14949 + Interview Questions in Maths in Class 11 Page 190 InterviewSolution

9451.	Period of sin sqrt(x) + cos sqrt( x) =
Answer» `PI` `2PI` 1 Does not exist Answer :D

Discussion

9452.	{:("Column - I ","Column - II "),("A) The number of pairs (x, y)satisfying the equation sin x + sin y = sin (x + y) and \|x\| + \|y\| = 1 ","P) 6 "),("B) The number of values of x satisfying " e^((1)/(sqrt(2)))(e ^(sin x)+ e ^(cos x)) = 2 i n (- pi , pi) is ,"Q) 4 "),("C) The number of values of" x in ( - pi, pi) "satisfying " cos^(7) x + sin^(4) x = 1is ,"R) 3 "),("D) The number of values of " x in ( - pi, pi) "satisfying " cos^(50) x - sin^(50) x = 1 ,"S) 2 " ):}
Answer» <P> ANSWER :A- p; B - s; C - R; D - r

Discussion

9453.	Find Spearman's rank correlation coefficient .
Answer» ANSWER :Spearman's rank correlation COEFFICIENT (r ) = `0.99`

Discussion

9454.	If (sin alpha) x^(2) - 2 x + b gt 2 for all the real values of x le 1 and alpha in (0, pi//2) cup (pi//2,pi) , then the possible real values of b is/are
Answer» 2 3 4 5 Answer :C::D

Discussion

9455.	A tower, of x metres high, has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant y metres from the foot of the tower. Then the length of the flagstaff in metres in
Answer» ` ( y(X^(2) - y^(2)))/( x^(2) +y^(2))` ` ( x( y^(2) +x^(2)))/( y^(2)- x^(2))` ` (x( x^(2) +y^(2)))/( x^(2) - y ) ` ` ( x(x^(2)-y^(2)))/( x^(2) + y^(2))` ANSWER :B

Discussion

9456.	Find the values of x and y if 2x+4iy = -i^(3)x-y+3
Answer» ANSWER :`X=(4)/(3), y= (1)/(3)`

Discussion

9457.	Translate the following statements into symbolic form: Rahul passed in Hindi and English.
Answer» ANSWER :RAHUL PASSED in HINDI and ENGLISH.

Discussion

9458.	The plane x+2y-kz+3=0 is perpendicular to the line whose direction ratio are (2,4,3) then k =
Answer» 5 `10/3` 1 0 Answer :B

Discussion

9459.	For 0 lt x lt pi the values ofx which satisfy the relation 9^(1 + \| cos x \| + \| cos^(2) x \| + cos^(3) x \| + …."upto" infty )= 3^(4) are given by
Answer» `pm pi//4, pm 2 pi //3` `pm pi //6, pm 2 pi //3` `pm pi // 3, pm 2 pi //3` `pm pi//2, pm 2 pi //3` ANSWER :C

Discussion

9460.	Find the slope of the lines : (a) Passing through the points (3, -2) and (-1, 4),
Answer» ANSWER :`-(3)/(2)`

Discussion

9461.	If theta is the angle between the lines x/a+y/b=1 and x/b+y/a=1 find the value of sin theta. when a gtb.
Answer» ANSWER :`(a^(2)-B^(2))/(a^(2)+b^(2))`

Discussion

9462.	ABCDEF is a regular hexagon. O is centre and P.V. of A, B are bar(i)-bar(j)+2bar(k), 2bar(i)+bar(j)+bar(k)" then "bar(BC)=
Answer» `-BAR(i)+bar(J)+2BAR(K)` `-bar(i)+bar(j)-2bar(k)` `-bar(i)+bar(j)+bar(k)` `-bar(i)+bar(j)` ANSWER :A

Discussion

9463.	(5,10) and (5,-10) are end points of latus rectum of parabola y^2 = 20x .
Answer» ANSWER :TRUE STATEMENT

Discussion

9464.	If sin x = 3/5, cos y =- (12)/(13), where x and y both lie in second quadrant, find the vlaue of sin (x +y).
Answer» ANSWER :`56/65`

Discussion

9465.	If the points (1,1,k) and (-3,0,1) are equidistant from the plane barr.(3bari+4barj-12bark)+13=0 then k =
Answer» `1` `2` `3` `5` ANSWER :A

Discussion

9466.	The sum of solutions of sin pi x + cos pi x = 0in [0, 100] is
Answer» 4375 4975 5000 5025 Answer :D

Discussion

9467.	Find atleast two equations of the straight lines in the family of the lines y=5x+b, for which b and the x-coordinate of the point of intersection of the lines with 3x-4y=6 are integers.
Answer» ANSWER :20x-4y-4y-23=0 5x-y-10=0

Discussion

9468.	Find the derivative of f from the first principle, where f is given by f(x)=x+(1)/(x)
Answer» ANSWER :`1-(1)/(X^(2))`

Discussion

9469.	Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0,- 4) and B (8,0).
Answer» ANSWER :`- 1/2`

Discussion

9470.	An equation of a line whose segment between the coordinate axis is divided by the point ((1)/(2),(1)/(3)) in the ratio 2:3 is
Answer» `6x + 9y=5` `9x+6y=5` `4X + 9 y=5` `9x + 4Y =5` ANSWER :C

Discussion

9471.	If x gt 0 then tan h^(-1) ((x^(2) - 1)/(x^(2) + 1)) =
Answer» `log_(e )(2x)` `log_(e )x` `log_(e )(3X)` `log_(e )(5x)` Answer :B

Discussion

9472.	If y=sqrt((1+cos2 theta)/(1-cos2 theta)) then (dy)/("d"theta) at theta = (3pi)/4 is
Answer» 2 -2 ±2 None of these Answer :A

Discussion

9473.	Examinethe continuityof the following (i) x + sin x (ii)x^(2) cos x(iii)e^(x) tan x (iv)e^(2x) + x^(2) (v)x. In x (vi)( sin x)/x^(2) (vii)(x^(2) -16)/(x+4) ( viii) \|x +2 \| + \| x -1\| (ix) (\|x+2\|)/(\|x+1\|)(x)cot x + tan x OR find the pointsof discontinuityof the function f, where (i)f(x) = {{:(4x+5, if xle 3) , (4x - 5,ifxgt 3) :} (ii)f(x) = {{:(x+2, if x ge2) , ( x^(2) , if x lt2):} f(x)= {{:(x^(3) - 3,ifx le 2) , (x^(2) +1 , if x gt 2):} (iv) if f(x) = {{:(sin x , 0 le x le pi/4),( cos x , pi/4 lt x lt pi/2):}
Answer» Answer :(i)` X inRR` (ii)cos x (III) ` pi/2` (iv)` x in RR` (v) `f(x)` (VI) 0 (vii) -4 (viii)` x in RR` (ix) `-1` (x) ` - ( npi)/2` (b) (i)x =3 (ii)4 (iii) 5 (iv) ` ( 0, pi/2)`

Discussion

9474.	lim_(x to 0)(xe^(x)-log(1+x))/(x^(2))=
Answer» `(3)/(2)` `(2)/(3)` 0 1 Answer :A

Discussion

9475.	Prove that cos^(2)76^(@)+cos^(2)16^(@)-cos76^(@)cos16^(@)=(3)/(4)
Answer» `1//2` 0 `-1//4` `3//4` ANSWER :D

Discussion

9476.	Find perpendicular distance from point (3,-1) to the line 12 x -5y-7=0.
Answer» ANSWER :`(34)/(13)`.

Discussion

9477.	If cos alpha+cos beta=0=sin alpha+sin beta, then cos 2 alpha+cos 2beta is equal to
Answer» `-2 sin (alpha + BETA)` `-2 COS (alpha + beta)` `2 sin(alpha +beta)` `2COS(alpha +beta)` Answer :B

Discussion

9478.	Write the contrapositive and converse of the following statements: If x is a prime number, then x is odd.
Answer» ANSWER :The contrapositive is If a number x is not ODD, then x is not a prime number. The CONVERSE is If a number x in odd, then it is a prime number

Discussion

9479.	Find the distance from the origin to each of the point: (0, 4,-4)
Answer» ANSWER :`sqrt29`

Discussion

9480.	If 2sec^(2) A - sec^(4) A - 2cosec^(2) A + cosec^(4) A = 15//4, then tan A is equal to
Answer» `1//sqrt(2)` `1//2` `1//2sqrt(2)` `-1//sqrt(2)` ANSWER :A::D

Discussion

9481.	A line passes through the point (2,2) and is perpendicular to the line 3x + y = 3 . Its y-intercept is
Answer» `(1)/(3)` `(2)/(3)` 1 `(4)/(3)` ANSWER :D

Discussion

9482.	For alpha = pi//7 which of the following hold (s) good ?
Answer» `tanalphatan2alphatan3alpha=tan3alpha-tan2alpha-tanalpha` `"cosec"ALPHA = "cosec"2alpha+"cosec" 4alpha` `COS alpha - cos 2 alpha + cos 3 alpha =1//2` `8 cos alpha cos 2alpha cos 4 alpha =1` Answer :A::B::C

Discussion

9483.	The minimum and maximum values of sin (x+(pi)/(4) ) sin ( x - (pi)/(4)) are
Answer» `-1, 1` `-(1)/(2), (1)/(2)` `-(3)/(2), (3)/(2)` `-(1)/(4), (1)/(4)` Answer :B

Discussion

9484.	A and B are two sets such that n(A)= 5 and n(B)= 2. If(a,2), (b, 3), (c, 2), (d, 2), (e, 2)are elements of A xx B then find A and B.
Answer» Answer :A= {a,B,c,d,E} B= {2, 3}

Discussion

9485.	Find the ratio in which the pointC(6,-17,-4) divides the line segment joining the points A (2, 3,4) and B (3 , -2 , 2) .
Answer» ANSWER :`=-3:4`

Discussion

9486.	If x = sqrt((1 - t^2)/(1 + t^2)), y = (sqrt(1 + t^2) - sqrt(1 - t^2))/(sqrt(1 + t^2) + sqrt(1 -t^2)) then (dy)/(dx) =
Answer» ANSWER :`(-2)/(1+x)^2`

Discussion

9487.	Two unbiased dice are thrown . Find the probability that six may be obtained as product ,
Answer» ANSWER :`=(1)/(9)`.

Discussion

9488.	Find the locus of the point (cosectheta-sintheta,sectheta-costheta),theta is a parameter
Answer» ANSWER :1

Discussion

9489.	If f(x) =(10^(x)-10^(-x))/(10^(x) +10^(-x)) then f^(-1)(x)=
Answer» `log_(10)(2-x)` `1/2 log_(10)((1+x)/(1-x))` `1/2 log_(10) (2X-1)` `1/4 log_(10)((2x)/(2-x))` ANSWER :B

Discussion

9490.	The value of the expression tan^(6)20^(@) - 33tan^(4)20^@+27^(2)20^@ is
Answer» 0 1 2 3 Answer :D

Discussion

9491.	Rewrite each of the following statements in the form p if and only if q: p: If you watch television, then you mind is free and if you mind is free, then you watch television.
Answer» ANSWER :You WATCH TELEVISION if and only if your MIND in FREE.

Discussion

9492.	If (p,q), (acostheta,bsintheta),(bcostheta,asintheta) are the vertices of a triangle, where theta is a parameter then the locus of the centriod of the triangle
Answer» `(3x-p)^(2)+(3y-q)^(2)=(a+b)^(2)` `X^(2)+y^(2)=9(a+b)^(2)` `(3x+p)^(2)+(3y+q)^(2)=(a+b)^(2)` `x(x-a)+y(y+b)=0` Answer :1

Discussion

9493.	Represent the complex numberZ = 1 = isqrt(3)in the polar form .
Answer» ANSWER :the COMPLEX NUMBER is `z=2(COS pi/3 + I SIN pi/3)`

Discussion

9494.	Consider the complex number z_1 = 3+i and z_2 = 1+i .Find 1/z_2
Answer» ANSWER :`1/2-1/2i`

Discussion

9495.	Every progression is a sequence but the converse, i.e., every sequences is also a progression need not necessarily be true
Answer» ANSWER :1

Discussion

9496.	Compute the following limits. Lt_(xtooo)(6x^(2)-cos3x)/(x^(2)+5)
Answer» ANSWER :6

Discussion

9497.	Let 0lt theta_(1)lt theta_(2)lt theta_(3)lt …….. Denote the positive solution of the equation 3+3cos theta=2sin^(2) theta.The value of theta_(3)+theta_(7) is
Answer» `6PI` `7pi` `8pi` `4PI` ANSWER :A

Discussion

9498.	Ifthree geometric meansinsertedbetween 1 and256 , then find the common ratio
Answer» ANSWER :2

Discussion

9499.	The value of a third order determinan t is 11 then find the value of the square of the determinent formed by the cofactors
Answer» ANSWER :`(121)^(2)`

Discussion

9500.	1^(2) + 3^(2) + 5^(2)+……..up to n terms is……..
Answer» `(N(n+ 1)(2n+1))/(2)` `(n(2n-1)(2n+1))/(3)` `((n-1)^(2)(2n+1))/(6)` `((2n+1)^(3))/(3)` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Period of sin sqrt(x) + cos sqrt( x) =

Find Spearman's rank correlation coefficient .

If (sin alpha) x^(2) - 2 x + b gt 2 for all the real values of x le 1 and alpha in (0, pi//2) cup (pi//2,pi) , then the possible real values of b is/are

A tower, of x metres high, has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant y metres from the foot of the tower. Then the length of the flagstaff in metres in

Find the values of x and y if 2x+4iy = -i^(3)x-y+3

Translate the following statements into symbolic form: Rahul passed in Hindi and English.

The plane x+2y-kz+3=0 is perpendicular to the line whose direction ratio are (2,4,3) then k =

For 0 lt x lt pi the values ofx which satisfy the relation 9^(1 + | cos x | + | cos^(2) x | + cos^(3) x | + …."upto" infty )= 3^(4) are given by

Find the slope of the lines : (a) Passing through the points (3, -2) and (-1, 4),

If theta is the angle between the lines x/a+y/b=1 and x/b+y/a=1 find the value of sin theta. when a gtb.

ABCDEF is a regular hexagon. O is centre and P.V. of A, B are bar(i)-bar(j)+2bar(k), 2bar(i)+bar(j)+bar(k)" then "bar(BC)=

(5,10) and (5,-10) are end points of latus rectum of parabola y^2 = 20x .

If sin x = 3/5, cos y =- (12)/(13), where x and y both lie in second quadrant, find the vlaue of sin (x +y).

If the points (1,1,k) and (-3,0,1) are equidistant from the plane barr.(3bari+4barj-12bark)+13=0 then k =

The sum of solutions of sin pi x + cos pi x = 0in [0, 100] is

Find atleast two equations of the straight lines in the family of the lines y=5x+b, for which b and the x-coordinate of the point of intersection of the lines with 3x-4y=6 are integers.

Find the derivative of f from the first principle, where f is given by f(x)=x+(1)/(x)

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0,- 4) and B (8,0).

An equation of a line whose segment between the coordinate axis is divided by the point ((1)/(2),(1)/(3)) in the ratio 2:3 is

If x gt 0 then tan h^(-1) ((x^(2) - 1)/(x^(2) + 1)) =

If y=sqrt((1+cos2 theta)/(1-cos2 theta)) then (dy)/("d"theta) at theta = (3pi)/4 is

lim_(x to 0)(xe^(x)-log(1+x))/(x^(2))=

Prove that cos^(2)76^(@)+cos^(2)16^(@)-cos76^(@)cos16^(@)=(3)/(4)

Find perpendicular distance from point (3,-1) to the line 12 x -5y-7=0.

If cos alpha+cos beta=0=sin alpha+sin beta, then cos 2 alpha+cos 2beta is equal to

Write the contrapositive and converse of the following statements: If x is a prime number, then x is odd.

Find the distance from the origin to each of the point: (0, 4,-4)

If 2sec^(2) A - sec^(4) A - 2cosec^(2) A + cosec^(4) A = 15//4, then tan A is equal to

A line passes through the point (2,2) and is perpendicular to the line 3x + y = 3 . Its y-intercept is

For alpha = pi//7 which of the following hold (s) good ?

The minimum and maximum values of sin (x+(pi)/(4) ) sin ( x - (pi)/(4)) are

A and B are two sets such that n(A)= 5 and n(B)= 2. If(a,2), (b, 3), (c, 2), (d, 2), (e, 2)are elements of A xx B then find A and B.

Find the ratio in which the pointC(6,-17,-4) divides the line segment joining the points A (2, 3,4) and B (3 , -2 , 2) .

If x = sqrt((1 - t^2)/(1 + t^2)), y = (sqrt(1 + t^2) - sqrt(1 - t^2))/(sqrt(1 + t^2) + sqrt(1 -t^2)) then (dy)/(dx) =

Two unbiased dice are thrown . Find the probability that six may be obtained as product ,

Find the locus of the point (cosectheta-sintheta,sectheta-costheta),theta is a parameter

If f(x) =(10^(x)-10^(-x))/(10^(x) +10^(-x)) then f^(-1)(x)=

The value of the expression tan^(6)20^(@) - 33tan^(4)20^@+27^(2)20^@ is

Rewrite each of the following statements in the form p if and only if q: p: If you watch television, then you mind is free and if you mind is free, then you watch television.

If (p,q), (acostheta,bsintheta),(bcostheta,asintheta) are the vertices of a triangle, where theta is a parameter then the locus of the centriod of the triangle

Represent the complex numberZ = 1 = isqrt(3)in the polar form .

Consider the complex number z_1 = 3+i and z_2 = 1+i .Find 1/z_2

Every progression is a sequence but the converse, i.e., every sequences is also a progression need not necessarily be true

Compute the following limits. Lt_(xtooo)(6x^(2)-cos3x)/(x^(2)+5)

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

Ifthree geometric meansinsertedbetween 1 and256 , then find the common ratio

The value of a third order determinan t is 11 then find the value of the square of the determinent formed by the cofactors

1^(2) + 3^(2) + 5^(2)+……..up to n terms is……..