28278 + Interview Questions in Maths in Class 12

1.	Select the correct answer:Degree of (d^2y/(dx^2))^2+sin(dy/(dx))+x=0
Answer» `1` `1` `2` not defined Answer :D

Discussion

2.	Findpositive real numbers 'a' and 'b' such thatf(x) =ax-bx^(3) has four extrema on [-1,1] at each of which\|f(x)\|=1
Answer» ANSWER :`a=3 , b=4 `

Discussion

3.	The minimumvalueof7costheta+ 24 sinthetais
Answer» 25 `-25` `6` `0` ANSWER :D

Discussion

4.	If the roots of the equation sqrt((x)/(1-x))+sqrt((1-x)/(x))=(5)/(2) are p and q(q gt q) and the roots of the equation (p+q)x^(4)-pqx^(2)+(p)/(q)=0 are alpha,beta,gamma,delta, then (sum alpha)^(2)-sum alpha beta+alpha beta gamma delta=
Answer» 0 `(104)/(25)` `(25)/(4)` `(16)/(5)` ANSWER :B

Discussion

5.	int(x^(3m)+x^(2m)+x^(m))(2x^(2m)+3x^(n)+6)^(1//m)dx(xgt0)(m in N)
Answer» ANSWER :)`(1)/(6(m+1))[2x^(3M)+3x^(2m)+6x^(m)]^(m+1//m)+C`

Discussion

6.	Find the total number of times the digit '2' appears in the set of integers {1,2, ….2016}. For example, the digit '2' appears twice in the integer 229.
Answer» ANSWER :619

Discussion

7.	Integrate the following functions: sin^-1(cosx)
Answer» Solution :`sin^-1(cosx)` =`sin^-1 sin(pi/2-x) = pi/2-x` THEREFORE` INT sin^-1 (cosx) DX,` ` = pi/2x-x^2/2+c`

Discussion

8.	The middle term in the expansion of (x + 1/x)^(2n) is
Answer» `""^(2N)C_n` `""^(2n)C_nx ` `(""^(2n)C_n)/(X)` `""^(2n)C_(n-1)x ` ANSWER :A

Discussion

9.	A is one of 5 horses that entered the race and for it to be rided by one of the two jokeys P & Q and odds in favour of P rides it is 2 to 1. If P rides, A, all the horses are likely to win. If Q rides A, A' s chance of winning is tripled. The odds in favour of A's winning is
Answer» `1 : 3` `3 :1` `1 : 2` `2 : 1` ANSWER :C

Discussion

10.	Can a sum difference, product or quotient of irrational numbers be a rational number?
Answer» ANSWER :YES

Discussion

11.	Write down and simplify 6^("th") term in ((2x)/(3)+(3y)/(2))^(9)
Answer» SOLUTION :N/A

Discussion

12.	If x= a t^(2), y= 2 a t" then " (dy)/(dx) = …., where t ne 0
Answer» `(1)/(t)` t `-t` a Answer :A

Discussion

13.	If (2 le r le n) , then ""^(n)C_(r)+2""^(n)C_(r+1)+""^(n)C_(r+2) is equal to
Answer» `2.""^(N)C_(R+2)` `""^(n+1)C_(r+1)` `""^(n+2)C_(r+2)` `""^(n+1)C_(r)` ANSWER :C

Discussion

14.	If P(A) = 3/5P(B) = 1/5. Find P(A cap B) if A an B are independent events.
Answer» ANSWER :`3/25`

Discussion

15.	Find the vector equation of the plane passing through the intersection of the palnes vecr.(2hati+2hatj-hat3k) = 7, vecr.(2hati+5hatj+3hatk) = 9 and through the point (2, 1, 3)
Answer» ANSWER :LET the required EQUATION be `vecr.[(2hati+2hatj-3hatk)+LAMBDA(2hati+5hatj+3hatk)] = 7+9lambda`

Discussion

16.	If int e^(sqrt(x)) " dx = K.e"^(sqrt(x))f(x ) + c then K f(x) =
Answer» 2, `SQRT(X)- `1 `2 , sqrt(x) + 1` `2 , x + 1` `2 , x^(2) -1` ANSWER :A

Discussion

17.	A particle is acted upon by constant forces 4hati+hatj-3hatk and 3hati+hatj-hatk which displace it from a point hati+2hatj+3hatk to the point 5hati+4hatj+hatk. The work done in standard units by the forces is given by
Answer» 40 units 30 units 25units 15 units Solution :TOTAL force, `F = (4hati + hatj - 3hatk) + (3hati + hatj- hatk)` `F = 7hati +2hatj- 4hatk` The PARTICLEIS displacedfrom `A(hati + 2hatj + 3hatk) - (hati + 2hatj + 3hatk) = 4hati +2hatj- 2HATK` `:.` Work DONE`= F . AB=(7hati + 2hatj - 4hatk ). (4hati + 2hatj - 2hatk)` `= 28 + 4+ 8 = 40` units

Discussion

18.	Find the order and degree (it defined) of the differential equation((d^(2)y)/(dx^(2)) )^(3) + ((dy)/(dx))^(2) + sin ((dy)/(dx))+ 1 = 0 .
Answer» ANSWER :ORDER 2; DEGREE is not DEFINED.

Discussion

19.	Find the number of odd positive integral solutions of a + b + c + d = 20.
Answer» ANSWER :165

Discussion

20.	The value of x, where the function : f(x) = (tan x log (x-2))/(x^(2) - 4x + 3) is discontinuous, is given by :
Answer» `(- oo, 2)` `(-oo, 2) UU {3}` `(-oo, 2) uu {3, n pi + (pi)/(2), n ge 1}` NONE of these ANSWER :C

Discussion

21.	Find the following integrals int(ax^(2)+bx+c)dx
Answer» ANSWER :`a(x^(3))/(3)+b(x^(2))/(2)+cx+c_(1)`

Discussion

22.	Express the -3+ipoints geometrically in the Argand plane.
Answer» SOLUTION :`-3+i=(-3,1)`

Discussion

23.	If overline(a), overline(b), overline(c) are non-coplanar vectors and the points with position vectors 3overline(a)+4overline(b)-2overline(c), overline(a)+lambdaoverline(b)+3overline(c),overline(a)-6overline(b)+6overline(c) and 2overline(a)+3overline(b)-overline(c)are coplanar, the lambda=
Answer» `-2` `2` `-3` `3` ANSWER :A

Discussion

24.	If vec(a)=hati+2hatj+hatk and vec(b)=hati-2hatj-3hatk then (vec(a)+vec(b)*(vec(a)-vec(b)) = ………..
Answer» `-2` `-8` 8 2 Answer :B

Discussion

25.	Consider the curves C_1 : y^2 and C_2: x^2 +y^2-6x+1=0 Assertion(A) The common tangents to the curves C_1 and C_2 areothogonal. Reason ( R ) x-y+1=0 and x+y+1=0 are the common tangents to the curves C_1 and C_2 The correct answer is
Answer» (A) is true, (R ) is true and (R ) is the CORRECT EXPLANATION of (A) (A) is true , (R ) is true but (R ) is not a correct explanation of (A) (A) is true but ( R) is FALSE (A) is false but (R ) is true. ANSWER :A

Discussion

26.	Find the real values of theta , such that (3 + 2i sin theta)/(1 - 2i sin theta) is purely Real
Answer» ANSWER :A

Discussion

27.	A person who has been taken Maths or Computer can apply for M.Sc computer science
Answer» Solution :Here we MEAN that the students who have been taken both MATHS and COMPUTER science can apply for M.Sc somputer science , as well as the students who have taken only one of these subject . So , in this case , we are USING inclusive "OR"

Discussion

28.	What is the domain of the function sin^(2)x?
Answer» ANSWER :`[-1, 1]`

Discussion

29.	The value ofx + y + zis 15 if a, x, y, z, b are in A.P. while the value of(1)/(x) + (1)/(y) + (1)/(z) + (1)/(z) is (5)/(3)if a, x, y, z, b are in H.P. the value of a and b are
Answer» 9,1 7,4 8,2 `-1,3` ANSWER :1

Discussion

30.	(A) : The mod amplitude form of (1 + 7i)/((2- i)^(2)) is sqrt2 c is (3pi)/(4) (R) : The mod-amplitude form z = a+ ib is rcis thetawhere r = \|z\| , theta is amplitude of z
Answer» A is true , R is true and R correct explanation of A A is true , R is true and R is not correct EXPLANATIONOF A A is true , R is false A is false, R is true ANSWER :A

Discussion

31.	Find the transpose of each of each of the following matrics: [[-1,5,6],[sqrt3,5,6], [2,3,-1]]
Answer» SOLUTION :`[[-1,sqrt3,2], [5,5,3], [6,6,-1]]`

Discussion

32.	Choose the correct answer. Smaller area enclosed by the circle x^2+y^2 =4 and the line x+y=2 is:
Answer» `2(PI-2)` `pi-2` `2pi-1` `2(pi +2)` ANSWER :B

Discussion

33.	Find the sum 1 xx 2 xx .^(n)C_(1) + 2 xx 3xx .^(n)C_(2) + "….." + 2 xx (n+1) xx .^(n)C_(n).
Answer» Solution :METHODI : `1 xx 2 xx .^(n)C_(1)+ 2 xx 3 xx .^(n)C_(2) + "...." + n xx (n+1) xx .^(n)C_(n)` `= underset(r=1)OVERSET(n)sumr(r+1)..^(n)C_(r)` `= underset(r=1)overset(n)sum(r+1)[n..^(n-1)C_(r-1)]` `= n underset(r=1)overset(n)sum((r-1)+2).^(n-1)C_(r-1)` `= nxxunderset(r=1)overset(n)sum[(r-1)..^(n-1)C_(r-1)+2..^(n-1)C_(r-1)]` `= nxx n(n-1)underset(r=2)overset(n)sum.^(n-2)C_(r-2)+(2n)underset(r=1)overset(n)sum.^(n-1)C_(r-1)` `=n xx (n-1) xx 2^(n-2) + 2nxx 2^(n-1)` ` = n(n+3)xx2^(n-2)` Method II : We have `(1+x)^(n) = .^(n)C_(0) + .^(n)C_(1)x + .^(n)C_(2)x^(2) + "....." + .^(n)C_(n)x^(n)` Differentiatingw.r.t.x we get `n(1+x)^(n-1) = .^(n)C_(1) + 2 xx .^(n)C_(2)x + 3 xx .^(n)C_(3)x^(2)"....." + nxx .^(n)C_(n) xx x^(n-1)` Multipyingwith `x^(2)`,we have `n(1+x)^(n-1) x^(2) = .^(n)C_(1) x^(2) + 2 xx .^(n)C_(2)x^(3) + 3xx .^(n)C_(3)x^(4)"...."+n xx .^(n)C_(n)x^(n+1)` Differentiating w.r.t. ,we get `m(n-1)(1+x)^(n-2)x^(2) +2x xx n(1+x)^(n-1)` `= 2.^(n)C_(1)x + 2 xx 3xx .^(n)C_(2)x^(2) + 3 xx 4 xx .^(n)C_(3)x^(3) + "...." + n(n+1) xx .^(n)C_(n)x^(n)` Now putting ` x = 1`, we get `1 xx 2 xx .^(n)C_(1) + 2 xx 3 xx .^(n)C_(2) + "...." + n xx (n+1) xx .^(n)C_(n)` `= n (n+3) xx 2^(n-2)`

Discussion

34.	Find the equation of line of the shortest distancebetween the lines (x - 1)/( -2) = (y + 3)/( 2) = ( z - 4)/( -1) and (x + 3)/( 6) = (y - 2)/( 2) = (z + 5)/( 3)
Answer» Answer :`(x +(61)/(16))/(1)=(y-(41)/(20))/(0)=(z)/(-2)`

Discussion

35.	The value of p and q so that the function f(x) = {{:((1\|sin x\|)^((p)/(sin x)),(-pi)/(6) lt x lt 0),(e^((sin 2x)/(sin 3x)), 0 lt x lt (pi)/(6)):} is continuous at x = 0, are
Answer» <P>`p = (1)/(3), q = E^(2//3)` `p = 0, q = e^(2//3)` `p = (2)/(3), q = e^(-2//3)` `p = - (2)/(3), q = e^(2//3)` Answer :d

Discussion

36.	Find the area of the smaller region bounded by the ellipse (x^(2))/(9) + (y^(2))/(4) = 1 and the line (x)/(3) + (y)/(2) = 1
Answer» ANSWER :`3/2 (pi-2)`

Discussion

37.	f(x) = e^(-1//x^2) sin(1//x) for x ne 0 and f(0) =0 . The function f(x) is
Answer» DIFFERENTIABLE at x = 0 not differentiable at x = 0 INSUFFICIENT DATA None of these Answer :A

Discussion

38.	IfS_1 and S_2 are the foci of the hyperbola whose transverse axis length is 4 and conjugate axis length is 6,S_3 and S_4 are the foci of the conjugate hyperbola , then the area of the quadrilateral S_1, S_2 , S_3 ,S_4is
Answer» 24 26 22 12 Answer :B

Discussion

39.	Prove that .^(n)C_(0) + (.^(n)C_(1))/(2) + (.^(n)C_(2))/(3) + "……" + (.^(n)C_(n))/(n+1) = (2^(n+1)-1)/(n+1).
Answer» SOLUTION :Method I : We have `T_(R ) = (.^(n)C_(r-1))/(r ) = (.^(n+1)C_(r))/(n+1)` `:.`Requiredsum `= underset(r=1)overset(n+1)sumT_(r)` ` = underset(r=1)overset(n+1)sum(.^(n+1)CR)/(n+1)` ` = (.^(n+1)C_(1) + .^(n+1)C_(2) + "….." + .^(n+1)C_(n+1))/(n+1)` ` = ((.^(n+1)C_(0) + .^(n+1)C_(1) + .^(n+1)C_(2) + "......" + .^(n+1)C_(n+1))-1)/(n+1)` `= (2^(n+1) - 1)/(n+1)` Method II : We have `(1+X)^(n)= .^(n)C_(0) + .^(n)C_(1)x+.^(n)C_(2)x^(2)+"...."+.^(n)C_(n)x^(n)` ` :. underset(0)overset(1)INT(1+x)^(n)dx = underset(0)overset(1)int(.^(n)C_(0) + .^(n)C_(1)x+.^(n)C_(2)x^(2) + "...." + .^(n)C_(n)x^(n))dx` `rArr [((1+x)^(n+1))/(n+1)]_(0)^(1)=[.^(n)C_(0)x+(.^(n)C_(1)x^(2))/(2)+(.^(n)C_(2)x^(3))/(3) + "....."+ (.^(n)C_(n)x^(n+1))/(n+1)]_(0)^(1)` `rArr (2^(n+1))/(n+1) -1/(n+1)=.^(n)C_(0)+(.^(n)C_(1))/(2)+(.^(n)C_(2))/(3)+ "......" + (.^(n)C_(n))/(n+1)`

Discussion

40.	Every body in a room shakes hands with every body else. The total number of hand shakes is 66. The total number of persons in the room is
Answer» 11 12 13 14 Answer :B

Discussion

41.	The mapping f: R rarrR , g, R rarr R are defined by f(x) = 5-x^2and g(x)=3x -4, then find the value of (fog)(-1)
Answer» 40 `-44` `-40` `-45` ANSWER :B

Discussion

42.	If two points are taken on the mirror axis of the ellipse (x^(2))/(25)+(y^(2))/(9)=1 at the same distance from the centre as the foci, then the sum of the sequares of the perpendicular distance from these points on any tangent to the ellipse is
Answer» 25 18 50 80 Answer :C

Discussion

43.	Integrate the following functions w.r.t.x (e^(5logx) - e^(4logx))/(e^(3logx) - e^(2logx))
Answer» SOLUTION :`(E^(5 logx) - e^(4 logx))/(e^(3 logx) -e^(2logx)) = (x^5-x^4)/(x^3-x^2)` =`(x^2(x^3-x^2))/(x^3-x^2) = x^2` `e^(a logx) = e^(logx^a) = x^a` therefore The REQUIRED integral =`int x^2 dx = x^3/3 +C`

Discussion

44.	a gt 1is a real numberf(x) = log_(a)x^2 , where x gt 0 If f^(-1)(x) is a inverse of f(x) andb and c are real numbers then f^(-1) (b+c) = ......
Answer» `F^(-1)(B) .f^(-1)(C)` `f^(-1)(b)+f^(-1)(c)` `1/(f(b+))` NONE of these Solution :N/A

Discussion

45.	( sin 70^(@) + cos 40^(@) )/( cos 70^(@) + sin 40^(@))=
Answer» 3 `SQRT(3)` `1/(sqrt(3))` `1//2` ANSWER :B

Discussion

46.	T_m denotesthenumber of trianglesthat can beformedwiththe verticesof aregularpolygonof msides. If T_(m+1)- T_m=15thenm=
Answer» 3 6 9 12 Answer :B

Discussion

47.	Find two positive numbers x and y such that x+y=60 and xy^(3) is maximum.
Answer» ANSWER :15 and 45

Discussion

48.	intdx/(cos^2x)
Answer» SOLUTION :`INT(DX)/(cos^2x)`=`intsec^2xdx=tanx+C`

Discussion

49.	Four persons A,B,C,D cut a pack of 52 cards successively in that order given. If the person who cuts a spade first wins, find their probability of winning.
Answer» ANSWER :`(27)/(175)`

Discussion

50.	(y''')^(2) + (y'')^(3) + (y')^(4) + y^(5) = 0
Answer» ANSWER :ORDER 3; DEGREE 2

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Select the correct answer:Degree of (d^2y/(dx^2))^2+sin(dy/(dx))+x=0

Findpositive real numbers 'a' and 'b' such thatf(x) =ax-bx^(3) has four extrema on [-1,1] at each of which|f(x)|=1

The minimumvalueof7costheta+ 24 sinthetais

If the roots of the equation sqrt((x)/(1-x))+sqrt((1-x)/(x))=(5)/(2) are p and q(q gt q) and the roots of the equation (p+q)x^(4)-pqx^(2)+(p)/(q)=0 are alpha,beta,gamma,delta, then (sum alpha)^(2)-sum alpha beta+alpha beta gamma delta=

int(x^(3m)+x^(2m)+x^(m))(2x^(2m)+3x^(n)+6)^(1//m)dx(xgt0)(m in N)

Find the total number of times the digit '2' appears in the set of integers {1,2, ….2016}. For example, the digit '2' appears twice in the integer 229.

Integrate the following functions: sin^-1(cosx)

The middle term in the expansion of (x + 1/x)^(2n) is

A is one of 5 horses that entered the race and for it to be rided by one of the two jokeys P & Q and odds in favour of P rides it is 2 to 1. If P rides, A, all the horses are likely to win. If Q rides A, A' s chance of winning is tripled. The odds in favour of A's winning is

Can a sum difference, product or quotient of irrational numbers be a rational number?

Write down and simplify 6^("th") term in ((2x)/(3)+(3y)/(2))^(9)

If x= a t^(2), y= 2 a t" then " (dy)/(dx) = …., where t ne 0

If (2 le r le n) , then ""^(n)C_(r)+2""^(n)C_(r+1)+""^(n)C_(r+2) is equal to

If P(A) = 3/5P(B) = 1/5. Find P(A cap B) if A an B are independent events.

Find the vector equation of the plane passing through the intersection of the palnes vecr.(2hati+2hatj-hat3k) = 7, vecr.(2hati+5hatj+3hatk) = 9 and through the point (2, 1, 3)

If int e^(sqrt(x)) " dx = K.e"^(sqrt(x))f(x ) + c then K f(x) =

A particle is acted upon by constant forces 4hati+hatj-3hatk and 3hati+hatj-hatk which displace it from a point hati+2hatj+3hatk to the point 5hati+4hatj+hatk. The work done in standard units by the forces is given by

Find the order and degree (it defined) of the differential equation((d^(2)y)/(dx^(2)) )^(3) + ((dy)/(dx))^(2) + sin ((dy)/(dx))+ 1 = 0 .

Find the number of odd positive integral solutions of a + b + c + d = 20.

The value of x, where the function : f(x) = (tan x log (x-2))/(x^(2) - 4x + 3) is discontinuous, is given by :

Find the following integrals int(ax^(2)+bx+c)dx

Express the -3+ipoints geometrically in the Argand plane.

If overline(a), overline(b), overline(c) are non-coplanar vectors and the points with position vectors 3overline(a)+4overline(b)-2overline(c), overline(a)+lambdaoverline(b)+3overline(c),overline(a)-6overline(b)+6overline(c) and 2overline(a)+3overline(b)-overline(c)are coplanar, the lambda=

If vec(a)=hati+2hatj+hatk and vec(b)=hati-2hatj-3hatk then (vec(a)+vec(b)*(vec(a)-vec(b)) = ………..

Consider the curves C_1 : y^2 and C_2: x^2 +y^2-6x+1=0 Assertion(A) The common tangents to the curves C_1 and C_2 areothogonal. Reason ( R ) x-y+1=0 and x+y+1=0 are the common tangents to the curves C_1 and C_2 The correct answer is

Find the real values of theta , such that (3 + 2i sin theta)/(1 - 2i sin theta) is purely Real

A person who has been taken Maths or Computer can apply for M.Sc computer science

What is the domain of the function sin^(2)x?

The value ofx + y + zis 15 if a, x, y, z, b are in A.P. while the value of(1)/(x) + (1)/(y) + (1)/(z) + (1)/(z) is (5)/(3)if a, x, y, z, b are in H.P. the value of a and b are

(A) : The mod amplitude form of (1 + 7i)/((2- i)^(2)) is sqrt2 c is (3pi)/(4) (R) : The mod-amplitude form z = a+ ib is rcis thetawhere r = |z| , theta is amplitude of z

Find the transpose of each of each of the following matrics: [[-1,5,6],[sqrt3,5,6], [2,3,-1]]

Choose the correct answer. Smaller area enclosed by the circle x^2+y^2 =4 and the line x+y=2 is:

Find the sum 1 xx 2 xx .^(n)C_(1) + 2 xx 3xx .^(n)C_(2) + "….." + 2 xx (n+1) xx .^(n)C_(n).

Find the equation of line of the shortest distancebetween the lines (x - 1)/( -2) = (y + 3)/( 2) = ( z - 4)/( -1) and (x + 3)/( 6) = (y - 2)/( 2) = (z + 5)/( 3)

The value of p and q so that the function f(x) = {{:((1|sin x|)^((p)/(sin x)),(-pi)/(6) lt x lt 0),(e^((sin 2x)/(sin 3x)), 0 lt x lt (pi)/(6)):} is continuous at x = 0, are

Find the area of the smaller region bounded by the ellipse (x^(2))/(9) + (y^(2))/(4) = 1 and the line (x)/(3) + (y)/(2) = 1

f(x) = e^(-1//x^2) sin(1//x) for x ne 0 and f(0) =0 . The function f(x) is

IfS_1 and S_2 are the foci of the hyperbola whose transverse axis length is 4 and conjugate axis length is 6,S_3 and S_4 are the foci of the conjugate hyperbola , then the area of the quadrilateral S_1, S_2 , S_3 ,S_4is

Prove that .^(n)C_(0) + (.^(n)C_(1))/(2) + (.^(n)C_(2))/(3) + "……" + (.^(n)C_(n))/(n+1) = (2^(n+1)-1)/(n+1).

Every body in a room shakes hands with every body else. The total number of hand shakes is 66. The total number of persons in the room is

The mapping f: R rarrR , g, R rarr R are defined by f(x) = 5-x^2and g(x)=3x -4, then find the value of (fog)(-1)

If two points are taken on the mirror axis of the ellipse (x^(2))/(25)+(y^(2))/(9)=1 at the same distance from the centre as the foci, then the sum of the sequares of the perpendicular distance from these points on any tangent to the ellipse is

Integrate the following functions w.r.t.x (e^(5logx) - e^(4logx))/(e^(3logx) - e^(2logx))

a gt 1is a real numberf(x) = log_(a)x^2 , where x gt 0 If f^(-1)(x) is a inverse of f(x) andb and c are real numbers then f^(-1) (b+c) = ......

( sin 70^(@) + cos 40^(@) )/( cos 70^(@) + sin 40^(@))=

T_m denotesthenumber of trianglesthat can beformedwiththe verticesof aregularpolygonof msides. If T_(m+1)- T_m=15thenm=

Find two positive numbers x and y such that x+y=60 and xy^(3) is maximum.

intdx/(cos^2x)

Four persons A,B,C,D cut a pack of 52 cards successively in that order given. If the person who cuts a spade first wins, find their probability of winning.

(y''')^(2) + (y'')^(3) + (y')^(4) + y^(5) = 0