is ([vecc-veca, vecb, vecd])/(\|vecbxxvecd\|)
Answer» (i) and (II) are CORRECT (III) and (IV) are correct (i) and (iii) are correct (ii) and (iv) are correct SOLUTION :N/A

Discussion

40.	Prove that (mn)! Is divisible by (n!)^(m) " and" (m!)^(n).
Answer» SOLUTION :Number of ways of distribution of (mn) distinct objects equally AMONG N PERSONS `=((mn)!)/((m!)^(n)n!)xxn!=((mn)!)/((m!)^(n))`. Obviously, this value is integer. So, (mn)! Is divisible by `(m!)^(n)` Similarly, number of ways of distribution of (mn) objects equally among m persons `=((mn)!)/((n!)^(m)m!)xxm!=((mn)!)/((n!)^(m))` So, (mn)! is also divisible by `(n!)^(m)`.

Discussion

41.	Solve as directed : x/2 + 7/2 lt 3x-1 in R
Answer» SOLUTION :x/2 + 7/2 `lt` 3x-1 `rArr (3x + 14)/6 lt (3x-1)` `rArr 3x + 14 lt 18x - 6` `rArr 3x -18x lt -6-14` `rArr -15x lt -20 `rArr (-15x)/(-15) gt (-20)/(-15)` `rArr x gt 4/3` If x `in` R , the solution SET is S = (4/3 , `INFTY`) = {x:x `in` R and x`gt` 4/3}

Discussion

42.	int(x^(4)+x^(2)+1)/(x^(2)+1)dx=......+c
Answer» `(1)/(3)X^(3)+(1)/(2)+x^(2)+x+c` `(1)/(3)x^(3)-(1)/(2)+x^(2)+x+c` `(1)/(3)x^(3)+(1)/(2)-x^(2)+x+c` None of these Answer :A

Discussion

43.	The value of int_(0)^(pi//3)[sqrt(3)tanx]dx (where [.] denotes the greatest integer function)
Answer» `(5PI)/(6)` `(5pi)/(6)-TAN^(-1)((2)/(SQRT(3)))` `(pi)/(2)-tan^(-1)((2)/(sqrt(3)))` `(5pi)/(3)` Answer :3

Discussion

44.	If f: RR to RR" is defined by f(x){{:(,(x-2)/(x^(2)-3x+2),"if "x in R-{1,2}),(,2,"if x=1"),(,1,"if x=2"):}" then " underset(x to 2)"Lt"(f(x)-f(2))/(x-2)=
Answer» 0 `-1` 1 `-1//2` ANSWER :B

Discussion

45.	Mean and variance of one binomial distribution are (4)/(3) and (20)/(21) respectively then p = ………….. where p is parameter.
Answer» `(7)/(5)` `(2)/(7)` `(4)/(7)` `(5)/(7)` Answer :B

Discussion

46.	Evaluate the following inegrals int cos mx cosnx dx
Answer» ANSWER :`(1)/(2)[(SIN(m+n)x)/(m+n)-(sin(m-n)x)/(m-n)]+c`

Discussion

47.	Evaluation of definite integrals by subsitiution and properties of its : If f(x) is an odd function then int_(-(pi)/(2))^(pi/(2))f(cosx)dx=.........
Answer» 0 `int_(0)^(pi/2)f(COSX)DX` `2int_(0)^(pi/2)f(sinx)dx` `int_(0)^(pi)f(cosx)dx` Answer :C

Discussion

48.	Let bara,barb,barc are the three vectors such that \|bara}=\|barb\|=\|barc\|=2 and angle between bara and barb is pi//3,barb and barc is pi//3 and bara and barc pi//3.
Answer» ANSWER :A-r B-p C-q D-p

Discussion

49.	Examine whether the following system of equations are consistent or inconsistent and if consistent, find the complete solution, x+y+z = 1, 2x+y+z = 2, x+2y+2z = 1.
Answer» ANSWER :`x=1,y=-k,z=k`

Discussion

50.	Differentiate w.r.t x, the following function: (i) sqrt(3x+2) + (1)/(sqrt(2x^(2) + 4)) (ii) e^(sec^(2)x)+ 3 cos^(-1)x (iii) log_(7) (log x)
Answer» Answer :(i) `(3)/(2 sqrt(3x + 2))- (2x)/((2x^(2) + 4)^((3)/(2)))`, (II) `2sec^(2)X. tan XE^(SEC^(2)x) - 3 ((1)/(sqrt(1-x^(2))))` (iii) `(1)/(x log 7 log x)`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Show that the area enclosed by y^(2)=4ax and its latus rectum is (8a^(2))/(3) sq units.

Write the component statement "2 is an even number and a prime number"compound statements and check whether the compound statement is true or false.

Find the number of ways in which 6 men can sit at a round table so that all shall not have the same neighbours in any two arrangements

Evaluate :|{:( 0, sin alpha , - cos alpha ), ( - sin alpha , 0 ,sin beta) , (cos alpha , -sin beta ,0):}|

Let f(x)=(2x)/(2x^(2)+5x+2) and g(x)=(1)/(x+1).

If |z + 1| = sqrt2 | z- 1| and z is a complex number , then the locus of z is

(dy)/(dx) + 3y = e^(-2x)

Compute the volume of the solid generated by revolving about the x-axis the area bounded by the axes of coordinates and the parabola x^((1)/(2)) +y^((1)/(2)) = a^((1)/(2)).

Find the number of ways of arranging all the letters of the word MATHEMATICS

Let Delta=|{:(a,a+b,a+3d),(a+d,a+2d,a),(a+2d, a, a+d):}| then :

State the converse, inverse and contrapositive of A parallelogram which is inscribed in a circle is a rectangle propositions. Stating it as a conditional, wherever necessary.

Examine the following functions for continuity. f(x)= (1)/(x-5), x ne 5

If the relation f'(a+b) =f'( a)+ f '(b) and(d)/(dx)(f(x))=f'(x) ,then f(x) =

(31)^((1)/(5)) has approximate value ………..

Bag A contains 2 white and 3 red balls, and bag B contains 4 white and 5 red balls. One ball is drawn at randow from one of the bags and it is found to be red. Find the probability that it was drawn from bag B.

The sum of odd integers from 1 to 2001 is

Solve(x^(3)-3xy^(2))dx+(3x^(2)y-y^(3))dy=0

Two tangents are drawn from a point (-2, -1) to the curve y^(2)=4x. If alpha is the angle between them, then |tan alpha| is equal to :

Prove that 3lerlen ""^(n-3)C_(r)+3""^(n-3)C_(r-1)+3""^(n-3)C_(r-2)+""^(n-3)C_(r-3)=""^(n)C_(r)

If(1+ sin^(@))/( cos 6^(@))=tan A =sqrt((1+ sinB)/(1- sin B)), where A and B in (0.90^(@)), then

Evaluate the following integrals intx logx dx

If (2x+3)/(5) lt (4x-1)/(2) , then x lies in the interval

solvethe differentialequation(dy)/(dx) +ysec x= tanx,0 lex lepi/2

which of the following statement is//are correct?

A vanadium ...............

The periodofthefunctionf(x)= a^({ tan( pix) } +x -[x] ),whereagt0 ,[x]denotesthe greatest integer functionandx is realnumber, is

Integrate the function 1/(sqrt((2-x)^(2)+1))

Area of a rectangle having vertices A, B, C and D with position vectors -hati+(1)/(2)hatj+4hatk,hati+(1)/(2)hatj+4hatk, hati-(1)/(2)hatj+4hatk and -hati-(1)/(2)hatj+4hatk, respectively is ………..

int(x+sqrt(x+1))/(x+2) dx is equal to:

If line (x-3)/(2)=(y-4)/(3)=(z-5)/(4)lines in the plane 4x+4y-cz-d=0, then values of c,d are

If the coefficient of variation and standard deviation are 60 and 21 respectively, the arithmetic mean of distribution is

Number n is selected from the set {1,2, ….200}. and the number 2^(n)+3^(n)+5^(n) is formed. Find the total number of ways of selecting n so that the formed number is divisible by 4

lim _(y to1) ((1)/(y^2-1)-(2)/(y^4-1))=

[vec(a)-vec(b).vec(b)-vec(c).vec(a)+vec(c)]" equals"

Integrate the following functions 1/(x+xlogx)

Prove that (mn)! Is divisible by (n!)^(m) " and" (m!)^(n).

Solve as directed : x/2 + 7/2 lt 3x-1 in R

int(x^(4)+x^(2)+1)/(x^(2)+1)dx=......+c

The value of int_(0)^(pi//3)[sqrt(3)tanx]dx (where [.] denotes the greatest integer function)

If f: RR to RR" is defined by f(x){{:(,(x-2)/(x^(2)-3x+2),"if "x in R-{1,2}),(,2,"if x=1"),(,1,"if x=2"):}" then " underset(x to 2)"Lt"(f(x)-f(2))/(x-2)=

Mean and variance of one binomial distribution are (4)/(3) and (20)/(21) respectively then p = ………….. where p is parameter.

Evaluate the following inegrals int cos mx cosnx dx

Evaluation of definite integrals by subsitiution and properties of its : If f(x) is an odd function then int_(-(pi)/(2))^(pi/(2))f(cosx)dx=.........

Let bara,barb,barc are the three vectors such that |bara}=|barb|=|barc|=2 and angle between bara and barb is pi//3,barb and barc is pi//3 and bara and barc pi//3.

Examine whether the following system of equations are consistent or inconsistent and if consistent, find the complete solution, x+y+z = 1, 2x+y+z = 2, x+2y+2z = 1.

Differentiate w.r.t x, the following function: (i) sqrt(3x+2) + (1)/(sqrt(2x^(2) + 4)) (ii) e^(sec^(2)x)+ 3 cos^(-1)x (iii) log_(7) (log x)