28278 + Interview Questions in Maths in Class 12

1.	Write the principal value branch of f(x)=sin^(-1)x.
Answer» ANSWER :`ABS(X) GE 1`

Discussion

2.	If omega be the imaginary cube root of 1, the value of (7+11omega+3omega^(2))/(13+7omega+11omega^(2))+(7+11omega+13omega^(2))/(11+13omega+7omega^(2)) will be
Answer» 2 3 0 `-1` ANSWER :D

Discussion

3.	(x + 3y^(2))(dy)/(dx) = y ( y rt 0).
Answer» ANSWER :`X = 3Y^(2) + CY`

Discussion

4.	Blocks A and B each have same mass m=1 kg determine the largest horizontal force P(in newton) which can be appied to B so that A wil not slip up on B . Neglect any friction.
Answer» ANSWER :`15.00`

Discussion

5.	Let f(x)=f(x) f(y) for all x and y. If f(x) is continuous at x=1. then f(x) is continuous
Answer» `PHI` R `R-{0}` `R-{1}` ANSWER :B

Discussion

6.	Which statement is/are incorrect for given conplex ? Co(C_(2)O_(4))(en)Cl_(2)]^(-1)
Answer» Oxidation state of central ATOM is + 3. Coordination number of central atom is 4. Bidentate ligand and Monodentate ligand both are present in this complex. Ambidentate ligand and POSITIVE ligand are present in it. Solution :`[Co(C_(2)O_(4))(en)Cl_(2)]^(-1)` Oxidation state of Co x-2+0-2=-1 x=+3 `C_(2)O_(4)^(-2)` and en = bidentate ligand `Cl^(-)` = monodentate]

Discussion

7.	Express the 1-i points geometrically in the Argand plane.
Answer» SOLUTION :`1-i=(1,-1)`

Discussion

8.	Each side of DeltaABC is the polarof the opposite vertex with respect to a circle with centre P. For the DeltaABC the point P is
Answer» centroid circumcentre incentre orthocentre Answer :D

Discussion

9.	Find the derivative of the following functions with respect to x sqrt((x+1)/(x-1))
Answer» ANSWER :`(-1)/(SQRT(x+1) (x-1)^((3)/(2)))`

Discussion

10.	If \|{:(4-x,4+x,4+x),(4+x,4-x,4+x),(4+x,4+x,4-x):}\|=0 then find values of x
Answer» ANSWER :`thereforex=0" or "x=-12`

Discussion

11.	Differentiate the following w.r.t.x (cot^-1x)^2
Answer» SOLUTION :`d/dx[(cot^-1x)^2]=2cot^-1xd/dx(cot^-1x)=2cot^-1"X"XX(-1)/(1+x^2)=(-2cot^-1x)/(1+x^2)`

Discussion

12.	The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?
Answer» ANSWER :150

Discussion

13.	An aqueous solution containing1 M NiSO_(4) & 1 M S_(2) O_(8)^(2-) is electrolysed using palladium electrode, at 25^(@)C {:(Ni^(+2)+2e^(-) rarrNi,,E^(@)=-0.25 V),(2H^(+)+2e^(-)rarrH_(2),,E^(@)=0.00 V ),(O_(2)+4H^(+)+4e^(-)rarr2H_(2)O,,E^(@)=1.23 V),(Pd^(+2)+2e^(-) rarrPd,,E^(@) = 0.92 V),(S_(2)O_(8)^(2-)+2e^(-) rarr 2SO_(4)^(2-),,E^(@)=2 V):} pH of solution is 7. Select the correct statementon the basis of above given information. (Ignore over voltage & neglect variation ofE_(Pd^(+2)//Pd)^(@) with concentration)
Answer» REACTION at anode is `Pd rarr Pd^(+2)+2e^(-)` Reaction at anode is `2H_(2)O rarrO_(2)+4H^(+)+4e^(-)` Reaction at CATHODE is `Ni^(+2)+2e^(-) rarr Ni` Reaction at cathode is `2H^(+) + 2e^(-) rarrH_(2)` Answer :B::C

Discussion

14.	Prove that the chord joining pointsP(alpha) and Q (beta)on the ellipse subtends a right angle at the vertex A(a,0) then tan((alpha)/(2)) tan((beta)/(2))=(-b^(2))/(a^(2))
Answer» ANSWER :`-(B^(2))/(a^(2))`

Discussion

15.	The pair of tangents from origin to x^(2)+y^(2)+4x+2y-3=0 is
Answer» `(2x+y)^(2)=3(X^(2)+y^(2))` `(2x+y)^(2)=33(x^(2)+y^(2))` `(2x-y)^(2)=-3(x^(2)-y^(2))` not existing Answer :D

Discussion

16.	The curves y=x^3-3x^2-8x-4,y=3x^2+7x+4 touch at the point (-1, 0). The equation of the common tangent is
Answer» A and R are TRUE and R is the CORRECT EXPLANATION of A A and R are true and R is not correct explanation of A A is true but R is FALSE A is false but R is true Answer :A

Discussion

17.	Let f:[1,3]to[0,oo) be continuous and differentiabl function. If (f(3)-f(1))(f^(2)(3)+f^(2)(1)+f(3)f(1))=kf^(2)(c)f'(c) where c in (1,3), then the value of k is "_____"
Answer» ANSWER :6

Discussion

18.	The minimum value of z = 2x + 4y subject to constraints x+2y ge 10, 3x+y ge 10, x ge 0, y ge 0 is ………..
Answer» 20 40 Not exists 30 Answer :A

Discussion

19.	Let a, b, c be distinct non-negative numbers. If the vectors ahat(i)+ahat(j)+chat(k),hat(i)+hat(k),chat(i)+chat(j)+bhat(k) lie in a plane, then C is
Answer» A.M. of a, B G.M. of a, b H.M. of a, b zero Answer :B

Discussion

20.	Find the number of ways of forming a committee of 5 persons from a group of 4 Indians and 3 Russians such that there are atleast 3 Indians in the committee.
Answer» ANSWER :15

Discussion

21.	Discuss the continuity of the functionf(x) = \|x -1\|"at" x=1
Answer» Solution :By definition f(x) `{:{(x-1,XGE 1), (-(x-1), x lt1):}` CLEARLY, the function is DEFINED at 1 and f(1)=0 LEFT hand limit of at 1 is `underset(x to 1^(-))limf(x) = underset(x to1) LIM (-x+1)=0` Similarly the right hand limit of f at 1. is `underset(x to 1^(+))limf(x) = underset(x to 1^(+))lim ( x-1)=0 ` Thus, the left hand limit, right hand limit and the value of the function coincide at x =1 . Hence the function is continuous at x =1 .

Discussion

22.	A 10 kW transmitter emits radio waves of 500 m wavelength. The number of photons emitted per second by the transmitter is of the order of :-
Answer» `10^(25)` `10^(31)` `10^(43)` `10^(37)` SOLUTION :`E = N((HC)/(LAMBDA))`.

Discussion

23.	Evaluate the following inegrals int(x^(2)+2)/(x^(2)+1)dx
Answer» ANSWER :`x+tan^(-1)x+c`

Discussion

24.	Find all the points of discontinuity of the function f defined by {{:(x+2," if "x lt 1),(0," if "x=1),(x-2," if "x gt 1):}.
Answer» ANSWER :HENCE, x=1 is the only POINT of DISCONTINUITY of F.

Discussion

25.	If alpha and beta are the roots of x^(2)+x+1=0, then alpha^(16)+beta^(16)=
Answer» `(-1-isqrt3)/2` 1 -1 `(-1+isqrt3)/2` ANSWER :C

Discussion

26.	Let A and B be two sub-sets of C defined as follows: A = {z in C :(1+3i)z + (1-3i)barz=10} and B ={z in C : \|z\|=1}, then
Answer» `A CAP B = phi` `A = B` `A cap B` is a singleton `A cap B` CONSITS of EXACTLY two points. Answer :A

Discussion

27.	Let a=3^(1//224)+1 and for all n ge 3, let f(n)=""^(n)C_(0)a^(n-1)-""^(n)C_(1)a^(n-2)+""^(n)C_(2)a^(n-3)+...+(_1)^(n-1)""^(n)C_(n-1)a^(0). If the value of f(2016)+f(2017)=3^(k), the value of K is
Answer» 6 8 9 10 Answer :C

Discussion

28.	There are 2 locks on the door and the door keys are among the 6 differentones you carry in your pocket . In a hurry one key is dropped somewhere by you. The probability that you can still open the door is
Answer» `1//2` `4//9` `2//3` `1//4` ANSWER :C

Discussion

29.	The point (2a, a) lies inside the region bounded by the parabola x^(2) = 4y and its latus rectum. Then,
Answer» `0 LT=a lt=1` `0 lt a lt 1` `a gt 1` `a lt 0 ` ANSWER :B

Discussion

30.	Observe the following statements: statement I: The radical centre of S-=x^2+y^2-1=0 S' -= x^2+y^2+6x-2y-1=0 S''-=x^2+y^2-12x+4y-1=0 does not exist. statement II : The radical centre of three circles whose centers are collinear does not exist because radical axes of each pair of circles are parallel.
Answer» I is true, II is true, But II is not the CORRECT explaination for I I and II are true. II is correct EXPLANATION of I I is true, II is false I is false, II is true Answer :B

Discussion

31.	Find the domain and range of the following function : f : R rarr R , f(x) = -\|x\|
Answer» SOLUTION :N/A

Discussion

32.	Find k if the following pairs of circles are orthogonal x^(2)+y^(2)-6x-8y+12=0,x^(2)+y^(2)-8x+6y+k=0
Answer» ANSWER :`k=-24`

Discussion

33.	Refers to question 11. How many of circuit of type A and of type B, should be produced by the manufacture, so as to maximise hi profit? Determine the profit.
Answer» Solution :Referrein to solution 11, we have Maximise Z=50x+60y, subject to `2x+y le 20, x+2y le 12, x+3y le 15 , x ge 0, y ge 0` From the shaded region it is CLEAR that feasible region determine by the system of constraints is OABCD and is bouned and the COORDINATES of corner points are (0,0) (10,0), `((28)/(3),(4)/(3))`,(6,3)and (0,5) respectively. `"since" x+2y=12 and 2x+y=20 Rightarrow x=(28)/(3),y=(4)/(3)and x+3y=15 and x+2y=12 Rightarrow y=3 and x=6] Since, the manufacture is required to produce two types of CIRCUITS A and B it is clear that parts of resistor, transistor and capacitor cannot be in friction, so the required MAXIMUM profit is 480 where circuits of types B is 3.

Discussion

34.	An open top box of maximum possible volume from a square piece of tin of side 'a' is to be made by cutting equal squares out of the corners and then folding up the tin to form the sides.The length of a side of square cut out is
Answer» `a//6` `a//4` `a//3` `a//2` ANSWER :A

Discussion

35.	CaOCl_(2)overset(Delta)underset(CoCl_(2))rarrproduct, The product are
Answer» `CaCl_(2)` `O_(2)` `Ca(ClO_(3))_(2)` All of these Answer :AB

Discussion

36.	Examine the existence of the following limits:lim_(xto0+) log_ax
Answer» SOLUTION :`lim_(xto0+) log_ax` `lim_(hto0) log_ah=-infty` `THEREFORE` The LIMIT EXISTS.

Discussion

37.	Evalute the following integrals int e^(2 log" cot x")dx =
Answer» COT X - x + C cot x + x + c TAN x - x + c `-`cot x -x+c ANSWER :D

Discussion

38.	If R and S are two symmetric relation then
Answer» `R_(o)S` is SYMMETRIC RELATION `S_(o)R` is a symmetric relation `R_(o)S^(-)` is symmetric relation `R_(o)S` is a symmetric relation if and ONLYB if `R_(o)S S_(o)R` ANSWER :D

Discussion

39.	The number of ways in which a 7 people can sit around a round table is
Answer» `""^(16)C_(11)` `""^(16)C_(5)` `""^(16)C_(9)` `""^(20)C_(8)` Answer :C

Discussion

40.	The separate equations of the lines represented by the line equation (x+1)^(2)+(x+1)(y-2)-2(y-2)^(2)=0 are
Answer» `2x+y-4=0 and 5x-3y+1=0` `2x-y+4=0 and 5x+3y-1=0` `2x+y+4=0 and 5x-3y-1=0` `2x-y-4=0 and 5x+3y+1=0` ANSWER :B

Discussion

41.	Integrate the functions sqrt((1-sqrtx)/(1+sqrtx))
Answer» ANSWER :`-2sqrt(1-x)+COS^(-1)sqrtx+sqrt(x-x^(2))+C`

Discussion

42.	Find the value of c for which the vectors vec(a)=(c log_(2)x)hati-6hatj+3hatk and vec(b)=(log_(2)x)hati+2hatj+(2c log_(2)x)hatk makes an obtuse angle for any (x in 0, oo).
Answer» ANSWER :`C in (-(4)/(3),0)`

Discussion

43.	The sum of the first three terms of a G.P. is 16 and the sum of the next three terms is 128. (i) Determine the first term and common ratio. (ii) Find also the sum of n terms of the G.P.
Answer» ANSWER :(i) `a = 16/7` (II) `16/7 (2^(N) - 1)`

Discussion

44.	Let f :[1,oo] to[2,oo]differentiable function such that f (1) = 2 .If [1,oo] to[2,oo]
Answer» Solution :Given , f `(1)=(1)/(3)and6 int_(1)^(x)f(t)dt = 3xf (x) -x^(3),AAx le 1`Using Newton - Leibnitz formula. Differentiating both sides `rArr6(x)*1-0=3f(x)+3xf'(x)-3x^(2)` `RARR 3xf' (x) -3 f(x) = 3x^(2) rArr f' (x) -(1)/(x)f(x)=x` `rArr (xf'(x)-f'(x))/(x^(2))=1rArr (d)/(dx){(x)/(x)}=1` On INTEGRATING both sides , we get `rArr (f(x))/(x')=x+c`"" [`:' f(1)=(1)/(3)]` `(1)/(3)=1+crArrc=(2)/(3)ANDF(x)=x^(2)-(2)/(3)x` `:. f(2)=4-(4)/(3)=(8)/(3)` NOTEHere , f (1) = 2 , does not satisfy given function. `:. f(1) = (1)/(3)` For that f (x)`=x^(2)-(2)/(3)x andf(2)=4-(4)/(3)=(8)/(3)`

Discussion

45.	The normal at point P on a given parabola meet the axis of parabola at Q. Then prove that a line through Q and perpendicular to this normal always touches a fixed a parabola whose length of latusrectum is same as that of given parabola.
Answer» ANSWER :`y^2=4a(2a-x)`

Discussion

46.	Find the equation of circle passing through intersection points of line ax + by + c =0with coordinate axes and through origin.
Answer» ANSWER :` rArr AB ( x^(2) + y^(2))+ C ( bx+ ay ) = 0`

Discussion

47.	The simplified form of i^(n)+i^(n+1)+i^(n+2)+i^(n+3) is
Answer» 1)0 2)1 3)`-1` 4)i Answer :A

Discussion

48.	If the expansion in powers of x of the function (1)/((1-ax)(1-bx)) is a_(0)+a_(1)x+a_(2)x^(2)+a_(3)x^(3)+.....+a_(n) thencoefficient of x^(n) is
Answer» `(a^(N+1)-B^(n+1))/(b-a)` `(b^(n+1)-a^(n+1))/(b-a)` `(b^(n)-a^(n))/(b-a)` `(a^(n)-b^(n))/(b-a)` ANSWER :B

Discussion

49.	Evalute the following integrals int (x^(5))/(x^(3) - 1) dx
Answer» ANSWER :`(1)/(3)X^(3)+(1)/(3)log\|x^(3)-1\|+c`

Discussion

50.	Find Lt(n rarr oo) sum_(r=0)^(n-1)(1)/(sqrt(n^(2) - r^(2))
Answer» ANSWER :`(PI)/(2)`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Write the principal value branch of f(x)=sin^(-1)x.

If omega be the imaginary cube root of 1, the value of (7+11omega+3omega^(2))/(13+7omega+11omega^(2))+(7+11omega+13omega^(2))/(11+13omega+7omega^(2)) will be

(x + 3y^(2))(dy)/(dx) = y ( y rt 0).

Blocks A and B each have same mass m=1 kg determine the largest horizontal force P(in newton) which can be appied to B so that A wil not slip up on B . Neglect any friction.

Let f(x)=f(x) f(y) for all x and y. If f(x) is continuous at x=1. then f(x) is continuous

Which statement is/are incorrect for given conplex ? Co(C_(2)O_(4))(en)Cl_(2)]^(-1)

Express the 1-i points geometrically in the Argand plane.

Each side of DeltaABC is the polarof the opposite vertex with respect to a circle with centre P. For the DeltaABC the point P is

Find the derivative of the following functions with respect to x sqrt((x+1)/(x-1))

If |{:(4-x,4+x,4+x),(4+x,4-x,4+x),(4+x,4+x,4-x):}|=0 then find values of x

Differentiate the following w.r.t.x (cot^-1x)^2

The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?

Prove that the chord joining pointsP(alpha) and Q (beta)on the ellipse subtends a right angle at the vertex A(a,0) then tan((alpha)/(2)) tan((beta)/(2))=(-b^(2))/(a^(2))

The pair of tangents from origin to x^(2)+y^(2)+4x+2y-3=0 is

The curves y=x^3-3x^2-8x-4,y=3x^2+7x+4 touch at the point (-1, 0). The equation of the common tangent is

Let f:[1,3]to[0,oo) be continuous and differentiabl function. If (f(3)-f(1))(f^(2)(3)+f^(2)(1)+f(3)f(1))=kf^(2)(c)f'(c) where c in (1,3), then the value of k is "_____"

The minimum value of z = 2x + 4y subject to constraints x+2y ge 10, 3x+y ge 10, x ge 0, y ge 0 is ………..

Let a, b, c be distinct non-negative numbers. If the vectors ahat(i)+ahat(j)+chat(k),hat(i)+hat(k),chat(i)+chat(j)+bhat(k) lie in a plane, then C is

Find the number of ways of forming a committee of 5 persons from a group of 4 Indians and 3 Russians such that there are atleast 3 Indians in the committee.

Discuss the continuity of the functionf(x) = |x -1|"at" x=1

A 10 kW transmitter emits radio waves of 500 m wavelength. The number of photons emitted per second by the transmitter is of the order of :-

Evaluate the following inegrals int(x^(2)+2)/(x^(2)+1)dx

Find all the points of discontinuity of the function f defined by {{:(x+2," if "x lt 1),(0," if "x=1),(x-2," if "x gt 1):}.

If alpha and beta are the roots of x^(2)+x+1=0, then alpha^(16)+beta^(16)=

Let A and B be two sub-sets of C defined as follows: A = {z in C :(1+3i)z + (1-3i)barz=10} and B ={z in C : |z|=1}, then

Let a=3^(1//224)+1 and for all n ge 3, let f(n)=""^(n)C_(0)a^(n-1)-""^(n)C_(1)a^(n-2)+""^(n)C_(2)a^(n-3)+...+(_1)^(n-1)*""^(n)C_(n-1)*a^(0). If the value of f(2016)+f(2017)=3^(k), the value of K is

There are 2 locks on the door and the door keys are among the 6 differentones you carry in your pocket . In a hurry one key is dropped somewhere by you. The probability that you can still open the door is

The point (2a, a) lies inside the region bounded by the parabola x^(2) = 4y and its latus rectum. Then,

Find the domain and range of the following function : f : R rarr R , f(x) = -|x|

Find k if the following pairs of circles are orthogonal x^(2)+y^(2)-6x-8y+12=0,x^(2)+y^(2)-8x+6y+k=0

Refers to question 11. How many of circuit of type A and of type B, should be produced by the manufacture, so as to maximise hi profit? Determine the profit.

An open top box of maximum possible volume from a square piece of tin of side 'a' is to be made by cutting equal squares out of the corners and then folding up the tin to form the sides.The length of a side of square cut out is

CaOCl_(2)overset(Delta)underset(CoCl_(2))rarrproduct, The product are

Examine the existence of the following limits:lim_(xto0+) log_ax

Evalute the following integrals int e^(2 log" cot x")dx =

If R and S are two symmetric relation then

The number of ways in which a 7 people can sit around a round table is

The separate equations of the lines represented by the line equation (x+1)^(2)+(x+1)(y-2)-2(y-2)^(2)=0 are

Integrate the functions sqrt((1-sqrtx)/(1+sqrtx))

Find the value of c for which the vectors vec(a)=(c log_(2)x)hati-6hatj+3hatk and vec(b)=(log_(2)x)hati+2hatj+(2c log_(2)x)hatk makes an obtuse angle for any (x in 0, oo).

The sum of the first three terms of a G.P. is 16 and the sum of the next three terms is 128. (i) Determine the first term and common ratio. (ii) Find also the sum of n terms of the G.P.

Let f :[1,oo] to[2,oo]differentiable function such that f (1) = 2 .If [1,oo] to[2,oo]

The normal at point P on a given parabola meet the axis of parabola at Q. Then prove that a line through Q and perpendicular to this normal always touches a fixed a parabola whose length of latusrectum is same as that of given parabola.

Find the equation of circle passing through intersection points of line ax + by + c =0with coordinate axes and through origin.

The simplified form of i^(n)+i^(n+1)+i^(n+2)+i^(n+3) is

If the expansion in powers of x of the function (1)/((1-ax)(1-bx)) is a_(0)+a_(1)x+a_(2)x^(2)+a_(3)x^(3)+.....+a_(n) thencoefficient of x^(n) is

Evalute the following integrals int (x^(5))/(x^(3) - 1) dx

Find Lt(n rarr oo) sum_(r=0)^(n-1)(1)/(sqrt(n^(2) - r^(2))

Let a=3^(1//224)+1 and for all n ge 3, let f(n)=""^(n)C_(0)a^(n-1)-""^(n)C_(1)a^(n-2)+""^(n)C_(2)a^(n-3)+...+(_1)^(n-1)""^(n)C_(n-1)a^(0). If the value of f(2016)+f(2017)=3^(k), the value of K is