28278 + Interview Questions in Maths in Class 12

1.	Evaluate the following integrals. int(1)/(4x^(2)-4x-7)dx
Answer» ANSWER :`(1)/(8sqrt(2))LOG\|(2x-1-2sqrt(2))/(2x-1+2sqrt(2))\|+C`

Discussion

2.	underset(n=1)overset(oo)sum.^(n)C_(0)+.^(n)C_(1)+underset(.^(n)P_(n))(.^(n)C_(2))+....+.^(n)C_(n)=
Answer» `E-1` `e+1` `e^(2)-1` `e^(2)+1` ANSWER :C

Discussion

3.	The rank of the matrix[(1,2,3),(lambda , 2 , 4),(2,-3,1)] is 3 if :
Answer» `LAMBDA NE 18/11` `lambda ne 18/11` `lambda =-18/11` NONE of these ANSWER :A

Discussion

4.	An equilateral triangle is inscribed in the parabola y^(2) = 8x with one of its vertices is the vertex of the parabola. Then, the length or the side or that triangle is
Answer» `24 SQRT(3)` `16sqrt(3)` `8sqrt(3)` `4(sqrt(3))` ANSWER :B

Discussion

5.	The value of theta satisfying : \|(sin3theta,-2,3),(cos2theta,8,-7),(2,14,11)\|=0is :
Answer» `(NPI)/2` `npi+pi//6` `2npi+pi//6` `npi+(-1)^(N)pi//6 " or " npi, n in I.` ANSWER :D

Discussion

6.	Determine the truth values of p
Answer» SOLUTION :

Discussion

7.	Let f(x) be a non-negative continuous function such that the area bounded by the curve y=f(x), x-axis and the ordinates x=(pi)/(4) and x = bet gt (pi)/(4) is beta sin beta +(pi)/(4) cos beta +sqrt(2) beta then f((pi)/(2))=
Answer» `(PI)/(4)+SQRT(2)-1` `(pi)/(4)-sqrt(2)+1` `-(pi)/(4)-sqrt(2)+1` `-(pi)/(4)+sqrt(2)+1` Answer :4

Discussion

8.	Evaluate the following inegrals intx^(2)sinx^(3)dx
Answer» ANSWER :`-(1)/(3)COS(x^3)+C`

Discussion

9.	The random variable X can take only the values 0, 1, 2. Given that P(X = 0) = P(X = 1) = p and that E(X^(2)) = E(X), find the value of p.
Answer» ANSWER :`(1)/(2)`

Discussion

10.	""^(29)C_(5)+sum_(r=0)^(4)""^((33-r))C_(4)=
Answer» `""^(32)C_(4)` `""^(35)C_(5)` `""^(34)C_(4)` `""^(34)C_(5)` Answer :D

Discussion

11.	\|{:(a,-b,a-b),(b,c,b-c),(2,1,0):}\|=0 then a,b,c are in …………..
Answer» G.P A.P H.P None of these ANSWER :A

Discussion

12.	Find the number of 4 letter words that can be formed using the letters of the word EQUATION. How many of these words begin with E ? How many end with N ? How many begin with E and end with N ?
Answer» ANSWER :N=30

Discussion

13.	Find the second order derivatives of the functions log (log x)
Answer» ANSWER :`(-(1 + LOG X))/((x log x)^(2))`

Discussion

14.	Verify mean value theorem for each of the functions: f(x)= x^(3)-2x^(2)-x + 3,x in [0, 1]
Answer» ANSWER :`(1)/(3)`

Discussion

15.	A man of height 180 cm walks at a uniform rate of 12 km/hr away from the lamp post of height 450 cm . Then I : Rate at which the length of shadow increases is 8 km/hr II : Rate at which the tip of shadow is moving is 20 km /hr
Answer» only I is TRUE only II is true both I and II are true NEITHER I nor II true Answer :C

Discussion

16.	Find the value of int_(0)^(pi) (x)/(1+sin x) dx
Answer» `PI/2` `pi` `2PI` `4PI` ANSWER :B

Discussion

17.	The tangent to the hyperbola xy=c^2 at the point P intersects the x-axis at T and y- axis at T'.The normal to the hyperbola at P intersects the x-axis at N and the y-axis at N' . The areas of the triangles PNT and PN'T' are Delta and Delta' respectively, then 1/Delta+1/(Delta)' is (A) equal to 1 (B) depends on t (C) depends on c D) equal to 2
Answer» EQUAL to 1 DEPENDS on t depends on C equal to 2 Answer :C

Discussion

18.	If m=""^(n)C_(2),"then """^(m)C_(2)=
Answer» `3.""^(N)C_(4)` `""^(m+1)C_(4)` `3.""^(n+1)C_(4)` `3.""^(n+1)C_(3)` ANSWER :C

Discussion

19.	int(1-cos x)cosec^(2)xdx=.....+c
Answer» `tan((x)/(2))` `COT((x)/(2))` `(1)/(2)tan((x)/(2))` `2TAN((x)/(2))` Answer :A

Discussion

20.	Find the general solution of y log y dx - x dy = 0
Answer» ANSWER :`y = E^(CX)`

Discussion

21.	The value of x , where x > 0 and tan (sec^(-1)(1/x))=sin(tan^(-1)(2)) is
Answer» `SQRT5` `sqrt5/3` `1` `2/3` ANSWER :B

Discussion

22.	The number of ways in which 2n objects of one type, 2n of another type and 2n of a third type can be divided between 2 persons so that each may have 3n objects is alpha n^(2)+beta n +gamma. Find the value of (alpha+beta+gamma).
Answer» ANSWER :7

Discussion

23.	A street-light is hung 20 ft. above the ground .An object falls freely under the gravity, starting from rest at the same height as the lamp and at a horizontal distance of 5 ft. from it . When the object has fallen through 16 ft, the speed of the shadow of the object on the ground is
Answer» `12 FT.//SEC`. ` 11 ft. //sec` `10 ft. //sec`. `12 .5 ft.//sec`. ANSWER :D

Discussion

24.	Let z=(11-3i)/(1+i). If alpha is a real number such z-ialpha is real, then the value of alpha is
Answer» `4` `-4` `7` `-7` ANSWER :D

Discussion

25.	If x = a is a solution of the equation sin^(-1)""x/3+sin^(-1)""(2x)/3=sin^(-1)x, then the roots of the equation x^(2)-ax-1=0 are
Answer» `pm1` `1/2, 1` `PM 1/2` `-1/2, 1` ANSWER :A

Discussion

26.	Let matrixA=[(x,3,2),(1,y,4),(2, 2,z)], " if " xyz=2lambda and 8x+4y+3x=lambda+28, then (adj A) A equals :
Answer» `[(LAMBDA+1,0,0),(0,lambda+1,0),(0,0,lambda+1)]` `[(lambda,0,0),(0,lambda,0),(0,0,lambda)]` `[(lambda^(2),0,0),(0,lambda^(2),0),(0,0,lambda^(2))]` `[(lambda+2,0,0),(0,lambda+2,0),(0,0,lambda+2)]` ANSWER :B

Discussion

27.	Find the area of the tirangle with vertices A (1,1,2),B (2,3,5) and C(1,5,5).
Answer» ANSWER :`(SQRT(61))/(2)`

Discussion

28.	Findthe area of the region{(x,y) \|x^2 ley le x}.
Answer» ANSWER :`2/3 ` SQ. UNIT

Discussion

29.	Integrate the functions (xcos^(-1)x)/(sqrt(1-x^(2)))
Answer» Answer :`-[sqrt(1-x^(2))cos^(-1)x+x]+C`

Discussion

30.	Direction cosines of the line parallel to line frac{x-5}{2}=frac{y+3}{-3}=frac{z-5}{6}
Answer» `LT2, -3, 6gt` `lt5, -3, 5gt` `ltfrac{2}{7}, frac{-3}{7}, frac{6}{7}gt` `larr5, 3, -5gt` ANSWER :C

Discussion

31.	A random variable X has the probability distribution
Answer» 0.31 0.62 0.82 0.41 Answer :C

Discussion

32.	Let r be the range of n(AA n ge 1) observations x_(1), x_(2), ...., x_(n). If S= sqrt((sum_(i=1)^(n)(x_(i)-bar(x))^(2))/(n-1)), then
Answer» `S LT R SQRT((n^(2)+1)/(n-1))` `S ge r sqrt((n)/(n-1))` `S = r sqrt((n)/(n-1))` `S lt r sqrt((n)/(n-1))` ANSWER :D

Discussion

33.	If two normals drawn to the y^(2) =8x at ( 2,4)and (18, 12) intersect at P(x_1, y_1) then foot of the 3rd normal through p is
Answer» `( 32, 16) ` ` ( 32, -16) ` ` ( -16, 32) ` ` ( 2, 4) ` ANSWER :B

Discussion

34.	"coth"^(-1) 3 + "tanh"^(-1) (1)/(3)-"cosech"^(-1) (-sqrt3)=
Answer» `log_(E ) ((2)/(sqrt3))` `log_(e ) 2sqrt3` 0 `log_(e ) 3sqrt3` Answer :B

Discussion

35.	Find the point on the curve 4x^(2) + a^(2)y^(2) = 4a^(2), 4lta^(2)lt8, that is farthest from the point (0,-2).
Answer» ANSWER :(0,2)

Discussion

36.	If f(x)=(1+ tan x) [1+ tan(pi/4 - x)] and g(x) is a function with domain R, then int_(0)^(1) x^(3) g o f (x) dx=
Answer» `1/2 G(pi/4)` `1/4 g(2)` `1/4g(1)` 1 Answer :B

Discussion

37.	Lt_(n rarr oo)[(1^(99)+2^(99)+3^(99)+...+n^(99))/(n^(100))]
Answer» ANSWER :`(1)/(100)`

Discussion

38.	(x ^ 2+x + 1 ) /((x - 1)(x -2) (x -3))=(A)/(x-1) + (B)/(x-2) + (C )/(x - 3 )rArr A + C =
Answer» 4 5 6 8 Solution : ` ( x ^ 2+ x+ 1 ) /((x - 1 )(x-2) (x - 3 ))= (A)/((x - 1 ))+ (B)/((x - 2 ))+(C )/((x - 3 )) ` `x ^ 2+x + 1=A( x - 2 )(x - 3 ) +B( x - 1 )(x - 3 ) +C( x- 1 )(x - 2 ) ` If`x = 1` ` rArr3=A (-1)( - 2 ) ` ` A =(3 ) /(2) ` If`x=3 ` ` 3 ^ 2+ 3 + 1=0+0+ C ( 3 - 1 )(3 - 2 ) ` `rArr 13 =2C ` `rArr C =(13 ) /(2) ` A + C `= (3 ) /(2)+ (13 )/(2) ` `thereforeA + C =8 `

Discussion

39.	For -(pi)/(2) lt x lt (3pi)/(2) the value of (d)/(dx){"tan"^(-1)(cosx)/(1+sinx)} is equal to
Answer» `(1)/(2)` `-(1)/(2)` 1 `(SINX)/((1+sinx)^(2)`

Discussion

40.	Evalute the following integrals int (1)/(x^(4) sqrt(x^(2) + 4))dx
Answer» ANSWER :`- (1)/(48) (1 + (4)/(X^(2)))^(3//2) + (1)/(16) (1 + (4)/(x^(2)))^(1//2) ` + c

Discussion

41.	A box contains 30 toys of same size in which 10 toys are white and all the remaining toys are blue. A toy is drawn at random from the box and it is replacecd in the box after noting down itscolour. If 5 toys are drawn in this way, then the probability of getting atmost 2 white toys is
Answer» A`(6/9)^(2)` B`(8/9)^(2)` C`(7/9)^(2)` D`(2/3)^(2)` ANSWER :B

Discussion

42.	If a,b,c,d > 0 , x in R and (a^2 + b^2 +c^2)x^2-2(ab+bc+cd)x+(b^2+c^2+d^2) le 0 then \|{:(33,14,loga ),(65,27,log b ),(97,40,log c):}\|=
Answer» SOLUTION :f(1) < 0 f(-1) < 0 f(0) > 0 < br> `alphain ` (-1,0) `beta in` (0,1) `[ALPHA ] + [beta]` -1+0=-1

Discussion

43.	Evaluate the integrals by using substitution int_(0)^(2)xsqrt(x+2) (Put x + 2 = t^(2))
Answer» ANSWER :`(16sqrt2)/15(sqrt2+1)`

Discussion

44.	Let z ne 1 be a complex number and let omeg= x+iy, y ne 0. If (omega- bar(omega)z)/(1-z) is purely real, then \|z\| is equal to
Answer» `\|OMEGA\|` `\|omega\|^(2)` `(1)/(\|omega\|^2)` `1` ANSWER :D

Discussion

45.	Find the equation of the circle which passes through the origin and intersects each of the following circles orthogonally. x^(2)+y^(2)-4x+6y+10,x^(2)+y^(2)+12y+6=0
Answer» ANSWER :`2(X^(2)+y^(2))-7x+2y=0`

Discussion

46.	Find (dy)/(dx): x= cos^(2) theta and y= sin^(2) theta
Answer» ANSWER :`-1`

Discussion

47.	Find the equation of the circle which passes through the origin and intersects the circles below, orthogonally. x^2 + y^2 - 4x - 6y - 3 = 0 . x^2 + y^2 - 8y + 12 = 0 .
Answer» ANSWER :`X^(2)+y^(2)+6x-3y=0`

Discussion

48.	((1+i)/(1-i))^4+((1-i)/(1+i))^4=
Answer» 0 1 2 4 Answer :C

Discussion

49.	Froma company15 soldiersany4 arefrom8 male&7 femaleapplicantsif theselectionis toconsistof eitherall malesor allfemales is
Answer» 1365 4095 5460 131040 Answer :C

Discussion

50.	Separate equations of lines jointly given by the equation hxy+gx+(fh)/gh y+f=0 are
Answer» `X=(-FH)/g,y=(-g)/h` `x=f/g,y=(-g)/h` `x=(-f)/h,h=(-g)/h` `fg=ch` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Evaluate the following integrals. int(1)/(4x^(2)-4x-7)dx

underset(n=1)overset(oo)sum.^(n)C_(0)+.^(n)C_(1)+underset(.^(n)P_(n))(.^(n)C_(2))+....+.^(n)C_(n)=

The rank of the matrix[(1,2,3),(lambda , 2 , 4),(2,-3,1)] is 3 if :

An equilateral triangle is inscribed in the parabola y^(2) = 8x with one of its vertices is the vertex of the parabola. Then, the length or the side or that triangle is

The value of theta satisfying : |(sin3theta,-2,3),(cos2theta,8,-7),(2,14,11)|=0is :

Determine the truth values of p

Let f(x) be a non-negative continuous function such that the area bounded by the curve y=f(x), x-axis and the ordinates x=(pi)/(4) and x = bet gt (pi)/(4) is beta sin beta +(pi)/(4) cos beta +sqrt(2) beta then f((pi)/(2))=

Evaluate the following inegrals intx^(2)sinx^(3)dx

The random variable X can take only the values 0, 1, 2. Given that P(X = 0) = P(X = 1) = p and that E(X^(2)) = E(X), find the value of p.

""^(29)C_(5)+sum_(r=0)^(4)""^((33-r))C_(4)=

|{:(a,-b,a-b),(b,c,b-c),(2,1,0):}|=0 then a,b,c are in …………..

Find the number of 4 letter words that can be formed using the letters of the word EQUATION. How many of these words begin with E ? How many end with N ? How many begin with E and end with N ?

Find the second order derivatives of the functions log (log x)

Verify mean value theorem for each of the functions: f(x)= x^(3)-2x^(2)-x + 3,x in [0, 1]

A man of height 180 cm walks at a uniform rate of 12 km/hr away from the lamp post of height 450 cm . Then I : Rate at which the length of shadow increases is 8 km/hr II : Rate at which the tip of shadow is moving is 20 km /hr

Find the value of int_(0)^(pi) (x)/(1+sin x) dx

If m=""^(n)C_(2),"then """^(m)C_(2)=

int(1-cos x)cosec^(2)xdx=.....+c

Find the general solution of y log y dx - x dy = 0

The value of x , where x > 0 and tan (sec^(-1)(1/x))=sin(tan^(-1)(2)) is

The number of ways in which 2n objects of one type, 2n of another type and 2n of a third type can be divided between 2 persons so that each may have 3n objects is alpha n^(2)+beta n +gamma. Find the value of (alpha+beta+gamma).

A street-light is hung 20 ft. above the ground .An object falls freely under the gravity, starting from rest at the same height as the lamp and at a horizontal distance of 5 ft. from it . When the object has fallen through 16 ft, the speed of the shadow of the object on the ground is

Let z=(11-3i)/(1+i). If alpha is a real number such z-ialpha is real, then the value of alpha is

If x = a is a solution of the equation sin^(-1)""x/3+sin^(-1)""(2x)/3=sin^(-1)x, then the roots of the equation x^(2)-ax-1=0 are

Let matrixA=[(x,3,2),(1,y,4),(2, 2,z)], " if " xyz=2lambda and 8x+4y+3x=lambda+28, then (adj A) A equals :

Find the area of the tirangle with vertices A (1,1,2),B (2,3,5) and C(1,5,5).

Findthe area of the region{(x,y) |x^2 ley le x}.

Integrate the functions (xcos^(-1)x)/(sqrt(1-x^(2)))

Direction cosines of the line parallel to line frac{x-5}{2}=frac{y+3}{-3}=frac{z-5}{6}

A random variable X has the probability distribution

Let r be the range of n(AA n ge 1) observations x_(1), x_(2), ...., x_(n). If S= sqrt((sum_(i=1)^(n)(x_(i)-bar(x))^(2))/(n-1)), then

If two normals drawn to the y^(2) =8x at ( 2,4)and (18, 12) intersect at P(x_1, y_1) then foot of the 3rd normal through p is

"coth"^(-1) 3 + "tanh"^(-1) (1)/(3)-"cosech"^(-1) (-sqrt3)=

Find the point on the curve 4x^(2) + a^(2)y^(2) = 4a^(2), 4lta^(2)lt8, that is farthest from the point (0,-2).

If f(x)=(1+ tan x) [1+ tan(pi/4 - x)] and g(x) is a function with domain R, then int_(0)^(1) x^(3) g o f (x) dx=

Lt_(n rarr oo)[(1^(99)+2^(99)+3^(99)+...+n^(99))/(n^(100))]

(x ^ 2+x + 1 ) /((x - 1)(x -2) (x -3))=(A)/(x-1) + (B)/(x-2) + (C )/(x - 3 )rArr A + C =

For -(pi)/(2) lt x lt (3pi)/(2) the value of (d)/(dx){"tan"^(-1)(cosx)/(1+sinx)} is equal to

Evalute the following integrals int (1)/(x^(4) sqrt(x^(2) + 4))dx

A box contains 30 toys of same size in which 10 toys are white and all the remaining toys are blue. A toy is drawn at random from the box and it is replacecd in the box after noting down itscolour. If 5 toys are drawn in this way, then the probability of getting atmost 2 white toys is

If a,b,c,d > 0 , x in R and (a^2 + b^2 +c^2)x^2-2(ab+bc+cd)x+(b^2+c^2+d^2) le 0 then |{:(33,14,loga ),(65,27,log b ),(97,40,log c):}|=

Evaluate the integrals by using substitution int_(0)^(2)xsqrt(x+2) (Put x + 2 = t^(2))

Let z ne 1 be a complex number and let omeg= x+iy, y ne 0. If (omega- bar(omega)z)/(1-z) is purely real, then |z| is equal to

Find the equation of the circle which passes through the origin and intersects each of the following circles orthogonally. x^(2)+y^(2)-4x+6y+10,x^(2)+y^(2)+12y+6=0

Find (dy)/(dx): x= cos^(2) theta and y= sin^(2) theta

Find the equation of the circle which passes through the origin and intersects the circles below, orthogonally. x^2 + y^2 - 4x - 6y - 3 = 0 . x^2 + y^2 - 8y + 12 = 0 .

((1+i)/(1-i))^4+((1-i)/(1+i))^4=

Froma company15 soldiersany4 arefrom8 male&7 femaleapplicantsif theselectionis toconsistof eitherall malesor allfemales is

Separate equations of lines jointly given by the equation hxy+gx+(fh)/gh y+f=0 are