14949 + Interview Questions in Maths in Class 11 Page 261 InterviewSolution

13001.	Consider the circle x^2+y^2-4x-6y-3 = 0 Find the radius of the circle
Answer» SOLUTION :`SQRT(13-k)`

Discussion

13002.	If A+B+C=720^(@) " then " tan A + tan B + tan C=
Answer» TANA TANB TanC Tan2A Tan2B Tan2C Tan2A + Tan2B + Tan2B CotA COTB CotC Answer :A

Discussion

13003.	If the volume of parallelopiped with conterminus edges 4hati+5hatj+hatk, -hatj+hatk and 3hati+9hatj+phatk is 34 cubic units then p is equal to
Answer» 5 `-6` `-13` 6 Answer :C

Discussion

13004.	If (1+2x-3x^(2))^(5)=1+a_(1)x+a_(2)x^(2)+….+a_(10)x^(10) then the value of a_(2)+a_(4)+……+a_(10)" is "………
Answer» 1024 511 `-511` 31 Answer :C

Discussion

13005.	Three cards are drawn fromadeck of 52 cards . Whatis the probability thatthey are all spades ?
Answer» ANSWER :`(""^(13)C_(3))/(""^(52C_(3))=(11)/(850)`

Discussion

13006.	If A +B + C = pi then secA(cos B cos C - sin B sin C) = .........
Answer» ANSWER :`-1`

Discussion

13007.	Centroid of the triangle with verticies P(1, -2, 1), Q(2, 3, -1) and R(1, -1, -1) is _____ .
Answer» ANSWER :`4/3,0,(-1)/3)`

Discussion

13008.	If I_(n) is the identity matrix of order n then the rank of I_(n) is
Answer» 1 `n+1` no SOLUTION `n-1` ANSWER :C

Discussion

13009.	What is the number of terms in the expansion of(3 + 2 sqrt(5) )^(18) - (3-2 sqrt(5) )^(18)
Answer» ANSWER :9

Discussion

13010.	If secxcos5x+1=0,"where "0ltxle(pi)/(2), then find the value of x.
Answer» ANSWER :`(PI)/(6)`

Discussion

13011.	If y = sin x[1/(sin x.sin 2x) + 1/(sin 2x .sin 3x) +...+ 1/(sin nx sin(n + 1)x)]then (dy)/(dx) =
Answer» `cotx - cot(N + 1)x` `(n + 1)"cosec"^2(n + 1)x - "cosec"^2X` `"cosec"^2 x- (n + 1)"cosec"^2(n + 1)x` `cotx + "cot"(n + 1) x` ANSWER :C

Discussion

13012.	A balloon is in the form of right circular cylinder of radius 1.5m and length 4m and is surmounted by hemispherical ends. If the radius is increased by 0.01m and the length by 0.05m, the percentage change in the volume of the balloon is
Answer» 2.385 2.489 2.0389 2.589 Answer :A

Discussion

13013.	The range of the function f(x) = \|\|__x__\| -x\|,x in RR is
Answer» [0,1] [` 0, INFTY]` [0,1] (0,1) ANSWER :C

Discussion

13014.	Locus of centroid of the triangle whose vertices are (acostheta,asintheta),(bsintheta,-bcostheta) and (2,0) where theta is a parameter is
Answer» `(3x-2)^(2)+y^(2)=a^(2)+B^(2)` `(3x-2)^(2)+3y^(2)=a^(2)+b^(2)` `(3x-2)^(2)+9Y^(2)=a^(2)+b^(2)` `(3x-2)^(2)+9y^(2)=a^(2)-b^(2)` Answer :3

Discussion

13015.	Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A′?
Answer» ANSWER : A' is the SET of all EQUILATERAL TRIANGLES.

Discussion

13016.	Solve the following equations Cos 2 theta + cos 8 theta = Cos 5 theta
Answer» Answer :`(2n+1)(PI)/(10),(2npi)/(3)pm(pi)/(9),NINZ`

Discussion

13017.	If a triangle of maximum area is inscribed in a circle of radius 30cm then the side of the triangle and perimeter are
Answer» 30,45 `10sqrt3,15` `2sqrt5,30` `30sqrt3,990sqrt3` ANSWER :D

Discussion

13018.	The managing director of 'KUMAR PRAKASHAN KENDRA' arranges an exam of 100 marks to know the talent of student in Mathematics and English Subjects. Each question has two option true and false. In .......... Numbers of ways student can answer the question.
Answer» ANSWER :`2^(100)`

Discussion

13019.	If X and Y are two sets such that n ( X ) = 17, n ( Y ) = 23 and n ( X ∪ Y ) = 38, find n ( X ∩ Y ).
Answer» ANSWER :2

Discussion

13020.	Find the term independent of x in the expansion of (3/(2 x^2) - 1/(3^x))^6.
Answer» ANSWER :`5/12`

Discussion

13021.	Which of the following can not be valid assignment of probabilities for outcomes of sample Space S={omega_(1),omega_(2),omega_(3),omega_(4),omega_(5),omega_(6),omega_(7)}
Answer» ANSWER :(a) YES, (B) Yes, (C) No, (d) No, (E) No.

Discussion

13022.	Length of latus rectum of ellipse 5x^2+9y^2=25is ......... .
Answer» ANSWER :`10/3`

Discussion

13023.	If graph of y = f(x) is symmetric about the point (5,0) and f'(7) = 3 , then the value of f'(3) is ..........
Answer» ANSWER :C

Discussion

13024.	Evaluate the following limits : Lim_(theta to pi/2)(cot theta)/(pi/2 - theta )
Answer» ANSWER :`=1`

Discussion

13025.	Solve z^(2)=z
Answer» ANSWER :`0,1,(1)/(2),+(SQRT(3))/(2)I,(1)/(2),-(sqrt(3))/(2)i`

Discussion

13026.	Solve x^(2) + x + 1=0
Answer» ANSWER :`=(-1 + SQRT(3)i)/2`

Discussion

13027.	How many numbers lying between 100 and 1000 can be formed with the digits 0, 1, 2, 3, 4, 5, if the repetition of the digits is not allowed?
Answer» ANSWER :100

Discussion

13028.	Which of the following sets are empty sets ? {x : x is neither prime nor composite number}.
Answer» ANSWER :it is not an EMPTY SET

Discussion

13029.	A ballon is observed simultaneously from the 3 points A,B,C on a staight road dirctly beneath it. The angles elevation at B is twice that at A and the angular elevation on at C is thrice that at A. If AB = 20, BC = 40 then the height of the ballon is
Answer» `3sqrt(15)` `5sqrt(15)` `8sqrt(15)` `15sqrt(5)` ANSWER :B

Discussion

13030.	Write the negation of the following statements: The number 2 is greater than 7.
Answer» ANSWER :The NUMBER 2 is not GREATER than 7.

Discussion

13031.	If tan theta =(1)/(sqrt(7)), find the value of ("cosec"^(2)theta-sec^(2)theta)/("cosec"^(2)theta+sec^(2)theta).
Answer» ANSWER :`3/4`

Discussion

13032.	Prove that cos 2x cos "" x/2 -cos 3x cos " (9x)/(2) = sin 5x sin ""(5x)/(2).
Answer» ANSWER :`SIN " (5X)/(2)=R.H.S.`

Discussion

13033.	If f: R to Ris defined by f(x) = \|x-3\| + \|x-4\|for x in R then lim_(x to 3^-) f(x) is equal to …………………. .
Answer» `-2` `-1` `0` `1` ANSWER :C

Discussion

13034.	From a pack of 52 playing cards, three cards are drawn at random. Find the probability of drawing a king, a queen and a knave.
Answer» ANSWER :`(""^(4)C_(1)XX""^(4)C_(1)xx""^(4)C_(1))/(""^(52)C_(3))=(16)/(5525)`

Discussion

13035.	If x^(2)+xy-2y^(2)+4x-y+k=0 represents a pair of straight lines, find k.
Answer» ANSWER :k=3

Discussion

13036.	The sum of the series, sin theta sec(3theta)+sin 3theta sec(3^(2)theta)+sin(3^(2)theta)sec(3^(3)theta)+……. upto n terms, is
Answer» `(1)/(2)[tan 3^(n)theta-tan 3^(n-1)theta]` `[TAN3^(n)theta-tan theta]` `(1)/(2)[tan 3^(n)theta-tan theta]` `(1)/(2)(tan 3^(n)theta-1)` ANSWER :B

Discussion

13037.	A speaks truth in 75 %casesand Bspeaks truthin 80 %cases. Probabilitythat theycontradicteach otherin a
Answer» `7/20` `13/20` `3/5` `2/5` ANSWER :A

Discussion

13038.	Period of cos x cos(60^(@) - x) cos (60^(@)+ x) is
Answer» `PI/2` `pi/3` `2pi/3` `pi` ANSWER :C

Discussion

13039.	Find the approximations of the following sqrt(25001)
Answer» ANSWER :5.0001

Discussion

13040.	The angle between any two diagonals of a cube is
Answer» ANSWER :`COS^(-1)((1)/(3))`

Discussion

13041.	Let 0lt x lt pi//4, then (sec2x-tan2x) equals
Answer» `TAN (x-(PI)/(4))` `tan ((pi)/(4)-x)` `tan (x + (pi)/(4))` `tan^(2) (x+(pi)/(4))` ANSWER :B

Discussion

13042.	Evaluate root(7)(0.00003587).
Answer» Solution :Let `x = root(7)(0.00003587).` Then, log `x = 1/7` log (0.00003587) `= 1/7 (bar(5).5548) = 1/7 (-5 + 0.5548)` `= 1/7 (-4.4452) = -0.6350` ` = -1 + (1 - 0.6350) = bar(1).3650` `RARR` x = ANTILOG `(bar(1).3650) = 0.2317.` HENCE, the required value is 0.2317.

Discussion

13043.	Evaluate the following limits : Lt_(xto0)(e^(-2x)-1)/x
Answer» ANSWER :-2

Discussion

13044.	Find the derivative of y=e^(Sin-1)x.
Answer» Answer :`(E ^(SIN ^(-1) x ))/( SQRT (1- x ^(2)))`

Discussion

13045.	Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? lim_(xrarr2)f(x).where f(x)={(4-x,xne2),(0,x=2):}
Answer» ANSWER :2

Discussion

13046.	Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A= { 1, 2, 3, 4}, B = { 2,4, 6, 8 } and C = { 3, 4, 5, 6 }. Find (A ∪ C)′
Answer» ANSWER :`{7, 8, 9 }`

Discussion

13047.	If A = {1,2,3}, B= {3,4,5}, then (A nn B) xx A is
Answer» `{(1,3),(2,3),(2,2)}` `{(3,1),(3,2),(3,3)}` `{(1,3),(3,1),(3,2)}` `{(1,3),(2,4),(3,5)}` ANSWER :B

Discussion

13048.	If sides of a trianglesare in the ratiox: y : sqrt( x^(2) +xy + y^(2))then greatestangle is
Answer» `100 ^(@) ` ` 150 ^(@) ` ` 120 ^(@) ` ` 135 ^(@) ` ANSWER :C

Discussion

13049.	Find the transformed equation of the straight line 2x - 3y + 5 = 0, when the origin is shifted to the point (3, -1) after translation of axes.
Answer» ANSWER :`2x-3y + 14=0`

Discussion

13050.	The shadow of the tower standing on a level ground is found to be 60 metres longer when the sun's altitude is 30^@ then when it is 45^@. The height of the tower is
Answer» `60 m ` ` 30M ` ` 60 SQRT3 m ` ` 30 ( sqrt3+1) m ` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

Consider the circle x^2+y^2-4x-6y-3 = 0 Find the radius of the circle

If A+B+C=720^(@) " then " tan A + tan B + tan C=

If the volume of parallelopiped with conterminus edges 4hati+5hatj+hatk, -hatj+hatk and 3hati+9hatj+phatk is 34 cubic units then p is equal to

If (1+2x-3x^(2))^(5)=1+a_(1)x+a_(2)x^(2)+….+a_(10)x^(10) then the value of a_(2)+a_(4)+……+a_(10)" is "………

Three cards are drawn fromadeck of 52 cards . Whatis the probability thatthey are all spades ?

If A +B + C = pi then secA(cos B cos C - sin B sin C) = .........

Centroid of the triangle with verticies P(1, -2, 1), Q(2, 3, -1) and R(1, -1, -1) is _____ .

If I_(n) is the identity matrix of order n then the rank of I_(n) is

What is the number of terms in the expansion of(3 + 2 sqrt(5) )^(18) - (3-2 sqrt(5) )^(18)

If secxcos5x+1=0,"where "0ltxle(pi)/(2), then find the value of x.

If y = sin x[1/(sin x.sin 2x) + 1/(sin 2x .sin 3x) +...+ 1/(sin nx sin(n + 1)x)]then (dy)/(dx) =

A balloon is in the form of right circular cylinder of radius 1.5m and length 4m and is surmounted by hemispherical ends. If the radius is increased by 0.01m and the length by 0.05m, the percentage change in the volume of the balloon is

The range of the function f(x) = ||__x__| -x|,x in RR is

Locus of centroid of the triangle whose vertices are (acostheta,asintheta),(bsintheta,-bcostheta) and (2,0) where theta is a parameter is

Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A′?

Solve the following equations Cos 2 theta + cos 8 theta = Cos 5 theta

If a triangle of maximum area is inscribed in a circle of radius 30cm then the side of the triangle and perimeter are

The managing director of 'KUMAR PRAKASHAN KENDRA' arranges an exam of 100 marks to know the talent of student in Mathematics and English Subjects. Each question has two option true and false. In .......... Numbers of ways student can answer the question.

If X and Y are two sets such that n ( X ) = 17, n ( Y ) = 23 and n ( X ∪ Y ) = 38, find n ( X ∩ Y ).

Find the term independent of x in the expansion of (3/(2 x^2) - 1/(3^x))^6.

Which of the following can not be valid assignment of probabilities for outcomes of sample Space S={omega_(1),omega_(2),omega_(3),omega_(4),omega_(5),omega_(6),omega_(7)}

Length of latus rectum of ellipse 5x^2+9y^2=25is ......... .

If graph of y = f(x) is symmetric about the point (5,0) and f'(7) = 3 , then the value of f'(3) is ..........

Evaluate the following limits : Lim_(theta to pi/2)(cot theta)/(pi/2 - theta )

Solve z^(2)=z

Solve x^(2) + x + 1=0

How many numbers lying between 100 and 1000 can be formed with the﻿ digits 0, 1, 2, 3, 4, 5, if the repetition of the digits is not allowed?

Which of the following sets are empty sets ? {x : x is neither prime nor composite number}.

A ballon is observed simultaneously from the 3 points A,B,C on a staight road dirctly beneath it. The angles elevation at B is twice that at A and the angular elevation on at C is thrice that at A. If AB = 20, BC = 40 then the height of the ballon is

Write the negation of the following statements: The number 2 is greater than 7.

If tan theta =(1)/(sqrt(7)), find the value of ("cosec"^(2)theta-sec^(2)theta)/("cosec"^(2)theta+sec^(2)theta).

Prove that cos 2x cos "" x/2 -cos 3x cos " (9x)/(2) = sin 5x sin ""(5x)/(2).

If f: R to Ris defined by f(x) = |x-3| + |x-4|for x in R then lim_(x to 3^-) f(x) is equal to …………………. .

From a pack of 52 playing cards, three cards are drawn at random. Find the probability of drawing a king, a queen and a knave.

If x^(2)+xy-2y^(2)+4x-y+k=0 represents a pair of straight lines, find k.

The sum of the series, sin theta sec(3theta)+sin 3theta sec(3^(2)theta)+sin(3^(2)theta)sec(3^(3)theta)+……. upto n terms, is

A speaks truth in 75 %casesand Bspeaks truthin 80 %cases. Probabilitythat theycontradicteach otherin a

Period of cos x cos(60^(@) - x) cos (60^(@)+ x) is

Find the approximations of the following sqrt(25001)

The angle between any two diagonals of a cube is

Let 0lt x lt pi//4, then (sec2x-tan2x) equals

Evaluate root(7)(0.00003587).

Evaluate the following limits : Lt_(xto0)(e^(-2x)-1)/x

Find the derivative of y=e^(Sin-1)x.

Use the graph to find the limits (if it exists).If the limit does not exist ,explain why? lim_(xrarr2)f(x).where f(x)={(4-x,xne2),(0,x=2):}

Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A= { 1, 2, 3, 4}, B = { 2,4, 6, 8 } and C = { 3, 4, 5, 6 }. Find (A ∪ C)′

If A = {1,2,3}, B= {3,4,5}, then (A nn B) xx A is

If sides of a trianglesare in the ratiox: y : sqrt( x^(2) +xy + y^(2))then greatestangle is

Find the transformed equation of the straight line 2x - 3y + 5 = 0, when the origin is shifted to the point (3, -1) after translation of axes.

The shadow of the tower standing on a level ground is found to be 60 metres longer when the sun's altitude is 30^@ then when it is 45^@. The height of the tower is

The range of the function f(x) = ||x| -x|,x in RR is

How many numbers lying between 100 and 1000 can be formed with the digits 0, 1, 2, 3, 4, 5, if the repetition of the digits is not allowed?