14949 + Interview Questions in Maths in Class 11 Page 234 InterviewSolution

11651.	The radius and height of a cone are measured as 8 cm, 8cm by a scale in which there is an error of 0.01cm in each cm. The error in the volume of the cone is
Answer»

Discussion

11652.	A is the set of prime number less than 10, B is the set of odd numbers less than 10 and C is the set of even numbers of less than 10. Which of the following statements are true? (i) A subset B (ii) B subset A (iii) A subset C (iv) C subset A (v) B subset C (vi) phi subset A
Answer» ANSWER :all FOUR CONDITIONS are EQUIVALENT.

Discussion

11653.	If 2tan theta-cot theta=-1 then theta=______
Answer» `NP-(PI)/4,npi+TAN^(-1)(1/2), n INZ` `npi+(pi)/4, n pi +tan^(-1)(1/2), ninZ` `npi-(pi)/4, npi-tan^(-1)(1/2), ninZ` `npi+(pi)/4, n pi-tan^(-1)(1/2),n in Z` Answer :A

Discussion

11654.	Three points P (h, k), Q(x_(1) , y_(1))" and " R (x_(2) , Y_(2)) lie on a line. Show that(h - x_(1)) (y_(2) - y_(1)) = (k - y_(1)) (x_(2) - x_(1)).
Answer» ANSWER :`(h - x_(1)) (y_(2) - y_(1)) = (K - y_(1)) (x_(2) - x_(1))`

Discussion

11655.	If ((1+i)/(1-i))^(100)=x +iythen (x,y) = .......
Answer» ANSWER :1

Discussion

11656.	If sin^(-1)(x-(x^2)/(2)+(x^3)/(4)-...infty)+cos^(-1)(x^2-(x^4)/(2)+(x^6)/(4)-...infty)=(pi)/(2) and 0ltxltsqrt(2), then x is equal to
Answer» `1//2` 1 `-1//2` `-1` ANSWER :B

Discussion

11657.	Assertion: ""^(24)C_(4) + overset(3)underset(r=0)(sum) ""^(27-r)C_(3) =""^(28)C_(4)Reason: ""^(n)C_(r) + ""^(n)C_(r-1) =""^(n+1)C_(r)
Answer» Both Assertion and REASON are INCORRECT Reason is incorrect Assertion is CORRECT Reason is correct, Assertion is incorrect Using Reason we can PROVE Assertion Answer :D

Discussion

11658.	If 0 le x le 2 pi, then the number of solution of 3 (sin x + cos x) - 2 (sin^(3)x + cos^(3) x)= 8 is
Answer» 0 1 2 4 Answer :A

Discussion

11659.	If Y= {1, 2, 3,………..,10} and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions. a in Y" but "a^(2) notin Y
Answer» Answer :`= {4, 5, 6, 7, 8, 9, 10}`

Discussion

11660.	If Y= {1, 2, 3,………..,10} and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions. a+1=6, a in Y
Answer» ANSWER :`= {5}`

Discussion

11661.	If (sin x)/(sin y)=(1)/(2), (cos x)/(cos y)=(3)/(2), where x,y in (0,(pi)/(4)), then the value of tan (x + y) is equal to
Answer» `sqrt(13)` `sqrt(14)` `sqrt(17)` `sqrt(15)` ANSWER :D

Discussion

11662.	If Y= {1, 2, 3,………..,10} and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions. a is less than 6 and a in Y
Answer» ANSWER :`= {1, 2, 3, 4, 5}`

Discussion

11663.	Let p be " Ananya is beautiful, " and let q be " Ananya is 165 centimetres tall. " Underwhat cooditions is the statement," Ananya is beauiful or 165 centimetres tall, " true?
Answer» Answer :If Ananya is beautiful and or 165 CM TALL .

Discussion

11664.	Calculate the cost of living index number from the following group data:
Answer» ANSWER :`231.2` APPROX.

Discussion

11665.	Statement-I: The perpendicular distance from A(1, 4, -2) to the line vec(BC), where B(2, 1, -2) and C(0, -5, 1) " is" 3(sqrt26)/(7) units Statement-II: If vec(a) is any vector then (vec(a) xx vec(i))^(2) + (vec(a) xx vec(j))^(2) + (vec(a) xx vec(k))^(2) = \|vec(a)\|^(2), then Which of above statements are true?
Answer» only I is true only II is true Both I and II are true neither I nor II is true Answer :D

Discussion

11666.	Solve the following system of equations by matrix inversion method 5x-6y+4z=15,7x+4y-3z=19,3x+y+6z=46
Answer» ANSWER :`z=6`

Discussion

11667.	The mean life of a sample of 60 bulbs was 650 h and the standard deviation was 8 h, If a second sample of 80 bulbs has a mean life of 660 h and standard deviation 7 h then find the over all standard deviation
Answer» Solution :Here `n_(1)=60barx_(1)=650,s_(1)=8 ` and `n_(2)=80,barx_(2)=660,s_(2)=7` `sigma=sqrt((n_(1)s_(1)^(2)+n_(2)s_(2)^(2))/(n_(1)+n_(2))+(n_(1)n_(2)(barx_(1) barx_(2))^(2))/(n_(1)+n_(2))^(2)` `sqrt((60xx(8)^(2)+80xx(7)^(2))/(60+80)+(60xx80(650-660)^(2))/((60+80)^(2)))` `sqrt((6xx64+8xx49)/(14)+(60xx80xx100)/(140xx140))` `sqrt((192+196)/7+(1200)/49)=sqrt(388/7+1200/49)` `sqrt((2716+1200)/49)=sqrt(3916/49)=62.58/7=8.9`

Discussion

11668.	If one complex number is in third quadrent then its conjugate complex number is in ............ quadrent.
Answer» ANSWER :SECOND

Discussion

11669.	Find the orthocentre of the triangle whose sides are 7x+y-10=0, x-2y+5=0, x+y+2=0
Answer» ANSWER :`((-2)/3,4/3)`

Discussion

11670.	If x=-1 is a root of the equation \|{:(2-x,3,3),(3,4-x,5),(3,5,4-x):}\|=0 then the other roots are
Answer» 0, 12 11, 12 0, 11 0, 11/2 Answer :C

Discussion

11671.	If 0ltcos^(-1)x lt 1 and 1+sin(cos^(-1)x)+sin^(2)(cos^(-1)x)+sin^(3)(cos^(-1)x)+…….oo=2, then the value of 12x^(2) is
Answer» ANSWER :9

Discussion

11672.	If (a^(n)+b^n)/ (a^(n-1) +b^(n-1)) is the A.M. between a and b, then find the value of n.
Answer» ANSWER :1

Discussion

11673.	How many number greater than 3,00,000 can be formed by using all the digits of the number 111223?
Answer» ANSWER :10 WAYS

Discussion

11674.	Find the standard deviation from the following datas:
Answer» SOLUTION :NA

Discussion

11675.	Which of the following pairs of sets are disjoint {1, 2, 3, 4} and {x : x is a natural number and 4 ≤ x ≤ 6 }
Answer» ANSWER :A and B are DISJOINT SET

Discussion

11676.	Construct a composite index number, as a weighted mean from the following data:
Answer» ANSWER :`122`

Discussion

11677.	X=tan 1, Y =tan 2, Z= tan 3 then the decending order is
Answer» X.Y.Z Z,Y,X X,Z,Y Y,Z,X Answer :C

Discussion

11678.	There letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.
Answer» ANSWER :`=(2)/(3)`

Discussion

11679.	If there is an error 0.01 cm in the measurement of the radius 10 cm of a cylinder of fixed height 20 cm then error in the volume is
Answer» ANSWER :`4PI` CUBIC CM, 0.002, 02

Discussion

11680.	Find the coefficient of x^10 in the expansion of (1+x+x^2 +x^3 + ……+x^10)^4 .
Answer» ANSWER :5

Discussion

11681.	The value of k if the equation 2cosx +cos2kx=3 has only one solution is
Answer» 0 2 `SQRT(2)` `1//2` ANSWER :C

Discussion

11682.	Any two collinear vectors are
Answer» L.D L.I both 1 and 2 neither 1 nor 2 Answer :A

Discussion

11683.	Fill in the blanks of the following For any two complex numbers z_(1),z_(2) and real numbers a,b\|az_(1)-bz_(2)\|^(2)+\|bz_(1)+az_(2)\|^(2)=....
Answer» ANSWER :`(a^(2)+B^(2)) (\|z_(1)\|^(2)+\|z_(2)\|^(2))`

Discussion

11684.	x + 2y le 10, x + y ge 1, x - y le 0, x ge 0, y ge 0
Answer» Solution :First inequation : `x + 2y le 10` Corresponding equation :`x + 2y = 10` This line PASSES through the points A(10, 0) and B(0, 5). Join AB. At POINT (0, 0) , from the inequation, 0le10 (True) `:.`The Solution of this inequation is that region of XY-plane divided by line AB in which (0, 0) lie. Second inequation : ` x + y ge 1` Corresponding equation: `x + y =1` This line passes through the points C(1, 0) and D(0, 1).join CD. At point (0, 0), From the inequation, `0 ge 1` (FALSE) `:.` The solution of this inequation is that region of XY-plane divided by line AB in which (0, 0) lie. Third inequation : `x- y le0` Corresponding inequation : `x - y = 0` This line passes through the points O(0, 0) and E(2, 2) . Join OE. At point (1, 0 ), from the inequation, `1 ge 0` (False) `:,` The solution of this inequation is that region of XY-plane divided by line OE in which (1, 0) does not lie. The solution of x`ge` 0, y `ge` 0 is in first quadrant `:.` The solution of GIVEN inequation is shown by the shaded region.

Discussion

11685.	In Argand figure complex number (1+2i)/(1-i) lies in ......... quadrent.
Answer» First Second Third Fourth Answer :B

Discussion

11686.	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 D – A
Answer» ANSWER :`={5, 10, 20}`

Discussion

11687.	If the radius of sphere is 3 cm. If an error of 0.03 cm is made in measuring the radius of the sphere, then the percentage error in its surface area is
Answer» 2 0.02 0.002 0.0002 Answer :A

Discussion

11688.	Examine whether the following statements are true or false: { a, e } ⊂ {x : x is a vowel in the English alphabet}
Answer» ANSWER :1

Discussion

11689.	Ifx= cot theta + cos theta , y= cot theta - cos theta , " then " (x^(2)-y^(2))^(2)=
Answer» 4ab 8ab 16 ab ab Answer :C

Discussion

11690.	Evaluate the following limits. Lt_(xtoa)((x+2)^(7//3)-(a+2)^(7//3))/(x-a)
Answer» ANSWER :`7/3(a+2)^(4//3)`

Discussion

11691.	If the altitudes of a triangle are in arithmetic progression, then the sides of the triangle are in
Answer» ARITHMETIC GEOMETRIC HARMONIC A.G.P Answer :B

Discussion

11692.	If baraxxbarr=barb+lamdabara, bara.barr=3, abs(bara)=1, barb.barr=
Answer» `bara.barb` `2(bara.barb)` `3(bara.barb)` 1 Answer :C

Discussion

11693.	Two lines passes through (0,0), (2,3) and (2,-2), (3,5). Find measure of an angle between them.
Answer» Answer :`TAN^(-1)""((11)/(23))` OR `pi - tan^(-1) ""((11)/( 23))`

Discussion

11694.	Expand 2^(3n) by writing 2^(3n)=(1+7)^n
Answer» SOLUTION :`2^(3N)=1+^nC_1 7+^nC_2. 7^2+.....+7^n`

Discussion

11695.	Write the contrapositive and converse of the following statements: If the two lines are parallel, then they do not intersect in the same plane.
Answer» ANSWER :The CONTRAPOSITIVE is If two lines intersect in the same plane, then they are not PARALLEL The CONVERSE is If two lines do not interesect in the same plane, then they are parallel

Discussion

11696.	How many 2- digits numbers can be formed from the digits 8,1,3,5 and 4 assumingrepetitions of digits is not allowed?
Answer» ANSWER :` 20 `

Discussion

11697.	the periodof \|sin x \|+ \|cos x\| is
Answer» `(PI)/(2)` `pi` `(3PI)/(2)` `2PI` ANSWER :1

Discussion

11698.	Evaluate C(19,17)+ C(19,18)
Answer» ANSWER :`190`

Discussion

11699.	Find the derivative of the w.r.t.x x ^(n) n ^(x) log nx
Answer» ANSWER :`X ^(n-1)`

Discussion

11700.	((n+2)!)/( (n-1)!) is divisible by
Answer» `6` `11` `24` `26` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

The radius and height of a cone are measured as 8 cm, 8cm by a scale in which there is an error of 0.01cm in each cm. The error in the volume of the cone is

A is the set of prime number less than 10, B is the set of odd numbers less than 10 and C is the set of even numbers of less than 10. Which of the following statements are true? (i) A subset B (ii) B subset A (iii) A subset C (iv) C subset A (v) B subset C (vi) phi subset A

If 2tan theta-cot theta=-1 then theta=______

Three points P (h, k), Q(x_(1) , y_(1))" and " R (x_(2) , Y_(2)) lie on a line. Show that(h - x_(1)) (y_(2) - y_(1)) = (k - y_(1)) (x_(2) - x_(1)).

If ((1+i)/(1-i))^(100)=x +iythen (x,y) = .......

If sin^(-1)(x-(x^2)/(2)+(x^3)/(4)-...infty)+cos^(-1)(x^2-(x^4)/(2)+(x^6)/(4)-...infty)=(pi)/(2) and 0ltxltsqrt(2), then x is equal to

Assertion: ""^(24)C_(4) + overset(3)underset(r=0)(sum) ""^(27-r)C_(3) =""^(28)C_(4)Reason: ""^(n)C_(r) + ""^(n)C_(r-1) =""^(n+1)C_(r)

If 0 le x le 2 pi, then the number of solution of 3 (sin x + cos x) - 2 (sin^(3)x + cos^(3) x)= 8 is

If Y= {1, 2, 3,………..,10} and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions. a in Y" but "a^(2) notin Y

If Y= {1, 2, 3,………..,10} and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions. a+1=6, a in Y

If (sin x)/(sin y)=(1)/(2), (cos x)/(cos y)=(3)/(2), where x,y in (0,(pi)/(4)), then the value of tan (x + y) is equal to

If Y= {1, 2, 3,………..,10} and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions. a is less than 6 and a in Y

Let p be " Ananya is beautiful, " and let q be " Ananya is 165 centimetres tall. " Underwhat cooditions is the statement," Ananya is beauiful or 165 centimetres tall, " true?

Calculate the cost of living index number from the following group data:

Solve the following system of equations by matrix inversion method 5x-6y+4z=15,7x+4y-3z=19,3x+y+6z=46

The mean life of a sample of 60 bulbs was 650 h and the standard deviation was 8 h, If a second sample of 80 bulbs has a mean life of 660 h and standard deviation 7 h then find the over all standard deviation

If one complex number is in third quadrent then its conjugate complex number is in ............ quadrent.

Find the orthocentre of the triangle whose sides are 7x+y-10=0, x-2y+5=0, x+y+2=0

If x=-1 is a root of the equation |{:(2-x,3,3),(3,4-x,5),(3,5,4-x):}|=0 then the other roots are

If 0ltcos^(-1)x lt 1 and 1+sin(cos^(-1)x)+sin^(2)(cos^(-1)x)+sin^(3)(cos^(-1)x)+…….oo=2, then the value of 12x^(2) is

If (a^(n)+b^n)/ (a^(n-1) +b^(n-1)) is the A.M. between a and b, then find the value of n.

How many number greater than 3,00,000 can be formed by using all the digits of the number 111223?

Find the standard deviation from the following datas:

Which of the following pairs of sets are disjoint {1, 2, 3, 4} and {x : x is a natural number and 4 ≤ x ≤ 6 }

Construct a composite index number, as a weighted mean from the following data:

X=tan 1, Y =tan 2, Z= tan 3 then the decending order is

There letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.

If there is an error 0.01 cm in the measurement of the radius 10 cm of a cylinder of fixed height 20 cm then error in the volume is

Find the coefficient of x^10 in the expansion of (1+x+x^2 +x^3 + ……+x^10)^4 .

The value of k if the equation 2cosx +cos2kx=3 has only one solution is

Any two collinear vectors are

Fill in the blanks of the following For any two complex numbers z_(1),z_(2) and real numbers a,b|az_(1)-bz_(2)|^(2)+|bz_(1)+az_(2)|^(2)=....

x + 2y le 10, x + y ge 1, x - y le 0, x ge 0, y ge 0

In Argand figure complex number (1+2i)/(1-i) lies in ......... quadrent.

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 D – A

If the radius of sphere is 3 cm. If an error of 0.03 cm is made in measuring the radius of the sphere, then the percentage error in its surface area is

Examine whether the following statements are true or false: { a, e } ⊂ {x : x is a vowel in the English alphabet}

Ifx= cot theta + cos theta , y= cot theta - cos theta , " then " (x^(2)-y^(2))^(2)=

Evaluate the following limits. Lt_(xtoa)((x+2)^(7//3)-(a+2)^(7//3))/(x-a)

If the altitudes of a triangle are in arithmetic progression, then the sides of the triangle are in

If baraxxbarr=barb+lamdabara, bara.barr=3, abs(bara)=1, barb.barr=

Two lines passes through (0,0), (2,3) and (2,-2), (3,5). Find measure of an angle between them.

Expand 2^(3n) by writing 2^(3n)=(1+7)^n

Write the contrapositive and converse of the following statements: If the two lines are parallel, then they do not intersect in the same plane.

How many 2- digits numbers can be formed from the digits 8,1,3,5 and 4 assumingrepetitions of digits is not allowed?

the periodof |sin x |+ |cos x| is

Evaluate C(19,17)+ C(19,18)

Find the derivative of the w.r.t.x x ^(n) n ^(x) log nx

((n+2)!)/( (n-1)!) is divisible by