28278 + Interview Questions in Maths in Class 12

1.	Ifare the n Arithmetic means between a and b, then 2sum_(I - 1)^(n)a_(i) =
Answer» `AB` `N(a + B)` `NAB` `(a + b)/n` ANSWER :B

Discussion

2.	If the circumcentre of the triangle whose vertices are (0, 2), (3, 5) and (5, 8) is (h, k) then (h^(2)+k^(2)) is equal to
Answer» ANSWER :`462.50`

Discussion

3.	If alpha, beta, gamma are acute angles and cos theta = sin beta//sin alpha, cos phi = sin gamma//sin alpha and cos (theta-phi)= sin beta sin gamma, then tan^(2)alpha-tan^(2)beta-tan^(2) gamma is equal to
Answer» -1 0 1 None of these Answer :B

Discussion

4.	Let the equations of perpendicular bisectors of sides AC and of Delta ABCbe x+y=3 and x-y=1 respectively Then vertex A is is (0,0) The circumcentre of the DeltaABC is
Answer» `(1,1)` `(2,1)` `(0,0)` `(0,1)` ANSWER :B

Discussion

5.	Let the equations of perpendicular bisectors of sides AC and AB of Delta ABC bex+y=3 and x-y=1 respectivelyThen vertex A is is (0,0) Length of side BC of the DeltaABC is
Answer» `SQRT2` `SQRT8` `sqrt12` `sqrt20` ANSWER :D

Discussion

6.	The value of 'c' in Lagrange's thorem for f(x) = lx^(2) + mx + n [l ne 0]on [a,b] is
Answer» `a//2` `b//2` `(a-b)/(2)` `(a+b)/(2)` ANSWER :D

Discussion

7.	Let A(x_(1),y_(1)) and B(x_(2),y_(2)) be two points on the parabola y^(2) = 4ax. If the circle with chord AB as a dimater touches the parabola, then \|y_(1)-y_(2)\| is equal to
Answer» `4a` `8A` `6sqrt(2)a` not a constant Solution :Equation of circle with AB as diameter is `(x-x_(1)) (x-x_(2)) + (y-y_(1)) (y-y_(2)) =0`. Solving it with `y^(2) =4ax`, we get `16a^(2) (y-y_(1)) (y-y_(2)) + (y^(2) -y_(1)^(2)) (y^(2)-y_(2)^(2)) =0` `rArr (y-y_(1)) (y-y_(2)) [16a^(2) + (y+y_(1)) (y+y_(2))] = 0` `rArr (y+y_(1)) (y+y_(2)) + 16a^(2) =0` `rArr y^(2) + (y_(1)+y_(2)) y + y_(1)y_(2) + 16a^(2) =0` The roots of the equation are equal if `(y_(1)+y_(2))^(2) = 4y_(1)y_(2) + 64A^(2) rArr \|y_(1)-y_(2)\| = 8a`.

Discussion

8.	Let ABC be a triangle whose centroid is G, orhtocentre is H and circumcentre is the origin 'O'. If D is any point in the plane of the triangle such that no three of O, A, C and D are collinear satisfying the relation vec(AD) + vec(BD) + vec(CH ) + 3 vec(HG)= lamda vec(HD), then what is the value of the scalar 'lamda'?
Answer» SOLUTION :L.H.S = ` vecd - veca + vecd - vecb + vech - vecc + 3 (vecg - vech)` `"" = 2 vecd - ( veca + vecb + vecc) + 3 (( veca + vecb + vecc))/(3) - 2 vech` `"" =2 vecd - 2 vech = 2(vecd - vech) =2 VEC(HD)` `RARR lamda =2 `

Discussion

9.	Measure of anlge betweenthe line (x-1)/5 = (y+2)/2 = (z+5)/14
Answer» `SIN^(-1)(1/15)` `cos^(-1)(2/15)` `sin^(-1)(2/15)` `cos^(-1)(1/15)` ANSWER :A::B::C::D

Discussion

10.	Show that\| aunderset( x) overset(a) +2x,bundersetyoversetb+2y,cunderset zoversetc+2z\|=0
Answer» ANSWER :`DELTA =Delta _1`

Discussion

11.	Statement I If A gt 0 , B gt 0 and A+B= pi/3, then the maximum value of tan A tan B is 1/3. Statement II If a_(1)+a_(2)+a_(3)+...+a_(n)=k(constant), then thevalue a_(1)a_(2)a_(3)...a_(n) is greatest when a_(1)=a_(2)=a_(3)=...+a_(n)
Answer» Both Statement I and Statement II are INDIVIDUALLY true and R is the CORRECT explanation of Statement I. Both Statement I and Statement IIare individually true but Statement II is not the correct explanaton of Statement I. Statement I is true but Statement II is false. Statement I is false but Statement II is true. Answer :B

Discussion

12.	If D is a determinant of order three and Delta is a determinant formed by the cofactors of determinant D then
Answer» `Delta=D^(2)` `D=0` implies `Delta=0` if `D=27`, then `Delta` is PERFECT cube None of these Answer :A::B::C

Discussion

13.	Let * be a operation defined on the set of non zero rational numbers by a * b = (ab)/4Find the identity element.
Answer» Answer :`E = 4 in Q` is the IDENTITY ELEMENT.

Discussion

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

Discussion

15.	Usingintregrationfind theareaofregionboundedby thetriagnlewhoseverticesare (1,0) ,(2,2)and (3,1)
Answer» ANSWER :`3/2`

Discussion

16.	If a chord of the parabola y^(2) = 4ax touches the parabola y^(2) = 4bx, show that the tangents at its extremities meet on the parabola by^(2) = 4a^(2) x
Answer» <P> Answer :The locus of `P( x_(1) , y_(1) )` is `by^(2) = 4A^(2) X`

Discussion

17.	Equation of the line passing through (1,1,1) and perpendicular to 2x-3y+z=5 is
Answer» `(x-1)/(-1)=(y-1)/(1)=(z-1)/(1)` `(x-1)/(1)=(y-1)/(3)=(z-1)/(2)` `(x-1)/(3)=(y-1)/(3)=(z-1)/(1)` `(x-1)/(-1)=(y-1)/(1)=(z-1)/(1)` ANSWER :D

Discussion

18.	Lt_(ntooo)sum_(r=1)^(n)(1)/(n)[sqrt ((n+r)/(n-r))]
Answer» `pi/2` `2PI` `pi/2 -1` `pi/2 +1` ANSWER :D

Discussion

19.	There are 2 red, 4 green balls in bag A, bag B, there are 5 red and 7 green balls.If one ball is randomly replaced from A into B and a ball is drawn from B then the probability for the ball to be red is
Answer» `17/40` `14/40` `19/45` `16/39` ANSWER :D

Discussion

20.	If all the letters of the word 'QUEST' are arranged in all possible ways and put in dictionary order, then find the rank of the given word
Answer» ANSWER :43

Discussion

21.	Let f be the continuous and differentiable function such that f(x)=f(2-x), forall x in R and g(x)=f(1+x), then
Answer» g(x) is an ODD FUNCTION f(x) is an even function f(x) is symmetric about x=1 None of the above Answer :B::C

Discussion

22.	For any two non-zero vectors a and b, \|a\|b+\|b\|a and \|a\|b-\|b\|a are
Answer» parallel PERPENDICULAR non-parallel None of these Solution :Let `P=\|a\|B+\|b\|a andq=\|a\|b-\|b\|a` THUS ` p.q =(\|a\|b+\|b\|a)` ` =\|a\|^(2)(b.b)-\|a\|\|b\|(b.a)+\|b\|\|a\|(a.b)-\|b\|^(2)\|a\|^(2)(a.a)` `=\|a\|^(2)\|b\|^(2)-\|a\|\|b\|(a.b)+\|a\|\|b\|(a.b)-\|b\|^(2)\|a\|^(2)=0` `implies p BOT q [:' ifC.d =0implies c ` isperpendicular to d ] Hence,\|a\| `b+\|b\| a and\|a\|b-\|b\|a` areperpendiculartoeachotherfor any non-zerovectors a andb.

Discussion

23.	Three positive acute angles alpha, beta and gamma satisfy the relation tan. (beta)/(2)=(1)/(3)cot.(alpha)/(2)and cot.(gamma)/(2)=(1)/(2)(3tan.(alpha)/(2)+cot.(alpha)/(2)). Then, the value of alpha+beta+gamma is equal to
Answer» `PI` `2PI` `(pi)/(2)` `(3PI)/(2)` ANSWER :A

Discussion

24.	Solve x^9-x^5+x^4-1=0
Answer» `cispi/5,CIS(3pi)/(5),cispi,cis(7pi)/(5),cis(9pi)/(5),PM 1,pm i` `cispi/3,cis(2pi)/(3),cispi,cis(7pi)/(3),cis(9pi)/(3),pm 1` `cispi/2,cis(3pi)/(2),cispi,cis(7pi)/(2),cis(9pi)/(2),pm 1` `1,i,cispi/2,cis(3pi)/(2),cispi,cis(7pi)/(2)` Answer :A

Discussion

25.	y = e^(2x)(a + bx)
Answer» ANSWER :`y" - 4Y' + 4y = 0`

Discussion

26.	(i) Find the equation of the tangent and normal at (2, 1) on the ellipse 2x^(2) + 3y^(2) = 11 (ii) Find the equaiton of the tangent and normal at (-1,2) on the ellipse x^(2) + 8y^(2) = 33
Answer» Answer :(i) 4x + 3 y - ll = 0 ,3 x -4 y = 2 (II) x -1 6 y + 33 = 0,16x+ y + 14 = 0

Discussion

27.	Leta, bandcbe suchthat(1)/((1 - x ) (1 -2x)(1 - 3x)) = (a ) /( 1- x )+(b)/(1- 2x )+(c )/( 1- 3x ),then(a )/(1) + (b)/(3)+(c )/(5)is equal to
Answer» ` (1)/(15) ` `(1)/(6) ` `(1)/(5) ` `(1)/(3) ` SOLUTION : ` ( 1)/((1- X )(1- 2x )(1 - 3x) )=(a ) /((1-x ))+(b)/(( 1-2x)) +(C )/((1-3x))… (1)` substituingx= 2 inequation(1) `(1)/((1 - 2)(1 - 2(2)) (1 - 3(2)))=(a)/((1- 2))+(b)/((1-2(2))) + (c )/((1-3(2))) ` ` rArr(1)/(-15)= - a+ (b)/((-3))+ (c )/((-5)) ` ` rArr(1)/(15) = (a)/(1) + (b)/(3)+ (c )/(5) `

Discussion

28.	A zoo has 20 zebras ,12 jiraffes ,11 lions and 3 tigers.The number of ways a tourist can visit these animals so that he must see at least one tiger
Answer» `21xx13xx12xx3` `7.2^(43)` `7.21xx13xx12-1` `6.2^(43)` ANSWER :B

Discussion

29.	The probability that a police inspector Ravi will catch a thief in a day is 1/4 and the probability he will catch a robber in that day is 1/5 and the probability that he will catch both a thief and a robber in a day is 1/15 then what is the probability that Ravi will catch at least 1 mischief?
Answer» `23//60` `19//60` `7//20` NONE of these Answer :A

Discussion

30.	The value of -2[sin ^(6) ((pi)/(2) +alpha )+ sin ^(6) (5pi-alpha ) ] is eqqual to -
Answer» 2 1 0 4 Answer :B

Discussion

31.	The maximum value of the functions x^(2) e^(-2x), x gt 0is ……….
Answer» `(1)/(E )` `(1)/(2e)` `(1)/(e^(2))` `(4)/(e^(4))` ANSWER :C

Discussion

32.	Using properties of determinants prove abs[[x,y,x+y],[y,x+y,x],[x+y,x,y]]=-2(x^3+y^3)
Answer» SOLUTION :`-2(x^3+y^3)`

Discussion

33.	(4+7i)-(6+2i) What complex number is equivalent to the expression above if i=sqrt-1?
Answer» 2 2-5i `-2+5i` `-10-9i` ANSWER :C

Discussion

34.	Express the following matrices as the sum of a symmetric and a skew symmetric matrix: [(1,5),(-1,2)]
Answer» ANSWER :A=[(1,2),(2,2)]+[(0,3),(-3,0)]`

Discussion

35.	(dy)/(dx) - 3y cot x = sin 2x, y = 2 when x = (pi)/(2)
Answer» Answer :`y = 4 sin^(3)X - 2SIN^(2)x`

Discussion

36.	The transformed equation of x^(2) + 4xy + y^(2) - 2x +2y-6=0 when the axes are rotated through an anlge pi//4 is
Answer» a,B,C b,c,a a,c,b c,a,b Answer :D

Discussion

37.	Assume that each child born is equally likely to be boy or a girl . If a family has two children, what is the conditional probability that both are girls given thatthe youngest is a girl?
Answer» ANSWER :(i) `(1)/(2)` (II) `(1)/(3)`

Discussion

38.	From a pack of 52 well shuffeled cards, cards are drawn one by one without replacement. It 4 th drawn card is found to be ace, then what is probability that there are no more acess left in the pack, is :-
Answer» `(1)/(.^(48)C_(3)+3.^(49)C_(2)+1)` `(1)/(.^(48)C_(3)+.^(49)C_(2)+1)` `(1)/(3.^(48)C_(3)+.^(49)C_(2)+1)` `(1)/(.^(52)C_(4)+1)` SOLUTION :`(.^(4)C_(3).^(1)C_(1)l^(52)C_(4))/((.^(4)C_(3).^(1)C_(1)+.^(4)C_(2).^(48)C_(1).^(2)C_(1)+.^(4)C_(1).^(48)C_(2).^(3)C_(1)+.^(48)C_(3).^(4)C_(1))/(.^(52)C_(4)))` `4/(4+12.^(48)C_(1)+12.^(48)C_(2)+4.^(48)C_(3))` `1/(1+3 .^(49)C_(2)+ .^(48)C_(3))`.

Discussion

39.	Select the correct atatement for Ne.
Answer» It is not isoelectronic with `H_(2)O` LAST ELECTRON enters in s-orbital The VALUE of 'm' must be zero for last electron The value of 'l' must be '1' for last electron Answer :D

Discussion

40.	If z_(1) and z_(2) satisfy the equation 2\|z+3\|=\|"Re"(z)\| and arg(z+3)/(1+i)=pi/2, then arg (z_(1)+3)/(z_(2)+3) is equal to
Answer» 0 `+-PI/2` `+-pi` `+-pi/4` ANSWER :C

Discussion

41.	The value of sqrt((1)/(3) (sqrt(27)+sqrt(15) ) is
Answer» `PM 3^(-1//4) (SQRT((5)/(2)) + sqrt((1)/(2)))` `pm (sqrt((5)/(2)) + sqrt((1)/(2)) )` `pm 2^(1//4) (sqrt((5)/(2) ) + sqrt((1)/(2)) )` `pm 3^(-1//4) (sqrt((3)/(2) )+ sqrt((1)/(2)))` Answer :A

Discussion

42.	Let P(k): 2 + 4 + 6 + ... + 2k = kk + 1) + 2, then the statement P(m + 1) will be true if
Answer» <P>P(1) is true P(2)is true P(m ) is true Noneof these Answer :C

Discussion

43.	Choose the correct answer. if n is even Answer all the questions, int_(0)^((pi)/(2))sin^(n)xdx is ……
Answer» `(n)/(n-1).(n-2)/(n-3).(n-4)/(n-5)….(PI)/(2)` `(n-1)/(n).(n-3)/(n-2).(n-5)/(n-4)….(1)/(2)(pi)/(2)` `(n)/(n-1).(n-2)/(n-3).(n-4)/(n-5)….(3)/(2).1` `(n-1)/(n).(n-3)/(n-2).(n-5)/(n-4)….(2)/(3).1` ANSWER :B

Discussion

44.	int (g(x)-f(x))dx=
Answer» `(1)/(2sqrt(3))log \|(X^(2)-sqrt(3)x-3)/(x^(2)+sqrt(3)x+3)\|+c` `(1)/(3) TAN^(-1) ((x^(2)-3X)/(3x))+c` `(1)/(2sqrt(3))log \|(x^(2)-sqrt(3)x+3)/(x^(2)+sqrt(3)x+3)\|+c` `(1)/(3) tan^(-1) ((x^(2)+3x)/(3x))+c` Answer :C

Discussion

45.	An Apache helicopter of enemy is flying along the curve given by y=x^(2)+7. A solider, placed at (3, 7), wants to shoot down the helicopter when it is nearest to him. Find the nearest distance.
Answer» ANSWER :`SQRT(5)`

Discussion

46.	Evaluate the following integrals (v) int_(0)^(log 2) cosh 2 x dx.
Answer» ANSWER :`15/16`

Discussion

47.	If A = {:[(1, 2), (3,4)]:} , then 2A^(-1) =
Answer» 3I - A 5 I - A A - 5I 3A + I Solution :`A^(2) - 5A - 2I = 0rArrA - 5 I - 2A^(-1) = 0` 2A^(-1) = A - 5I`

Discussion

48.	Sum of n terms of the serise sqrt(2) + sqrt(8) + sqrt(18) + sqrt(32) + .... is
Answer» `(n(n + 1))/2` `2n(n + 1)` `(n(n + 1))/SQRT(2)` 1 Answer :C

Discussion

49.	A boxcontainso red marblesnumberfrom 1 through 6 and 4whitemarbles12through15 .Find theprobabilitythat amarbledrawnat random is whiteand oldnumber :
Answer» `(1)/(6)` 6 `(1)/(5)` 5 Answer :C

Discussion

50.	Two tangents are drawn from a point (-4, 3) to the parabola y^(2)=16x. If alpha is the angle between them, then the value of cos alpha is
Answer» 0 `(1)/(2)` `(SQRT3)/(2)` `(1)/(SQRT2)` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Ifare the n Arithmetic means between a and b, then 2sum_(I - 1)^(n)a_(i) =

If the circumcentre of the triangle whose vertices are (0, 2), (3, 5) and (5, 8) is (h, k) then (h^(2)+k^(2)) is equal to

If alpha, beta, gamma are acute angles and cos theta = sin beta//sin alpha, cos phi = sin gamma//sin alpha and cos (theta-phi)= sin beta sin gamma, then tan^(2)alpha-tan^(2)beta-tan^(2) gamma is equal to

Let the equations of perpendicular bisectors of sides AC and of Delta ABCbe x+y=3 and x-y=1 respectively Then vertex A is is (0,0) The circumcentre of the DeltaABC is

Let the equations of perpendicular bisectors of sides AC and AB of Delta ABC bex+y=3 and x-y=1 respectivelyThen vertex A is is (0,0) Length of side BC of the DeltaABC is

The value of 'c' in Lagrange's thorem for f(x) = lx^(2) + mx + n [l ne 0]on [a,b] is

Let A(x_(1),y_(1)) and B(x_(2),y_(2)) be two points on the parabola y^(2) = 4ax. If the circle with chord AB as a dimater touches the parabola, then |y_(1)-y_(2)| is equal to

Measure of anlge betweenthe line (x-1)/5 = (y+2)/2 = (z+5)/14

Show that| aunderset( x) overset(a) +2x,bundersetyoversetb+2y,cunderset zoversetc+2z|=0

Statement I If A gt 0 , B gt 0 and A+B= pi/3, then the maximum value of tan A tan B is 1/3. Statement II If a_(1)+a_(2)+a_(3)+...+a_(n)=k(constant), then thevalue a_(1)a_(2)a_(3)...a_(n) is greatest when a_(1)=a_(2)=a_(3)=...+a_(n)

If D is a determinant of order three and Delta is a determinant formed by the cofactors of determinant D then

Let * be a operation defined on the set of non zero rational numbers by a * b = (ab)/4Find the identity element.

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

Usingintregrationfind theareaofregionboundedby thetriagnlewhoseverticesare (1,0) ,(2,2)and (3,1)

If a chord of the parabola y^(2) = 4ax touches the parabola y^(2) = 4bx, show that the tangents at its extremities meet on the parabola by^(2) = 4a^(2) x

Equation of the line passing through (1,1,1) and perpendicular to 2x-3y+z=5 is

Lt_(ntooo)sum_(r=1)^(n)(1)/(n)[sqrt ((n+r)/(n-r))]

There are 2 red, 4 green balls in bag A, bag B, there are 5 red and 7 green balls.If one ball is randomly replaced from A into B and a ball is drawn from B then the probability for the ball to be red is

If all the letters of the word 'QUEST' are arranged in all possible ways and put in dictionary order, then find the rank of the given word

Let f be the continuous and differentiable function such that f(x)=f(2-x), forall x in R and g(x)=f(1+x), then

For any two non-zero vectors a and b, |a|b+|b|a and |a|b-|b|a are

Three positive acute angles alpha, beta and gamma satisfy the relation tan. (beta)/(2)=(1)/(3)cot.(alpha)/(2)and cot.(gamma)/(2)=(1)/(2)(3tan.(alpha)/(2)+cot.(alpha)/(2)). Then, the value of alpha+beta+gamma is equal to

Solve x^9-x^5+x^4-1=0

y = e^(2x)(a + bx)

(i) Find the equation of the tangent and normal at (2, 1) on the ellipse 2x^(2) + 3y^(2) = 11 (ii) Find the equaiton of the tangent and normal at (-1,2) on the ellipse x^(2) + 8y^(2) = 33

Leta, bandcbe suchthat(1)/((1 - x ) (1 -2x)(1 - 3x)) = (a ) /( 1- x )+(b)/(1- 2x )+(c )/( 1- 3x ),then(a )/(1) + (b)/(3)+(c )/(5)is equal to

A zoo has 20 zebras ,12 jiraffes ,11 lions and 3 tigers.The number of ways a tourist can visit these animals so that he must see at least one tiger

The probability that a police inspector Ravi will catch a thief in a day is 1/4 and the probability he will catch a robber in that day is 1/5 and the probability that he will catch both a thief and a robber in a day is 1/15 then what is the probability that Ravi will catch at least 1 mischief?

The value of -2[sin ^(6) ((pi)/(2) +alpha )+ sin ^(6) (5pi-alpha ) ] is eqqual to -

The maximum value of the functions x^(2) e^(-2x), x gt 0is ……….

Using properties of determinants prove abs[[x,y,x+y],[y,x+y,x],[x+y,x,y]]=-2(x^3+y^3)

(4+7i)-(6+2i) What complex number is equivalent to the expression above if i=sqrt-1?

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: [(1,5),(-1,2)]

(dy)/(dx) - 3y cot x = sin 2x, y = 2 when x = (pi)/(2)

The transformed equation of x^(2) + 4xy + y^(2) - 2x +2y-6=0 when the axes are rotated through an anlge pi//4 is

Assume that each child born is equally likely to be boy or a girl . If a family has two children, what is the conditional probability that both are girls given thatthe youngest is a girl?

From a pack of 52 well shuffeled cards, cards are drawn one by one without replacement. It 4 th drawn card is found to be ace, then what is probability that there are no more acess left in the pack, is :-

Select the correct atatement for Ne.

If z_(1) and z_(2) satisfy the equation 2|z+3|=|"Re"(z)| and arg(z+3)/(1+i)=pi/2, then arg (z_(1)+3)/(z_(2)+3) is equal to

The value of sqrt((1)/(3) (sqrt(27)+sqrt(15) ) is

Let P(k): 2 + 4 + 6 + ... + 2k = kk + 1) + 2, then the statement P(m + 1) will be true if

Choose the correct answer. if n is even Answer all the questions, int_(0)^((pi)/(2))sin^(n)xdx is ……

int (g(x)-f(x))dx=

An Apache helicopter of enemy is flying along the curve given by y=x^(2)+7. A solider, placed at (3, 7), wants to shoot down the helicopter when it is nearest to him. Find the nearest distance.

Evaluate the following integrals (v) int_(0)^(log 2) cosh 2 x dx.

If A = {:[(1, 2), (3,4)]:} , then 2A^(-1) =

Sum of n terms of the serise sqrt(2) + sqrt(8) + sqrt(18) + sqrt(32) + .... is

A boxcontainso red marblesnumberfrom 1 through 6 and 4whitemarbles12through15 .Find theprobabilitythat amarbledrawnat random is whiteand oldnumber :

Two tangents are drawn from a point (-4, 3) to the parabola y^(2)=16x. If alpha is the angle between them, then the value of cos alpha is