28278 + Interview Questions in Maths in Class 12

1.	A variable line lx+my=1 (where l and m are parameters) intersect a circle x^(2)+y^(2)-4x+3=0 at the points P and Q. The chord PQ subtends a right angle at the origin. If the locus of foot of perpendicular drawn from origin on the given variable lines is lambdax^(2)+muy^(2)-4x+3=0, then find the value of (lambda+mu).
Answer» Solution :Homogenising circle with variable line `x^(2)+y^(2)-4x(lx+my)+3(lx+my)^(2)=0` SINCE OP and OQ are at right angle. `:."Coefficient of "x^(2)+"coeff. Of "y^(2)=0` `(1-4l+3l^(2))+(1+3m^(2))=0` `3l^(2)+3m^(2)-4l+2=0""…(1)` Let FOOT of perpendicular is (h,k) `:.""lh+mk=1""...(2)` Equation of OM is `y=(m)/(l)x` `mh=lk""...(3)` From (2) and (3) we get `l=(h)/(h^(2)+k^(2))" and "m=(k)/(h^(2)+k^(2))` `l^(2)+m^(2)=(1)/(h^(2)+k^(2))" using this in (1)"` `(3)/(h^(2)+k^(2))-(4h)/(h^(2)+k^(2))+2=0` `:."""Required LOCUS is "2x^(2)+2y^(2)-4x+3=0` `:.""lambda=mu=2` `:.""lambda+mu=4`

Discussion

2.	Ifthe mean, variance, standard deviation of 3,4,5 are denoted by a,b,c then.
Answer» `a LT B lt C` `c lt b lt a` `b lt c lt a` `a lt c lt b` ANSWER :A

Discussion

3.	The plane 2x - (1- lambda) y+ 3 lambda z= 0 is passing through the line of intersectoin of ...... Planes.
Answer» `2x-y = 0 , y-3Z = 0` `2x-y + 3z = 0 ,y=0` `2x-y+3z = 0,y - 3z = 0` NONE of these Answer :A

Discussion

4.	Find (dy)/(dx) of y = l og_2x
Answer» SOLUTION :`d/dx(log_2x)=1/(xlog2)`

Discussion

5.	If vecaveca=0andvecavecab=0 , then what can be concluded about the vectorvecb?
Answer» ANSWER :VECTOR `VECB` can be any vector

Discussion

6.	Show that the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-4)/(5)=(y-1)/(2)=z intersect. Also, find their point of intersection,Hint for solution : If shortest distance between two lines is zero then they are intersecting lines.
Answer» ANSWER :`=(-1,-1,-1)`

Discussion

7.	Determine order and degree (if defined) of differential equations y'' + 5y = 0
Answer» ANSWER :ORDER 2; DEGREE 1

Discussion

8.	Examine the consistency of the system of linear equtions in 1 to 6 x+2y=2 2x+3y=3
Answer» ANSWER :`-1 NE 0`

Discussion

9.	Find the range of values of the term independent of x in (x sin^(-1)p+(cos^(-1)p)/(x))^(10) where p in [-1, 1].
Answer» SOLUTION :N/A

Discussion

10.	I: The condition that the roots of x^(3) -px^(2) + qx - r = 0 are such that the sum of two of the roots is 0 is pq = r . II: The condition that ax^(4)+ bx^(3) + cx^(2) + dx + e = 0may have a pair of equal roots is ad^(2) = b^(2) e.
Answer» only I is TRUE only II is true both I and II are true NEITHER I nor II true Answer :3

Discussion

11.	For two events A and B, let P(A) = 3/5, P(B) = 2/3, then which of the following is correct?
Answer» `P(a cap BARB) LE (1)/(3)` `P(A CUP B) GE (2)/(3)` `(4)/(15) le P(A cap B) le (3)/(5)` `(1)/(10) leP(barA//B) le (3)/(5)` Answer :A::B::C::D

Discussion

12.	An instructor has a question bank consisting of 300 easy True/False questions, 200 difficult True/False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?
Answer» ANSWER :`(5)/(9)`

Discussion

13.	Prove that for 3 le" r " le n, ""^((n-3))C_(r)+.""^((n-3))C_((r-1))+3. ""^((n-3))C_((r-2))+""^((n-3))C_((r-3))=""^(n)C_(r).
Answer» ANSWER :`THEREFORE LHS = RHS`

Discussion

14.	If A and B are two independent events with P(A) =1/3 and P(B) = 1/4 , then P(B/A) is equal to
Answer» `1/4` `1/3` `3/4` 1 Answer :C

Discussion

15.	If for different values of alpha, the locus of point of intersection of two straight lines sqrt(3)ax+ay-4 sqrt(3)alpha=0is hyperbola with eccentricity e, then e is equal to
Answer» ANSWER :2.24

Discussion

16.	Bag A contains 4 white and 7 black balls. Bag B contains 5 white and 6 black balls. A die is rolled . If 2 or 5 turns up then choose bag A otherwise choose bag B. If one ball is drawn at random from the selected bag, then find the probability that it is black.
Answer» ANSWER :`(19)/(33)`

Discussion

17.	Find the magnitude of the vector :(1)/(sqrt(3))hat(i)+(1)/(sqrt(3))hat(j)-(1)/(sqrt(3))hat(k)
Answer» ANSWER :1

Discussion

18.	The straight lines whose direciton cosines are given by al + bm + cn = 0 , fmn + gnl + hlm = 0 if ............
Answer» `f/a + G/b + h/c = 0` `(a^2)/(f) + (b^2)/(g) + (c^2)/(h) = 0` `a^2(g + h) + b^2(h+g) + c^2(f + g)=0` NONE of these Answer :A

Discussion

19.	The matrix P=[{:(0,0,4),(0,4,0),(4,0,0):}]is a ………..
Answer» SQUARE matrix diagonal matrix unit matrix None Answer :A

Discussion

20.	int_(0)^(1)x(1-x)^(n)dx
Answer» ANSWER :`1/((n+1)(n+2))`

Discussion

21.	If ""^(-3) ^(n)C_(r+1) then-
Answer» `-sqrt3 le x le sqrt3` `-oo lt x lt -2` `2 lt x lt oo` `1/N +3 le x ^(2) le 4 (n GE 2)` ANSWER :D

Discussion

22.	Let A = ((a,b),(c,d)) ,a,b,c,d in R , a+d ne 4 . If A satisfies A^(2)-4A+3I_(2)=O_(2) then bc is equal to ______ .
Answer» ANSWER :`0.00`

Discussion

23.	Angle between tangents drawn from (0,-a) to parabola x^(2) =4ayis
Answer» `(PI)/(4)` `(pi)/(2)` `(pi)/(3)` `(pi)/(2)` Answer :B

Discussion

24.	The value of sum_(n=1)^(oo)(""^(n)C_(0)+.......+""^(n)C_(n))/(""^(n)P_(n))
Answer» `E^(2)` e `e^(2)-1` e - 1 Answer :C

Discussion

25.	Statement-I: If n si an odd interger greater then3 butnot a multiple of 3 , then (x+1)^(n)-x^(n)-1 is divisible by x^(3)+x^(2)=x. Statement - II: if nis an odd interger greater than 3 but not a multilpe of 3, we have 1+omega^(n)+omega^(2n)=0.
Answer» Statement -I is TRUE, Statement-II is true and Statement-II is a CORRECT EXPLANATION for Statement-I. Statement-I is true, Statement-II is true but Statement-II is not a correct explanation of Statement-I. Statement-I is true, Statement-II is false. Statement-I is false, Statement-II is true. Answer :C

Discussion

26.	Solve the following linear programming problem graphically: Maximise Z=4x+y subject to the constraints: x+yle50 3x+yle90 xge0, yge0
Answer» ANSWER :(30,0)

Discussion

27.	The value of hati.(hatjxxhatk)+hatj(hatixxhatk)+hatk(hatixxhatj)is
Answer» 0 `-1` 1 3 Answer :C

Discussion

28.	A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, scooter or by other means of transport are respectively (3)/(10), (1)/(5), (1)/(10) and (2)/(5). The probabilities that he will be late are (1)/(4), (1)/(3) and (1)/(12), if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he is late. What is the probability that he comes by train?
Answer» ANSWER :`(1)/(2)`

Discussion

29.	Consider the binary operation * : R xx R rarr R and o : R xx R rarr R defined as a * b = \|a-b\| and a o b = a, AA a, b in R. Is o distributive over * ? Justify your answer.
Answer» ANSWER :o is not DISTRIBUTIVE over *

Discussion

30.	In triangleABC, if ar (triangleABC)=8. Then, a^(2)sin(2B)+ b^(2)sin(2A) is equal to
Answer» 2 16 32 128 Answer :C

Discussion

31.	If any two chords be drawn through two points on major axis of an ellipse equidstant from centre, then tan((alpha)/(2))tan((beta)/(2))tan((gamma)/(2))tan((delta)/(2)) = _____, ( where alpha, beta, gamma, delta are ecentric angles of extremities of chords )
Answer» ANSWER :1

Discussion

32.	If a,b,c are real
Answer» a = b = C 2b = 3a + c `b^(2) = SQRT(ac//8)` none of these Answer :A

Discussion

33.	A buisness man gets a profit of Rs. 2800 with probability 0.5, loss of Rs. 5000 with probability 0.3. and neither profit nor loss with probability 0.2. Find mean of his income.
Answer» ANSWER :`-100`

Discussion

34.	Determine whether (t_n) is an arithmetic sequence if: t_n=an^2+bn
Answer» SOLUTION :`t_n=an^2+impliest_(N+1)=a(n+1)^2+B(n+1)impliest_(a+1)-t_a=a{(n+1)^2-n^2}+{n+1-n}=a(2n+1)+b` which is not INDEPENDENT of n. `THEREFORE(t_a)` is not an A.P.

Discussion

35.	If \|bar(x)\|=7.\|bar(y)\|=sqrt(2),bar(x)xx bar(y)=(6,2,3) then \|bar(x).bar(y)\|^(2)= ………. .
Answer» 98 7 147 49 Answer :D

Discussion

36.	If \|bar(a)\|=1 and bar(a)xx bar(b)=(1,2,3) then bar(a)xx[bar(a)xx(bar(a)xx bar(b))] = ……. .
Answer» (1, 2, 3) `(-1, -2, -3)` `(0, 0, 0)` (1, 0, 0) ANSWER :B

Discussion

37.	Find the area bounded by y=sinx,y=0,x=pi/2
Answer» SOLUTION :AREA = `int_0^(pi/2)sin x dx=[-COSX]_0^(pi/2)` = - COS`pi/2+cos theta=1`

Discussion

38.	Using the method of integration find the area bounded by the curve \|x\|+\|y\|= 1. [Hint: The required region is bounded by lines x + y = 1, x - y = 1, -x + y = 1 and -x -y =1].
Answer» ANSWER :2

Discussion

39.	A particle moves along the curve y=x^2+2x. Then the point on the curve such that x and y coordinates of the particle change with the same rate, is
Answer» (1, 3) `(1/2,5/2)` `(-1/2,-3/4)` `(-1,-1)` ANSWER :C

Discussion

40.	If vectors vec(a),vec(b),vec(c) are non-coplanar, then ([vec(a)+2vec(b).vec(b)+2vec(c).vec(c)+2vec(a)])/([vec(a).vec(b).vec(c)])=
Answer» 3 9 8 6 Answer :B

Discussion

41.	If int sqrt(x) logx dx = K.x^(3//2) f(x) + c then K,f(x) =
Answer» `(1)/(3), "log X "+ (2)/(3)` `(1)/(3), "log x "- (2)/(3)` `(2)/(3), "log x "+ (2)/(3)` `(2)/(3), "log x "- (2)/(3)` ANSWER :D

Discussion

42.	Findproducts : [[1,2],[3,4]][[1,3],[1,4]]
Answer» SOLUTION :`[[1,2],[3,4]][[1,3],[1,4]]` `=[[1.1+2.1""1.3+2.4],[3.1+4.1" "3.3+4.4]]=[[3,11],[7,25]]`

Discussion

43.	int e^(f(x)) dx = (x^(6))/(6) +C, find f(x).
Answer» SOLUTION :N/A

Discussion

44.	Determine the area of parallelogram whose adjacent sides are the vector 2hati,hatj
Answer» SOLUTION :LET `veca` = `2hati` and `vecb` = `hatj` Then AREA of the parallelogram whose adjacent sides are `veca` and `vecb` = `\|vecaxxvecb\|` = `\|2hatixxhatj\|` = `\|2hatk\|` = 2 sq. UNITS

Discussion

45.	x_(1),x_(2),….,x_(n) are n observations with mean vec(x) and standard deviation sigma. Match the items of List - I with those of List - II The correct answer is
Answer» `{:(A,B,C,D),("(i)","(V)","(II)","(III)"):}` `{:(A,B,C,D),("(i)","(IV)","(iii)","(ii)"):}` `{:(A,B,C,D),("(iii)","(v)","(iv)","(ii)"):}` `{:(A,B,C,D),("(iii)","(v)","(ii)","(i)"):}` Answer :C

Discussion

46.	If 2a+3b+c=0, " then " axx b +b xx c+c xx a is equal to
Answer» `6(bxxc)` `3(bxxc)` `2(bxxc)` 0 Solution :Given , `2a+3b+c=0` `RARR 2a+3b=-c` Taking cross product with a and b respectively, we GET `2(axxa)+3(AXXB)=axxc` `rArr 3(axxb)=cxxa` .....(ii) and `2(bxxa)+3(bxxb)=-bxxc` `rArr 2(axxb)=bxxc` ......(ii) Now , `axxb+bxxc+cxxa` `=axxb+bxxc+3(axxb)` `=4(axxb)+bxxc` `=2(bxxc)+bxxc` `=3(bxxc)` .

Discussion

47.	There are 14 Railway stations along a line. Number of ways of selecting 3 stations out of them to stop the train such that no two stops are adjacent is
Answer» 120 220 320 420 Answer :B

Discussion

48.	Evaluate int cos^(2) x dx
Answer» ANSWER :`(cos^(4)xsinx)/(5)+(4)/(15)cos^(2)xsinx+(8)/(15)sinx+c`

Discussion

49.	int (1)/(sqrt(x)(x + 9))dx =
Answer» `(2)/(3) tan^(-1)(SQRT(x))+ C ` `(2)/(3) tan^(-1) ((sqrt(x))/(3)) + c ` `3 tan^(-1) sqrt(x)+ c` `tan^(-1) ((sqrt(x))/(3)) + c ` ANSWER :B

Discussion

50.	Statement-1 : If n(A) = 3, n(B) = 6, then minimum number of elements in A cup B is 6. Statement-2 : A = {x\|x in R, \|x\| lt 2} and B = {x\| x in R,\|x\| ge 2}. If A cup B = C - R, then C = {x\| x in R, 2 ge x lt 3}. Statement-3: The range off(x) = 2^((x^(2) - 2)^(3) + 8) is [1, oo)
Answer» TFT TTF TTT TFF Answer :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Ifthe mean, variance, standard deviation of 3,4,5 are denoted by a,b,c then.

The plane 2x - (1- lambda) y+ 3 lambda z= 0 is passing through the line of intersectoin of ...... Planes.

Find (dy)/(dx) of y = l og_2x

If veca*veca=0andveca*vecab=0 , then what can be concluded about the vectorvecb?

Show that the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-4)/(5)=(y-1)/(2)=z intersect. Also, find their point of intersection,Hint for solution : If shortest distance between two lines is zero then they are intersecting lines.

Determine order and degree (if defined) of differential equations y'' + 5y = 0

Examine the consistency of the system of linear equtions in 1 to 6 x+2y=2 2x+3y=3

Find the range of values of the term independent of x in (x sin^(-1)p+(cos^(-1)p)/(x))^(10) where p in [-1, 1].

I: The condition that the roots of x^(3) -px^(2) + qx - r = 0 are such that the sum of two of the roots is 0 is pq = r . II: The condition that ax^(4)+ bx^(3) + cx^(2) + dx + e = 0may have a pair of equal roots is ad^(2) = b^(2) e.

For two events A and B, let P(A) = 3/5, P(B) = 2/3, then which of the following is correct?

Prove that for 3 le" r " le n, ""^((n-3))C_(r)+.""^((n-3))C_((r-1))+3. ""^((n-3))C_((r-2))+""^((n-3))C_((r-3))=""^(n)C_(r).

If A and B are two independent events with P(A) =1/3 and P(B) = 1/4 , then P(B/A) is equal to

If for different values of alpha, the locus of point of intersection of two straight lines sqrt(3)ax+ay-4 sqrt(3)alpha=0is hyperbola with eccentricity e, then e is equal to

Bag A contains 4 white and 7 black balls. Bag B contains 5 white and 6 black balls. A die is rolled . If 2 or 5 turns up then choose bag A otherwise choose bag B. If one ball is drawn at random from the selected bag, then find the probability that it is black.

Find the magnitude of the vector :(1)/(sqrt(3))hat(i)+(1)/(sqrt(3))hat(j)-(1)/(sqrt(3))hat(k)

The straight lines whose direciton cosines are given by al + bm + cn = 0 , fmn + gnl + hlm = 0 if ............

The matrix P=[{:(0,0,4),(0,4,0),(4,0,0):}]is a ………..

int_(0)^(1)x(1-x)^(n)dx

If ""^(-3) ^(n)C_(r+1) then-

Let A = ((a,b),(c,d)) ,a,b,c,d in R , a+d ne 4 . If A satisfies A^(2)-4A+3I_(2)=O_(2) then bc is equal to ______ .

Angle between tangents drawn from (0,-a) to parabola x^(2) =4ayis

The value of sum_(n=1)^(oo)(""^(n)C_(0)+.......+""^(n)C_(n))/(""^(n)P_(n))

Statement-I: If n si an odd interger greater then3 butnot a multiple of 3 , then (x+1)^(n)-x^(n)-1 is divisible by x^(3)+x^(2)=x. Statement - II: if nis an odd interger greater than 3 but not a multilpe of 3, we have 1+omega^(n)+omega^(2n)=0.

Solve the following linear programming problem graphically: Maximise Z=4x+y subject to the constraints: x+yle50 3x+yle90 xge0, yge0

The value of hati.(hatjxxhatk)+hatj*(hatixxhatk)+hatk*(hatixxhatj)is

Consider the binary operation * : R xx R rarr R and o : R xx R rarr R defined as a * b = |a-b| and a o b = a, AA a, b in R. Is o distributive over * ? Justify your answer.

In triangleABC, if ar (triangleABC)=8. Then, a^(2)sin(2B)+ b^(2)sin(2A) is equal to

If any two chords be drawn through two points on major axis of an ellipse equidstant from centre, then tan((alpha)/(2))tan((beta)/(2))tan((gamma)/(2))tan((delta)/(2)) = _____, ( where alpha, beta, gamma, delta are ecentric angles of extremities of chords )

If a,b,c are real

A buisness man gets a profit of Rs. 2800 with probability 0.5, loss of Rs. 5000 with probability 0.3. and neither profit nor loss with probability 0.2. Find mean of his income.

Determine whether (t_n) is an arithmetic sequence if: t_n=an^2+bn

If |bar(x)|=7.|bar(y)|=sqrt(2),bar(x)xx bar(y)=(6,2,3) then |bar(x).bar(y)|^(2)= ………. .

If |bar(a)|=1 and bar(a)xx bar(b)=(1,2,3) then bar(a)xx[bar(a)xx(bar(a)xx bar(b))] = ……. .

Find the area bounded by y=sinx,y=0,x=pi/2

Using the method of integration find the area bounded by the curve |x|+|y|= 1. [Hint: The required region is bounded by lines x + y = 1, x - y = 1, -x + y = 1 and -x -y =1].

A particle moves along the curve y=x^2+2x. Then the point on the curve such that x and y coordinates of the particle change with the same rate, is

If vectors vec(a),vec(b),vec(c) are non-coplanar, then ([vec(a)+2vec(b).vec(b)+2vec(c).vec(c)+2vec(a)])/([vec(a).vec(b).vec(c)])=

If int sqrt(x) logx dx = K.x^(3//2) f(x) + c then K,f(x) =

Findproducts : [[1,2],[3,4]][[1,3],[1,4]]

int e^(f(x)) dx = (x^(6))/(6) +C, find f(x).

Determine the area of parallelogram whose adjacent sides are the vector 2hati,hatj

x_(1),x_(2),….,x_(n) are n observations with mean vec(x) and standard deviation sigma. Match the items of List - I with those of List - II The correct answer is

If 2a+3b+c=0, " then " axx b +b xx c+c xx a is equal to

There are 14 Railway stations along a line. Number of ways of selecting 3 stations out of them to stop the train such that no two stops are adjacent is

Evaluate int cos^(2) x dx

int (1)/(sqrt(x)(x + 9))dx =

Statement-1 : If n(A) = 3, n(B) = 6, then minimum number of elements in A cup B is 6. Statement-2 : A = {x|x in R, |x| lt 2} and B = {x| x in R,|x| ge 2}. If A cup B = C - R, then C = {x| x in R, 2 ge x lt 3}. Statement-3: The range off(x) = 2^((x^(2) - 2)^(3) + 8) is [1, oo)

If vecaveca=0andvecavecab=0 , then what can be concluded about the vectorvecb?

The value of hati.(hatjxxhatk)+hatj(hatixxhatk)+hatk(hatixxhatj)is