28278 + Interview Questions in Maths in Class 12

1.	int_(1)^(2) x^(-2).e^(1//x) dx=
Answer» `E+SQRT(e)` `sqrt(e)` `e-sqrt(e)` e Answer :C

Discussion

2.	If absA = m , absB =n ,what can you say about abs(P(A) X P(B))
Answer» SOLUTION :If `absA` = m , `absB` = n then `absP(A) = 2^m . absP(B) = 2^n THEREFORE absP(A) XX P(B) = 2^m xx 2^n = 2^(m+n)`

Discussion

3.	Find the number of arrangements by arranging all the letters of the word 'BANANA'
Answer» ANSWER :60

Discussion

4.	Let DeltaABC be inscribedin a circle having radius unity. The three internalbisectorsof the angles A, B and C are extended to intersect the circumcircleof DeltaABC at A_(1)B_(1) and C_(1) respectively. Then (A A_(1)"cos"(A)/(2)BB_(1)"cos"(B)/(2)+C C_(1)"cos"(C)/(2))/(sinA+sinB+sinC)=
Answer» ANSWER :2

Discussion

5.	Find a particular solution of the differential equation (x + 1)(dy)/(dx) = 2e^(-y) - 1, given that y = 0 when x = 0.
Answer» Answer :`y = log\|(2x + 1)/(X + 1)\|, x ne -1`

Discussion

6.	2. C_0+ 2^2 (C_1)/(2)+2^3. (C_2)/(3)+…....+2^(n+1). (C_n)/(n+1)=
Answer» `(1)/(n+1)` `(4^n)/(n+1)` `(3^(n+1)-1)/(n+1)` `(4^(n+1)-1)/(n+1)` ANSWER :C

Discussion

7.	2.C_0 + (2^2)/(2).C_1 + (2^3)/(3).C_2 + ……+(2^11)/(11).C_10 =
Answer» `((3^(11)+1))/(11)` `(3^(11)-1)/(11)` `(3^7 +1)/(7)` `(4^7 -1)/(7)` ANSWER :B

Discussion

8.	Find the range of x for which the binomial expansions of the following are valid .(7 - 4x)^(-5)
Answer» ANSWER :`((-7)/(4), 7/4)`

Discussion

9.	A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curvex^(2) + y^(2) = 4 and x + y = a . The set containing the value of a is
Answer» `{-2 , 2}` `{- 3, 3}` `{-4, 4}` `{-5,5}` ANSWER :A

Discussion

10.	When the voltage applied to an X-raytube increased fromV_(1)15.5 KV to V_(2) = 31 KV, the wavelength interval between the K_(alpha) line and theshort wavelength cut-off of the continuous X-ray spectrum increasesby a factor of 1.3. If the atomic number of the element of the target is 13N, where N is an integer find N (Take : hc = 1240 eV and R=1xx10^(7)//m)
Answer» Solution : `lambda_(TH)=(hc)/(eV_(a))` `(1)/(lambda_(K alpha))=R(Z-1)^(2)((1)/(1^(2))-(1)/(2^(2)))` `(143)/(10)(lambda_(K alpha)-lambda_(th))=(lambda_(Kalpha)-(lambda_(th))/(2))` `(3)/(10)lambda_(K alpha)=((13)/(10)-(1)/(2))lambda_(th)` `(3)/(10)((4xx10^(-7))/(3(z_(7))^(2)))=((8)/(10))(12.4xx10^(-7))/(15.5xx10^(3))RARR(5000)/(8)=(z-1)^(2)` `625=(z-1)^(2) " " rArr z = 26`

Discussion

11.	Consider the system of equations x_1+2x_2+3x_3=1 x_2+2x_3+3x_1=2 x_3=2x_1+3x_2=3, then mathc the following columns ,
Answer» <P>`{:(P,Q,R,S),(1,2,3,4):}` `{:(P,Q,R,S),(2,3,4,1):}` `{:(P,Q,R,S),(3,2,1,4):}` `{:(P,Q,R,S),(4,1,2,3):}` ANSWER :A

Discussion

12.	Find the area of the region bounded by y= x^(3),y = 0, x= 0 and x=2
Answer» ANSWER :4

Discussion

13.	a and b are unit vectors along OA, OB and OC bisects the angle AOB. The unit vector along OC is
Answer» `(a + B)/(2)` `(a - b)/(2)` `(a + b)/(\|a + b\|)` `(a - b)/(\|a-b\|)` ANSWER :C

Discussion

14.	16cos^(6)10^(@)-24cos^(4)10^(@)+9cos^(2)10^(@) is equal to
Answer» `1/4` `3/4` `1/2` `1` Solution :GIVEN expression `=(4cos^(3)10^(@)-3COS^(@))^(2)` `=(COS30^(@))^(2)` `=3/4`

Discussion

15.	L.P.P. is a process of finding
Answer» MAXIMUM VALUE of OBJECTIVE function minimum value of objective function optimal value of objective function only maximum value of objective function Answer :C

Discussion

16.	Let y=f(x) be satisfying differential equation e^(-x^(2))(dy)/(dx)=2xy^(2) such that f(0)=(1)/(2) Q. Which of the following statement is correct about f(x)?
Answer» `f(x)` is unbounded `f(x)` is bijective `f(x)` is odd None of these. Solution :`int(DY)/(y^(2))=int2xe^(x^(2))dx` `-(1)/(y)=E^(x^(2))+C` POINT `(0.(1)/(2))` lies on the curve `implies-2=1+C` `impliesC=-3` Hence `-(1)/(y)=e^(x^(2))-3` `impliesf(x)=(1)/(3-e^(x^(2)))` Hence, `f(x)` is even which means that it cannot be objective Also, denominator of `f(x)` becomes zero which implies that it cannot be bounded.

Discussion

17.	The uranium disintegrates at a rate proportional to the amount present at any instant. If m_(1)andm_(2) gms of uranium are present at time t_(1)andt_(2) respectively, then half life of uranium is
Answer» `((t_(1)-t_(2))log2)/log((m_(1))/(m_(2)))` `((t_(2)-t_(1))log2)/log((m_(1))/(m_(2)))` `((t_(1)-t_(2))log(m_(1)/m_(2)))/log2` `((t_(2)-t_(1))log(m_(1)/m_(2)))/log2` ANSWER :B

Discussion

18.	int [ (log x - 1)/(1 + (log x)^(2)) ]^(2) dx =
Answer» `(LOG X)/((log x)^(2) + 1) + C ` `(x)/(x^(2) + 1) + C ` `(xe^(x))/( x^(2)+1)` + C `(x)/((log x)^(2)) + c ` Answer :D

Discussion

19.	Transform the equation x^2+4xy+y^2-2x+2y+4=0 into the form (y'^2)/(b^2)-(x'^2)/(a^2)=1
Answer» ANSWER :where , `a^2=2and b^2=6`.

Discussion

20.	The maximum value of 27^(cos(2x))xx81^(sin(2x)) is …………
Answer» `-5` `(1)/(5)` `(1)/(25)` 243 Answer :D

Discussion

21.	You are given an unlimited supply of each of the digits 1, 2, 3, or 4. Using only these four digits, you construct n digit numbers. Such n digit numbers will be called BEAUTIFUL if it contains the digit composite number either an even number times or not at all. Number of n digit BEAUTIFUL numbers are
Answer» `2^(n)+1` `2^(n+1)+2` `2^(n-1)(2^(n)+1)` `2^(n+2)+4` ANSWER :C

Discussion

22.	Let bara.barb and barc are three unit vectors such that \|bara+barb+barc\|=sqrt3 such that (bara times barb).(barb times barc)+(barb times barc).(barc times bara)+(barc times bara).(bara.barb)=lamda
Answer» the maximum VALUE of `LAMDA` is 2 when `lamda` is maximum then the volume of parallelepiped determined by `BARA.barb and barc` is `sqrt3` when `lamda` is maximum then the value of `\|(2bara+3barb+4barc).(bara TIMES barb times 5barb times barc+5barc times bara)\|` is 32. None of these Answer :A::C

Discussion

23.	Let f: (-oo,oo) to (-oo,oo) be such that f(.) is continuous at 0 and let f((x+y)/2) = (f(x)+f(y))/2 for x , y in (-oo,oo) Statement-1: f(.) is continuous at every point on (-oo,oo) Statement-2: f(x+h)+f(0)=2 f(x)+f(2h) for x , h in (-oo, oo).
Answer» ANSWER :a

Discussion

24.	Let S_(n)=sum_(k=1)^(n)(-1)^(k-1).K^(2) for n gt=1. Given that S_(2n)=-n(2n+1) For n=1,2,3,cdotsthen S_(n)=
Answer» -3003 3003 -2926 2926 Answer :B

Discussion

25.	d/dx[sin^(-1)(cos x)]=
Answer» `-SIN X` -1 x `π/2-x` ANSWER :B

Discussion

26.	Find the number of ways to arrange 5 boys and 5 girl in a row such that all the girls must sit together
Answer» ANSWER :`lfloor6xxlfloor5`

Discussion

27.	The value of tan (1^(@)) + tan (89^(@)) is _______
Answer» `(1)/(SIN (2^(@)))` `(2)/(sin(1^(@)))` `(2)/(sin(2^(@)))` `(1)/(sin(1^(@)))` ANSWER :C

Discussion

28.	(d)/(dx)[x^(sinx)+(sinx)^(x)]=
Answer» `X^(SINX)[(sinx)/(x)+COSX"LOG"x]+(sinx)^(x)[xtanx+"log"(sinx)]` `x^(sinx)[xtanx+cosx "log"x]+(sinx)^(x)[(sinx)/(x)+"log"(sinx)]` `x^(sinx)[(x)/(sinx)+cosx "log" x]+(sinx)^(x)[xcot x+"log"(sinx)]` `x^(sinx)[(sinx)/(x)+sinx "log" x]+(sinx)^(x)[xcot x+"log"(cosx)]`

Discussion

29.	A line L makes intercept a and b on the coordinate axes. The axes are rotated through an angle theta in the positive direction, keeping the origin fixed. If the line L makes intercept p and q on the new coordinate axes, then 1/a^(2)+1/b^(2) =
Answer» <P>`1/(p^(2)q^(2))` `1/p^(2) -1/q^(2)` `1/p^(2)+1/q^(2)` `(PQ)/(p^(2)+q^(2))` Answer :C

Discussion

30.	If the roots of the quadratic equation 3x^(2)+2x+a^(2)-a=0 in x are of opposite signs, then a lies in the interval
Answer» `(-OO,-2)` `(-oo,0)` `(-1,0)` `(0,1)` ANSWER :D

Discussion

31.	The set of values of x in R satisfying the inequality x^(2)-4x-21 le 0 is
Answer» (3, 7] (-3, 7] [-7, 3] [-7, -3] ANSWER :B

Discussion

32.	Evaluate{:\|(2,4),(-1,2)\|:}
Answer» ANSWER :`8`

Discussion

33.	Find the particular solution of the differential equation (dy)/(dx) + y cot x = 2x + x^(2) cot x( x ne 0) given that y = 0when x = (pi)/(2).
Answer» ANSWER :`y = x^(2) - (pi^(2))/(4 SIN x)(sin x NE 0)`

Discussion

34.	Findthe areaof the regionboundedby thecurvesy= 5- x^2 , X - axisand thelinesx=2and x=3.
Answer» Answer :`(20)/(3) ( SQRT(5) -2) `Sq. units

Discussion

35.	If x > 0 , write the first negative term in the expansion of (1 + 2x)^(23//2)
Answer» ANSWER :14TH TERM

Discussion

36.	Let f(x)=int_(0)^(x)(cost)/(t)dt,(x gt0), then for x = (2n+1) (pi)/(2)f(x) has
Answer» maxima when n = 0, 2,4, 6, .. NEITHER maxima nor MINIMA when n = - 1, -3,-5,…… minima when n =0,2,4,6,…… none of these Answer :A

Discussion

37.	Integrate the following intsin(x/2)dx
Answer» Solution :`intsintheta 2 d THETA` `2(-COSTHETA)+C`=-2COS(x/2)+C`

Discussion

38.	(i) Let z_1 (i=1,2,3,3) represent the vertices a square all of which lie on the sides of the triangle with vertices (0,0), (2,1), (3,0) . Give that z_1 and z_2 are purify real, find z_3 and z_4. (ii) Find the roots common to the equations x^6 - x^3 + x^2 -1=0, x^4 =1.
Answer» ANSWER :`z_3 = (9)/(4) + (3)/(4)i , z_4= (3)/(2) = (3)/(4) i` `1,-1`

Discussion

39.	Complete set of values of g(x) is
Answer» `(-INFTY,-1]CUP[3,infty)` `(-infty,-1)cup(3,infty)` `[-1,3]` `(-infty.infty)` ANSWER :A

Discussion

40.	a xx {b xx (C xx a) + (p xx q)} =
Answer» (a.q) P - (a.p) q + (B.a) `(a xx C) - (b xx c)` (a.q) p - (a.p) q + (b.a) `(a xx c)` `a xx (p xx q) + [a b c] c` NONE of these Answer :B

Discussion

41.	The value of c in the Langrange's mean value theorem for f(x)=root()(x-2) in the interval [2,6] is
Answer» `9/12` `5/2` 3 4 Answer :C

Discussion

42.	Show that the function defined by f(x)= cos(x^(2)) is a continuous function.
Answer» ANSWER :`F(X) = COS (x^(2))`

Discussion

43.	If ain R^(+) and f:R rarrR is defined by f(x)=(a^(2x))/(a^(2x)+a) , then Sigma_(r=1)^(10)f((1)/(11))=
Answer» 11 10 5.5 5 Answer :D

Discussion

44.	Integrate the following functions : int(sin(sqrtx))/(sqrtx)dx
Answer» ANSWER :`-2cossqrtx+c`

Discussion

45.	Prove the following: 2tan^(-1)x=cos^(-1)((1-x^(2))/(1+x^(2))),xge0
Answer» ANSWER :`X^(x cos x)[cos x. (1+ LOG x)-x sin xlog x]-(4x)/((x^(2)-1)^2)`.

Discussion

46.	ABC is an isosceles right anlged triangle with AB = BC = 1 . If P is any point on AC, then min (max {(area APQ) , (area PQBR) , area PRC )}} is
Answer» `2/9` `1/9` `1/3` NONE of these Answer :A

Discussion

47.	If three distinct positive numbers a,b,c are in A.P. Such that abc=4,then value of b is always
Answer» GREATER than`(2)^(2//3)` LESS than `(2)^(2//3)` EQUAL to `(2)^(2//3)` equal to `(2)^(3//2)` ANSWER :A

Discussion

48.	Minimise Z = 3x + 2y subject to the constraints : x+y ge 8"…(1)" 3x+5y le 15"…(2)" x ge 0, y ge 0"…(3)"
Answer» Answer :It has no FEASIBLE REGION SUBJECT to the given CONSTRAINTS.

Discussion

49.	If a line makes alpha,beta,gamma,delta angles with four diagonals of a cube, then cos2alpha+cos2beta+cos2gamma+cos2delta=
Answer» `-(2)/(3)` `(2)/(3)` `-(4)/(3)` `(4)/(3)` ANSWER :C

Discussion

50.	If x,y,z are three consecutive positive integers then (1)/(2)log_(e)x+(1)/(2)log_(e)z+(1)/(2xz+1)+(1)/(3)((1)/(2xz+1))^(3)+....=
Answer» `log_(a )y` `log_(E )(1//y)` `log_(e )y` 1 Answer :C

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

int_(1)^(2) x^(-2).e^(1//x) dx=

If absA = m , absB =n ,what can you say about abs(P(A) X P(B))

Find the number of arrangements by arranging all the letters of the word 'BANANA'

Let DeltaABC be inscribedin a circle having radius unity. The three internalbisectorsof the angles A, B and C are extended to intersect the circumcircleof DeltaABC at A_(1)B_(1) and C_(1) respectively. Then (A A_(1)"cos"(A)/(2)BB_(1)"cos"(B)/(2)+C C_(1)"cos"(C)/(2))/(sinA+sinB+sinC)=

Find a particular solution of the differential equation (x + 1)(dy)/(dx) = 2e^(-y) - 1, given that y = 0 when x = 0.

2. C_0+ 2^2 (C_1)/(2)+2^3. (C_2)/(3)+…....+2^(n+1). (C_n)/(n+1)=

2.C_0 + (2^2)/(2).C_1 + (2^3)/(3).C_2 + ……+(2^11)/(11).C_10 =

Find the range of x for which the binomial expansions of the following are valid .(7 - 4x)^(-5)

A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curvex^(2) + y^(2) = 4 and x + y = a . The set containing the value of a is

Consider the system of equations x_1+2x_2+3x_3=1 x_2+2x_3+3x_1=2 x_3=2x_1+3x_2=3, then mathc the following columns ,

Find the area of the region bounded by y= x^(3),y = 0, x= 0 and x=2

a and b are unit vectors along OA, OB and OC bisects the angle AOB. The unit vector along OC is

16cos^(6)10^(@)-24cos^(4)10^(@)+9cos^(2)10^(@) is equal to

L.P.P. is a process of finding

Let y=f(x) be satisfying differential equation e^(-x^(2))(dy)/(dx)=2xy^(2) such that f(0)=(1)/(2) Q. Which of the following statement is correct about f(x)?

The uranium disintegrates at a rate proportional to the amount present at any instant. If m_(1)andm_(2) gms of uranium are present at time t_(1)andt_(2) respectively, then half life of uranium is

int [ (log x - 1)/(1 + (log x)^(2)) ]^(2) dx =

Transform the equation x^2+4xy+y^2-2x+2y+4=0 into the form (y'^2)/(b^2)-(x'^2)/(a^2)=1

The maximum value of 27^(cos(2x))xx81^(sin(2x)) is …………

Let bara.barb and barc are three unit vectors such that |bara+barb+barc|=sqrt3 such that (bara times barb).(barb times barc)+(barb times barc).(barc times bara)+(barc times bara).(bara.barb)=lamda

Let f: (-oo,oo) to (-oo,oo) be such that f(.) is continuous at 0 and let f((x+y)/2) = (f(x)+f(y))/2 for x , y in (-oo,oo) Statement-1: f(.) is continuous at every point on (-oo,oo) Statement-2: f(x+h)+f(0)=2 f(x)+f(2h) for x , h in (-oo, oo).

Let S_(n)=sum_(k=1)^(n)(-1)^(k-1).K^(2) for n gt=1. Given that S_(2n)=-n(2n+1) For n=1,2,3,cdotsthen S_(n)=

d/dx[sin^(-1)(cos x)]=

Find the number of ways to arrange 5 boys and 5 girl in a row such that all the girls must sit together

The value of tan (1^(@)) + tan (89^(@)) is _______

(d)/(dx)[x^(sinx)+(sinx)^(x)]=

A line L makes intercept a and b on the coordinate axes. The axes are rotated through an angle theta in the positive direction, keeping the origin fixed. If the line L makes intercept p and q on the new coordinate axes, then 1/a^(2)+1/b^(2) =

If the roots of the quadratic equation 3x^(2)+2x+a^(2)-a=0 in x are of opposite signs, then a lies in the interval

The set of values of x in R satisfying the inequality x^(2)-4x-21 le 0 is

Evaluate{:|(2,4),(-1,2)|:}

Find the particular solution of the differential equation (dy)/(dx) + y cot x = 2x + x^(2) cot x( x ne 0) given that y = 0when x = (pi)/(2).

Findthe areaof the regionboundedby thecurvesy= 5- x^2 , X - axisand thelinesx=2and x=3.

If x > 0 , write the first negative term in the expansion of (1 + 2x)^(23//2)

Let f(x)=int_(0)^(x)(cost)/(t)dt,(x gt0), then for x = (2n+1) (pi)/(2)f(x) has

Integrate the following intsin(x/2)dx

(i) Let z_1 (i=1,2,3,3) represent the vertices a square all of which lie on the sides of the triangle with vertices (0,0), (2,1), (3,0) . Give that z_1 and z_2 are purify real, find z_3 and z_4. (ii) Find the roots common to the equations x^6 - x^3 + x^2 -1=0, x^4 =1.

Complete set of values of g(x) is

a xx {b xx (C xx a) + (p xx q)} =

The value of c in the Langrange's mean value theorem for f(x)=root()(x-2) in the interval [2,6] is

Show that the function defined by f(x)= cos(x^(2)) is a continuous function.

If ain R^(+) and f:R rarrR is defined by f(x)=(a^(2x))/(a^(2x)+a) , then Sigma_(r=1)^(10)f((1)/(11))=

Integrate the following functions : int(sin(sqrtx))/(sqrtx)dx

Prove the following: 2tan^(-1)x=cos^(-1)((1-x^(2))/(1+x^(2))),xge0

ABC is an isosceles right anlged triangle with AB = BC = 1 . If P is any point on AC, then min (max {(area APQ) , (area PQBR) , area PRC )}} is

If three distinct positive numbers a,b,c are in A.P. Such that abc=4,then value of b is always

Minimise Z = 3x + 2y subject to the constraints : x+y ge 8"…(1)" 3x+5y le 15"…(2)" x ge 0, y ge 0"…(3)"

If a line makes alpha,beta,gamma,delta angles with four diagonals of a cube, then cos2alpha+cos2beta+cos2gamma+cos2delta=

If x,y,z are three consecutive positive integers then (1)/(2)log_(e)x+(1)/(2)log_(e)z+(1)/(2xz+1)+(1)/(3)((1)/(2xz+1))^(3)+....=