14949 + Interview Questions in Maths in Class 11 Page 244 InterviewSolution

12151.	Fill up the blanks in following table: P(A)" "P(B)" "P(A nn B" "P(A uu B) (i) 1/3" "1/5" "1/15" "… (ii) 0.35" "..." "0.25" "0.6 (iii) 0.5" "0.35" "..." "0.7.
Answer» ANSWER :(i) `7/15`, (II) 0.5, (III) 0.15

Discussion

12152.	If an error of (1/10)% is made in measuring the radius of a sphere, the percentage error in volume is
Answer» 0.3 0.03 0.003 0.0003 Answer :A

Discussion

12153.	Find the domains of the following functions f(x) = sqrt( x- 2)
Answer» ANSWER :`[2,OO)`

Discussion

12154.	The sum of angles of elevation of the top of a tower from two points distance a and b from the base and in the same straight line with it is 90^@. Then the height of the tower is :
Answer» `a^(2)B` `ab^(2)` `SQRT(ab)` `ab` ANSWER :C

Discussion

12155.	If x = e^(t)sint, y =e^(t)costthen (d^2y)/(dx^2) att = piis
Answer» `2E^(pi)` `e^(pi)/2` `1/(2e^(pi))` `2/(e^pi)` ANSWER :D

Discussion

12156.	Evaluate the following limits : Lim_(x to 3) (x^(5) -243)/(x^(2)-9)
Answer» ANSWER :`135/2`

Discussion

12157.	Line passess from fixed point (2, 3) intersects axis of points P and Q. If O is origin and OPRQ will be rectangle then locus of point R is ..........
Answer» `3X + 2y = 6` `2x + 3Y = XY` `3x + 2y = xy` `3x + 2y = 6XY` Answer :C

Discussion

12158.	A farm house uses atleast 800 kg of special food daily. The special food is a mixture of corn and soyabean with the following compositions The dietary requirements of the special food stipulate atleast 30% protein and at most 5% fibre. Determine the daily minimum cost of the food mix.
Answer» ANSWER :RS 11294

Discussion

12159.	Prove the following ("sin"5x+"sin"3x)/(cos5x-cos3x)="tan"4x
Answer» ANSWER :`="TAN"4x=RHS`

Discussion

12160.	If the area of a triangleis 6.sq unitsand itsinradiusis 2 unitsthen itsperimeteris
Answer» `1` ` 2` ` 3` ` 6` ANSWER :D

Discussion

12161.	Use mathematical induction, to find 41^(n) - 14^(n) is a multiple of
Answer» `2,8` `27` `26` `14` ANSWER :B

Discussion

12162.	Write the first five terms of each of the sequenceswhose n^(th)terms are: a_n = n / (n+1)
Answer» Answer :`(1)/(2), (2)/(3), (3)/(4), (4)/(5) and (5)/(6)`

Discussion

12163.	Distance of the origin from the line (1+sqrt3)y+(1-sqrt3)x=10 " along the line " y=sqrt3x+k is
Answer» `5//sqrt2` `5//sqrt2+k` 10 5 Answer :D

Discussion

12164.	If sin alpha = A sin (alpha+beta), A ne 0 then Which of the following is the value of tan (alpha+beta) ?
Answer» `(SIN BETA)/(COS beta-A)` `(sin ALPHA cos alpha)/(A cos beta - sin^(2)alpha)` `(sin alpha cos alpha)/(A cos beta + sin^(2)alpha)` `(sin alpha)/(cos alpha - A)` Answer :B

Discussion

12165.	The solution of the inequality (sec^(-1)x)^(2)-6sec^(-1)x+8 gt 0 is
Answer» `(-INFTY, SEC2) CUP[1, infty)` `(sec2,1)` `[sec2,1]` `(-infty, sec2] cup [1, infty)` ANSWER :A

Discussion

12166.	Reprsent the complex numbner z=1+isqrt(3) in the polar form.
Answer» ANSWER :`(COS((PI)/(3))+I SIN((pi)/(3)))`

Discussion

12167.	An experiment consists of rolling a die and then tossing a coin if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.
Answer» ANSWER :{1HH, 1HT, 1TH, 1TT, 2H, 2T, 3HH, 3HT, 3TH, 3TT, 4H, 4T, 5HH, 5HT, 5TH, 5TT, 6H, 6T}

Discussion

12168.	An urn contains 7 white, 5 black and 3 read balls. Two balls are drawn at random. Find the probability that. (i) Both the balls are red. (ii) One balls is red and other is black. One ball is white.
Answer» Answer :(i) `(1)/(35)` (II) `(1)/(7)` (III) `(8)/(15)`

Discussion

12169.	Find the coefficient of : x^(10) " in " (x^(2)-2)^(11)
Answer» ANSWER :29568

Discussion

12170.	r("cot"(A)/(2)"cot"(B)/(2)"cot"(C)/(2))=
Answer» `DELTA` s 2s `2DELTA` ANSWER :B

Discussion

12171.	Statement-I : If (2,3,5),(3,5,2) and (5,2,3) are the vertices of a triangle then its circumcentre is (10/3,10/3,10/3) Statement-I : If (2,3,5),(3,5,2) and (5,2,3) are the vertices of a triangle then itperimeter is 3sqrt3 Which of the above statements is correct :
Answer» Only I Only II Both I and II Neither I nor II Answer :A

Discussion

12172.	Write down all the subsets of the following sets phi
Answer» ANSWER :`PHI`

Discussion

12173.	sin 2x + cos x =0
Answer» ANSWER :`X = NPI + (-1) ^(N) (7pi)/(6) or (2n +1) (pi)/(2), n in Z`

Discussion

12174.	If 0 lt alpha lt (pi)/(6) then alpha(cosec alpha) is
Answer» less than `(PI)/(6)` GREATER than `(pi)/(6)` less that `(pi)/(3)` greater than `(pi)/(3)` ANSWER :C

Discussion

12175.	Show that tha angles between the diagonals of a rectangular parallelopiped having sides a,b and c are cos^(-1)((\|alpha\|)/(a^(2)+b^(2)+c^(2))), where alpha=pma^(2)pmb^(2)pmc^(2)and\|alpha\|!=a^(2)+b^(2)+c^(2). Hence find the angle between the diagonals of a cube.
Answer» ANSWER :`COS^(-1)(1)/(3).`

Discussion

12176.	Find the consumer price index number for 1991 on the base of 1990 from the following data, using the method of weighted relatives.
Answer» ANSWER :`137.37`

Discussion

12177.	Cos^(-1)(cos""(10pi)/7)+Sin^(-1)(sin""(35pi)/11)+Tan^(-1)(tan""(24pi)/13)+Cot^(-1)(cot""(26pi)/5) is
Answer» `(4PI)/7+(PI)/55-(2pi)/13` `(4pi)/7-(pi)/55-(2pi)/13` `(4pi)/7-(pi)/55+(2pi)/13` `-(4pi)/7+(pi)/55+(2pi)/13` Answer :A

Discussion

12178.	Find distance from point (3, 5) to the line 2x + 3y = 14 and the distance to the line parallel to x - 2y = 1.
Answer» ANSWER :`SQRT5`

Discussion

12179.	Find the coordinates of the centre , foci, and ends points of latus rectum of the hyperbola 9x^(2)-16y^(2)+18x-64y-199=0 . Also find thelength of axes.
Answer» Answer :`(-1,-2); (4,-2),(-6,-2) ; (4,(1)/(4)), (4,(17)/(-4)),(-6,(1)/(4)),(-6,-(17)/(4))`; 8 UNITS ,6 units

Discussion

12180.	If f(x) = 2+ cos^(2) x + sec^(2) x, its value always is
Answer» `f(x) LT 1` `f(x) = 1` `2 GT f(x) gt 1` `f(x) ge 4` ANSWER :D

Discussion

12181.	If y= x^(n),then ratio of relative errors in y and x is
Answer» `1:1` `2:1` `1:N` `n:1` ANSWER :D

Discussion

12182.	Write the place of numbers underlined?1 ul2 3 ul7 ul2
Answer» Answer :`(a)3, (b) pm 2, (C ) 6 " or " 1`

Discussion

12183.	Write the general term in the expansion of(x^2 - yx)^12. x != 0.
Answer» ANSWER :`(-1)^R` `^6`Cundersetr.`x^12-2r` .`y^r`

Discussion

12184.	If an error of 0.01cm is made in measuring the perimeter of a circle and the perimeter is measured as 44cm then find the approximate error and relative error in its area.
Answer» ANSWER :0.07,0.0004545

Discussion

12185.	Which of the following functions are identical ?
Answer» `f(x)= ln x^(2)` and `g(x)=2 ln x` `f(x)=log_(x)e` and `g(x)=(1)/(log_(e)x)` `f(x)= SIN(cos^(-1)x)` and `g(x)= cos(sin^(-1)x)` NONE of these Answer :B::C

Discussion

12186.	The minimum value of 7/(4sinx+3cosx-6) is
Answer» -7 `7//9` `7//5` `1//9` ANSWER :A

Discussion

12187.	Prove that (1 + i)^4 = -4
Answer» ANSWER :`2(COS(PI)3/+isinpi/3)`

Discussion

12188.	Ifsqrt( 5 - 2 sinx) = 6 sin x - 1then x =
Answer» ` N PI + ( - 1)^(n) (pi)/( 6) , n in Z` ` n pi + ( - 1)^(n) (pi)/( 3) , n in Z` ` n pi + ( - 1)^(n) ( 2 pi)/( 3) , n in Z` ` n pi + ( - 1)^(n) (5 pi)/( 6) , n in Z` Answer :A

Discussion

12189.	I : Through three non-collinear points only one plane exists II : Through three collinear points only one plane exists Which of the following is correct?
Answer» both I, II are TRUE Neither I nor II is true I is true, II is FALSE I is false, II is true ANSWER :C

Discussion

12190.	(1+ tan alpha tan beta)^(2) + (tan beta - tan beta)^(2)=
Answer» `TAN^(2) ALPHA tan^(2) BETA` `sec^(2) alpha + sec^(2) beta` `sec^(2)alpha sec^(2)beta` `tan^(2) alpha +tan^(2) beta` ANSWER :C

Discussion

12191.	Determine thesmallest postive value of x which satisfies the equation sqrt(1 + sin 2 x) - sqrt( 2) cos3 x = 0
Answer» `(pi)/4` `(pi)/16` `(pi)/3` `(pi)/8` ANSWER :B

Discussion

12192.	The range of the functions. Observe the following lists. The correct match for list I from list II:
Answer» A-4,B-1,C-2,D-5 A-4,B-3,C-2,D-5 A-4,B-3,C-5,D-2 A-3,B-1,C-4,D-2 Answer :A

Discussion

12193.	If in DeltaABC a = 9 , b = 7 and sinA = 3/4then DeltaABC is right angle .
Answer» ANSWER :FALSE STATEMENT

Discussion

12194.	The periodof 6 cos^(4)(x ) -7 sin^(4)( x) is
Answer» `(PI)/(2)` `pi` `(3PI)/(2)` `2PI` ANSWER :2

Discussion

12195.	Identify the Quantifiers in the following statements: There exists a triangle which is not an isosceles triangle.
Answer» ANSWER :EXISTENTIAL quanifier is USED

Discussion

12196.	Evaluate the following:i) sin\ pi/12ii) sin\ pi/8, iii) cos\ pi/8,iv) cos\ pi/(24
Answer» SOLUTION :i) `(sqrt(3)-1)/(2sqrt(2)`, II) `sqrt(2-sqrt(2))/(2)`, iii) `sqrt(2+sqrt(2))` , iv) `sqrt(4+sqrt(6)+sqrt(2))/(8)`

Discussion

12197.	Find the standard deviation for the following data:
Answer» ANSWER :6.12

Discussion

12198.	If the equation to the locus of points equidistant from the points (-2,3), (6,-5) is ax+by+c=0 where agt0 then, the ascending order of a, b, c is
Answer» a,B,c c, b, a b, c, a a, c, b Answer :2

Discussion

12199.	cos^(2)A+cos^(2)B-cos^(2)C=1-2sinA sinB cosC
Answer» SOLUTION :NA

Discussion

12200.	Showthat sin 5x + cos(sqrt(5) pi x)is non-periodic .
Answer» ANSWER :1

Discussion

Explore topic-wise InterviewSolutions in .

Fill up the blanks in following table: P(A)" "P(B)" "P(A nn B" "P(A uu B) (i) 1/3" "1/5" "1/15" "… (ii) 0.35" "..." "0.25" "0.6 (iii) 0.5" "0.35" "..." "0.7.

If an error of (1/10)% is made in measuring the radius of a sphere, the percentage error in volume is

Find the domains of the following functions f(x) = sqrt( x- 2)

The sum of angles of elevation of the top of a tower from two points distance a and b from the base and in the same straight line with it is 90^@. Then the height of the tower is :

If x = e^(t)sint, y =e^(t)costthen (d^2y)/(dx^2) att = piis

Evaluate the following limits : Lim_(x to 3) (x^(5) -243)/(x^(2)-9)

Line passess from fixed point (2, 3) intersects axis of points P and Q. If O is origin and OPRQ will be rectangle then locus of point R is ..........

A farm house uses atleast 800 kg of special food daily. The special food is a mixture of corn and soyabean with the following compositions The dietary requirements of the special food stipulate atleast 30% protein and at most 5% fibre. Determine the daily minimum cost of the food mix.

Prove the following ("sin"5x+"sin"3x)/(cos5x-cos3x)="tan"4x

If the area of a triangleis 6.sq unitsand itsinradiusis 2 unitsthen itsperimeteris

Use mathematical induction, to find 41^(n) - 14^(n) is a multiple of

Write the first five terms of each of the sequenceswhose n^(th)terms are: a_n = n / (n+1)

Distance of the origin from the line (1+sqrt3)y+(1-sqrt3)x=10 " along the line " y=sqrt3x+k is

If sin alpha = A sin (alpha+beta), A ne 0 then Which of the following is the value of tan (alpha+beta) ?

The solution of the inequality (sec^(-1)x)^(2)-6sec^(-1)x+8 gt 0 is

Reprsent the complex numbner z=1+isqrt(3) in the polar form.

An experiment consists of rolling a die and then tossing a coin if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

An urn contains 7 white, 5 black and 3 read balls. Two balls are drawn at random. Find the probability that. (i) Both the balls are red. (ii) One balls is red and other is black. One ball is white.

Find the coefficient of : x^(10) " in " (x^(2)-2)^(11)

r("cot"(A)/(2)"cot"(B)/(2)"cot"(C)/(2))=

Statement-I : If (2,3,5),(3,5,2) and (5,2,3) are the vertices of a triangle then its circumcentre is (10/3,10/3,10/3) Statement-I : If (2,3,5),(3,5,2) and (5,2,3) are the vertices of a triangle then itperimeter is 3sqrt3 Which of the above statements is correct :

Write down all the subsets of the following sets phi

sin 2x + cos x =0

If 0 lt alpha lt (pi)/(6) then alpha(cosec alpha) is

Show that tha angles between the diagonals of a rectangular parallelopiped having sides a,b and c are cos^(-1)((|alpha|)/(a^(2)+b^(2)+c^(2))), where alpha=pma^(2)pmb^(2)pmc^(2)and|alpha|!=a^(2)+b^(2)+c^(2). Hence find the angle between the diagonals of a cube.

Find the consumer price index number for 1991 on the base of 1990 from the following data, using the method of weighted relatives.

Cos^(-1)(cos""(10pi)/7)+Sin^(-1)(sin""(35pi)/11)+Tan^(-1)(tan""(24pi)/13)+Cot^(-1)(cot""(26pi)/5) is

Find distance from point (3, 5) to the line 2x + 3y = 14 and the distance to the line parallel to x - 2y = 1.

Find the coordinates of the centre , foci, and ends points of latus rectum of the hyperbola 9x^(2)-16y^(2)+18x-64y-199=0 . Also find thelength of axes.

If f(x) = 2+ cos^(2) x + sec^(2) x, its value always is

If y= x^(n),then ratio of relative errors in y and x is

Write the place of numbers underlined?1 ul2 3 ul7 ul2

Write the general term in the expansion of(x^2 - yx)^12. x != 0.

If an error of 0.01cm is made in measuring the perimeter of a circle and the perimeter is measured as 44cm then find the approximate error and relative error in its area.

Which of the following functions are identical ?

The minimum value of 7/(4sinx+3cosx-6) is

Prove that (1 + i)^4 = -4

Ifsqrt( 5 - 2 sinx) = 6 sin x - 1then x =

I : Through three non-collinear points only one plane exists II : Through three collinear points only one plane exists Which of the following is correct?

(1+ tan alpha tan beta)^(2) + (tan beta - tan beta)^(2)=

Determine thesmallest postive value of x which satisfies the equation sqrt(1 + sin 2 x) - sqrt( 2) cos3 x = 0

The range of the functions. Observe the following lists. The correct match for list I from list II:

If in DeltaABC a = 9 , b = 7 and sinA = 3/4then DeltaABC is right angle .

The periodof 6 cos^(4)(x ) -7 sin^(4)( x) is

Identify the Quantifiers in the following statements: There exists a triangle which is not an isosceles triangle.

Evaluate the following:i) sin\ pi/12ii) sin\ pi/8, iii) cos\ pi/8,iv) cos\ pi/(24

Find the standard deviation for the following data:

If the equation to the locus of points equidistant from the points (-2,3), (6,-5) is ax+by+c=0 where agt0 then, the ascending order of a, b, c is

cos^(2)A+cos^(2)B-cos^(2)C=1-2sinA sinB cosC

Showthat sin 5x + cos(sqrt(5) pi x)is non-periodic .