28278 + Interview Questions in Maths in Class 12

1.	Let f: R to R be defined as f (x)= 3x. Choose the correct answer.
Answer» F is one-one ONTO f is many-one onto f is one-one but not onto f is NEITHER one-one nor onto. ANSWER :A

Discussion

2.	If sum_(i=1)^(18) (x_(i) - 8) = 9 andsum_(i=1)^(18) (x_(i) - 8)^(2) = 45 then the standard deviation of x_(1), x_(2),…,x_(18) is
Answer» `(4)/(9)` `(9)/(4)` `(3)/(2)` `(1)/(2)` Answer :C

Discussion

3.	(pvvr)^^(qvvr)=
Answer» `PVV(q^^r)` `p^^(qvvr)` `(p^^q)VVR` none of these Answer :C

Discussion

4.	f(x+y)=f(x).f(y) for all x,yinR and f(5)=2,f'(0)=3 then f'(5) is equal to
Answer» `G'(X)` `g(x)` `F(x)` `f'(x)` ANSWER :C

Discussion

5.	If the product of two of 6x^(4) - 29x^(3) + 40x^(2) - 7x - 12 = 0is 2 then the roots are
Answer» 4/3, 3/2, 1 + `sqrt(2), 1 - sqrt(2)` `-4//3, 3//2, 1 + sqrt(2), 1 - sqrt(2)` `4//3, -3//2, 1 + sqrt(2), 1 - sqrt(2)` `- 4// 3, -3//2, 1 + sqrt(2) , 1- sqrt(2)` Answer :1

Discussion

6.	If two ogives of a data intersect (37, 51), the total number of observation in the data is ___________
Answer» ANSWER :`102`

Discussion

7.	The triangle formed by the points 3+3i,2+2i,1+3i in the argand diagram is
Answer» ISOSCELES equilateral right ANGLED right angled isosceles Answer :D

Discussion

8.	From a rectangular sheet of dimensions 30cm times 80cm, four squares of sides x cm are removed at the corners, and the sides are then turned up so as to form an open rectangular box. What is the value of x, so that the volume of the box is the greatest?
Answer» 20/3 `10//3` `15//2` 5 Answer :A

Discussion

9.	Using vectors, find the value of k, such that the points (k,-10,3),(1,-1,3) and (3, 5, 3) are collinear.
Answer» ANSWER :`k=-2`

Discussion

10.	If y= cos^(-1) x, Find (d^(2)y)/(dx^(2)) in terms of y alone.
Answer» ANSWER :`-COT y "COSEC"^(2) y`

Discussion

11.	The x-raybeam emerging iiom anX-ray tube
Answer» is monochmmatic. CONTAINS all wavelengths smaller a CERTAIN maximum wavelength contains all wavelengths LARGER then a certain minimum wavelength contains all wavelengths LYING between a minimum and a maximum wavelength. Answer :C

Discussion

12.	If 5 different things are placed at random in 3 different boxes then the probability of placing them such that no box remains empty is
Answer» `(31)/(81)` `(50)/(81)` `(40)/(81)` `(20)/(81)` ANSWER :B

Discussion

13.	(1)/(sqrt((x-1)(x-2)))
Answer» Solution :` int(1)/(sqrt((x-1)(x-2)))DX` `= int(1)/(sqrt(x^(2)-3x+2))dx` `= int (1)/(sqrt((x^(2) -3x+(9)/(4))+2-(9)/(4)))dx` `= int (1)/(sqrt((x-(3)/(2))^(2) -((1)/(2))^(2)))dx` `=log \| x-(3)/(2) +sqrt((x-(3)/(2))^(2) -((1)/(2))^(2))\|+c` ` =log\|x-(3)/(2) +sqrt(x^(2)-3x+2)\|+c`

Discussion

14.	A matrixA = ({:(2,3),(5,-2):})is such that A^(-1)= lambda Athen what is the value of lambda.
Answer» 19 9 ` (1)/(19)` `-(1)/(19)` ANSWER :C

Discussion

15.	vec(a)_\|_vec(b) and vec(c),\|vec(a)\|=2,\|vec(b)\|=3,\|vec( c )\|=4. The angle between vec(b) and vec( c ) is (2pi)/(3) then \|[vec(a) vec(b) vec( c )]\|= …………
Answer» `4sqrt(3)` `6sqrt(3)` `12SQRT(3)` `18sqrt(3)` ANSWER :C

Discussion

16.	If three six-faced fair dice are thrown together, the probability that the sum of the numbers appearing on the dice is 16 is
Answer» `1/36` `1/11` `1/12` `5/36` ANSWER :A

Discussion

17.	Let f,g : [-1,2] tobe continuous functions which are twice differentiable on the interval (-1,2). Let the values of f and g at the pointsand 2 be as given in the following table: In each of the intervals(-1,0) and (0, 2) the function (f-3g) never vanishes. Then the correct statements(s) is(are) :
Answer» f'(X)-3g'(x)=0 has exactly three solution in`(-1,0) CUP (0,2)` `f'(x)-3g'(x)=0` has exactly one solution in(-1,0) f'(x)-3g'(x)=0 has exactly one solution in (0, 2) f'(x)-3g'(x)=0 has exactly TWO solutions INAND exactly two solutions in (0, 2) Answer :B::C

Discussion

18.	For every natural number n, n (n ^(2) -1) is divisible by
Answer» ANSWER :6

Discussion

19.	I is the incentre of DeltaABCandP_(1),P_(2)andP_(3) respectively are the radii of the circumcircles of the DeltaIBC,DeltaICAandDeltaIAB . Then P_(1)P_(2)P_(3)=
Answer» `RR^(2)` `2R^(2)R` `2Rr` `R^(2)r` ANSWER :b

Discussion

20.	Compute the magnitude of oversetrarra =overset^^i+overset^^j+overset^^k,vector
Answer» SOLUTION :`\|veca\|=sqrt(1^2+1^2+1^2)=SQRT3`

Discussion

21.	Determine if the set A={1,2,3…..}is a proper subset of the set B={x:x is a rational number}
Answer» SOLUTION :A is a proper SUBSET of B as all the ELEMENTS of A ae in B.

Discussion

22.	A positive divisor of integer 60 is selected at random. Find the probability that selected divisor is an even integer but not divisible by 4.
Answer» ANSWER :`(1)/(3)`

Discussion

23.	A =[a_(ij)]_(mxxn)is a square matrix ,if
Answer» `MLTN` `mgtn` `m=n` NONE of these Answer :C

Discussion

24.	Find the slope of the tangent to curve y = x^(3) – x + 1 at the point whose x-coordinate is 2.
Answer» ANSWER :11

Discussion

25.	Examine the continuity of the function f(x) = {(3x+5",","if " x ge 2),(x^(2) ,"if " x lt 2):} at x= 2
Answer» ANSWER :x=2

Discussion

26.	If x.a = 0, x xx b = c xx b then x =
Answer» `C - (c.a)/(B.a) b` `c - (c.a)/(c.b) a` `a - (c.a)/(c.b) b` `b - (c.a)/(c.b) b` ANSWER :A

Discussion

27.	If [.] denotes the greatest integer function and f(x)={:{(3(x)-(5\|x\|)/(x)","x ne 0),(" "2","x= 0):} then int_(-3//2)^(2) f(x)dx is equal to
Answer» `-(11)/(2)` `-(7)/(2)` -6 `-(17)/(2)` Answer :A

Discussion

28.	Find the area of the region bounded by y_(2) = 9x, x = 2, x = 4 and the x-axis in the first quadrant.
Answer» ANSWER :`16-4sqrt2`

Discussion

29.	If the equation ax^2 + bx + c = 0 ( a gt 0) has two roots alpha and beta such that alpha < -2 and beta> 2, then
Answer» `b^2 - 4ac = 0` `b^2 - 4ac lt 0` `b^2 - 4ac GT 0` `b^2 - 4ac GE 0` ANSWER :C

Discussion

30.	If I=int_(0)^(1)sqrt(1+x^(3))dx then
Answer» `I gt 1` ` I != (sqrt(5))/(2)` `1 gt (sqrt(7))/(2)` `I=0` Answer :A

Discussion

31.	If . int(cos^(2)xsinx)/(sinx-cosx)dx=Alog\|sinx-cosx\|+(1)/(8)(sin2x+cos2x)+C, then A is equal to
Answer» ANSWER :0.25

Discussion

32.	Find A , if [{:(4),(1),(3):}]A=[{:(-4,8,4),(-1,2,1),(-3,6,3):}]
Answer» ANSWER :`=[-1 " "2 " " 1]`

Discussion

33.	If t_(n)=(1)/(4)(n+2)(n+3) for n = 1, 2, 3,… then (1)/(t_(1))+(1)/(t_(2))+….+(1)/(t_(2003)) is equal to
Answer» `(4006)/(3006)` `(4003)/(3007)` `(4006)/(3008)` `(4006)/(3009)` ANSWER :D

Discussion

34.	If \|x\| is so small that all terms containing x^2 and higher powers of x can be neglected , then the approximate value of ((3 - 5x)^(1//2))/((5 - 3x)^2),where x = (1)/(sqrt363) , is
Answer» `(SQRT3)/(25)` `(1+30sqrt3)/(75)` `(1-30sqrt3)/(75)` `(1+30sqrt3)/(750)` ANSWER :D

Discussion

35.	Find the number of ways of arranging 6 boys and 6 girls around a circular table so that boys and girls sit alternately
Answer» ANSWER :`5!xx6!`

Discussion

36.	Find the second order derivatives of the following functions: sin(x^(2) + 5)
Answer» ANSWER :`2 cos (X^(2)+ 5)- 4x^(2) SIN (x^(2) + 5)`

Discussion

37.	If ""^nP_5:""^(n-1)P_5=3:2 then find n.
Answer» ANSWER :15

Discussion

38.	If A = { Ø, {Ø}} then the power set of A is
Answer» A `{PHI,{phi},A}` `{phi,{phi},{{phi}},A}` `{phi,{phi}}` ANSWER :C

Discussion

39.	If the matrix A=[(3,-3),(-3,3)] and A^(2)=lamdaA, then write value of 'lamda'.
Answer» ANSWER :`lamda=6`

Discussion

40.	If shoppers enter a store at an average rate of r shoppers per minute and each stays in the store for an average time of T minutes, the average number of shoppers in the store, N, at any one time is given by the formula N rT = . This relationship is known as Little’s law. The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes. The store owner uses Little’s law to estimate that there are 45 shoppers in the store at any time. The owner of the Good Deals Store opens a new store across town. For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes. The average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time? (Note: Ignore the percent symbol when entering your answer. For example, if the answer is 42.1%, enter 42.1)
Answer»

Discussion

41.	If 3A-B=[(5,0),(1,1)] and B=[(4,3),(2,5)], then find the matrix A.
Answer» ANSWER :`[(3,1),(1,2)]`

Discussion

42.	\|veca\| = \|vecb\| = veca = vecb.
Answer» SOLUTION :`VECA` = `VECB` IMPLIES `\|veca\|` = `\|vecb\|`

Discussion

43.	If sintheta+2costheta=1,then what is 2sintheta-costheta equal to ?
Answer» 0 1 2 4 Solution :Let`sintheta+2costheta=1` . . . (i) Consider `2sintheta-costheta=alpha("let")`.. . (ii) SQUARING and adding `SIN^(2)theta+4cos^2)theta+4sinthetacostheta+4sin^(2)theta+cos^(2)theta-4sinthetacostheta=1+alpha^(2)`. `rArr(sin^(2)theta+cos^(2)theta)+4(cos^(2)theta+sin^(2)theta)=1+alpha^(2)`. `rArr1+4=1+alpha^(2)rArralpha^(2)=4rArralpha=2`.

Discussion

44.	If shoppers enter a store at an average rate of r shoppers per minute and each stays in the store for an average time of T minutes, the average number of shoppers in the store, N, at any one time is given by the formula N rT = . This relationship is known as Little’s law. The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes. The store owner uses Little’s law to estimate that there are 45 shoppers in the store at any time. Little’s law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spend an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store?
Answer»

Discussion

45.	Find the conic represented by the equation sqrt( ax) + sqrt( by) = 1?
Answer» ANSWER :the GIVEN EQUATION REPRESENTS a PARABOLA.

Discussion

46.	C_2+2. C_3 + 3. C_4 + ….+ 14. C_15=
Answer» `2^14. 13+1` `2^13. 12+1` `2^11 . 13+2` none Answer :A

Discussion

47.	If a, b, c, d, x are distinct non zero real numbers suchthat (a^(2)+b^(2)+c^(2))x^(2)-2 (ab+bc+cd)x +(b^(2)+c^(2)+d^(2)) le 0, then a, b, c, d are in
Answer» A.P. H.P. G.P. NONE of these ANSWER :C

Discussion

48.	Fifteen coupons are numbered 1,2,. . . . 15 respectively seven coupons are selected at random one at time withreplacement. The probabilitythat thelargest number appearingon a selected coupons is 9 is
Answer» `((9)/(16))^(6)` `((8)/(15))^(7)` `((3)/(5))^(7)` `(9^(7) - 8^(7))/(15^(7))` Answer :D

Discussion

49.	Is the function f defined by f(x)= {(x",","if" x le 1),(5",","if" x gt 1):} continuous at x=0 ? At x= 1 ? At x=2 ?
Answer» ANSWER :x=2

Discussion

50.	A curve is difined parametrically by x=e^(sqrtt),y=3t-log_(e)(t^(2)), where t is a parameter. Then the equation of the tangent line drawn to the curve at t = 1 is
Answer» `y=(2)/(E)x+1` `y=(2)/(e)x-1` `y=(e)/(2)x+1` `y=(e)/(2)x-1` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let f: R to R be defined as f (x)= 3x. Choose the correct answer.

If sum_(i=1)^(18) (x_(i) - 8) = 9 andsum_(i=1)^(18) (x_(i) - 8)^(2) = 45 then the standard deviation of x_(1), x_(2),…,x_(18) is

(pvvr)^^(qvvr)=

f(x+y)=f(x).f(y) for all x,yinR and f(5)=2,f'(0)=3 then f'(5) is equal to

If the product of two of 6x^(4) - 29x^(3) + 40x^(2) - 7x - 12 = 0is 2 then the roots are

If two ogives of a data intersect (37, 51), the total number of observation in the data is ___________

The triangle formed by the points 3+3i,2+2i,1+3i in the argand diagram is

From a rectangular sheet of dimensions 30cm times 80cm, four squares of sides x cm are removed at the corners, and the sides are then turned up so as to form an open rectangular box. What is the value of x, so that the volume of the box is the greatest?

Using vectors, find the value of k, such that the points (k,-10,3),(1,-1,3) and (3, 5, 3) are collinear.

If y= cos^(-1) x, Find (d^(2)y)/(dx^(2)) in terms of y alone.

The x-raybeam emerging iiom anX-ray tube

If 5 different things are placed at random in 3 different boxes then the probability of placing them such that no box remains empty is

(1)/(sqrt((x-1)(x-2)))

A matrixA = ({:(2,3),(5,-2):})is such that A^(-1)= lambda Athen what is the value of lambda.

vec(a)_|_vec(b) and vec(c),|vec(a)|=2,|vec(b)|=3,|vec( c )|=4. The angle between vec(b) and vec( c ) is (2pi)/(3) then |[vec(a) vec(b) vec( c )]|= …………

If three six-faced fair dice are thrown together, the probability that the sum of the numbers appearing on the dice is 16 is

Let f,g : [-1,2] tobe continuous functions which are twice differentiable on the interval (-1,2). Let the values of f and g at the pointsand 2 be as given in the following table: In each of the intervals(-1,0) and (0, 2) the function (f-3g) never vanishes. Then the correct statements(s) is(are) :

For every natural number n, n (n ^(2) -1) is divisible by

I is the incentre of DeltaABCandP_(1),P_(2)andP_(3) respectively are the radii of the circumcircles of the DeltaIBC,DeltaICAandDeltaIAB . Then P_(1)P_(2)P_(3)=

Compute the magnitude of oversetrarra =overset^^i+overset^^j+overset^^k,vector

Determine if the set A={1,2,3…..}is a proper subset of the set B={x:x is a rational number}

A positive divisor of integer 60 is selected at random. Find the probability that selected divisor is an even integer but not divisible by 4.

A =[a_(ij)]_(mxxn)is a square matrix ,if

Find the slope of the tangent to curve y = x^(3) – x + 1 at the point whose x-coordinate is 2.

Examine the continuity of the function f(x) = {(3x+5",","if " x ge 2),(x^(2) ,"if " x lt 2):} at x= 2

If x.a = 0, x xx b = c xx b then x =

If [.] denotes the greatest integer function and f(x)={:{(3(x)-(5|x|)/(x)","x ne 0),(" "2","x= 0):} then int_(-3//2)^(2) f(x)dx is equal to

Find the area of the region bounded by y_(2) = 9x, x = 2, x = 4 and the x-axis in the first quadrant.

If the equation ax^2 + bx + c = 0 ( a gt 0) has two roots alpha and beta such that alpha < -2 and beta> 2, then

If I=int_(0)^(1)sqrt(1+x^(3))dx then

If . int(cos^(2)xsinx)/(sinx-cosx)dx=Alog|sinx-cosx|+(1)/(8)(sin2x+cos2x)+C, then A is equal to

Find A , if [{:(4),(1),(3):}]A=[{:(-4,8,4),(-1,2,1),(-3,6,3):}]

If t_(n)=(1)/(4)(n+2)(n+3) for n = 1, 2, 3,… then (1)/(t_(1))+(1)/(t_(2))+….+(1)/(t_(2003)) is equal to

If |x| is so small that all terms containing x^2 and higher powers of x can be neglected , then the approximate value of ((3 - 5x)^(1//2))/((5 - 3x)^2),where x = (1)/(sqrt363) , is

Find the number of ways of arranging 6 boys and 6 girls around a circular table so that boys and girls sit alternately

Find the second order derivatives of the following functions: sin(x^(2) + 5)

If ""^nP_5:""^(n-1)P_5=3:2 then find n.

If A = { Ø, {Ø}} then the power set of A is

If the matrix A=[(3,-3),(-3,3)] and A^(2)=lamdaA, then write value of 'lamda'.

If 3A-B=[(5,0),(1,1)] and B=[(4,3),(2,5)], then find the matrix A.

|veca| = |vecb| = veca = vecb.

If sintheta+2costheta=1,then what is 2sintheta-costheta equal to ?

Find the conic represented by the equation sqrt( ax) + sqrt( by) = 1?

C_2+2. C_3 + 3. C_4 + ….+ 14. C_15=

If a, b, c, d, x are distinct non zero real numbers suchthat (a^(2)+b^(2)+c^(2))x^(2)-2 (ab+bc+cd)x +(b^(2)+c^(2)+d^(2)) le 0, then a, b, c, d are in

Fifteen coupons are numbered 1,2,. . . . 15 respectively seven coupons are selected at random one at time withreplacement. The probabilitythat thelargest number appearingon a selected coupons is 9 is

Is the function f defined by f(x)= {(x",","if" x le 1),(5",","if" x gt 1):} continuous at x=0 ? At x= 1 ? At x=2 ?

A curve is difined parametrically by x=e^(sqrtt),y=3t-log_(e)(t^(2)), where t is a parameter. Then the equation of the tangent line drawn to the curve at t = 1 is