28278 + Interview Questions in Maths in Class 12

1.	Statement I : (2x-1)/((x+1)(x^(2)+2))=(A)/(x+1)+(3x+c)/(x^(2)+2) then A= -1 Statement II : (Ax)/((x+2)(2x-3))=(2)/(x+2)+(3)/(2x-3) then A= 7 Statement III : The number of partial fractions of (x^(2)+1)/((x-1)^(4)) is 3. Which of the above statements are true.
Answer» I, II are true II, III are true III, I are true All are true Answer :D

Discussion

2.	Find the sum of the value (s) of a so that the equation (x^(2) + 2ax + 2a + 3) (x^(2) + 2ax + 4a +5 ) = 0 has only 3 real distinct roots.
Answer» ANSWER :`0005`

Discussion

3.	Let lt a_n gt be a sequence such that a_1=1and a_n+1 =cos a_n, n gt 1 . If a=lim_(xtooo) a_n, then a belongs to the interval
Answer» `(0,pi//6)` `(pi//6,pi//3)` `(pi//3,pi//2)` `(pi//2,4pi//3)` ANSWER :B

Discussion

4.	Evaluate int_(0)^((5pi)/(12))[tan x] dx
Answer» Answer :`(5PI)/(4) - (PI)/(4) - TAN^(-1) 3-tan^(-1) 2 = (pi)/(4)`

Discussion

5.	f:(-oo ,0] to[0,oo]is definedas f(x)= x^2. Thedomainand rangeof itsinverse is
Answer» DOMAIN`(f^(-1))=[0,oo),` rangeof ` (f^(-1))=(-00,0]` Domainof `(f^(-1))=[0,oo),` rangeof ` (f^(-1))=(-oo,oo]` Domainof ` f^(-1)=[0,oo)`, rangeof ` (f^(-1))=(0,oo)` `f^(-1)` doesnotexist ANSWER :A

Discussion

6.	Let f(x)=(x^(2)-2\|x\|)(2\|x\|-2)-9(2\|x\|-2)/(x^(2)-2\|x\|). (i) f(x) gt 0 (ii)f(x) ge 0 (iii)f(x) lt 0 (iv) f(x) le 0
Answer» Answer :`X in d(-oo,-3) cup (-2,-1)cup (1,2) cup (3,oo)`

Discussion

7.	If alpha, beta, gamma are roots of equation x^(3)- 10x^(2) + 7x + 8 = 0 . If a =alpha + beta + gamma, b = alpha^(2)+ beta^(2)+ gamma^(2), c = (1)/(alpha) + (1)/(beta) + (1)/(gamma) , d = (alpha)/(beta gamma) + (beta)/(gamma beta)+ (gamma )/(alpha beta) then a + b + c + d =
Answer» `(765)/(8)` `(576)/(8)` `(675)/(8)` `(657)/(8)` Answer :3

Discussion

8.	Using 0, 1, 2, how many different +ve integers which are smaller than 2xx10^8and divisible by 3 can be written
Answer» ANSWER :4373

Discussion

9.	int ((1-x)/(1+x^(2)))^(2) e^(x)dx
Answer» Answer :`E^(X)(1)/(1+x^(2))+C`

Discussion

10.	Show that the DeltaABC is an isosceles triangle if the determinant Delta=\|{:(1,1,1),(1+cosA,1+cosB,1+cosC),(cos^2A+cosA,cos^2B+cosB,cos^2C+cosC):}\|=0
Answer» ANSWER :`thereforeA=B=C`

Discussion

11.	Two roads OA and OB intersect at an angle 60^(@). A car driver approaches O from A, where OA = 800 metres, at a uniform speed of 20 m/sec. Simultaneasly, O runner starts running from O towards B at uniform speed of 5 m/sec. Find the time when the car and the runner are closest.
Answer» ANSWER :`(240)/(7)` SECOND.

Discussion

12.	If A= {:[( 1,0,1),(0,1,2),(0,0,4)]:},then show that \|3A\| =27\|A\|
Answer» ANSWER :`=108`

Discussion

13.	If n is a positive integer prove that (1+i)^(2n)+(1-i)^(2n)=2^(n+1)cos((n pi)/(2))
Answer» ANSWER :`2^(N+1).COS((n PI)/(2))`

Discussion

14.	The modulus of the vectors bar(a) and bar(b) are 2 and 3 respectively. If \|2(bar(a)xx bar(b))\|+\|3(bar(a).bar(b))\|=k then the maximum value of k = …………..
Answer» `SQRT(13)` `2sqrt(13)` `6sqrt(13)` `10sqrt(13)` ANSWER :C

Discussion

15.	If {sin ( alpha-beta)+cos(alpha+2beta)sin beta}^(2)=4 cos alpha sin beta (alpha+beta). Then, prove that tan alpha+tan beta=(tan beta)/((sqrt(2)cos beta-1)^(2)), alpha beta in (0 , pi//4).
Answer» ANSWER :

Discussion

16.	Solve the differential equation (dy)/(dx) + y sec x = tan x, 0 le x lt (pi)/(2).
Answer» ANSWER :`y (SEC X + TAN x ) = sec x + tan x - x + C`

Discussion

17.	If the radius of a sphere is raised from 10 cm to 10.02 cm when heated, then the percentage increase in volume is
Answer» 0.2 0.6 0.05 `pi//10` ANSWER :B

Discussion

18.	Prove each of the following relation: cos^(-1)x=sec^(-1)1/x=pi-sin^(-1)sqrt(1-x^(2))=pi+"tan"^(-1)(sqrt(1-x^(2)))/x="cot"^(-1)x/(sqrt(1-x^(2))) when -1ltxlt0
Answer» SOLUTION :NA

Discussion

19.	int e^(-3x)cos^(3)xdx
Answer» Answer :`(3E^(-3X))/(40)(sinx-3 COSX)+C`

Discussion

20.	Salivary glands are situated :-
Answer» Just insidethe BUCCAL CAVITY Just OUTSIDE the ORAL cavity Just INSIDE the oesophagoues Just outside the oesophagous Answer :A

Discussion

21.	Find the area of the region bounded by y=e^(x) and y = x between x = 0 and x = 1.
Answer» ANSWER :`(E- (3)/(2))`

Discussion

22.	Show that for a differentiable functin f (x), int _(0) ^(n) f '(x) {[x] -x + (1)/(2) } dx = int _(0) ^(n) f (x) dx + 1/2 f (0 ) + 1/2 f (n) - sum _(r =0) ^(n) f (e), where [**] denotes the greatest integer function and n in N)
Answer» ANSWER :`F (X ) DX `

Discussion

23.	Let A, B, C be finite sets. Suppose that n(A)=11,n(B)=16,n(C )=21,n(AnnB)=9andn(BnnC)=10. Then the possible value of n(AuuBuuC) is
Answer» 27 28 29 Any of the three VALUES 27, 28, 29 is possible ANSWER :D

Discussion

24.	If a = 2i + 3j + 5k, b = - I + j + k, c = 4i + 2j + 3k then (a xx b) xx c =
Answer» 8I - 19j - k `-I -4J + 4k` 7i + 3I - k `-I - 5j - 5K` Answer :B

Discussion

25.	overset((pi)/(4))underset(-(pi)/(4))int log (sin x+cosx)dx
Answer» ANSWER :`:. I=(pi)/(4) LOG _(e)((1)/(2))`

Discussion

26.	Find the values of x for which y = [x(x – 2)]^(2)is an increasing function.
Answer» ANSWER :0 `lt x lt 1` and `x gt 2`

Discussion

27.	Find the equation of a curve passing through the point (0,-2). Given that at any point (x,y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.
Answer» ANSWER :`y^(2) - X^(2) = 4`

Discussion

28.	If int_(0)^(1)[4x^(3)-f(x)dx=(4)/(7)] then find the area of region bounded by y=f(x),x-axis and coordinatex = 1 and x = 2.
Answer» ANSWER :`7.5`

Discussion

29.	f(x)= {((1- cos 4x)/(8x^(2))",",x ne 0),(k",",x= 0):}. If the function f(x) is continuous at x= 0, then find k.
Answer» ANSWER :k=1

Discussion

30.	Evaluate the following definite integrals . int_(2)^(3)x^(2)dx
Answer» ANSWER :`19/3`

Discussion

31.	There are several tea cups in the kitchen, some with handle and the others without handles. The number of ways of selecting two cups without a handle and three with a handle is exactly 1200.What is the maximum possible number of cups in the kitchen?
Answer» ANSWER :29

Discussion

32.	If Y=[{:(4,3),(2,5):}]and3X-Y=[{:(5,0),(1,1):}]then find X.
Answer» ANSWER :`X=[{:(3,1),(1,2):}]`

Discussion

33.	Integrate the functions cot x log sin x
Answer» ANSWER :`1/2(logsinx)^(2)+C`

Discussion

34.	overset(pi)underset(-pi)int sin^(3)xcos^(2)xdx=...
Answer» ANSWER :`overset(pi)underset(-pi)INT F(x)dx=0`

Discussion

35.	Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find, P(AuuB)
Answer» <P> SOLUTION :`P(ANNB)`B)-`P(AnnB)` =P(A)+P(B)-P(A)P(B) =0.3+0.4-`0.3xx0.4`

Discussion

36.	The probability that a bulb produced by a factory will fuse after 150 days is 0.05. Find the probability that out of 5 such bulbs (i) none (ii) not more than one (iii) more than one (iv) at least one will fuse after 150 days of use.
Answer» Answer :(i) `(0.95)^(5)` (II) `(45)/(512)` (iii) `(243)/(1024)` (IV) `1-(0.95)^(5)`

Discussion

37.	If A+B+C=pi then find the value of \|{:(sin^2A,sinAcosA,cos^2A),(sin^2B,sinBcosB,cos^2B),(sin^2C,sinCcosC,cos^2C):}\|
Answer» ANSWER :SIN(A-B)sin(C-A)sin(C-B)

Discussion

38.	If two dice are rolled thrice, then the mean of X where X denotes the number of times even numbers obtained on both dice is
Answer» `(1)/(4)` `(3)/(4)` `(1)/(2)` `(1)/(5)` ANSWER :B

Discussion

39.	Find the centre and radius of the circle x^(2) + y^(2) + 2x-4y-4=0
Answer» ANSWER :`sqrt9 =3`

Discussion

40.	Differentiate (x^2-5x+8)(x^3+7x+9) by expanding the product to obtain a single polynomial
Answer» SOLUTION :GIVEN FUNCTION `=x^5+7x^3+9x^2-5x^4-35x^2-45x+8x^3+56x+72=x^5-5x^4+15x^3-26x^2+11x+72therefore` REQUIRED DERIVATIVE `=5x^4-20x^3+45x^2-52x+11`

Discussion

41.	Let P (a sec theta, b tan theta) and Q (a sec phi, b tan theta) where theta+phi=pi/2, be two points on the hyperola x^(2)/a^(2)-y^(2)/b^(2)=1, If (h,k) is the point of intersection of normals of P and Q then find the value of k.
Answer» ANSWER :`K=- ((a^(2)+B^(2))/(b))`

Discussion

42.	A unitvectorperpendicularto both thevectors2 hati-3hatj+6hatk and 3hatj-4hatj is -
Answer» `(1)/(SQRT(34)) (3hati-4hatj+3hatk)` `(1)/(sqrt(34)) (3hati+4hatj-3hatk)` `(1)/(sqrt(34)) (3hati-4hatj-3hatk)` `(1)/(sqrt(34)) (-3hati+4hatj+3hatk)` ANSWER :D

Discussion

43.	Find \|vecx\|, if for a unit vector veca,(vecx-veca)*(vecx+veca)=12.
Answer» ANSWER :`SQRT(13)`

Discussion

44.	If tanx+tan(x+pi/3)+tan(x+(2pi)/3)=3, thentan 3x is equal to
Answer» 3 1 2 0 Answer :C

Discussion

45.	Check the validity of p:100 is a multiple of 5 and 4.
Answer» SOLUTION :Here the connective is .and. Step -1: 100 is a multiple of 5(True) Step -2: 100 is a multiple of 4(True) `:.`100 is a multiple of 5 and 4 is true, i.e. the STATEMENT .p. is valid.

Discussion

46.	The solution of tan ^(2) 9x = cos 2x -1is
Answer» `(NPI)/(3), n in I` `(npi)/(6), n in I` `npi, n in I` None of these ANSWER :D

Discussion

47.	Letf(x)={{:((x^(n)cos((1)/(x)))/(0^(tan^(m)x)),,xne0 ),(0,,x=0):}
Answer» `nlem` `mltnlem+1` `nlt2m` `nlt2m+1` Solution :`UNDERSET(xto0)Lim(X^(N)cos((1)/(x)))/(((tanx)/(x))^(m).x^(m))=underset(xto0)Limx^(n-m)cos((1)/(x))` `:." "n-mgt0` so that f(x) is continuous at x=0 But f(x) is non-derivable at x=0, so `f'(0)=underset(xto0)Lim(x^(n)cos((1)/(x)))/(((tanx)/(x))^(m).x^(m).x)=underset(xto0)Limx^(n-m-1)cos((1)/(x))` `n-m-1le0` os that f'(0) does not EXIST `n-mle1`

Discussion

48.	Prove that each diagonal element of a skew-stmmetric matrix is zero.
Answer»

Discussion

49.	If int(cos x - sin x)/(sqrt(8-sin 2x))dx = sin^(-1)((sin x + cos x)/(a)) + C, then a =
Answer» Solution :Let `I=int (COS x - SIN x)/(SQRT(8-sin 2x))dx` `rArr I = int(1)/(sqrt(3^(2)-(sin x + cos x)^(2)))d(sin x + cos x)` `rArr I = sin^(-1)((sin x + cos x)/(3))+C` HENCE. A = 3

Discussion

50.	Let x,y,z be real numbers such that 3x, 4y and 5z from a geometric progression while x,y,z form an H.P. If the value of ((x)/(z) +(z)/(x)) can be expressed as a lowest rational p/q, then (p+q) has the value equal to
Answer» 29 39 49 59 Answer :C

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Statement I : (2x-1)/((x+1)(x^(2)+2))=(A)/(x+1)+(3x+c)/(x^(2)+2) then A= -1 Statement II : (Ax)/((x+2)(2x-3))=(2)/(x+2)+(3)/(2x-3) then A= 7 Statement III : The number of partial fractions of (x^(2)+1)/((x-1)^(4)) is 3. Which of the above statements are true.

Find the sum of the value (s) of a so that the equation (x^(2) + 2ax + 2a + 3) (x^(2) + 2ax + 4a +5 ) = 0 has only 3 real distinct roots.

Let lt a_n gt be a sequence such that a_1=1and a_n+1 =cos a_n, n gt 1 . If a=lim_(xtooo) a_n, then a belongs to the interval

Evaluate int_(0)^((5pi)/(12))[tan x] dx

f:(-oo ,0] to[0,oo]is definedas f(x)= x^2. Thedomainand rangeof itsinverse is

Let f(x)=(x^(2)-2|x|)(2|x|-2)-9(2|x|-2)/(x^(2)-2|x|). (i) f(x) gt 0 (ii)f(x) ge 0 (iii)f(x) lt 0 (iv) f(x) le 0

If alpha, beta, gamma are roots of equation x^(3)- 10x^(2) + 7x + 8 = 0 . If a =alpha + beta + gamma, b = alpha^(2)+ beta^(2)+ gamma^(2), c = (1)/(alpha) + (1)/(beta) + (1)/(gamma) , d = (alpha)/(beta gamma) + (beta)/(gamma beta)+ (gamma )/(alpha beta) then a + b + c + d =

Using 0, 1, 2, how many different +ve integers which are smaller than 2xx10^8and divisible by 3 can be written

int ((1-x)/(1+x^(2)))^(2) e^(x)dx

Show that the DeltaABC is an isosceles triangle if the determinant Delta=|{:(1,1,1),(1+cosA,1+cosB,1+cosC),(cos^2A+cosA,cos^2B+cosB,cos^2C+cosC):}|=0

Two roads OA and OB intersect at an angle 60^(@). A car driver approaches O from A, where OA = 800 metres, at a uniform speed of 20 m/sec. Simultaneasly, O runner starts running from O towards B at uniform speed of 5 m/sec. Find the time when the car and the runner are closest.

If A= {:[( 1,0,1),(0,1,2),(0,0,4)]:},then show that |3A| =27|A|

If n is a positive integer prove that (1+i)^(2n)+(1-i)^(2n)=2^(n+1)cos((n pi)/(2))

The modulus of the vectors bar(a) and bar(b) are 2 and 3 respectively. If |2(bar(a)xx bar(b))|+|3(bar(a).bar(b))|=k then the maximum value of k = …………..

If {sin ( alpha-beta)+cos(alpha+2beta)sin beta}^(2)=4 cos alpha sin beta (alpha+beta). Then, prove that tan alpha+tan beta=(tan beta)/((sqrt(2)cos beta-1)^(2)), alpha beta in (0 , pi//4).

Solve the differential equation (dy)/(dx) + y sec x = tan x, 0 le x lt (pi)/(2).

If the radius of a sphere is raised from 10 cm to 10.02 cm when heated, then the percentage increase in volume is

Prove each of the following relation: cos^(-1)x=sec^(-1)1/x=pi-sin^(-1)sqrt(1-x^(2))=pi+"tan"^(-1)(sqrt(1-x^(2)))/x="cot"^(-1)x/(sqrt(1-x^(2))) when -1ltxlt0

int e^(-3x)cos^(3)xdx

Salivary glands are situated :-

Find the area of the region bounded by y=e^(x) and y = x between x = 0 and x = 1.

Show that for a differentiable functin f (x), int _(0) ^(n) f '(x) {[x] -x + (1)/(2) } dx = int _(0) ^(n) f (x) dx + 1/2 f (0 ) + 1/2 f (n) - sum _(r =0) ^(n) f (e), where [**] denotes the greatest integer function and n in N)

Let A, B, C be finite sets. Suppose that n(A)=11,n(B)=16,n(C )=21,n(AnnB)=9andn(BnnC)=10. Then the possible value of n(AuuBuuC) is

If a = 2i + 3j + 5k, b = - I + j + k, c = 4i + 2j + 3k then (a xx b) xx c =

overset((pi)/(4))underset(-(pi)/(4))int log (sin x+cosx)dx

Find the values of x for which y = [x(x – 2)]^(2)is an increasing function.

Find the equation of a curve passing through the point (0,-2). Given that at any point (x,y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

If int_(0)^(1)[4x^(3)-f(x)dx=(4)/(7)] then find the area of region bounded by y=f(x),x-axis and coordinatex = 1 and x = 2.

f(x)= {((1- cos 4x)/(8x^(2))",",x ne 0),(k",",x= 0):}. If the function f(x) is continuous at x= 0, then find k.

Evaluate the following definite integrals . int_(2)^(3)x^(2)dx

There are several tea cups in the kitchen, some with handle and the others without handles. The number of ways of selecting two cups without a handle and three with a handle is exactly 1200.What is the maximum possible number of cups in the kitchen?

If Y=[{:(4,3),(2,5):}]and3X-Y=[{:(5,0),(1,1):}]then find X.

Integrate the functions cot x log sin x

overset(pi)underset(-pi)int sin^(3)xcos^(2)xdx=...

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find, P(AuuB)

The probability that a bulb produced by a factory will fuse after 150 days﻿ is 0.05. Find the probability that out of 5 such bulbs﻿ (i) none ﻿ (ii) not more than one﻿ (iii) more than one﻿ (iv) at least one﻿ will fuse after 150 days of use.﻿

If A+B+C=pi then find the value of |{:(sin^2A,sinAcosA,cos^2A),(sin^2B,sinBcosB,cos^2B),(sin^2C,sinCcosC,cos^2C):}|

If two dice are rolled thrice, then the mean of X where X denotes the number of times even numbers obtained on both dice is

Find the centre and radius of the circle x^(2) + y^(2) + 2x-4y-4=0

Differentiate (x^2-5x+8)(x^3+7x+9) by expanding the product to obtain a single polynomial

Let P (a sec theta, b tan theta) and Q (a sec phi, b tan theta) where theta+phi=pi/2, be two points on the hyperola x^(2)/a^(2)-y^(2)/b^(2)=1, If (h,k) is the point of intersection of normals of P and Q then find the value of k.

A unitvectorperpendicularto both thevectors2 hati-3hatj+6hatk and 3hatj-4hatj is -

Find |vecx|, if for a unit vector veca,(vecx-veca)*(vecx+veca)=12.

If tanx+tan(x+pi/3)+tan(x+(2pi)/3)=3, thentan 3x is equal to

Check the validity of p:100 is a multiple of 5 and 4.

The solution of tan ^(2) 9x = cos 2x -1is

Letf(x)={{:((x^(n)cos((1)/(x)))/(0^(tan^(m)x)),,xne0 ),(0,,x=0):}

Prove that each diagonal element of a skew-stmmetric matrix is zero.

If int(cos x - sin x)/(sqrt(8-sin 2x))dx = sin^(-1)((sin x + cos x)/(a)) + C, then a =

Let x,y,z be real numbers such that 3x, 4y and 5z from a geometric progression while x,y,z form an H.P. If the value of ((x)/(z) +(z)/(x)) can be expressed as a lowest rational p/q, then (p+q) has the value equal to

The probability that a bulb produced by a factory will fuse after 150 days is 0.05. Find the probability that out of 5 such bulbs (i) none (ii) not more than one (iii) more than one (iv) at least one will fuse after 150 days of use.