28278 + Interview Questions in Maths in Class 12

1.	The locus of mid points of the chords of theellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1which pass through foot of a directrix
Answer» ANSWER :`(XE)/(A)=(X^(2))/(a^(2))+(y^(2))/(B^(2))`

Discussion

2.	The sum of the fourth powers of the roots of the equation x^(3)- x^(2) -2x + 2=0 is:
Answer» ANSWER :9

Discussion

3.	If I_(1),I_(2),I_(3) are the intercept on x-axis, y-axis, y=x w.r.t x^(2)+y^(2)-14x-10y+24=0 then
Answer» `I_(2)gtI_(3)gtI_(1)` `I_(3)gtI_(1)gtI_(2)` `I_(1)gtI_(3)gtI_(2)` `I_(3)gtI_(2)gtI_(1)` ANSWER :B

Discussion

4.	IFalpha , betaare therootsofx^2 +px +q=0and also ofx^(2n)+P^n x^n + q ^n=0andif( alpha )/(beta ), ( beta ) /( alpha)arethe rootsofx^n+ 1 + (x +1)^n =0thenn is
Answer» anoddinteger EN eveninteger ANYINTEGER NONE of these ANSWER :B

Discussion

5.	int (dx)/(x^(2) sqrt(4 + x^(2)))=
Answer» `(1)/(4) sqrt(4 + X^(2)) + C ` `(-1)/(4) sqrt(4 + x^(2)) + c ` `(-1)/(4x) sqrt(4 + x^(2)) + c ` `(9)/(4x) sqrt(4 + x^(2)) + c ` ANSWER :C

Discussion

6.	Principle of mathematical induction is used
Answer» to prove any STATEMENT to prove results which are TRUE for all real numbers to prove that statements which are FORMULATED in terms of n, where n is positive INTEGER None of these ANSWER :C

Discussion

7.	y= int_(x)^(x^(2)) sqrt(5-t^(2))dt then the value of (dy)/(dx) at x= sqrt(2) is
Answer» `1-sqrt(3)` `sqrt(3)(2 sqrt(6) -1)` `2sqrt(2)-sqrt(3)` `2sqrt(2)+sqrt(3)` ANSWER :C

Discussion

8.	Write{1,2,3,4,5}set in the intention(or specification form).
Answer» SOLUTION :`{X:xin N , LE x le 5}`

Discussion

9.	The sum of the digits in the unit's place of all the 4-digit numbersformed by using the numbers 3,4,5 and 6 withoutrepetitionis
Answer» 432 108 36 18 Answer :B

Discussion

10.	Find all zeros of the polynomial x^6-3x^5-5x^4+22x^3-39x^2-39x+135 , if it is known that 1 + 2i and sqrt3 are two of its zeros.
Answer» ANSWER :`(1pmsqrt37)/2`

Discussion

11.	(i) int(2x-5x) (3+2x) (1-x) dx, (ii) int sqrt(x) (ax^(2) + bx + c) dx (iii) int (sqrtx - 3sqrt(x^(4)) + 7/(3sqrt(x^(2))) - 6e^(x) + 1) dx
Answer» SOLUTION :N//A

Discussion

12.	India and Pakistan play a series of 'n' one day matches and probability than India wins a match against Pakistan is 1/2. For n = 7, probadility that India wins atleast three conseutive matches is
Answer» `4/2^7` `17/2^6` `47/2^7` None Answer :B

Discussion

13.	India and Pakistan play a series of 'n' one day matches and probability than India wins a match against Pakistan is 1/2. If 'n' is not fixed and series ends when any one of the team completes its 4^(th) win then probability that India wins the series is
Answer» `4/2^7` `47/2^7` `47/2^6` None Answer :C

Discussion

14.	India and Pakistan play a series of 'n' one day matches and probability than India wins a match against Pakistan is 1/2. If n = 7, them probability that India wins atleast three consercutive matches is
Answer» `17/2^6` `47/2^7` `47/2^6` None Answer :B

Discussion

15.	A set of lines x+y-2+lambda_(1)(2x+y-3)=0 represents incident rays on ellipse S=0 and 2x+3y-23+lambda_(2)=0 represents the set of refelction rays from the ellipse where lambda_(1), lambda_(2) in R. If P(3,7) is a point on the ellipse normal at which meets the major axis at N.
Answer» Elecentriciy of ELLIPSE is `SQRT((5)/(2sqrt(5)+1))` N divides line segment JOINING two foci in the ratio `2 sqrt(2):1` Area of triangle formed by point P and two foci 5 Elecentricity of ellips is `(sqrt(5))/(2sqrt(2)+1)` Answer :A::B::C

Discussion

16.	There are 4 mangoes, 3 apples, 2 oranges in a bag, fruits of the same variety being identical. In how many different ways can a selection of fruits be made if atleast one of each kind is to be selected
Answer» ANSWER :24

Discussion

17.	There are 4 mangoes, 3 apples 2 oranges in bag, fruits of the same variety being identical. In how many different ways can a selection of fruits be made if atleast one fruit is to be selected.
Answer» ANSWER :48

Discussion

18.	((2+3i)/(2-3i))-((2-3i)/(2+3i)) in the form of a + ib
Answer» `(24I)/(13)` `(27i)/(13)` `(28I)/(13)` `(30i)/(13)` ANSWER :A

Discussion

19.	If ax^2+2hxy+by^2+2gx+2fy+c=0 represents two parallel lines then prove that af^2=bg^2.
Answer» ANSWER :`"BG"^(2)`

Discussion

20.	Let f(x) = {((tan x - cot x)/(x-pi/4), ",", x != pi/4),(a, ",",x = pi/4):} The value of a so that f(x) is continuous at x = (pi)/4, is
Answer» 2 4 3 1 Answer :B

Discussion

21.	If a_r is the coefficient x^r in the expansion of (1+x+x^2)^n then a_1 - 2a_2 + 3a_3 -…..-2na_(2n) =
Answer» 0 N `-n` 2n Answer :C

Discussion

22.	A long cylinderical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis. The liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotatins per second, then the difference in the heights between the centre and the sides, in cm. will be :
Answer» `2.0` `0.1` `0.4` `1.2` SOLUTION :NA

Discussion

23.	Line 4x+5y-7=0 meets the coordinate axes at A and B. Through the mid - point of AB a line is drawn perpendicular to it meeting the line 2x+y=0 at Q(alpha, beta), the value of 1//alpha-1//beta is equal to
Answer» ANSWER :60

Discussion

24.	If the curves ax^(2)+by^(2)=1 and a'x^(2)+b'y^(2)=1 are orthogonally then …………
Answer» `(1)/(a)-(1)/(B)=(1)/(a')-(1)/(b')` `(1)/(a)+(1)/(b)=(1)/(a')+(1)/(b')` `(1)/(b)-(1)/(b)=(1)/(a')+(1)/(b')` `(1)/(a)+(1)/(b)=(1)/(a')-(1)/(b')` ANSWER :B

Discussion

25.	Using integration find the area of the region which is bounded bt x-axisthe tangent and normal to the circle x^(2)+y^(2)=4 drawn at (1,sqrt3).
Answer» ANSWER :`2SQRT3`.

Discussion

26.	Choose the correct answer int (sin^2x-cos^2x)/(sin^2x cos^2x) dxa)tanx+cotx+cb)tanx+cosecx+cc)cotx-tanx+c d) tanx+secx+c
Answer» tanx+cotx+c tanx+cosecx+c -tanx+cotx+c tanx+secx+c Answer :A

Discussion

27.	int_(0)^(pi//2) sin^8 xcos^2 xdx is equal to
Answer» `pi/512` `3pi/512` `5pi/512` `7pi/512` ANSWER :D

Discussion

28.	EvaluateP(A cup B), if 2P(A) = P(B)=(5)/(13) and P(A\|B)=(2)/(5)
Answer» ANSWER :`(11)/(26)`

Discussion

29.	Find thearea of theregionboundedbycirclex^2+y^2= 8xandparabolay^2 = 4x.
Answer» ANSWER :`32/3 SQ. UNIT

Discussion

30.	Evaluate : int_(0)^(pi/2)cos^(2)xdx.
Answer» ANSWER :`pi/4`

Discussion

31.	The radical centre of the circle x^2 + y^2 + 4x + 7 =0, 2 x^2 + 2y^2 + 3x + 5y+ 9 =0 and x^2 + y^2 + y =0 is
Answer» `( -2 , -1)` `( -2, 1)` `( 2, -1)` `(2, 1)` ANSWER :A

Discussion

32.	f(x) satisfies the relation f(x)-lamda int_(0)^(pi//2)sinxcostf(t)dt=sinx If f(x)=2 has the least one real root, then
Answer» `LAMDA EPSILON[1,4]` `lamda epsilon[-1,2]` `lamda epsilon[0,1]` `lamda epsilon [1,3]` Solution :`f(X)-lamda int_(0)^(pi//2)sinx COST f (t) dt=sinx` or `f(x)-lamda sinx int_(0)^(pi//2) cost f(t)dt=sinx` or `f(x)=Asinx=sinx` or `f(x)=(A+1)sinx` where `A=lamdaint_(0)^(pi//2) cost f(t)dt` or `A=lamda int_(0)^(pi//2) cos (A+1)sin dt` `=(lamda(A+1))/2int_(0)^(pi//2) sin 2tdt` `=(lamda(A+1))/2[(-cos 2t)/2]_(0)^(pi//2)` `=(lamda(A+1))/2` `:. A=(lamda)/(2-lamda)` `:.f(x)=((lamda)/(2-lamda)+1)sinx=(2/(2-lamda))sinx` `(2/(2-lamda))sinx=2` or `sinx=(2-lamda)` or `\|2-lamda\|le1` or `-1le lamda-2le 1` or `1 le lamda le 3` `int_(0)^(pi//2) f(x)dx=3` or `int_(0)^(pi//2) 2/(2-lamda) sinxdx=3` or `-[2/(2-lamda) cosx]_(0)^(pi//2) =3` or `2/(2-lamda)=3`

Discussion

33.	Out of 10 persons sitting at a round table, three persons are selected at random then the probability that no two of them are consecutive is
Answer» `(7)/(12)` `(7)/(10)` `(5)/(7)` `(5)/(12)` ANSWER :D

Discussion

34.	Let S = sum _(r=1)^(30) (""^(30+r)C_(r) (2r-1))/(""^(30)C_(r)(30+r)),K=sum_(r=0)^(30) (""^(30)C_(r))^(2) and G=sum_(r=0)^(60) (-1)^(r)(""^(60)C_(r) )^(2) The value fo (G-S)is
Answer» 0 1 `2^(30)` `2^(60)` Solution :`because S = sum _(R=1)^(30) (""^(30+r)C_(r) (2r-1))/(""^(30)C_(r)(30+r))=sum_(r=0)^(30) (""^(30+r)C_(r))/(""^(30)C_(r))(1-(30-r+1)/(30+r))` `=sum_(r=0)^(30)[ (""^(30+r)C_(r))/(""^(30)C_(r)) -(""^(30+r)C_(r))/(""^(30)C_(r))cdot ((30-r+1))/((30+r))]` `=sum_(r=0)^(30)[ (""^(30+r)C_(r))/(""^(30)C_(r)) -""^((30+r)/(r)cdot ^(29+r)C_(r-1))/(""^(30)C_(r))cdot ((30-r+1))/(30+r)]` `=sum_(r=0)^(30)[ (""^(30+r)C_(r))/(""^(30)C_(r)) -( ""^(29+r)C_(r-1))/(""^(30)C_(r-1)) ][because (""^(n)C_(r))/(""^(n)C_(r-1))=(n-r+1)/r]` For n = 30 `((31-r)/rcdot ""^(30)C_(r)=""^(30)C_(r-1))` `=(""^(30+30)C_(30))/ (""^(30)C_(30)) - (""^(29-1)C_(0))/(""^(30)C_(0))= ""^(60)C_(30)-1` `K = sum _(r=1) ^(30) (""^(30)C_(r))^(2) = ""^(60)C_(30) and G = sum_(r=0)^(60) (-1)^(r) (""^(60)C_(r))^(2)` `(""^(60)C_(0))^(2) - (""^(60)C_(1))^(2)+(""^(60)C_(2))^(2)-...+(""^(60)C_(60))=""^(60)C_(30)` [`because n=60` is even ] `G-S = "" ^(60)C_(1) - ("" ^(60)C_(30)-1) =1`

Discussion

35.	Find the mean deviation from the median for the following data (##VIK_MAT_IIA_QB_C08_SLV_004_Q01.png" width="80%">
Answer» ANSWER :`4.97`

Discussion

36.	Show that for a ge 1, f(x)=sqrt(3)sin x - cos x - 2ax + b is decreasing in R.
Answer» ANSWER :`F'(X)LE0`

Discussion

37.	The point on the curve y = x ^(2) + 4x + 3 which is nearest from the line y = 3x + 2 is
Answer» `((1)/(2), (5)/(4))` `(-(1)/(2), (5)/(4))` `(2, -(5)/(3))` `(2, (5)/(3))` ANSWER :B

Discussion

38.	How many of the following orders are correct ? (a) H – F lt H – Cl lt H – Br lt H – I (Bond length) (b) H – F lt H – Cl lt H – Br lt H – I (Acidic strength) (c) H – F lt H – Br lt H – Cl lt H – F (Bond strength) (d) H – F gt H – Cl gt H – Br gt H – I (thermodynamic stability) (e) H – F lt H – Cl lt H – Br lt H – I (reducing power) (f) H – F gt H – I gt H – Br gt H – Cl (Melting Point) (g) H – F gt H – I gt H – Br gt H – Cl (Boiling point)
Answer» Solution :CORRECT ORDER of MELTING point is : `HI GT HF gt HBR gt HCI`

Discussion

39.	A regular polygon of 10 sides is constructed No. of ways 3 vertices be selected so that no two vertices are consecutive is
Answer» 40 50 60 45 Answer :B

Discussion

40.	If ""^(18)C_(15)+2(""^(18)C_(16))"+"^(17)C_(16)+1=""^(n)C_(3) then n is
Answer» 19 20 18 24 Answer :B

Discussion

41.	Transform the equation 3x+4y+12=0 into slope intercept form
Answer» ANSWER :`(4)/(3)x+4`

Discussion

42.	A curve passes through the poit (5,3) and at any point (x,y) on it the product of its slope and the ordinate is equal to abscissa of the curve is
Answer» parabola ellipse hyperbola circle Answer :C

Discussion

43.	Expand(i) (x/3+3y/2)^(5) ,(ii)(x^(2)+2/x)^(4) using pascle's triangle.
Answer» ANSWER :`(x^(5))/(32)+(15X^(4)y)/(32)+(45X^(3)y^(2))/(16)+(135x^(2)y^(3))/(16)+(405xy^(4))/(32)+(243y^(5))/(32)`

Discussion

44.	int_(0)^(2pi)(1)/(1+e^(sinx))dx=
Answer» ANSWER :`PI`

Discussion

45.	Let F: R to Rbe definedbyf(x)={:{ (alpha + (sin[x])/x , " if "x gt 0), ( 2, " if " x =0), ( beta + [ (sin x-x)/x^(3)] ,"if " x lt 0):} where, [x]denotes the integral part of x. If f continuousat x =0,thenbeta = alphais equal to
Answer» `-1` 1 0 2 Answer :B

Discussion

46.	Let T_(n) denote the number of triangles which can be formed by using the vertices of a regular polygon of n sides. If T_(n + 1) - T_(n) = 36, then n is equal to
Answer» 4 5 6 7 Answer :D

Discussion

47.	If a point (1,4) lies inside the circle x^(2) +y^(2)- 6x -10 y +p=0and the circle does not touch or intersect the coordinate axes , then the set of all possible values of p is the interval.
Answer» `(0,25) ` ` ( 25,39) ` ` (9,25) ` ` (25, 29 ) ` ANSWER :C

Discussion

48.	Find the shortest distance of the point (0, c) from the curve y=x^(2), where 0lecle5.
Answer» ANSWER :`(SQRT(4c-1))/(2)`

Discussion

49.	Discuss the continuity of the cosine, cosecant, secant and cotangent functions: f(x)= sec x =(1)/(cos x), x in R- {(2n+1) (pi)/(2), n in I}
Answer» Answer :`F(x)= sec x, c in R- {(2n+1) (PI)/(2), n in I}`

Discussion

50.	Let lim _( x to oo) n ^((1)/(2 )(1+(1 )/(n))). (1 ^(1) . 2 ^(2) . 3 ^(3)....n ^(n ))^((1)/(n ^(2)))=e^((-p)/(q)) where p and q are relative prime positive integers. Find the vlaur of \|p+q\|.
Answer» ANSWER :5

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The locus of mid points of the chords of theellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1which pass through foot of a directrix

The sum of the fourth powers of the roots of the equation x^(3)- x^(2) -2x + 2=0 is:

If I_(1),I_(2),I_(3) are the intercept on x-axis, y-axis, y=x w.r.t x^(2)+y^(2)-14x-10y+24=0 then

IFalpha , betaare therootsofx^2 +px +q=0and also ofx^(2n)+P^n x^n + q ^n=0andif( alpha )/(beta ), ( beta ) /( alpha)arethe rootsofx^n+ 1 + (x +1)^n =0thenn is

int (dx)/(x^(2) sqrt(4 + x^(2)))=

Principle of mathematical induction is used

y= int_(x)^(x^(2)) sqrt(5-t^(2))dt then the value of (dy)/(dx) at x= sqrt(2) is

Write{1,2,3,4,5}set in the intention(or specification form).

The sum of the digits in the unit's place of all the 4-digit numbersformed by using the numbers 3,4,5 and 6 withoutrepetitionis

Find all zeros of the polynomial x^6-3x^5-5x^4+22x^3-39x^2-39x+135 , if it is known that 1 + 2i and sqrt3 are two of its zeros.

(i) int(2x-5x) (3+2x) (1-x) dx, (ii) int sqrt(x) (ax^(2) + bx + c) dx (iii) int (sqrtx - 3sqrt(x^(4)) + 7/(3sqrt(x^(2))) - 6e^(x) + 1) dx

India and Pakistan play a series of 'n' one day matches and probability than India wins a match against Pakistan is 1/2. For n = 7, probadility that India wins atleast three conseutive matches is

India and Pakistan play a series of 'n' one day matches and probability than India wins a match against Pakistan is 1/2. If 'n' is not fixed and series ends when any one of the team completes its 4^(th) win then probability that India wins the series is

India and Pakistan play a series of 'n' one day matches and probability than India wins a match against Pakistan is 1/2. If n = 7, them probability that India wins atleast three consercutive matches is

A set of lines x+y-2+lambda_(1)(2x+y-3)=0 represents incident rays on ellipse S=0 and 2x+3y-23+lambda_(2)=0 represents the set of refelction rays from the ellipse where lambda_(1), lambda_(2) in R. If P(3,7) is a point on the ellipse normal at which meets the major axis at N.

There are 4 mangoes, 3 apples, 2 oranges in a bag, fruits of the same variety being identical. In how many different ways can a selection of fruits be made if atleast one of each kind is to be selected

There are 4 mangoes, 3 apples 2 oranges in bag, fruits of the same variety being identical. In how many different ways can a selection of fruits be made if atleast one fruit is to be selected.

((2+3i)/(2-3i))-((2-3i)/(2+3i)) in the form of a + ib

If ax^2+2hxy+by^2+2gx+2fy+c=0 represents two parallel lines then prove that af^2=bg^2.

Let f(x) = {((tan x - cot x)/(x-pi/4), ",", x != pi/4),(a, ",",x = pi/4):} The value of a so that f(x) is continuous at x = (pi)/4, is

If a_r is the coefficient x^r in the expansion of (1+x+x^2)^n then a_1 - 2a_2 + 3a_3 -…..-2na_(2n) =

Line 4x+5y-7=0 meets the coordinate axes at A and B. Through the mid - point of AB a line is drawn perpendicular to it meeting the line 2x+y=0 at Q(alpha, beta), the value of 1//alpha-1//beta is equal to

If the curves ax^(2)+by^(2)=1 and a'x^(2)+b'y^(2)=1 are orthogonally then …………

Using integration find the area of the region which is bounded bt x-axisthe tangent and normal to the circle x^(2)+y^(2)=4 drawn at (1,sqrt3).

Choose the correct answer int (sin^2x-cos^2x)/(sin^2x cos^2x) dxa)tanx+cotx+cb)tanx+cosecx+cc)cotx-tanx+c d) tanx+secx+c

int_(0)^(pi//2) sin^8 xcos^2 xdx is equal to

EvaluateP(A cup B), if 2P(A) = P(B)=(5)/(13) and P(A|B)=(2)/(5)

Find thearea of theregionboundedbycirclex^2+y^2= 8xandparabolay^2 = 4x.

Evaluate : int_(0)^(pi/2)cos^(2)xdx.

The radical centre of the circle x^2 + y^2 + 4x + 7 =0, 2 x^2 + 2y^2 + 3x + 5y+ 9 =0 and x^2 + y^2 + y =0 is

f(x) satisfies the relation f(x)-lamda int_(0)^(pi//2)sinxcostf(t)dt=sinx If f(x)=2 has the least one real root, then

Out of 10 persons sitting at a round table, three persons are selected at random then the probability that no two of them are consecutive is

Let S = sum _(r=1)^(30) (""^(30+r)C_(r) (2r-1))/(""^(30)C_(r)(30+r)),K=sum_(r=0)^(30) (""^(30)C_(r))^(2) and G=sum_(r=0)^(60) (-1)^(r)(""^(60)C_(r) )^(2) The value fo (G-S)is

Find the mean deviation from the median for the following data (##VIK_MAT_IIA_QB_C08_SLV_004_Q01.png" width="80%">

Show that for a ge 1, f(x)=sqrt(3)sin x - cos x - 2ax + b is decreasing in R.

The point on the curve y = x ^(2) + 4x + 3 which is nearest from the line y = 3x + 2 is

A regular polygon of 10 sides is constructed No. of ways 3 vertices be selected so that no two vertices are consecutive is

If ""^(18)C_(15)+2(""^(18)C_(16))"+"^(17)C_(16)+1=""^(n)C_(3) then n is

Transform the equation 3x+4y+12=0 into slope intercept form

A curve passes through the poit (5,3) and at any point (x,y) on it the product of its slope and the ordinate is equal to abscissa of the curve is

Expand(i) (x/3+3y/2)^(5) ,(ii)(x^(2)+2/x)^(4) using pascle's triangle.

int_(0)^(2pi)(1)/(1+e^(sinx))dx=

Let F: R to Rbe definedbyf(x)={:{ (alpha + (sin[x])/x , " if "x gt 0), ( 2, " if " x =0), ( beta + [ (sin x-x)/x^(3)] ,"if " x lt 0):} where, [x]denotes the integral part of x. If f continuousat x =0,thenbeta = alphais equal to

Let T_(n) denote the number of triangles which can be formed by using the vertices of a regular polygon of n sides. If T_(n + 1) - T_(n) = 36, then n is equal to

If a point (1,4) lies inside the circle x^(2) +y^(2)- 6x -10 y +p=0and the circle does not touch or intersect the coordinate axes , then the set of all possible values of p is the interval.

Find the shortest distance of the point (0, c) from the curve y=x^(2), where 0lecle5.

Discuss the continuity of the cosine, cosecant, secant and cotangent functions: f(x)= sec x =(1)/(cos x), x in R- {(2n+1) (pi)/(2), n in I}

Let lim _( x to oo) n ^((1)/(2 )(1+(1 )/(n))). (1 ^(1) . 2 ^(2) . 3 ^(3)....n ^(n ))^((1)/(n ^(2)))=e^((-p)/(q)) where p and q are relative prime positive integers. Find the vlaur of |p+q|.