14949 + Interview Questions in Maths in Class 11 Page 177 InterviewSolution

8801.	If the A.M. and G.M. between two numbers are respectively 17 and 8, find the numbers.
Answer» ANSWER :32,2,

Discussion

8802.	Let a fiunction f defined by f(x)=(x-\|x\|)/(x) "for" x ne0 and f(0) =2 then f is
Answer» CONTINUOUS no where continuous EVERY where continuous for all, X EXCEPT at x=1 continuous for all, x except at x=0 Answer :D

Discussion

8803.	If bara is perpendicular to barbxxbarc, then which of the following is true
Answer» `baraxx(barbxxbarc)=-bari` `baraxx(barbxxbarc)=bari` `BARA.(barbxxbarc)=0` `baraxx(barbxxbarc)=bar0` Answer :C

Discussion

8804.	If cos hx=(3)/(2) find the values of (i) Sinh (2x) ""(ii) Cosh (2x)
Answer» ANSWER :`(i) 3sqrt(5) (II) (7)/(2)`

Discussion

8805.	Find the median from the following frequency distribution : {:(x,3,4,5,6,7,8,9,10,11),(f,13,90,81,117,66,27,6,2,2):}
Answer» ANSWER :6

Discussion

8806.	Find the mean deviation about the median for the data in Question
Answer» Solution : Here `N=26` `:.` Median `M=(N/2 "th TERM" + (N/2+1) "th term")/2` `=(26/2 "th term"+(26/2+1)"th term")/2` `=(13 "th term"+14 "th term")/2` `=(7+7)/2=7` Now mean DEVIATION `=(sumf_(i)\|x_(i)-M\|)/(sumf_(i))=84/26=3.23`

Discussion

8807.	If the line(x)/( a) + (y)/( b) =passes through the points (2, -3) and (4,-5) then ( a, b) is
Answer» `(1,1)` `(-1, 1)` `(1,-1)` `(-1,-1)` ANSWER :D

Discussion

8808.	Find the mean deviation about the median for the data in Question
Answer» Solution : Here `N=29` `:.` MEDIAN `M=(N+1)/2` TH TERM `=(29+1)/2` th term `=15` th term `=30` Mean deviation`=(sumf_(i)\|x_(i)-M\|)/(sumf_(i))=148/29=5.10`

Discussion

8809.	A family is using Liquefied petroleum gas (LPG) of weight 14.2 kg for consumption (Full weight 29.5 kg includes the empty cylinders tare weight of 15.3 kg.). IF it is usedwith cosntant rate then it lasts for 24 days. Then the new cylinder is replaced (i) Findthe equation relating the quantity of gas in the cylinder to the days. (ii) Draw the graph for first 96 days.
Answer» ANSWER :`F(x+24)`

Discussion

8810.	Evaluate the following limits : Lim_(x to 0) (sin 2x)/x
Answer» ANSWER :2

Discussion

8811.	Find n if ""^(n-1)P_(3) : ""^(n)P_(4)=1:9.
Answer» ANSWER :THEREFORE N = 9

Discussion

8812.	If A is (a_(ij))_(mxxn),B=(b_(ij)_(nxxp)),C=(c_(ij)_(pxxq))Then (ABC)^(T) will of……. Order.
Answer» `Q^(2)xxm^(2)` `mxxp` `mxxq` `qxxm` ANSWER :D

Discussion

8813.	If a,b,c are non-zero real numbers such that int_(0)^(1) ( 1+ cos^(8) x) (ax^(2) + bx + c ) dx = int _(0)^(2) (1+cos^(8)x) (ax^(2) + bx + c ) dx = 0 ,then the equation ax^(2) + bx +c = 0 will have
Answer» ONE ROOT between 0 and 1 and other root between 1 and 2 both the ROOTS between 0 and 1 both roots between 1 and 2 both the roots between `(3, oo )` Answer :A

Discussion

8814.	Find the probability that when a hand of 7 cards is drawn from a well shuffled deck of 52 cards it contains : (i) All queens (ii) 3 Queens (iii) At least 3 Queens
Answer» Answer :(i) `(1)/(7735)` (II) `(9)/(1547)` (III) `(46)/(7735)`

Discussion

8815.	Write the first six terms of an A.P. in which a=5 ,d =4
Answer» ANSWER :5,9,13, 17, 21, 25

Discussion

8816.	If f(x)= 3x^(4)- 5x^(2) + 9 then find f(x-1).
Answer» ANSWER :`3x^(4) -12X^(3) + 13X^(2)-2x + 7`

Discussion

8817.	A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio 1: n. Find the equation of the line.
Answer» ANSWER :`(1 + N) x + 3 (1 + n) y = n + 11`

Discussion

8818.	A is the point (-1, 0) and B is the point (1, 1). Find a point on the line 4x+5y=4, which is equidistant from A and B.
Answer» ANSWER :`(-1/(4), 1)`

Discussion

8819.	Let A, B and C be three events associated to a random experiment. Statement-1 : If A cap B sube C, " then " P(C )ge P(A)+P(B)-1. Statement-2 : If P{(A cap B) cup (B cap C) cup (C cap A)} le " min" {P(A cup B),P(B cup C),P(C cup A)}
Answer» Statement-1 is TRUE, Statement-2 is True, Statement-2 is a CORRECT EXPLANATION for Statement-1. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1. Statement-1 is True, Statement-2 is FALSE. Statement-1 is False, Statement-2 is True. Answer :B

Discussion

8820.	sin "" (pi)/(14) .sin "" (3pi)/(14).sin"" (5pi)/(14).sin""(7pi)/(14).sin"" (9pi)/(14).sin""(11pi)/(14).sin""(13pi)/(14)=
Answer» `1//64` `3//64` `5//64` `7//64` ANSWER :A

Discussion

8821.	Check the validity of the statements given below by the method given against it: p: The sum of an irrational number and a rational number is irrational (by) contradiction method)
Answer» ANSWER :SUM of irrationa and RATIONAL NUMBER is IRRATIONAL.

Discussion

8822.	{x in R: x-[x] =5}=
Answer» R, the set of all real NUMBERS `phi`, the empty set `( x in R : x lt 0)` `( x in R : x GE 0)` Answer :B

Discussion

8823.	If in a triangle ABC, BC = 5, AC = 4, AB = 3. D, E are the points on BC such that BD = DE = EC, angle CAE = theta. Then
Answer» `AE^(2) = 73/3` `AE^(2) = 73/9` `tan THETA = 3//8` `AD = (2sqrt13)/3` ANSWER :B::C::D

Discussion

8824.	(i) int (3x + 7)/(x^2 - 3x + 2) dx "" (ii) int (x + 3)/((x + 2)^2 (x + 1)) dx.
Answer» ANSWER :(i) `13 log \|X - 2\| - 10 log \|x - 1\| + c` (ii) `- 2 log \|x + 2\| + 1/(x + 2) + 2 log \|x + 1\| + c`.

Discussion

8825.	Examine the continuity of the following: e^(2x)+x^2
Answer» Answer :`F(X) = E^(2X) + x^(2)`is continuous for all ` x in RR ` .

Discussion

8826.	A photocopy store charge Rs 1.50 per copy for the first 10 copies and Rs 1.00 per copy after the 10th copy . Let x be the total cost of photocopying . (i) Draw graph of the cost as x goes from 0 to 50 copies . (ii) Find the cost of making 40 copies.
Answer» ANSWER :RS 45

Discussion

8827.	Find the sum of x,y intercepts made by the lines x+y=a,x+y=ar,x+y=ar^(2), on coordinates axes, when r=1/2,a!=0.
Answer» ANSWER :4N

Discussion

8828.	If z=(1+2i)/(1-(1-i)^(2)) then arg (z).....
Answer» 0 `(PI)/(2)` `pi` NONE of these Answer :A

Discussion

8829.	Describe the sample space for the indicated experiments A coin is tossed and a die is thrown
Answer» Answer :{H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}

Discussion

8830.	IfC = A- B = 60 ^(@)" then "(a-b)/ (c )=
Answer» ` ( 1)/(SQRT3) ` ` sqrt3` ` (2)/(sqrt3) ` ` - ( 2)/(sqrt3) ` ANSWER :A

Discussion

8831.	3 sqrt(3) sin^(3) x + cos^(3) x + 3 sqrt(3) sin x cos x = 1
Answer» `X+(2k-1)PI-(pi)/6uux=2m pi, m in I, k in I` `x+(2k+1)pi-(pi)/3uux=2mpi, m in I,k INI` `x+(2k+1)pi-(pi)/4uux=2m pi, m in I, k in I` `x+(2k+1)pi-(pi)/2uux=2mpi, m in I, k in I` ANSWER :B

Discussion

8832.	In the following, state whether A = B or not: A = {2, 4, 6, 8, 10} B={ x : x is positive even integer and x ≤ 10}
Answer» ANSWER :YES

Discussion

8833.	Let F(x) = f(x).g(x).h(x)x in R, where f(x) , g(x) & h(x) are differentiable function. At some point x_0, F'(x_0) = 21 F(x_0) , f'(x_0) = 4f(x_0),g'(x_0) = -7g(x_0), h'(x_0)= k.h(x_0) then k/4 =
Answer» ANSWER :`=24`

Discussion

8834.	Show that the determinant of skew - symmetric matrix of order three is always zero.
Answer» ANSWER :`=0`

Discussion

8835.	Assertion (A) : \|{:(1,2,2),(2,3,4),(3,5,6):}\|=0 Reason (R) : If the elements of a column of a square matrix are k times the elements of another column then the value of the determinant of the matrix is 0.
Answer» Both A and R true and R is the CORRECT EXPLANATION of A Both A and R are true but R is not correct explanation of A A is true but R is false A is false but R is true Answer :A

Discussion

8836.	Ifsqrt(1- x ^(2)) + sqrt(1- y ^(2) ) = a (x -y) then(dy)/(dx)=
Answer» `SQRT((1-x^2)/(1-y^2))` `sqrt((1-x^2)(1-y^2))` `sqrt((1-y^2)/(1-x^2))` `1/(sqrt((1-x^2)(1-y^2)))` ANSWER :C

Discussion

8837.	Let a=min {x^(2)+2, x in R} and b lim_( theta+ theta)(1-cos theta)/(theta^(2)), the value of overset(n) underset(r=0) sum a^(r), b^(n-r) is lim_( n to oo)n^(2){sqrt((1-"cos"^(1)/(n))sqrt((1-"cos"(1)/(n))sqrt((1-"cos"(1)/(n)).... alpha )))}
Answer» `(2^(n+1)+1)/(3.2^(n))` `(2^(n+1)-1)/(3.2^(n))` `(4^(n+1)-1)/(3.2^(n))` `(4^(n+1)+1)/(3.2^(n))` Answer :C

Discussion

8838.	sin^(2)24^(@)-cos^(2)84^(@)=?
Answer» `(sqrt(5)-1)/(8)` `(sqrt(5)+1)/(8)` `(sqrt(5)-1)/(4)` NONE of these Solution :N//A

Discussion

8839.	Find the equation of a line parallel to the line x cos alpha+ y sin alpha=p and passing through the mid-point of the line segment joining the points (1,5) and (3,-3).
Answer» ANSWER :`X COS ALPHA+y SIN alpha=2 cos alpha+sin alpha`

Discussion

8840.	[barbxxbarcbarcxxbarabaraxxbarb]=[barabarbbarc]^(k) then k=
Answer» 1 2 3 4 Answer :B

Discussion

8841.	If 4^(th) term of (ax+1/x)^(n) is 5/2 then find a and n .
Answer» ANSWER :`a = 1/2 , N = 6`

Discussion

8842.	Assertion (A) : A and B are given points in a space. Then locus of P such thatangleAPB=90^(@)is a sphere with AB as diameter.
Answer» Both A and R are true and R is the corect explanation of A Both A and R are TRU and R is not the CORRECT explanation of A a is true but RIS false A is false but R is true Answer :A

Discussion

8843.	Points of discontinuties of the functionf(x) = 4x + 7[x] + 2 log (1 + x)are
Answer» 0 1 `-3//2` all the above ANSWER :D

Discussion

8844.	If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find A – C
Answer» Answer :`={3, 9, 15, 18, 21}`

Discussion

8845.	IfA and B are two mutuallyexclusiveeventssuchthat P(B) = 2P(A) and A uu B = S, thenP(B)is
Answer» `(3)/(2)` `(1)/(3)` `(2)/(3)` `(1)/(2)` ANSWER :C

Discussion

8846.	Let A={x,y,z} and B={1,2}. Find the number of relations from A to B.
Answer» ANSWER :No. of RELATIONS from A into `B=2^(6)`

Discussion

8847.	Eccentricity of curve given equation y^2=9xis 1.
Answer» ANSWER :TRUE STATEMENT

Discussion

8848.	If ((n),(5))=((n),(13)) then ""^(n)C_2 = ........
Answer» ANSWER :TRUE STATEMENT

Discussion

8849.	If the lines x+3y-9=0, 4x+by-2=0, and 2x-y-4=0 are concurrent, then the equation of the line passing through the point (b,0) and concurrent with the given lines, is
Answer» `2x+y+10=0` `4x-7y+20=0` `x-y+5=0` `x-4y+5=0` ANSWER :D

Discussion

8850.	Find the mean variance of the frequency distribution given below:
Answer» ANSWER :4.043

Discussion

Explore topic-wise InterviewSolutions in .

If the A.M. and G.M. between two numbers are respectively 17 and 8, find the numbers.

Let a fiunction f defined by f(x)=(x-|x|)/(x) "for" x ne0 and f(0) =2 then f is

If bara is perpendicular to barbxxbarc, then which of the following is true

If cos hx=(3)/(2) find the values of (i) Sinh (2x) ""(ii) Cosh (2x)

Find the median from the following frequency distribution : {:(x,3,4,5,6,7,8,9,10,11),(f,13,90,81,117,66,27,6,2,2):}

Find the mean deviation about the median for the data in Question

If the line(x)/( a) + (y)/( b) =passes through the points (2, -3) and (4,-5) then ( a, b) is

Find the mean deviation about the median for the data in Question

Evaluate the following limits : Lim_(x to 0) (sin 2x)/x

Find n if ""^(n-1)P_(3) : ""^(n)P_(4)=1:9.

If A is (a_(ij))_(mxxn),B=(b_(ij)_(nxxp)),C=(c_(ij)_(pxxq))Then (ABC)^(T) will of……. Order.

If a,b,c are non-zero real numbers such that int_(0)^(1) ( 1+ cos^(8) x) (ax^(2) + bx + c ) dx = int _(0)^(2) (1+cos^(8)x) (ax^(2) + bx + c ) dx = 0 ,then the equation ax^(2) + bx +c = 0 will have

Find the probability that when a hand of 7 cards is drawn from a well shuffled deck of 52 cards it contains : (i) All queens (ii) 3 Queens (iii) At least 3 Queens

Write the first six terms of an A.P. in which a=5 ,d =4

If f(x)= 3x^(4)- 5x^(2) + 9 then find f(x-1).

A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio 1: n. Find the equation of the line.

A is the point (-1, 0) and B is the point (1, 1). Find a point on the line 4x+5y=4, which is equidistant from A and B.

Let A, B and C be three events associated to a random experiment. Statement-1 : If A cap B sube C, " then " P(C )ge P(A)+P(B)-1. Statement-2 : If P{(A cap B) cup (B cap C) cup (C cap A)} le " min" {P(A cup B),P(B cup C),P(C cup A)}

sin "" (pi)/(14) .sin "" (3pi)/(14).sin"" (5pi)/(14).sin""(7pi)/(14).sin"" (9pi)/(14).sin""(11pi)/(14).sin""(13pi)/(14)=

Check the validity of the statements given below by the method given against it: p: The sum of an irrational number and a rational number is irrational (by) contradiction method)

{x in R: x-[x] =5}=

If in a triangle ABC, BC = 5, AC = 4, AB = 3. D, E are the points on BC such that BD = DE = EC, angle CAE = theta. Then

(i) int (3x + 7)/(x^2 - 3x + 2) dx "" (ii) int (x + 3)/((x + 2)^2 (x + 1)) dx.

Examine the continuity of the following: e^(2x)+x^2

A photocopy store charge Rs 1.50 per copy for the first 10 copies and Rs 1.00 per copy after the 10th copy . Let x be the total cost of photocopying . (i) Draw graph of the cost as x goes from 0 to 50 copies . (ii) Find the cost of making 40 copies.

Find the sum of x,y intercepts made by the lines x+y=a,x+y=ar,x+y=ar^(2), on coordinates axes, when r=1/2,a!=0.

If z=(1+2i)/(1-(1-i)^(2)) then arg (z).....

Describe the sample space for the indicated experiments A coin is tossed and a die is thrown

IfC = A- B = 60 ^(@)" then "(a-b)/ (c )=

3 sqrt(3) sin^(3) x + cos^(3) x + 3 sqrt(3) sin x cos x = 1

In the following, state whether A = B or not: A = {2, 4, 6, 8, 10} B={ x : x is positive even integer and x ≤ 10}

Let F(x) = f(x).g(x).h(x)x in R, where f(x) , g(x) & h(x) are differentiable function. At some point x_0, F'(x_0) = 21 F(x_0) , f'(x_0) = 4f(x_0),g'(x_0) = -7g(x_0), h'(x_0)= k.h(x_0) then k/4 =

Show that the determinant of skew - symmetric matrix of order three is always zero.

Assertion (A) : |{:(1,2,2),(2,3,4),(3,5,6):}|=0 Reason (R) : If the elements of a column of a square matrix are k times the elements of another column then the value of the determinant of the matrix is 0.

Ifsqrt(1- x ^(2)) + sqrt(1- y ^(2) ) = a (x -y) then(dy)/(dx)=

Let a=min {x^(2)+2, x in R} and b lim_( theta+ theta)(1-cos theta)/(theta^(2)), the value of overset(n) underset(r=0) sum a^(r), b^(n-r) is lim_( n to oo)n^(2){sqrt((1-"cos"^(1)/(n))sqrt((1-"cos"(1)/(n))sqrt((1-"cos"(1)/(n)).... alpha )))}

sin^(2)24^(@)-cos^(2)84^(@)=?

Find the equation of a line parallel to the line x cos alpha+ y sin alpha=p and passing through the mid-point of the line segment joining the points (1,5) and (3,-3).

[barbxxbarcbarcxxbarabaraxxbarb]=[barabarbbarc]^(k) then k=

If 4^(th) term of (ax+1/x)^(n) is 5/2 then find a and n .

Assertion (A) : A and B are given points in a space. Then locus of P such thatangleAPB=90^(@)is a sphere with AB as diameter.

Points of discontinuties of the functionf(x) = 4x + 7[x] + 2 log (1 + x)are

If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find A – C

IfA and B are two mutuallyexclusiveeventssuchthat P(B) = 2P(A) and A uu B = S, thenP(B)is

Let A={x,y,z} and B={1,2}. Find the number of relations from A to B.

Eccentricity of curve given equation y^2=9xis 1.

If ((n),(5))=((n),(13)) then ""^(n)C_2 = ........

If the lines x+3y-9=0, 4x+by-2=0, and 2x-y-4=0 are concurrent, then the equation of the line passing through the point (b,0) and concurrent with the given lines, is

Find the mean variance of the frequency distribution given below: