14949 + Interview Questions in Maths in Class 11 Page 13 InterviewSolution

601.	Evaluate the following limits : Lim_(x to oo) ((x+1)(2x+3))/((x+2)(3x+4))
Answer» ANSWER :`2/3`

Discussion

602.	The number of values of alpha in [0,2pi] for whilch 2sin^(3)alpha-7sin^(2)alpha+7 sin alpha=2, is
Answer» 6 4 3 1 Answer :C

Discussion

603.	If a and b are distinct integers, prove that a-b is a factor of a^n - b^n , whenever n is a positive integer.
Answer» ANSWER :` :. (a-B) " is a FACTOR of "`a^(N)-b^(n)`

Discussion

604.	If f: N to Z is defined by: f(n) ={{:(2, if, n=3k, k in Z),(10-n, if, n=3k+1, k in Z),(0, if, n=3k, k in Z):}, then {n in N: f(n) gt 2)=
Answer» {3,6,4} {1,4,7} {4,7} {7} ANSWER :B

Discussion

605.	If f(x) = 2(7 cos x + 24 sinx ) (7 sin x-24 cos x),for every x inR, then maximum value of (f(x) )^(1//4) is _________
Answer» ANSWER :5

Discussion

606.	Find equaiton of hyperbola satisfying given conditons Focus (1,2) eccentricity e = sqrt(3) and equation of the directrix is 2x + y - 1 = 0. (Hint : Use definition of the hyperbola).
Answer» Answer :`7x^(2) + 12xy - 2y^(2) - 2x + 4Y - 7 = 0`

Discussion

607.	if sin x= cox x, x in[o,pi] then is
Answer» 0 `PI/4` `pi/3` `pi` ANSWER :B

Discussion

608.	Find the coordinates of a point which divides internally the points (1,3,7),(6,3,2) in the ratio 2:3.
Answer» ANSWER :`THEREFORE ` REQD, POINT `(3,3,5)`

Discussion

609.	If cos alpha = (3)/(5) , cos beta = (4)/(5) ,find the value ofcos ""(( alpha - beta)/( 2)), assumingalpha and beta to be acute angles.
Answer» ANSWER :`(7 SQRT2)/(10)`

Discussion

610.	Assertion (A) : Vector component of barb per pendicular to bara is (baraxx(barbxxbara))/(abs(bara)^(2)) Reason (R) : bara xx (barb xxbarc) =(bara· barc)barb -(bara· barb)barc, Reason (R) : bara xx (barb xxbarc) =(bara· barc)barb -(bara. barb)barc,abs(a xx b) l=abs(bara)abs(b)sintheta The correct answer is
Answer» A,R are true, R is CORRECT EXPLANATION of A A,R are true, R is not correct explanation of A A is true, R is false A is false, R is true Answer :A

Discussion

611.	Show that the set of letters needed to spell “ CATARACT ” and the set of letters needed to spell “ TRACT” are equal.
Answer» ANSWER :`X= Y`

Discussion

612.	Evaluate the following limits : Lim_(x to oo) (sqrt(x^(2)+1)-root3(x^(3)-1))/(root4(x^(4)+1)-root5(x^(4)+1))
Answer» ANSWER :1

Discussion

613.	Two sides of a Rhombus ABCDare parallel to the line x-y=5 and 7x-y=3. The diagonals intersect at (2,1) then the equation of the diagonal are
Answer» x-y=1, 7x-y=13 x+y=3,x+7y=9 x+2y=4,2x-y=3 3x+4y=10,4x-3y=5 Answer :C

Discussion

614.	The minimum value of the function f(x)=3tanx+4cotx where x in(0,pi/2)
Answer» 7 `2sqrt(12)` `6sqrt2` 12 Answer :B

Discussion

615.	Find the probability of getting 5 at most 3 times in four throws of a dice.
Answer» SOLUTION :N/a

Discussion

616.	If z_(1)=2 + 7i and z_(2)=1- 5i, then verify that \|(z_(1))/(z_(2))\|= (\|z_(1)\|)/(\|z_(2)\|)
Answer» ANSWER :`SQRT((53)/(26))`

Discussion

617.	Sum the series to infinity : sqrt(2)- (1)/(sqrt(2))+(1)/(2(sqrt(2)))-(1)/(4sqrt(2))+ ....
Answer» ANSWER :`(2sqrt(2))/(3)`

Discussion

618.	If the co-ordinates of the orthocentre of an equilaateral triangleformed by the line y=0,37x-36y+37xx36=0 and 64x-63y+64xx63=0 is (a,b) then a-b-4535 is
Answer» ANSWER :6

Discussion

619.	Find the term independent of x in the expansion of the following binomials: (ii) ( sqrt((x)/(3) ) - sqrt(3)/(2x ))^(12)
Answer» ANSWER :`T_5 = (55)/(16)`,

Discussion

620.	What is the 20^(th) term of the sequence defined by a_(n)= (n-1) (2-n) (3+n) ?
Answer» ANSWER :`-7866`

Discussion

621.	If tan^(2)(pi(x+y))+cot^(2)(pi)x+y=1+sqrt((2x)/(1+x^(2))) where x,y are real then the least positive value of y is
Answer» 1 `1/4` `1/2` `3/5` ANSWER :B

Discussion

622.	Derive a formula for the angle between two lines with slopes m_(1) and m_(2). Hence the slopes of the lines which make an angle pi/4 with the line x-2y+5=0
Answer» ANSWER :`L= ABS(-m_(2))`

Discussion

623.	If x is measured in degree , then d/(dx) (cosx) is equal to
Answer» `- SINX ` `-(180)/PI sinx` `-pi/(180) sinx` `sinx` ANSWER :C

Discussion

624.	Prove that cot^(4)theta+cot^(2)theta="cosec"^(4)theta-"cosec"^(2)theta
Answer» ANSWER :LEFT SIDE.

Discussion

625.	Which of the following is/are not functions ([.] denotes the greatest integer and fractional part functions, respectively)?
Answer» `(1)/(ln[1-\|X\|])` `(x !)/({x})` `x ! {x}` `(ln (x-1))/(SQRT((1-x^(2))))` ANSWER :A::B::D

Discussion

626.	If the points (1, 2) and (3, 4)were to be on the same side of the line 3x-5y+a=0then
Answer» `7ltalt11` `a=7` `a=1` `alt7` or `agt11` ANSWER :D

Discussion

627.	sec h^(-1)((1)/(sqrt(2))) =
Answer» `log_(E)(sqrt(2)-1)` `log_(e)(sqrt(2) + 1)` `log_(e)(sqrt(3) +1)` `log_(e)(sqrt(3) - 1)` Answer :B

Discussion

628.	Let 0 lt theta_(1) lt theta_(2) lt theta_(3) lt. . . . denote the positive solution of the equation 3 + 3 cos theta = 2 sin ^(2) theta . The value of theta_(3) + theta_(7) is
Answer» `6 pi` `7 pi` `8 pi` `4 pi` ANSWER :A

Discussion

629.	The sides of a parallelogram are given by 2x^(2)-5xy+2y^(2)=0 and 2x^(2)-4xy+2y^(2)+3x+3y-9=0 then the equation of the diagonal not passing through the origin is
Answer» `x-y=1` `x+y=3` `x+y+3=0` `x+y=2` ANSWER :B

Discussion

630.	lim_(xto1)((sqrt(x)-1)(2x-3))/(2x^(2)+x-3)=……
Answer» 1 `(1)/(10)` `-(1)/(10)` Does not exists Answer :C

Discussion

631.	Two coin (a one rupee coin and a two rupee coin) are tossed once. Find a sample space.
Answer» ANSWER :S = {HH. HT, TH, TT}

Discussion

632.	The number of integral points (integral point means both the coordinates should be integers )exactly in the interior of the triangle withvertice(0,0), (0,21) and (21,0) is
Answer» ANSWER :190

Discussion

633.	For each of the following compound statements first identify the connecting words and then break it into component statements. All rational numbers are real and all real numbers are not complex.
Answer» ANSWER : ''And''. The component STATEMENTS are: All RATIONAL NUMBERS are REAL. All real numbers are not complex.

Discussion

634.	If f :[ - 2a, 2a] to R is an odd function such that f (x) = f (2a -x)forx in [a, 2a]. If the left hand derivative of f (x) at x =a is zero, then show that the left hand derivative of f (x) at x =-a is also zero
Answer» ANSWER :`THEREFORE F'(-a^(0)) =0`

Discussion

635.	If y= sqrt((a-x)(x-b))-(a-b)tan^(-1)sqrt((a-x)/(x-b))(a gtb) then(dy)/(dx) =
Answer» `SQRT((a-x)/(x-b))` `sqrt((a-x)(x-b))` 0 1 Answer :A

Discussion

636.	Evaluate the following limits : lim_( x to 0 ) (sqrt(1+ax) - sqrt(1-ax))/x
Answer» ANSWER :`1/a (SQRT(1+a^(2))-sqrt(1-a^(2)))`

Discussion

637.	Find the number of terms in the expansion of the following : (z+3y)^(8)-(z-3y)^(8)
Answer» ANSWER :4

Discussion

638.	The variance of the given data 2,5,7,9 is 25.1 . Then find the variance of the data 4,10,14,18.
Answer»

Discussion

639.	If A=sin^(2) theta + cos^(4) theta, then for all values oftheta, where
Answer» `1leAle2` `3/4leAle1` `0leAle1` `1/4leAle1/2` ANSWER :B

Discussion

640.	Show that the angle of rotation of the axes to eliminate xy term in the equationax^(2)+2hyxy by^(2)=0is 1/2tan^(-1)((2h)/(a-b)) when a ne b and pi/4 when a = b.
Answer» ANSWER :`PI/4`.

Discussion

641.	In the expansion of (x+a)^(100)+(x-a)^(100) , there are ………… terms
Answer» 50 202 51 None of these ANSWER :C

Discussion

642.	If C=60^(@), " then show that"(a)/(b+c)+(b)/(c+a)=1
Answer» `2` `0` ` -1` ` 1` ANSWER :D

Discussion

643.	If ((2,lambda,-3),(0,2,5),(1,1,3)) is a singular matrix, then lambda is
Answer» `lambda =2 ` `lambda NE 2` `lambda = (-8)/(5)` `lambda ne (-8)/(5)` ANSWER :A::B::D

Discussion

644.	The vector bar(i)+xbar(j)+3bar(k) is rotated through angle theta and doubled in magnitude, then it ecomes 4(i)+(4x-2)bar(j)+2bar(k). The value of x is
Answer» `2, -2//3` `1//3, 2` `2//3, 0` `2, 7` ANSWER :A

Discussion

645.	Express the following as functions of angles less than 45^(@) : tan(3598^(@))
Answer» ANSWER :`-TAN2^(@)`

Discussion

646.	A piece of paper is in the shape of a square of side 1 m long. It is cut at the four corners to make a regular polygon of eight sides (octagon), then the area of the polygon is
Answer» `2(SQRT2 - 1)m^(2)` `(sqrt2 - 1)m^(2)` `1/sqrt2 m^(2)` NONE of these ANSWER :a

Discussion

647.	Write the first three terms of the sequence a_(n)=(-1)^(n-1) 5^(n+1)
Answer» ANSWER :`25,-125,625,3125,15625`

Discussion

648.	Ifa lt b " thenf(x) "f(x) = sqrt((x -a)/(b-x))is continuous on
Answer» (a,B) [a,b] [a,b) (a,b] ANSWER :C

Discussion

649.	Reduce the equation of the straight line 3x+4y+15=0 to normal form and find the perpendicular distance of the line from the origin.
Answer» ANSWER : `-3/(5)x-4/(5)y=3, p=3`

Discussion

650.	If A= {-1, 2, 3} and B= {1, 3}, the determine A xx B
Answer» ANSWER :`{(-1,1), (-1, 3), (2,1),(2,3),(3,1),(3,3)}`

Discussion

Explore topic-wise InterviewSolutions in .

Evaluate the following limits : Lim_(x to oo) ((x+1)(2x+3))/((x+2)(3x+4))

The number of values of alpha in [0,2pi] for whilch 2sin^(3)alpha-7sin^(2)alpha+7 sin alpha=2, is

If a and b are distinct integers, prove that a-b is a factor of a^n - b^n , whenever n is a positive integer.

If f: N to Z is defined by: f(n) ={{:(2, if, n=3k, k in Z),(10-n, if, n=3k+1, k in Z),(0, if, n=3k, k in Z):}, then {n in N: f(n) gt 2)=

If f(x) = 2(7 cos x + 24 sinx ) (7 sin x-24 cos x),for every x inR, then maximum value of (f(x) )^(1//4) is _________

Find equaiton of hyperbola satisfying given conditons Focus (1,2) eccentricity e = sqrt(3) and equation of the directrix is 2x + y - 1 = 0. (Hint : Use definition of the hyperbola).

if sin x= cox x, x in[o,pi] then is

Find the coordinates of a point which divides internally the points (1,3,7),(6,3,2) in the ratio 2:3.

If cos alpha = (3)/(5) , cos beta = (4)/(5) ,find the value ofcos ""(( alpha - beta)/( 2)), assumingalpha and beta to be acute angles.

Show that the set of letters needed to spell “ CATARACT ” and the set of letters needed to spell “ TRACT” are equal.

Evaluate the following limits : Lim_(x to oo) (sqrt(x^(2)+1)-root3(x^(3)-1))/(root4(x^(4)+1)-root5(x^(4)+1))

Two sides of a Rhombus ABCDare parallel to the line x-y=5 and 7x-y=3. The diagonals intersect at (2,1) then the equation of the diagonal are

The minimum value of the function f(x)=3tanx+4cotx where x in(0,pi/2)

Find the probability of getting 5 at most 3 times in four throws of a dice.

If z_(1)=2 + 7i and z_(2)=1- 5i, then verify that |(z_(1))/(z_(2))|= (|z_(1)|)/(|z_(2)|)

Sum the series to infinity : sqrt(2)- (1)/(sqrt(2))+(1)/(2(sqrt(2)))-(1)/(4sqrt(2))+ ....

If the co-ordinates of the orthocentre of an equilaateral triangleformed by the line y=0,37x-36y+37xx36=0 and 64x-63y+64xx63=0 is (a,b) then a-b-4535 is

Find the term independent of x in the expansion of the following binomials: (ii) ( sqrt((x)/(3) ) - sqrt(3)/(2x ))^(12)

What is the 20^(th) term of the sequence defined by a_(n)= (n-1) (2-n) (3+n) ?

If tan^(2)(pi(x+y))+cot^(2)(pi)x+y=1+sqrt((2x)/(1+x^(2))) where x,y are real then the least positive value of y is

Derive a formula for the angle between two lines with slopes m_(1) and m_(2). Hence the slopes of the lines which make an angle pi/4 with the line x-2y+5=0

If x is measured in degree , then d/(dx) (cosx) is equal to

Prove that cot^(4)theta+cot^(2)theta="cosec"^(4)theta-"cosec"^(2)theta

Which of the following is/are not functions ([.] denotes the greatest integer and fractional part functions, respectively)?

If the points (1, 2) and (3, 4)were to be on the same side of the line 3x-5y+a=0then

sec h^(-1)((1)/(sqrt(2))) =

Let 0 lt theta_(1) lt theta_(2) lt theta_(3) lt. . . . denote the positive solution of the equation 3 + 3 cos theta = 2 sin ^(2) theta . The value of theta_(3) + theta_(7) is

The sides of a parallelogram are given by 2x^(2)-5xy+2y^(2)=0 and 2x^(2)-4xy+2y^(2)+3x+3y-9=0 then the equation of the diagonal not passing through the origin is

lim_(xto1)((sqrt(x)-1)(2x-3))/(2x^(2)+x-3)=……

Two coin (a one rupee coin and a two rupee coin) are tossed once. Find a sample space.

The number of integral points (integral point means both the coordinates should be integers )exactly in the interior of the triangle withvertice(0,0), (0,21) and (21,0) is

For each of the following compound statements first identify the connecting words and then break it into component statements. All rational numbers are real and all real numbers are not complex.

If f :[ - 2a, 2a] to R is an odd function such that f (x) = f (2a -x)forx in [a, 2a]. If the left hand derivative of f (x) at x =a is zero, then show that the left hand derivative of f (x) at x =-a is also zero

If y= sqrt((a-x)(x-b))-(a-b)tan^(-1)sqrt((a-x)/(x-b))(a gtb) then(dy)/(dx) =

Evaluate the following limits : lim_( x to 0 ) (sqrt(1+ax) - sqrt(1-ax))/x

Find the number of terms in the expansion of the following : (z+3y)^(8)-(z-3y)^(8)

The variance of the given data 2,5,7,9 is 25.1 . Then find the variance of the data 4,10,14,18.

If A=sin^(2) theta + cos^(4) theta, then for all values oftheta, where

Show that the angle of rotation of the axes to eliminate xy term in the equationax^(2)+2hyxy by^(2)=0is 1/2tan^(-1)((2h)/(a-b)) when a ne b and pi/4 when a = b.

In the expansion of (x+a)^(100)+(x-a)^(100) , there are ………… terms

If C=60^(@), " then show that"(a)/(b+c)+(b)/(c+a)=1

If ((2,lambda,-3),(0,2,5),(1,1,3)) is a singular matrix, then lambda is

The vector bar(i)+xbar(j)+3bar(k) is rotated through angle theta and doubled in magnitude, then it ecomes 4(i)+(4x-2)bar(j)+2bar(k). The value of x is

Express the following as functions of angles less than 45^(@) : tan(3598^(@))

A piece of paper is in the shape of a square of side 1 m long. It is cut at the four corners to make a regular polygon of eight sides (octagon), then the area of the polygon is

Write the first three terms of the sequence a_(n)=(-1)^(n-1) 5^(n+1)

Ifa lt b " thenf(x) "f(x) = sqrt((x -a)/(b-x))is continuous on

Reduce the equation of the straight line 3x+4y+15=0 to normal form and find the perpendicular distance of the line from the origin.

If A= {-1, 2, 3} and B= {1, 3}, the determine A xx B