14949 + Interview Questions in Maths in Class 11 Page 100 InterviewSolution

4951.	If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 }, find B ∪ D
Answer» ANSWER :`{3, 4, 5, 6, 7, 8, 9, 10}`

Discussion

4952.	Find x if the slope of the line passes from points A(x, 2) and B(6, -8) is -(5)/(4).
Answer» ANSWER :`-2`

Discussion

4953.	I : If (cos alpha )/(a)=(sin alpha )/(b) then a cos2 alpha + b cos 2 alpha =a II : If(sin alpha )/(a) =(cos alpha )/(b)thena sin 2 alpha + b cos 2 alpha = a
Answer» Only I is TRUE Only II is true Both I and II are true NEITHER I nor II are true ANSWER :A

Discussion

4954.	Find the standard deviation from the following data:
Answer» Solution : Let ASSUMED mean `a=3` Standard deviation `sigma=sqrt((sumf_(i)d_(i)^(2))/(sumf_(i))-((sumf_(i)d_(i))/(sumf_(i)))^(2))` `=sqrt(124/62-((-30)/62)^(2))=sqrt(2-0.2341)=1.33`

Discussion

4955.	If f(x)=4x^(3)-x^(2)-2x+1andg(x)=[{:(min [f(t),0letlex},0lexle1),(3-x,1ltxle2):} then g((1)/(4))+g((3)/(4))+g((5)/(4)) has
Answer» `7//4` `9//4` `13//4` `5//2` ANSWER :D

Discussion

4956.	Findlimit of the following if it exists: lim_(xto0)(e^(sin)-1)/(x)
Answer» ANSWER :1

Discussion

4957.	The value of (sin 1^(@) + sin 3^(@) + sin 5^(@) + sin 7^(@))/( cos 1^(@) .cos2^(@).sin4^(@)) is"________"
Answer» ANSWER :4

Discussion

4958.	The upper3//4of a ship's mast subtends at a point on the deck which is 40 metersfrom the mast an angletan ^(-1) (( 3)/(4)), the height of the mast abovethe deck in meters is ………
Answer» ` 40` ` 80 ` `120 ` ` 160` Answer :B

Discussion

4959.	The vertices of a triangle are A (0, 5), B (-1, -2) and C (11, 7). Write down the equations of BC and the perpendicular from A to BC and hence find the co-ordinates of the foot of the perpendicular.
Answer» ANSWER : `3x-4y=5,4x+3y=15;(3, 1)`

Discussion

4960.	InDelta ABC , if A = 3C" then "(a-c)/( 2c ) =
Answer» `"SIN"(B)/(2)` `"sin"(C)/(2)` `"cos"(B)/(2)` `"cos"(C)/(2)` ANSWER :A

Discussion

4961.	Find (x+y)^(5)+(x-y)^(5) . Hence evaluate (sqrt(2)+1)^(5)+(sqrt(2)-1)^(5)
Answer» Answer :`2(x^(5)+10x^(3)y^(2)+5XY^(4)),58sqrt(2)`

Discussion

4962.	Evaluate the following limits : Lim_(x to 1) (sin(e^(x)-1))/(log x)
Answer» ANSWER :1

Discussion

4963.	A parallelopiped is formed by the planes drawn through the points (2,3,5) and (5,9,7) parallel to the coordinate planes. The length of diagonal of the paralleopiped is
Answer» 7 `sqrt38` `sqrt155` `SQRT7` ANSWER :A

Discussion

4964.	Identity the type of 'or' used in the following statement and check whether the statement is true or false. ''To enter in to a public library children need an identity card from the school or a letter from the school authorities.
Answer» ANSWER :1

Discussion

4965.	Identify the type of 'or ' used in statement ''sqrt( 2)is a rational number or an irrational number
Answer» ANSWER :1

Discussion

4966.	The+ve value of a for which the image of (a,a-1) w.r.t the line x+y=6a is point (a^2+1,a) is
Answer» 0 1 2 -1 Answer :C

Discussion

4967.	If Sin^(-1)x+Tan^(-1)x=(pi)/2 then the value of x^(2) is
Answer» `SIN18^(@)` `COS36^(@)` `2sin18^(@)` `2cos36^(@)` ANSWER :C

Discussion

4968.	Consider a line with equation x - sqrt 3 y + 4 =0 Reduce the given equation into slope-intercept form and find the slope and y - intercept of the line
Answer» SOLUTION :`y = 1/sqrt3 X + 4/sqrt3, 1/sqrt3,4/sqrt3`

Discussion

4969.	Estimate standard deviation for the following frequency distribution.
Answer» ANSWER :2.77

Discussion

4970.	If b= 4 cms. \|__A =45^(@) , \|__B= 30 ^(@) , find a
Answer» ANSWER :` 4sqrt2`

Discussion

4971.	Integrate the following w.r.to .x.1/3cos(x/3-4)+7(7x+9)+e^((x)/(5)+3)
Answer» ANSWER :`SIN(x/4-4)+log\|7x+9\|+5e^(x/5+3)+C`

Discussion

4972.	If x = "cosec" theta - sintheta, y = "cosec"^(n)theta - sin^(n) theta then (x^2+4)((dy)/(dx))^2 -n^2y^2 =
Answer» `n^2` `2n^2` `3n^2` `4n^2` ANSWER :D

Discussion

4973.	How many 5 - digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once ?
Answer» ANSWER :`therefore` 336 NUMBERS are formed DIGIT 0 to 9.

Discussion

4974.	IfA=[a_(ij)]_(mxxn) is a matrix of rank r and B is a square submatrix of order r + 1, then
Answer» B is INVERTIBLE B is not invertible B many or MAY be invertible NONE of these Answer :B

Discussion

4975.	Find the value of sin "" (31pi)/(3).
Answer» ANSWER :`(SQRT3)/(2)`

Discussion

4976.	Let vec a and vec b be the position vectors of the points A and B. Prove that the position vectors of the points which trisects the line segment AB are (veca+2vecb)/(3)and (vecb+2veca)/(3).
Answer» ANSWER :`( VECA + 2vecb)/3`

Discussion

4977.	Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
Answer» ANSWER :2000

Discussion

4978.	~(~prArrq) has ….. expression logically equal .
Answer» ANSWER :FALSE

Discussion

4979.	If sin^(-1)(sin((2x^(2)+4)/(1+x^(2))))lt pi-3 then x satisfies.
Answer» `abs(x) gt 1` `abs(x) LT 1` `abs(x) le 1` `abs(x) GE 1` ANSWER :B

Discussion

4980.	If a+ib=c+id, then
Answer» `a^(2)+C^(2)=0` `B^(2)+c^(2)=0` `b^(2)+d^(2)=0` `a^(2)+b^(2)=c^(2)+d^(2)` ANSWER :D

Discussion

4981.	lim_(xrarr0)(sqrt(1+x)-1)/x
Answer» 0 1 `1/2` not defined Answer :C

Discussion

4982.	If \|bar(P)\| = 2, \|bar(q)\| = 3 and (bar(p),bar(q)) = (pi)/6, then find \|bar(p) xx bar(q)\|^(2)
Answer» 6 7 8 9 Answer :D

Discussion

4983.	If (bar(a), bar(i))=(bar(a), bar(j))=pi/4" then "(bar(a), bar(k))=
Answer» `pi/6` `pi/4` `pi/3` `pi/2` ANSWER :D

Discussion

4984.	Write the following sets in the set-builder form : {2, 4, 6, . . .}
Answer» ANSWER :`={x : x` is an EVEN natural NUMBER} or `={x : x= 2n, N in N}`

Discussion

4985.	If f(x)=kx^(3)-9x^(2)+9x+3 is monotonically increasing in R , then
Answer» `klt3` `kle2` `kge3` `kgt2` ANSWER :B

Discussion

4986.	Which of the following sentences are statements? Give reasons for your answer: Today is a windy day.
Answer» ANSWER :It is not CLEAR from the CONTEXT which day is referred and therefore, it is not a STATEMENT.

Discussion

4987.	If (1)/( 2 xx 4) + (1)/( 4 xx 6) + (1)/( 6 xx 8) + …. N terms = (kn)/( n+1)then k=
Answer» `(1)/(4)` `(1)/(2)` `1` `(1)/(8)` ANSWER :A

Discussion

4988.	If xgt0 then which of the following is true
Answer» `TAN^(-1)XGT(x)/(1+x^(2))` `tan^(-1)x=(x)/(1+x^(2))` `tan^(-1)XLT(x)/(1+x^(2))` `tan^(-1)x ne(x)/(1+x^(2))` Answer :A

Discussion

4989.	Express the following in the form a+bi (2 +3i) (3+7i)
Answer» ANSWER :`-15+23i`

Discussion

4990.	If e^(x+y) =xy then (dy)/(dx) =
Answer» `(y (1-X))/(x(y-1))` `(-y (1-x))/(x(y-1))` `(x (y-1))/(y(1-x))` `(-x (y-1))/(y(1+x))` ANSWER :A

Discussion

4991.	If f(x) = log_(x)(lnx) then f'(x) at x = e is
Answer» `1//E` e `-1//e` 0 Answer :A

Discussion

4992.	If X={8^(n)-7n-1\|n inN}and y= {49n-49\|n in N}. Then
Answer» `XsubY` `YsubX` `X=Y` `XcapY=phi` ANSWER :A

Discussion

4993.	Find the sum 5^(2)+ 6^(2) + 7^(2) + ... + 20^(2).
Answer» ANSWER :2840

Discussion

4994.	Find the unit vector perpendicular to the plane passing through the points (1,2,3), (2,-1,1) and (1,2,-4).
Answer» ANSWER :`+- ((3 VEC(i) + vec(J)))/(SQRT10)`

Discussion

4995.	For set A = { 1,2,3 4} B = {"x"in Z\|-2lexle2} and C= {1,2,3 } are subset of ……set .
Answer» ANSWER :[-2,4]

Discussion

4996.	Four cards are drawn from a full pack of cards . Find the probability thatall the four are kings,
Answer» ANSWER :`=1/270725`

Discussion

4997.	If tan(pi cos theta) =cot(pi sin theta), 0 lt theta lt(3pi)/4, then sin(theta+pi/4)=
Answer» `1/sqrt(2)` `-1/sqrt(2)` `1/(2sqrt(2))` `-1/(2sqrt(2))` ANSWER :C

Discussion

4998.	Find the equation of linePassing through (2, 2 sqrt3) and inclined with the x-axis at an angle of 75^(@).
Answer» ANSWER :`(SQRT3 + 1) X - ( sqrt3 - 1) y = 4 (sqrt3- 1)`

Discussion

4999.	Which of the following are sets ? Justify your answer. A collection of most dangerous animals of the world.
Answer» ANSWER :it is not a SET

Discussion

5000.	The orthocentre of the Delta^( l e) formed by (0,0), (8,0),(4,6) is
Answer» `(4,8//3)` `(3,4)` `(4,3)` `(-3,4)` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 }, find B ∪ D

Find x if the slope of the line passes from points A(x, 2) and B(6, -8) is -(5)/(4).

I : If (cos alpha )/(a)=(sin alpha )/(b) then a cos2 alpha + b cos 2 alpha =a II : If(sin alpha )/(a) =(cos alpha )/(b)thena sin 2 alpha + b cos 2 alpha = a

Find the standard deviation from the following data:

If f(x)=4x^(3)-x^(2)-2x+1andg(x)=[{:(min [f(t),0letlex},0lexle1),(3-x,1ltxle2):} then g((1)/(4))+g((3)/(4))+g((5)/(4)) has

Findlimit of the following if it exists: lim_(xto0)(e^(sin)-1)/(x)

The value of (sin 1^(@) + sin 3^(@) + sin 5^(@) + sin 7^(@))/( cos 1^(@) .cos2^(@).sin4^(@)) is"________"

The upper3//4of a ship's mast subtends at a point on the deck which is 40 metersfrom the mast an angletan ^(-1) (( 3)/(4)), the height of the mast abovethe deck in meters is ………

The vertices of a triangle are A (0, 5), B (-1, -2) and C (11, 7). Write down the equations of BC and the perpendicular from A to BC and hence find the co-ordinates of the foot of the perpendicular.

InDelta ABC , if A = 3C" then "(a-c)/( 2c ) =

Find (x+y)^(5)+(x-y)^(5) . Hence evaluate (sqrt(2)+1)^(5)+(sqrt(2)-1)^(5)

Evaluate the following limits : Lim_(x to 1) (sin(e^(x)-1))/(log x)

A parallelopiped is formed by the planes drawn through the points (2,3,5) and (5,9,7) parallel to the coordinate planes. The length of diagonal of the paralleopiped is

Identity the type of 'or' used in the following statement and check whether the statement is true or false. ''To enter in to a public library children need an identity card from the school or a letter from the school authorities.

Identify the type of 'or ' used in statement ''sqrt( 2)is a rational number or an irrational number

The+ve value of a for which the image of (a,a-1) w.r.t the line x+y=6a is point (a^2+1,a) is

If Sin^(-1)x+Tan^(-1)x=(pi)/2 then the value of x^(2) is

Consider a line with equation x - sqrt 3 y + 4 =0 Reduce the given equation into slope-intercept form and find the slope and y - intercept of the line

Estimate standard deviation for the following frequency distribution.

If b= 4 cms. |__A =45^(@) , |__B= 30 ^(@) , find a

Integrate the following w.r.to .x.1/3cos(x/3-4)+7(7x+9)+e^((x)/(5)+3)

If x = "cosec" theta - sintheta, y = "cosec"^(n)theta - sin^(n) theta then (x^2+4)((dy)/(dx))^2 -n^2y^2 =

How many 5 - digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once ?

IfA=[a_(ij)]_(mxxn) is a matrix of rank r and B is a square submatrix of order r + 1, then

Find the value of sin "" (31pi)/(3).

Let vec a and vec b be the position vectors of the points A and B. Prove that the position vectors of the points which trisects the line segment AB are (veca+2vecb)/(3)and (vecb+2veca)/(3).

Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5﻿ blue balls if each selection consists of 3 balls of each colour.﻿

~(~prArrq) has ….. expression logically equal .

If sin^(-1)(sin((2x^(2)+4)/(1+x^(2))))lt pi-3 then x satisfies.

If a+ib=c+id, then

lim_(xrarr0)(sqrt(1+x)-1)/x

If |bar(P)| = 2, |bar(q)| = 3 and (bar(p),bar(q)) = (pi)/6, then find |bar(p) xx bar(q)|^(2)

If (bar(a), bar(i))=(bar(a), bar(j))=pi/4" then "(bar(a), bar(k))=

Write the following sets in the set-builder form : {2, 4, 6, . . .}

If f(x)=kx^(3)-9x^(2)+9x+3 is monotonically increasing in R , then

Which of the following sentences are statements? Give reasons for your answer: Today is a windy day.

If (1)/( 2 xx 4) + (1)/( 4 xx 6) + (1)/( 6 xx 8) + …. N terms = (kn)/( n+1)then k=

If xgt0 then which of the following is true

Express the following in the form a+bi (2 +3i) (3+7i)

If e^(x+y) =xy then (dy)/(dx) =

If f(x) = log_(x)(lnx) then f'(x) at x = e is

If X={8^(n)-7n-1|n inN}and y= {49n-49|n in N}. Then

Find the sum 5^(2)+ 6^(2) + 7^(2) + ... + 20^(2).

Find the unit vector perpendicular to the plane passing through the points (1,2,3), (2,-1,1) and (1,2,-4).

For set A = { 1,2,3 4} B = {"x"in Z|-2lexle2} and C= {1,2,3 } are subset of ……set .

Four cards are drawn from a full pack of cards . Find the probability thatall the four are kings,

If tan(pi cos theta) =cot(pi sin theta), 0 lt theta lt(3pi)/4, then sin(theta+pi/4)=

Find the equation of linePassing through (2, 2 sqrt3) and inclined with the x-axis at an angle of 75^(@).

Which of the following are sets ? Justify your answer. A collection of most dangerous animals of the world.

The orthocentre of the Delta^( l e) formed by (0,0), (8,0),(4,6) is

If b= 4 cms. |A =45^(@) , |B= 30 ^(@) , find a

Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.