28278 + Interview Questions in Maths in Class 12

1.	Find the Cartesian coordinates of the centre of gravity of the figure enclosed by the curve = a cos^(3) varphi (a gt 0).
Answer» ANSWER :`(21)/(40)a`

Discussion

2.	Find the values of the following integrals (iv) int_(0)^(pi/4) sec^(3) x dx
Answer» `1/2 ln2` `(1)/(SQRT(2))+1/2 LN (sqrt(2)+1)` `(1)/(sqrt(2))- ln (sqrt(2)+1)` `ln (sqrt(2)+1)` ANSWER :B

Discussion

3.	If A and B are two events and A ne phi, B ne phi, then ………
Answer» <P>`P(A//B)= P(A) * P(B)` `P(A//B)= (P(A CAP B))/(P(B))` `P(A//B) * P(B//A)=1` `P(A//B) = (P(A))/(P(B))` ANSWER :B

Discussion

4.	Find the second order derivatives of the functions x^(20)
Answer» ANSWER :`380 X^(18)`

Discussion

5.	Find the rang of (2x^(2)-6x+5)/(x^(2)-3x+2).
Answer» ANSWER :`(-INFTY, -2] CUP (2, infty)`

Discussion

6.	What is the approximate perecent increase in average daily full - price ticket sales from 1990 to 1995 ?
Answer» `10%` `20%` `33%` `48%` ANSWER :D

Discussion

7.	Find the prabability of throwing atmost 2 sixes in 6 throws of a single die
Answer» Answer :`(35)/(18)((5)/(6))^(4)`

Discussion

8.	If cosx=tany,cosy=tanz,cosz=tanx, then the value of sinx is
Answer» `2cos18^(@)` `COS18^(@)` `SIN18^(@)` `2sin18^(@)` ANSWER :D

Discussion

9.	If the vectors vec(a)=hati+3hatj+hatk,vec(b)=2hati-hatj-hatk and vec( c )=lambda hati+7hatj+3hatk are coplannar then find lambda.
Answer» ANSWER :`lambda=0`

Discussion

10.	Ifalpha , beta , gammaare the rootsofx^3 -3x+1=0thentheequationwhoserootsare alpha- (1)/( beta gamma) , beta -(1)/(gammaalpha ) , gamma- (1)/( alpha beta )is
Answer» `x^3 - 3X +8=0` ` x^3 -6X +8=0` `x^3 -9X +8=0` `x^3- 12X + 8=0` ANSWER :D

Discussion

11.	If a point R(4,y,z) lies on the line segment joining the points P(2,-3,4) and Q(8,0,10), then (OR)^(2) = _______??
Answer» ANSWER :56

Discussion

12.	Find the number of ways of arranging the letters of the word 'KRISHNA'so that all the vowels come together
Answer» ANSWER :720

Discussion

13.	An article manufactured by a company consists of two parts A and B. In the process of manufacture 13 out of 104 parts of A and 5 out of 100 parts of B may be defective then the probability that the assembled product is not defective is
Answer» `(28)/(160)` `(33)/(160)` `(128)/(160)` `(133)/(160)` ANSWER :D

Discussion

14.	If x is numerically so small so that x^2 and higher powers of x can be neglected , then (1+(2x)/(3))^(3/2), (32 + 5x)^(-1/5) is approximately equal to :
Answer» `(32 + 31X)/(64)` `(32 +32x)/(64)` `(31 + 32x)/(64)` `(1-2x)/(64)` ANSWER :A

Discussion

15.	A random variable x follows binomial distribution with mean a and variance b then observe the following statements. Statement-I : a gt b gt 0 Statement-II : (a^(2))/(a-b) is a positive integer Statement-III : a+b=1 which of the above statments are true.
Answer» only I, II only II, III only I, III all the I, II, III Answer :A

Discussion

16.	A (-5,0) and B (3,0) are two of the verti- ces of a triangle ABC. Its area is 20 square units. The vertex Clies on the line x - y = 2. The coordinates of C are
Answer» (-7, -5) or (3,5) (-3,-5) or (-5, 7) (7,5) or (3,5) (-3, -5) or (7,5) Answer :D

Discussion

17.	(i) Find equation of line joining (1,2) and ( 3,6) using determinants . (ii) Find equation of line joining (3,1) and ( 9,3) using determinants.
Answer» ANSWER :` (i) y=2x , (II) x-3y =0`

Discussion

18.	The value of x satisfying the equation \|x-1\|^(log_(3)x^(2)-2log_(x)9)=(x-1)^(7) is
Answer» 27 81 9 `1//sqrt(3)` ANSWER :B

Discussion

19.	Origin is the orthocentre of the triangle formed by the points (5, -1), (-2, 3) and (-4, -7) then its ninepoint centre is
Answer» `(-1//3, -5//3)` (5, 3) (1, 1) `(-1//4, -5//4)` ANSWER :D

Discussion

20.	Integrate the function in Exercise. x^(2)e^(x)
Answer» ANSWER :`E^(X)(x^(2)-2x+2)+C`

Discussion

21.	If aspherical soap bubble expands at the rate of 2 cc//sec, then , when the radius is 10 cm, its diamater is increasing at the rate of
Answer» `100 PI cm//sec`. `(1)/(100pi) cm//sec`. `(pi)/(100) cm//sec` `(100)/(pi) cm//sec`. ANSWER :B

Discussion

22.	The value lim_(n to oo) int_(0)^(1) ( sin n x)/( sin nx + cos nx) dx is
Answer» ANSWER :`0.50`

Discussion

23.	A perpendicular drawn from any point P of the curve on the x-axis meets the x-axis at A. Length of the perpendicular from A on the tangent line at P is equal to ‘a’. If this curve cuts the y-axis orthogonally, find the equation to all possible curves, expressing the answer explicitly.
Answer» ANSWER :`y = +- a (E^x/a + e^ -x/a)/2 & y +- a`

Discussion

24.	Letalpha, betabe suchpi lt alpha- betalt 3 piifsinalpha + sin beta = (-21)/(65) , andcosalphaCos beta= (-27)/(65) then the valueofcos( alpha - beta)/(2) is
Answer» `(6)/( 65)` `(3)/(sqrt(130))` `-(3)/(sqrt(130))` `(-6)/(65)` ANSWER :C

Discussion

25.	Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of the probability of choosing box B. If a red ball is drawn from the selected box then find the probability that it has come from box B.
Answer» ANSWER :`10/31`

Discussion

26.	Let bara,barb,barc be three non-zero non-coplanar vectors and barp = bara + barb - 2barc, barq = 3bara - 2barb + barc and barr=bara-4barb+2barc
Answer» `3 : 1` `7 : 1` `11 : 1` `15 : 1` Answer :D

Discussion

27.	If \|veca xx vecb\|=veca-vecb then the angle between veca and vecb is :
Answer» `(PI)/(4)` `(pi)/(2)` `(3pi)/(4)` `(pi)/(6)` SOLUTION :N/A

Discussion

28.	If S _(1), S _(2) , S _(3)……., S _(2n) are the sums of infinite geometric series whose first terms are respectively 1,2,3,…..,2n and common ratio are respectively, 1/2, 1/3, …….., (1)/(2n +1), find the value of , S_(1) ^(2) + S_(2) ^(2) +…....+ S _(2n -1) ^(2).
Answer» ANSWER :`( N ( 2N +1) ( 4N +1))/(3) -1 `

Discussion

29.	Prove that the line through A(0, -1, -1) and B(4, 5, 1) intersects the line through C(3, 9, 4) and D(-4, 4, 4).
Answer» ANSWER :`=140-140=0` `THEREFORE` GIVEN LINES are INTERSECTING.

Discussion

30.	Solvethe followingequations 4x^3 -13x^2-13 x+4=0
Answer» ANSWER :`-1,4,1/4`

Discussion

31.	The maximum value of [ x(x-1)+1]^((1)/(3)) , 0 lt= x lt= 1is
Answer» `((1)/(3))^((1)/(3))` `(1)/(2)` 1 0 Answer :C

Discussion

32.	The maximum value of[x(x-1)+1]^(1/3), 0 le x le1 is:
Answer» `(1/3)^(1/3)` ` 1/2` 1 0 Solution :Let ` f(x) = [x(x-1)+1]^(1//3)=(x^(2)-x+1)^(1//3),0 LEX le1` Differentiate w.r.t.X, `f'(x) = 1/3 (x^(2)-x+1)^(1/3-1)(2x-1)=((2x-1))/(3(x^(2)-x+1)^(2/3))` f'(x) = 0, ` rArr2x - 1 = 0rArrx=1/2 in [0, 1]` Now, we find thevalues of f at `x= 1/2` and at the end points of the interval [0, 1] at ` x= 0,f(0) = (0-0+1)^(1//3) = 1` at ` x = 1, f(1) = (1-1+1)^(1//3) = 1` at ` x = 1/2,f(1/2)=(1/4-1/2+1)^(1/3) = (3/4)^(1/3)` `:. ` The maximum VALUE off(x) is, 1, at x = 0, 1.

Discussion

33.	A= sin 1 , B= cos 1 ,C=tan 1 then the ascending order is
Answer» A,B,C B,A,C C,A,B B,C,A Answer :C

Discussion

34.	Integrate the function (x+2)/(sqrt(4x-x^(2)))
Answer» ANSWER :`-sqrt(4x-x^(2))+4sin^(-1)((x-2)/2)+C`

Discussion

35.	Area of a rectangle having vertices A,B,C and D with position vectors-overset^^i+1/2overset^^j+4overset^^k,overset^^i+1/2overset^^j+4overset^^k,overset^^i-1/2overset^^j+4overset^^k"and"-overset^^i-1/2overset^^j+4overset^^k respectively is :a)1/2b)1c)2d)4
Answer» `1/2` 1 2 4 Answer :C

Discussion

36.	Use following sequence, A_n = 3 - 8n What is A_1 ?
Answer» ANSWER :`-5`

Discussion

37.	The line (x-2)/(3) = (y+1)/( 2) = (z-1)/(-1) intersects the curve xy = c ^(2) , z =0 if c =
Answer» `pmsqrt(7)` `pmsqrt(5)` `pmsqrt(5)` `pm1` ANSWER :B

Discussion

38.	For x,yepsilonR with 0 lt x lt (pi)/2 such that ((sinx)^(2y))/((cosx)^((y^(2))/2))+((cosx)^(2y))/((sinx)^((y^(2))/2))=sin2x, then y is ________.
Answer» Solution :APPLY `AMgeGm` `((SINX)^(2y))/((cosx)^((y^(2))/2))+((cosx)^(2y))/((sinx)^((y^(2))/2))=2(sinx.cosx)^(y-(y^(2))/4)` It follows that `sin 2x ge 2(sinx.cosx)^(y-(y^(2))/4)` `:' sin x .COS XLT 1implies1 le y - (y^(2))/4` or `(1-(y^(2))/2)^(2) le 0` `impliesy=2` and `sin=cosx` So there is a unique solution `x-(pi)/4, y=2`

Discussion

39.	If log_(sqrt3)((abs(z)^(2)-absz+1)/(2+absz))gt2, then the locus of z is
Answer» `absz=5` `abszlt5` `abszgt5` NONE of these Answer :C

Discussion

40.	The sum to n terms of the series 1/2 + 3/4 + 7/8 + 15/16 + ....... is
Answer» `N - 1 + 2^(-n)` 1 `n - 1` `1 + 2^(-n)` ANSWER :A

Discussion

41.	If a, b, c be the p^(th), q^(th)and r^(th)terms respectively of an A.P.and G.P. both, then the product of the roots of equation(a^(b) b^(c ) c^(a))x^(2)-(abc)x+(a^(c )b^(a) c^(b))=0 equals
Answer» `-1` 2 abc 1 Answer :d

Discussion

42.	A three digit numbers is equal to the sum of the factorial of their digits . If the sum of all such three digit numbers is lamda then find the sum of digit of lamda.
Answer» ANSWER :10

Discussion

43.	The value of sqrt(15 + 8i) + sqrt(15 - 8i) is equal to
Answer» 15 8 23 7 Answer :B

Discussion

44.	Statement 1: Any chord of the conic x^(2) +y^(2) +xy = 1through (0,0)is bisected at ( 0,0 ) Statement 2: The centre of a conic is a point through which every chord is bisected.
Answer» Both the statement are TRUE and statement 2 is the CORRECT explanation of statement 1 Both the statement are True but Statement 2 is Not the correct explanation of Statement 1 Statement 1 is true and Statement 2 is FALSE Statement 1 is false and statement 2 is true. Answer :A

Discussion

45.	If a_1,a_2,a_3,….,a_n are in G.P. are in a_i > 0 for each I, then the determinantDelta=\|{:(loga_n,log a_(n+2),log a_(n+4)),(log a_(n+6),log a_(n+8), log a_(n+10)),(log a_(n+12), log a_(n+14), loga_(n+16)):}\|
Answer» 0 `(sum_(i=1)^(n^2+n) a_i)` 1 2 Answer :A

Discussion

46.	If c ne 0 and p/(2x)= a/(x+c) + b/(x-c) has two equal roots, then find p.
Answer» `p=(sqrta - sqrtb)^2` `(sqrta + SQRT b)^2` `(sqrta +- sqrtb)^2` `0` ANSWER :D

Discussion

47.	Prove that : Find the 7^("th") term in the expansion of ((4)/(x^(3))+(x^(2))/(2))^(14).
Answer» SOLUTION :N/A

Discussion

48.	Show that the circles S -= x^2 + y^2 - 2x - 4y - 20 = 0"___"(1) andS^1 -= x^2 + y^2 + 6x + 2y - 90 = 0 "___"(2) touch each other internally. Find their point of contact and the equation of common tnagent.
Answer» ANSWER :`= (5,5)`

Discussion

49.	Determine P(E\|F) A coinis tossed three times, where E : at most two tails, F : at least one tail
Answer» ANSWER :`(6)/(7)`

Discussion

50.	A set A contains 4 elements another set B contains 5 elements . If a function from A to B is formed then the probability that the function is one one is
Answer» `(4)/(5)` `(24)/(125)` `(12)/(125)` `(6)/(125)` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the Cartesian coordinates of the centre of gravity of the figure enclosed by the curve = a cos^(3) varphi (a gt 0).

Find the values of the following integrals (iv) int_(0)^(pi/4) sec^(3) x dx

If A and B are two events and A ne phi, B ne phi, then ………

Find the second order derivatives of the functions x^(20)

Find the rang of (2x^(2)-6x+5)/(x^(2)-3x+2).

What is the approximate perecent increase in average daily full - price ticket sales from 1990 to 1995 ?

Find the prabability of throwing atmost 2 sixes in 6 throws of a single die

If cosx=tany,cosy=tanz,cosz=tanx, then the value of sinx is

If the vectors vec(a)=hati+3hatj+hatk,vec(b)=2hati-hatj-hatk and vec( c )=lambda hati+7hatj+3hatk are coplannar then find lambda.

Ifalpha , beta , gammaare the rootsofx^3 -3x+1=0thentheequationwhoserootsare alpha- (1)/( beta gamma) , beta -(1)/(gammaalpha ) , gamma- (1)/( alpha beta )is

If a point R(4,y,z) lies on the line segment joining the points P(2,-3,4) and Q(8,0,10), then (OR)^(2) = _______??

Find the number of ways of arranging the letters of the word 'KRISHNA'so that all the vowels come together

An article manufactured by a company consists of two parts A and B. In the process of manufacture 13 out of 104 parts of A and 5 out of 100 parts of B may be defective then the probability that the assembled product is not defective is

If x is numerically so small so that x^2 and higher powers of x can be neglected , then (1+(2x)/(3))^(3/2), (32 + 5x)^(-1/5) is approximately equal to :

A random variable x follows binomial distribution with mean a and variance b then observe the following statements. Statement-I : a gt b gt 0 Statement-II : (a^(2))/(a-b) is a positive integer Statement-III : a+b=1 which of the above statments are true.

A (-5,0) and B (3,0) are two of the verti-﻿ ces of a triangle ABC. Its area is 20 square﻿ units. The vertex Clies on the line﻿ x - y = 2. The coordinates of C are

(i) Find equation of line joining (1,2) and ( 3,6) using determinants . (ii) Find equation of line joining (3,1) and ( 9,3) using determinants.

The value of x satisfying the equation |x-1|^(log_(3)x^(2)-2log_(x)9)=(x-1)^(7) is

Origin is the orthocentre of the triangle formed by the points (5, -1), (-2, 3) and (-4, -7) then its ninepoint centre is

Integrate the function in Exercise. x^(2)e^(x)

If aspherical soap bubble expands at the rate of 2 cc//sec, then , when the radius is 10 cm, its diamater is increasing at the rate of

The value lim_(n to oo) int_(0)^(1) ( sin n x)/( sin nx + cos nx) dx is

A perpendicular drawn from any point P of the curve on the x-axis meets the x-axis at A. Length of the perpendicular from A on the tangent line at P is equal to ‘a’. If this curve cuts the y-axis orthogonally, find the equation to all possible curves, expressing the answer explicitly.

Letalpha, betabe suchpi lt alpha- betalt 3 piifsinalpha + sin beta = (-21)/(65) , andcosalphaCos beta= (-27)/(65) then the valueofcos( alpha - beta)/(2) is

Let bara,barb,barc be three non-zero non-coplanar vectors and barp = bara + barb - 2barc, barq = 3bara - 2barb + barc and barr=bara-4barb+2barc

If |veca xx vecb|=veca-vecb then the angle between veca and vecb is :

If S _(1), S _(2) , S _(3)……., S _(2n) are the sums of infinite geometric series whose first terms are respectively 1,2,3,…..,2n and common ratio are respectively, 1/2, 1/3, …….., (1)/(2n +1), find the value of , S_(1) ^(2) + S_(2) ^(2) +…....+ S _(2n -1) ^(2).

Prove that the line through A(0, -1, -1) and B(4, 5, 1) intersects the line through C(3, 9, 4) and D(-4, 4, 4).

Solvethe followingequations 4x^3 -13x^2-13 x+4=0

The maximum value of [ x(x-1)+1]^((1)/(3)) , 0 lt= x lt= 1is

The maximum value of[x(x-1)+1]^(1/3), 0 le x le1 is:

A= sin 1 , B= cos 1 ,C=tan 1 then the ascending order is

Integrate the function (x+2)/(sqrt(4x-x^(2)))

Area of a rectangle having vertices A,B,C and D with position vectors-overset^^i+1/2overset^^j+4overset^^k,overset^^i+1/2overset^^j+4overset^^k,overset^^i-1/2overset^^j+4overset^^k"and"-overset^^i-1/2overset^^j+4overset^^k respectively is :a)1/2b)1c)2d)4

Use following sequence, A_n = 3 - 8n What is A_1 ?

The line (x-2)/(3) = (y+1)/( 2) = (z-1)/(-1) intersects the curve xy = c ^(2) , z =0 if c =

For x,yepsilonR with 0 lt x lt (pi)/2 such that ((sinx)^(2y))/((cosx)^((y^(2))/2))+((cosx)^(2y))/((sinx)^((y^(2))/2))=sin2x, then y is ________.

If log_(sqrt3)((abs(z)^(2)-absz+1)/(2+absz))gt2, then the locus of z is

The sum to n terms of the series 1/2 + 3/4 + 7/8 + 15/16 + ....... is

If a, b, c be the p^(th), q^(th)and r^(th)terms respectively of an A.P.and G.P. both, then the product of the roots of equation(a^(b) b^(c ) c^(a))x^(2)-(abc)x+(a^(c )b^(a) c^(b))=0 equals

A three digit numbers is equal to the sum of the factorial of their digits . If the sum of all such three digit numbers is lamda then find the sum of digit of lamda.

The value of sqrt(15 + 8i) + sqrt(15 - 8i) is equal to

Statement 1: Any chord of the conic x^(2) +y^(2) +xy = 1through (0,0)is bisected at ( 0,0 ) Statement 2: The centre of a conic is a point through which every chord is bisected.

If a_1,a_2,a_3,….,a_n are in G.P. are in a_i > 0 for each I, then the determinantDelta=|{:(loga_n,log a_(n+2),log a_(n+4)),(log a_(n+6),log a_(n+8), log a_(n+10)),(log a_(n+12), log a_(n+14), loga_(n+16)):}|

If c ne 0 and p/(2x)= a/(x+c) + b/(x-c) has two equal roots, then find p.

Prove that : Find the 7^("th") term in the expansion of ((4)/(x^(3))+(x^(2))/(2))^(14).

Show that the circles S -= x^2 + y^2 - 2x - 4y - 20 = 0"___"(1) andS^1 -= x^2 + y^2 + 6x + 2y - 90 = 0 "___"(2) touch each other internally. Find their point of contact and the equation of common tnagent.

Determine P(E|F) A coinis tossed three times, where E : at most two tails, F : at least one tail

A set A contains 4 elements another set B contains 5 elements . If a function from A to B is formed then the probability that the function is one one is

A (-5,0) and B (3,0) are two of the verti- ces of a triangle ABC. Its area is 20 square units. The vertex Clies on the line x - y = 2. The coordinates of C are

Show that the circles S -= x^2 + y^2 - 2x - 4y - 20 = 0"_"(1) andS^1 -= x^2 + y^2 + 6x + 2y - 90 = 0 "_"(2) touch each other internally. Find their point of contact and the equation of common tnagent.