28278 + Interview Questions in Maths in Class 12

1.	Consider the circle C_(1):x ^(2) +y ^(2) -6x - 8y + 15=0, C_(2) : x ^(2) + y ^(2) - 6x - 8y + 20 =0 Now from any point P on C_(1), pair of tangents PA and PB are drawn onC_(2). Then locus of the orthocenter of triangle PAB is
Answer» `X ^(2) +y ^(2) - 6x - 8y + 20 =0` `x ^(2) + y^(2) - 6x - 8y + 10=0` `x ^(2) +y ^(2) - 6x - 8y + 5=0` NONE of these ANSWER :D

Discussion

2.	On [1,e] the gratest value of x^2log_ex, is
Answer» `e^2` `1/2log(1/sqrte)` `e^2logsqrte` e Answer :A

Discussion

3.	A set contains (2n+1) elements. If the number of subsets of this set which contain atmost n elements is 4096, then n is
Answer» 15 13 6 21 Answer :C

Discussion

4.	If 3 coins are tossed simultaneously and the number of heads turned up is denoted by the variable X, then find mean and variance of X.
Answer» ANSWER :2

Discussion

5.	Let A={(x,y):x gt 0,y gt0,x^(2)+y^(2)=1} and let B={(x,y):x gt 0,y gt0,x^(6)+y^(6)=1} then A nn B
Answer» A B `PHI` `{(0,1),(1,0)}` ANSWER :D

Discussion

6.	vec(AB)=3bari-barj+bark and vec(CD)= -3bari+2barj+4bark are two vectors. The position vectors of the points A and C are 6bari + 7barj + 4bark and -9bari + 2bark respectively. Find the position vector of a point P on the line AB and a point Q on the line CD such that vec(PQ) is perpendicular to vec(AB) and vec(CD) both.
Answer» ANSWER :`=(-6,-15,3)`

Discussion

7.	Which of the ..........
Answer» Solution :`P_(4)+3NaOH+3H_(2)O rarr 3NaH_(2)PO_(2)+PH_(3) uarr`

Discussion

8.	Two persons A and B are throwing an unbiased six faced dice alternatively, with the condition that the person who throws 3 first wins the game. If A starts the game, then probabilities of A and B to win the same are, respectively
Answer» `(6)/(11),(5)/(11)` `(5)/(11),(6)/(11)` `(8)/(11),(3)/(11)` `(3)/(11),(8)/(11)` ANSWER :C

Discussion

9.	Let t_(1)=(sin^(-1)x)^(sin^(-1)x), t_(2)=(sin^(-1)x)^(cos^(-1)x), t_(3)=(cos^(-1)x)^(sin^(-1)x) and t_(4)=(cos^(-1)x)^(cos^(-1)x) Match the column I with column II and mark the correct option from the given codes.
Answer» `{:(I,II,III,IV),(p,q,s,r):}` `{:(I,II,III,IV),(q,p,p,s):}` `{:(I,II,III,IV),(p,p,s,q):}` `{:(I,II,III,IV),(q,s,p,p):}` ANSWER :B

Discussion

10.	Which of the .............
Answer» Solution :It is TWO STEP REACTION and FIRST step is SLOW and rds.

Discussion

11.	Determine if A sub B or A cancel sub B where A={x:x "is an integer "},B={3x:x "is an integer"}
Answer» SOLUTION :`A cancelsub B`

Discussion

12.	Consider the system of equations sin x cos 2y=(a^(2)-1)^(2)+1, cos x sin 2y = a+1 The number of values of a for which the system has a solution is
Answer» 1 2 3 infinite Solution :The given system is `sin X COS 2Y=(a^(@)-1)^(2)+1`, and `cos x sin 2y=a+1` ...(i) Since the L.H.S. of both the equations does not exceed 1, the given system may have solutions only for a's such that `(a^(2)-1)^(2)+1 le 1 and -1 le a +1 le 1` ...(II) `(a^(2)-1)^(2)+1 le 1` or `(a^(2)-1)^(2) le 0` or `(a^(2)-1)^(2)=0` or `a=1` For `a=1`, equation `cos x sin 2y=a+1` does not hold. Thus, `a=-1` only and we get `sin x cos 2y=1` `cos x sin 2y =0` ...(iii) `sin x cos 2y =1` `rArr sin x=1, cos 2y =1` or `sin x=-1, cos 2y=-1` for which `cos x sin 2y=0`.

Discussion

13.	Which of the ..............
Answer» SOLUTION :Only 2, 3-Dichlorohexane has chiral CENTRES so it will ROTATE the plane of polarised LIGHT in the polarimeter tube experiment.

Discussion

14.	Evaluate int_(0)^(pi/2)logsinxdx
Answer» ANSWER :`-(PI)/(2)LOG2`

Discussion

15.	Show "tan"^(-1)1/2+"tan"^(-1)2/11+"tan"^(-1)4/3=pi/2.
Answer» ANSWER :`pi/2`

Discussion

16.	If p and q are chosen at random from the set {1,2,3,4,5,6,7,8,9,10} with replacement. Find the probability that the roots of x^(2)+px+q=0 are imaginary.
Answer» ANSWER :`(19)/(50)`

Discussion

17.	Number of circles touching all the lines x+4h+1=0, 2x+3y+3=0 and x-6y+3=0 is
Answer» 0 2 4 infinite Answer :B

Discussion

18.	Evaluate the following define integrals as limit of sums : lim_(n rarroo) sum_(i=1)^(n) 1/n ((n-i)/(n+i))
Answer» ANSWER :`-1+2 log_(E)2`

Discussion

19.	Letf :R to R be anyfunctionandg(x) =(1) /( f (x) ) thenwhichof thefollowingis / arenot true?
Answer» G is onto of F is onto g isone - oneif f is onto g is continuousifis CONTINUOUS g isdifferentiableif f isdifferentiable Answer :A::C::D

Discussion

20.	If 2 + i and sqrt5 - 2i are the roots of the equation (x^(2) +ax+ b)(x^(2) +cx+ d) = 0, where a, b, c, dare real constants, then product of all roots of the equation is
Answer» 40 `9sqrt5` 45 35 Answer :C

Discussion

21.	Find the principal value of cos^(-1)(-(1)/(2))+2sin^(-1)(-(1)/(2))
Answer» `(pi)/(2)` `(2PI)/(3)` `(3PI)/(4)` `(5PI)/(8)` Answer :A

Discussion

22.	Examine the consistency of the following system of equation x+y+z=1 2x +3y+2z =2 ax +ay +2az =4
Answer» SOLUTION :Here A=[[1,1,1],[2,3,2],[a,a,2a]] `THEREFORE \|A\|=1 \|[3,2],[a,2a]\|-1\|[2,2],[a,2a]\|+1\|[2,3],[a,a]\| `=(6a -2a)-(4a-2a)+(2a-3a) `=4a-2a-a=a!=0` (Clearly `a!= 0` because if a=0, then the THIRD equation would not exist)`therefore`The GIVEN system is consistent

Discussion

23.	In a bolt factory, there machines A, B, C, manufature 25%,35% and 40% of the total production respectively. Of their respective outputs, 5%, 4% and 2% are defective. A bolt is drawn at random from the total product and it is found to be defective. Find the probability that it was manufactured by the machine C.
Answer» Solution :Let `E_1,E_2 and E_3` be the EVENTS of drawing a bolt produced by machine A, B and C RESPECTIVELY. Then, `=P(E_1)=25/100=1/4,P(E_2)=35/100=7/20,and P(E_3)=40/100=2/5`. Let E be the event of drawing a DEFECTIVE bolt. Then, `P(E//E_1)` = probability of drawing a defective bolt, given that it is produced by the machine A `=5/100=1/20`. `P(E//E_2)` = probabilityof drawing a defective bolt, given that it is produced by the machine B `=4/100=1/25`. `P(E//E-3)` =probability of drawing a defective bolt, given that it is produced by the machine C `=2/100=1/50`. Probability that the bolt drawn is manufactured by C, given that it is defective `=P(E_3//E)` `(P(E//E_3)P(E_3))/(P(E_1).P(E//E_1)+P(E_2).P(E//E_2)+P(E_3).P(E//E_3))` [by Bayes's theorem] `((1/50xx2/5))/((1/20xx1/4)+(1/25xx7/20)+(1/50xx2/5))=(1/125xx2000/69)=16/69`. Hence, the REQUIRED probability is `16/69`.

Discussion

24.	Which of the ...................
Answer» SOLUTION :OBVIOUS

Discussion

25.	Let f(x) be a polynomial of degree 4 with f(2)=-1, f^(')(2)=0,f^('')(2)=2,f^(''')(2)=24, then the value of f^('')(1) is
Answer» 24 26 28 30 Solution :Let `f(x)=a(x-2)^(4)+b(x-2)(3)+C(x-2)^(2)+d(x-2)-1` `f(x)=12(x-2)^(2)-12(x-2)+2` `f^''(1)=26`

Discussion

26.	Integrationof rationalfunctions int(dx)/((1+x)(1+x^(2))(1+x^(3))).
Answer» ANSWER :`-(1)/(6(1-X))+(1)/(6) In ((1+x)^())/(1-x+x^(2))+(1)/(2) ARC tan x`

Discussion

27.	If A = [[1,1,0],[0,1,0],[1,0,1]] then A^(3) =
Answer» `[[1,3,0],[0,1,0],[3,3,1]]` `[[1,0,3],[3,1,3],[0,0,1]]` `[[3,3,1],[1,3,0],[0,1,0]]` `[[3,1,0],[3,3,1],[1,0,0]]` ANSWER :A

Discussion

28.	If f(x)=\|x-1\|+\|x-2\|+\|x-3\| when 2 lt x lt 3 is
Answer» `((1)/(3))^((1)/(3))` `(1)/(2)` 1 0 Answer :C

Discussion

29.	Find the coordinates of the points on the parabola y^(2)=2x whose focal distance is (5)/(2).
Answer» ANSWER :The REQUIRED POINTS are `(2,-2)` and `(2,2)`

Discussion

30.	For each of the differential equations given in x(dy)/(dx)+2y=x^(2)logx
Answer» ANSWER :`y = (x^(2))/(16)(4 log\|x\| - 1) + Cx^(-2)`

Discussion

31.	Find the area of the region{ (x,y):x^(2) +y^(2) lt1lt x +y} (ii) Find the area of the region { ( x,y): x^(2)+ y^(2) lt 2ax ,y^(2) gt ax ,x gt 0, ygt 0} (iii) Using integration find the area of the region{ x,y): y^(2) lt 4x ,4x^(2) +4y^(2) lt 9}.
Answer» Answer :` (1)/(4) (pi-2)` SQUARE units `(ii) (1)/(12) (3PI -8) ` square units ` (iii) [( 9)/( 4)cos ^(-1)""(1)/(3) +(SQRT( 2))/( 6)]` square units

Discussion

32.	If sin^(-1)x+cos^(-1)y=(2pi)/5," then "cos^(-1)x+sin^(-1)y is
Answer» 1)`(2pi)/5` 2)`(3pi)/5` 3)`(4PI)/5` 4)`(3pi)/10` ANSWER :B

Discussion

33.	If \|{:((1+x)^(17),(1+x)^(19),(1+x)^(23)),((1+x)^(23),(1+x)^(29),(1+x)^(34)),((1+x)^(41),(1+x)^(43),(1+x)^(47)):}\|=Ax^2+Bx+C then value of A = "........."
Answer» ANSWER :A=0

Discussion

34.	If the marginal revenue of a commodity is given by MR=20e^(-x/10)(1-x/10) , find the demand function .
Answer» ANSWER :`p=20e^(-x/10)`

Discussion

35.	The tangent at any point P on a standard ellipse with foci as S & S' meets the tangents at the vertcies A & A' in the points V & V', then
Answer» `L(AV). l(A'v') =b^2` `l(AV). l(A'v') =a^2` `ANGLE V'SV = 90^@` `V'S'SV` is a CYCLIC quadilateral Answer :A::C::D

Discussion

36.	Check the validity of "The sum of an irrational number and a rational number is irrational " by contradiction method.
Answer» Solution :Let the given STATEMENT is false. i.e. the SUM of an irrational NUMBER and a rational number is rational. implies An irrational number + a rational number = a rational number implies An irrational number =A rational number + rational number = A rational number Which is absurd. `:.` We arrive at a contradiction. This is due to our false assumption THUS, the given statement is TRUE.

Discussion

37.	Asserton (A) : The solution of (dy)/(dx) = (x+y)/(x) is e^(y//x) = cx Reason (R) : To solve (dy)/(dx) = (f(x,y))/(g(x,y)), where f(x,y) and g(x,y) are homogeneous function of same degree in x and y, put x =vy. Then the Statement among the following is
Answer» Both (A) and (R) are TRUE and R is correct EXPLANATION of A Both (A) and (R) are true and R is not correct explanation of A A is true, (R) is FALSE (A) is false (R) is true Answer :A

Discussion

38.	Match the statements/expressions in List I statements/expression in List II
Answer» Solution : Given `2(a^(2) -B^(2)) = c^(2)` `RARR 2 (sin^(2) X - sin^(2)Y) = sin^(2)Z` `rArr 2 sin (X + Y) sin (X - Y) = sin^(2) Z` `rArr 2 sin (pi - Z) sin (X -Y) = sin^(2) Z` `rArr sin (X- Y) = (sin Z)/(2)`...(i) `:. lamda = (sin (X -Y))/(sin Z) = (1)/(2)` Now `cos (n pi lamda) = 0` `rArr cos ((n pi)/(2)) = 0` `:. n = 1, 3, 5` `1 + cos 2X - 2 cos 2Y = 2 sin X sin Y` `2 cos^(2) X - 2 cos 2Y = 2 sin X sin Y` `1- sin^(2) X - 1 + 2 sin^(2) Y = sin X sin Y` `sin^(2) X + sin X sin Y = 2 sin^(2) Y` `sin X (sin X + sin Y) = 2 sin^(2) Y` `rArr a(a +b) = 2B^(2)` `rArr a^(2) + ab - 2b^(2) = 0` `rArr ((a)/(b))^(2) + (a)/(b) - 2 = 0` `rArr (a)/(b) = -2, 1` `rArr (a)/(b) = 1` Note : Solutions of the REMAINING parts are given in their respecitive chapters.

Discussion

39.	If OA=a, OB=b, OC=c arethe co-terminus edges of regular parallelopiped, then the shortest distance between the diagonal and the side OB not meeting the diagonal is
Answer» `(bc)/SQRT(b^(2) + c^(2))` `(CA)/sqrt(c^(2) + a^(2))` `(ab)/sqrt(a^(2) + b^(2))` `(abc)/sqrt(a^(2) + b^(2) + c^(2))` ANSWER :B

Discussion

40.	If OA=a, OB=b, OC=c are the co-terminus edges of regular parallelopiped, then the shortest distance between the diagonal and the side OA not meeting the diagonal is
Answer» `(bc)/sqrt(B^(2) +c^(2))` `(CA)/sqrt(c^(2) +a^(2))` `(ab)/sqrt(a^(2) + b^(2))` `(ABC)/sqrt(a^(2) + b^(2) +c^(2))` Answer :A

Discussion

41.	If a circle C_(1),x^(2)+y^(2)=16 intersects another circle C_(2) of radius 5 in such a manner that the common chord is maximum length and has slope 3/4, then show the centres of C_(2) are (9/5,(-12)/5),((-9)/5,12/5)
Answer» ANSWER :`=(-+9/5,12/5)`

Discussion

42.	Let f(x) = lt x gt^(""), where lt x gt^("") is the distance from x to the integer nearest to x, then lim_(x rarr 2) f(x) is :
Answer» 0 1 2 3 Answer :A

Discussion

43.	find thevalueof x for which\|(3,x),(x,1)\|=\|(3,2),(4,1)\|
Answer» ANSWER :`= +- 2 SQRT(2)`

Discussion

44.	If the planes vecr.(hati+2hatj-3hatk)=7 and vecr.(lambdahati+2hatj-7hatk)=26 are perpendicular to\| each other then find the value of lambda.
Answer» ANSWER :`lambda=17`

Discussion

45.	Verify Rolle's theorem of the function log(x^2+2)-log 3 on (-1,1)
Answer» ANSWER :`c=0 in(-1,1)`

Discussion

46.	Find the angle between the lines whose direction ratios are a, b, c and b-C, c-a, a-b.
Answer» Answer :`THEREFORE THETA=(pi)/(2)` `therefore` HENCE,both the lines are PERPENDICULAR.

Discussion

47.	If the extremities of a focal chord are (5pi)/(12) and (pi)/(12)then e =
Answer» `(1)/SQRT(2)` `sqrt(2/3)` `sqrt(3)/(4)` `sqrt(3)/(2)` Answer :B

Discussion

48.	If x ge 0, y ge 0, 2x+2y le 10, x+2y le 10, then the greatest value of F=x+y is
Answer» 5 `20//3` `5//2` 15 Answer :B

Discussion

49.	Which of the following is equivalent to 10+2(x-7)?
Answer» `-14x+10` `2x+24` `2x+3` `2x-4` ANSWER :D

Discussion

50.	Every one out of 15 telephone calls between 2.00 p.m and 4.00 p.m. in a week is busy. Find the probability that out of 6 randomly chosen telephone numbers, (i) exactly two are busy (ii) atleast three of them are busy.
Answer» ANSWER :i) `(14^(4))/(15^(5))`ii) `(20(14)^(3)+15(147)^(2)+6(14)+1)/(15^(6))`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Consider the circle C_(1):x ^(2) +y ^(2) -6x - 8y + 15=0, C_(2) : x ^(2) + y ^(2) - 6x - 8y + 20 =0 Now from any point P on C_(1), pair of tangents PA and PB are drawn onC_(2). Then locus of the orthocenter of triangle PAB is

On [1,e] the gratest value of x^2log_ex, is

A set contains (2n+1) elements. If the number of subsets of this set which contain atmost n elements is 4096, then n is

If 3 coins are tossed simultaneously and the number of heads turned up is denoted by the variable X, then find mean and variance of X.

Let A={(x,y):x gt 0,y gt0,x^(2)+y^(2)=1} and let B={(x,y):x gt 0,y gt0,x^(6)+y^(6)=1} then A nn B

Which of the ..........

Two persons A and B are throwing an unbiased six faced dice alternatively, with the condition that the person who throws 3 first wins the game. If A starts the game, then probabilities of A and B to win the same are, respectively

Let t_(1)=(sin^(-1)x)^(sin^(-1)x), t_(2)=(sin^(-1)x)^(cos^(-1)x), t_(3)=(cos^(-1)x)^(sin^(-1)x) and t_(4)=(cos^(-1)x)^(cos^(-1)x) Match the column I with column II and mark the correct option from the given codes.

Which of the .............

Determine if A sub B or A cancel sub B where A={x:x "is an integer "},B={3x:x "is an integer"}

Consider the system of equations sin x cos 2y=(a^(2)-1)^(2)+1, cos x sin 2y = a+1 The number of values of a for which the system has a solution is

Which of the ..............

Evaluate int_(0)^(pi/2)logsinxdx

Show "tan"^(-1)1/2+"tan"^(-1)2/11+"tan"^(-1)4/3=pi/2.

If p and q are chosen at random from the set {1,2,3,4,5,6,7,8,9,10} with replacement. Find the probability that the roots of x^(2)+px+q=0 are imaginary.

Number of circles touching all the lines x+4h+1=0, 2x+3y+3=0 and x-6y+3=0 is

Evaluate the following define integrals as limit of sums : lim_(n rarroo) sum_(i=1)^(n) 1/n ((n-i)/(n+i))

Letf :R to R be anyfunctionandg(x) =(1) /( f (x) ) thenwhichof thefollowingis / arenot true?

If 2 + i and sqrt5 - 2i are the roots of the equation (x^(2) +ax+ b)(x^(2) +cx+ d) = 0, where a, b, c, dare real constants, then product of all roots of the equation is

Find the principal value of cos^(-1)(-(1)/(2))+2sin^(-1)(-(1)/(2))

Examine the consistency of the following system of equation x+y+z=1 2x +3y+2z =2 ax +ay +2az =4

Which of the ...................

Let f(x) be a polynomial of degree 4 with f(2)=-1, f^(')(2)=0,f^('')(2)=2,f^(''')(2)=24, then the value of f^('')(1) is

Integrationof rationalfunctions int(dx)/((1+x)(1+x^(2))(1+x^(3))).

If A = [[1,1,0],[0,1,0],[1,0,1]] then A^(3) =

If f(x)=|x-1|+|x-2|+|x-3| when 2 lt x lt 3 is

Find the coordinates of the points on the parabola y^(2)=2x whose focal distance is (5)/(2).

For each of the differential equations given in x(dy)/(dx)+2y=x^(2)logx

Find the area of the region{ (x,y):x^(2) +y^(2) lt1lt x +y} (ii) Find the area of the region { ( x,y): x^(2)+ y^(2) lt 2ax ,y^(2) gt ax ,x gt 0, ygt 0} (iii) Using integration find the area of the region{ x,y): y^(2) lt 4x ,4x^(2) +4y^(2) lt 9}.

If sin^(-1)x+cos^(-1)y=(2pi)/5," then "cos^(-1)x+sin^(-1)y is

If |{:((1+x)^(17),(1+x)^(19),(1+x)^(23)),((1+x)^(23),(1+x)^(29),(1+x)^(34)),((1+x)^(41),(1+x)^(43),(1+x)^(47)):}|=Ax^2+Bx+C then value of A = "........."

If the marginal revenue of a commodity is given by MR=20e^(-x/10)(1-x/10) , find the demand function .

The tangent at any point P on a standard ellipse with foci as S & S' meets the tangents at the vertcies A & A' in the points V & V', then

Check the validity of "The sum of an irrational number and a rational number is irrational " by contradiction method.

Asserton (A) : The solution of (dy)/(dx) = (x+y)/(x) is e^(y//x) = cx Reason (R) : To solve (dy)/(dx) = (f(x,y))/(g(x,y)), where f(x,y) and g(x,y) are homogeneous function of same degree in x and y, put x =vy. Then the Statement among the following is

Match the statements/expressions in List I statements/expression in List II

If OA=a, OB=b, OC=c arethe co-terminus edges of regular parallelopiped, then the shortest distance between the diagonal and the side OB not meeting the diagonal is

If OA=a, OB=b, OC=c are the co-terminus edges of regular parallelopiped, then the shortest distance between the diagonal and the side OA not meeting the diagonal is

If a circle C_(1),x^(2)+y^(2)=16 intersects another circle C_(2) of radius 5 in such a manner that the common chord is maximum length and has slope 3/4, then show the centres of C_(2) are (9/5,(-12)/5),((-9)/5,12/5)

Let f(x) = lt x gt^("*"), where lt x gt^("*") is the distance from x to the integer nearest to x, then lim_(x rarr 2) f(x) is :

find thevalueof x for which|(3,x),(x,1)|=|(3,2),(4,1)|

If the planes vecr.(hati+2hatj-3hatk)=7 and vecr.(lambdahati+2hatj-7hatk)=26 are perpendicular to| each other then find the value of lambda.

Verify Rolle's theorem of the function log(x^2+2)-log 3 on (-1,1)

Find the angle between the lines whose direction ratios are a, b, c and b-C, c-a, a-b.

If the extremities of a focal chord are (5pi)/(12) and (pi)/(12)then e =

If x ge 0, y ge 0, 2x+2y le 10, x+2y le 10, then the greatest value of F=x+y is

Which of the following is equivalent to 10+2(x-7)?

Every one out of 15 telephone calls between 2.00 p.m and 4.00 p.m. in a week is busy. Find the probability that out of 6 randomly chosen telephone numbers, (i) exactly two are busy (ii) atleast three of them are busy.

Let f(x) = lt x gt^(""), where lt x gt^("") is the distance from x to the integer nearest to x, then lim_(x rarr 2) f(x) is :