14949 + Interview Questions in Maths in Class 11 Page 208 InterviewSolution

10351.	If x is real, then the minimum value of y=(x^(2)-x+1)/(x^(2)+x+1) is
Answer» `1//3` 3 `1//2` 1 Answer :A

Discussion

10352.	Let a.b and c be non-zero vectors such that (a xx b) xx c = (1)/(3) \|b\| \|c\| a. If theta is the acute angle between the vectors b and c then sin theta =
Answer» `(2 SQRT2)/(3)` `(1)/(3)` `(sqrt2)/(3)` `(2)/(3)` ANSWER :A

Discussion

10353.	A line is drawn through the point (1,2) to meet the co-ordinate axes at P and Q such that it forms a Delta^(1e) OPQ, where O is the origin. If the area of the Delta OPQ, is least, then the slope of the line PQ is
Answer» `(-1)/(4)` `-4` `-2` `(-1)/(2)` ANSWER :C

Discussion

10354.	A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A nn B) = 0.35 Find (i) P(A uu B (ii) P(A' nn B') (iii) P(A nn B') (iv) P(B nn A')
Answer» ANSWER :(I) 0.88 (II) 0.12 (III) 0.19 (V) 0.34

Discussion

10355.	1+ cso 56^(@) + cos 58^(@) - cos 66^(@)=
Answer» ` 2 COS 28^(@) cos 29^(@) cos 33^(@)` ` 4 cos 28^(@) cos 29^(@) cos 33^(@)` ` 4 cos 28^(@) cos 29^(@) SIN 33^(@)` ` 2 cos 28^(@) cos 29^(@) sin 33^(@)` ANSWER :C

Discussion

10356.	If xy(x-y)=2a^3(agt0) then y has minimum when x =
Answer» `(1)/(a)` `-a` `(a)/(2)` a Answer :B

Discussion

10357.	(i) Find the equation of hyperbola whose eccentricity is sqrt((13)/(12)) and the distance between foci is 26. (ii) The foci of a hyperbola coincide of the ellipse 9x^(2)+25y^(2)=225. If the eccentricity of the hyperbola is 2, then find its equation.
Answer» Answer :(i) `x^(2)-12Y^(2)=156` (ii) `2X^(2)-y^(2)=12`

Discussion

10358.	If P is a point on the ellipse (x^(2))/(16) + (y^(2))/(25) = 1 whose foci are S and S', thenPS + PS' = 8.
Answer» ANSWER :FALSE

Discussion

10359.	Find the middle term in the following expansion:(i) (x^(2)-1/x^2)^(10)(ii) ((x)/(a)+(a)/(x))^(12)(iii) ((a)/(x)+bx)^(2n)(iv) (x-(1)/(x))^(9)(v) (1-3x+3x^(2)-x^(3))^(6)(vi) (x^(2)-a)^(11)(vii) (2x-(3)/x^(2))^(15)
Answer» SOLUTION :N/a

Discussion

10360.	Primary events are mutually exclusive.
Answer» ANSWER :TRUE STATEMENT

Discussion

10361.	Show that the straight line y^2-4y+3=0" and "x^2+4xy+4y^2+5x+10y+4=0 form a parallelogram and find the length of its sides.
Answer» ANSWER :`2sqrt(5),3`

Discussion

10362.	Show that the area of the triangle formed by the lines y = m_(1) x + c_(1) , y = m_(2) x + c_(2) " and " x = 0" is " ((c_(1) - c_(2))^(2))/(2\|m_(1) - m_(2)\|)
Answer» ANSWER :`((c_(2) - c_(1))^(2))/(2\|m_(1) - m_(2)\|)`

Discussion

10363.	2^(2)+5^(2)+8^(2)+………………."to" 15terms.
Answer» ANSWER :10455

Discussion

10364.	If E and F are events such that P(E) = 1/4, P(F) = 1/2 and P(E and F)= 1/8, find (i) P(E or F),(ii) P(not E and not F).
Answer» ANSWER :(i) `5/8` (II) `3/8`

Discussion

10365.	3(sinx-cosx)^(4)+6(sinx+cosx)^(2)+4(sin^(6)x+cos^(6)x) =…………..
Answer» ANSWER :13

Discussion

10366.	If the circles x^(2) +y^(2) = a and x^(2) + y^(2) - 6x - 8y + 9 = 0touch externally then a =
Answer» 1 2 3 6 Answer :A

Discussion

10367.	If a+ib = (x+i)^(2)/(2x^(2)+1), prove that a^(2) + b^(2) = (x^(2)+1)^(2)/(2x^(2) + 1)^(2)
Answer» ANSWER :`((X^(2)+1)^(2))/((2X^(2)+1)^(2))`

Discussion

10368.	If theta_(1) and theta_(2) are two solutions of the equation a cos2theta+bsin2theta=c then tan theta_(1)+tan theta_(2) =
Answer» `(2B)/(c+a)` `(2A)/(b+c)` `(2C)/(a+b)` `(ABC)/(a+b+c)` ANSWER :A

Discussion

10369.	Two sides of a triangle are y=m_(1)x and y=m_(2)x,m_(1),m_(2) are the roots of the equation x^(2)+ax-1=0. For all values of a the orthocentre of the triangle lies at
Answer» (1,1) (2,2) `(3/2,3/2)` (0,0) ANSWER :D

Discussion

10370.	If the plane 7x + 11y + 13z = 3003 meets the coordinate axes in A, B, C then the centroid of the Delta ABC is
Answer» `(143, 91,77)` `(143, 77, 91)` `(91,143, 77)` `(143, 66, 91)` ANSWER :A

Discussion

10371.	On intersecting the plane with coordinate axes, then the areas of triangle formed on xy,yz,zx planes are 12, 4, 6 then equation of plane is
Answer» `(X)/(4)+(y)/(6)+(z)/(8)=1` `(x)/(6)+(y)/(4)+(z)/(2)=1` `(x)/(2)+(y)/(3)+(z)/(4)=1` `(x)/(2)+(y)/(4)+(z)/(6)=1` Answer :B

Discussion

10372.	Which of the following sentences are statement? Give reason for your answer: Sun is star.
Answer» ANSWER :TRUE.

Discussion

10373.	If two sides of a triangle are the roots of the equation 4x^2-(2sqrt6)x+1=0 and the included angle is 60^@, then the third side is
Answer» `SQRT(3)` `sqrt(3)//2` `1//sqrt(3)` `2//sqrt(3)` ANSWER :B

Discussion

10374.	Find the modulus of the following using the property of modulus (3+4i) (8-6i)
Answer» ANSWER :50

Discussion

10375.	Which of the following sentences are statements? Give reasons for your answer: Mathematics is a fun.
Answer» ANSWER :TRUE.

Discussion

10376.	If PM is the perpendicular from P(2,3) on to the lie x+y=3 the M=
Answer» `(2,1)` `(-1,4)` `(1,2)` `(4,-1)` ANSWER :C

Discussion

10377.	Rewrite the following statement with “if-then” in five different ways conveying the same meaning. If a natural number is odd, then its square is also odd.
Answer» ANSWER :(i) A natural NUMBER is odd IMPLIES that its square is odd. (II) A natural number is odd only if its square is odd. (iii) For a natural number to be odd it is necessary that its square is odd. (iv) For the square of a natural number to be odd, it is sufficient that the number is odd (v) If the square of a natural number is not odd, then the natural number is not odd.

Discussion

10378.	The value of f(2) so that f(x)=(2^(x+2)-16)/(4^(x)-16) is continuous at x=2 is
Answer» 0 1 `1//3` `1//2` ANSWER :D

Discussion

10379.	x_1,x_2,x_3,….x_n then (x_1-barx)+(x_2-barx)+(x_n-barx)=0.
Answer» ANSWER :TRUE STATEMENT

Discussion

10380.	The pair of straight line x^2-3xy+2y^2=0 and x^2-3xy+2y^2+x-2=0 from a :
Answer» SPUARE but not RHOMBUS rhombus parallelogram rectangle but not a square Answer :C

Discussion

10381.	Find the slope of a line whose inclination is 60^(@)
Answer» ANSWER : `SQRT(3)`

Discussion

10382.	If sin x + cos x = sqrt( y + (1)/(y))" for " x in [0, pi] . then
Answer» `X = PI //4` `y = 0` y = 1 `x = 3 pi // 4` Answer :A::C

Discussion

10383.	A = {3k\| k in N} B = {3k -1\|k in N} and C = {3k-2\| k in N}. Then A , B and C are disjoint sets .
Answer» ANSWER :TRUE STATEMENT

Discussion

10384.	The range of f(x)=-3 cos sqrt(3x+x+x^(2)) is
Answer» [-1,1] [-2,2] [-3,3] [-4,4] ANSWER :C

Discussion

10385.	If bara,barb,barcare three vectors such thatabsbara =1, absbarb = 2, absbarc =3 and bara+barb+barc = bar0 ,then bara.barb+barb.barc+barc.bara =
Answer» 0 2 3 6 Answer :D

Discussion

10386.	P is point on hyperbola 16x^(2) - 9y^(2) = 144. S_(1) and S_(2) are its foci then PS_(1) - PS_(2) = ………
Answer» 4 6 8 12 Answer :B

Discussion

10387.	Find the most general value of theta satisfying the equation tantheta=-1 and costheta=(1)/(sqrt(2)).
Answer» ANSWER :`2NPI+(7pi)/(4).NINZ`

Discussion

10388.	Consider the point A(3,2,-4) and B (9,8,-10) Find the co-ordinates of the points which divides AB internally in the ratio 2:3
Answer» SOLUTION :(-9,-10,8)

Discussion

10389.	Consider the point A(3,2,-4) and B (9,8,-10) Find the co-ordinates of the points which divides AB internally in the ratio 1:2
Answer» SOLUTION :(5,4,-6)

Discussion

10390.	The set of all numbers a such that a^(2) + 2a, 2a + 3 " and " a^(2) + 3a + 8are the sides of a triangle is ………..
Answer» `(5, INFTY)` `(- infty, 5)` `(-5, 5)` `[5, - infty]` ANSWER :A

Discussion

10391.	The point of intersection of the perpendiecular lines ax^(2)+3xy-2y^(2)-5x+5y+c=0 is
Answer» `((1)/(5),(7)/(5))` (1,7) (`-(1)/(5),(-7)/(5))` `((1)/(5),-(1)/(5))` ANSWER :A

Discussion

10392.	XOZ plane divides the join of (2,3,1 ) and (6,7,1 ) in the ratio
Answer» `3:7` `2:7` `-3:7` `-2:7` ANSWER :a

Discussion

10393.	A vector bar(a) has components a_(1), a_(2), a_(3) in the right handed system OXYZ. If the coordinate system is rotated about z-axis through an angle pi//2, the component of bar(a) in the new system are
Answer» `(a_(2), -a_(1), a_(3))` `(a_(2), a_(1), a_(3))` `(-a_(2), a_(1), a_(3))` `(-a_(2), -a_(1), a_(3))` ANSWER :A

Discussion

10394.	Differentiate (x^(2)-1)/(x^(2)+1) with respect to x:
Answer» `(4X)/(X^(2)+1)` `(4x)/(x^(2)-1)` `(x^(2)+1)/(x^(2)+1)` `(4x)/(x^(2)+1)^(2)` ANSWER :D

Discussion

10395.	Which term of the sequence sqrt2, (1)/(sqrt2), (1)/(2 sqrt2)……is (1)/(512 sqrt2) ?
Answer» ANSWER :11

Discussion

10396.	Assume that theta is a rational multiple of pi such that cos thetais a distinct rational . The number of values of cos thetais
Answer» 3 4 5 6 Answer :C

Discussion

10397.	Solve the inequality for x:3x-7 gt 2 (x-6), 6-x gt 11 -2x
Answer» ANSWER :`(5,OO)` `(##NCERT_TEL_MAT_XI_C06_E04_009_A01##)`

Discussion

10398.	A die is rolled. Let E be the event ''die shows 4'' and F be the event ''die shows even number''. Are E and F mutually exclusive ?
Answer» ANSWER :`:.` E and F are not MUTUALLY EXCLUSIVE.

Discussion

10399.	A : The general solution of sin x = -1 is n pi + (-1)^(n)(3pi)/(2), n in Z R : The principal solution of sin x = 0 lies in [-pi//2, pi//2]
Answer» A is FALSE but R is TRUE A is true but R is false Both A and R are true and R is correct explanation of A Both A and R are true but R is not the correct explanation of A Answer :A

Discussion

10400.	Show that x^(n)=1+n(1-(1)/(x))+(n(n+1))/(1.2)(1-(1)/(x))^(2)+….
Answer» ANSWER :`= X^(N)=LHS`

Discussion

Explore topic-wise InterviewSolutions in .

If x is real, then the minimum value of y=(x^(2)-x+1)/(x^(2)+x+1) is

Let a.b and c be non-zero vectors such that (a xx b) xx c = (1)/(3) |b| |c| a. If theta is the acute angle between the vectors b and c then sin theta =

A line is drawn through the point (1,2) to meet the co-ordinate axes at P and Q such that it forms a Delta^(1e) OPQ, where O is the origin. If the area of the Delta OPQ, is least, then the slope of the line PQ is

A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A nn B) = 0.35 Find (i) P(A uu B (ii) P(A' nn B') (iii) P(A nn B') (iv) P(B nn A')

1+ cso 56^(@) + cos 58^(@) - cos 66^(@)=

If xy(x-y)=2a^3(agt0) then y has minimum when x =

(i) Find the equation of hyperbola whose eccentricity is sqrt((13)/(12)) and the distance between foci is 26. (ii) The foci of a hyperbola coincide of the ellipse 9x^(2)+25y^(2)=225. If the eccentricity of the hyperbola is 2, then find its equation.

If P is a point on the ellipse (x^(2))/(16) + (y^(2))/(25) = 1 whose foci are S and S', thenPS + PS' = 8.

Find the middle term in the following expansion:(i) (x^(2)-1/x^2)^(10)(ii) ((x)/(a)+(a)/(x))^(12)(iii) ((a)/(x)+bx)^(2n)(iv) (x-(1)/(x))^(9)(v) (1-3x+3x^(2)-x^(3))^(6)(vi) (x^(2)-a)^(11)(vii) (2x-(3)/x^(2))^(15)

Primary events are mutually exclusive.

Show that the straight line y^2-4y+3=0" and "x^2+4xy+4y^2+5x+10y+4=0 form a parallelogram and find the length of its sides.

Show that the area of the triangle formed by the lines y = m_(1) x + c_(1) , y = m_(2) x + c_(2) " and " x = 0" is " ((c_(1) - c_(2))^(2))/(2|m_(1) - m_(2)|)

2^(2)+5^(2)+8^(2)+………………."to" 15terms.

If E and F are events such that P(E) = 1/4, P(F) = 1/2 and P(E and F)= 1/8, find (i) P(E or F),(ii) P(not E and not F).

3(sinx-cosx)^(4)+6(sinx+cosx)^(2)+4(sin^(6)x+cos^(6)x) =…………..

If the circles x^(2) +y^(2) = a and x^(2) + y^(2) - 6x - 8y + 9 = 0touch externally then a =

If a+ib = (x+i)^(2)/(2x^(2)+1), prove that a^(2) + b^(2) = (x^(2)+1)^(2)/(2x^(2) + 1)^(2)

If theta_(1) and theta_(2) are two solutions of the equation a cos2theta+bsin2theta=c then tan theta_(1)+tan theta_(2) =

Two sides of a triangle are y=m_(1)x and y=m_(2)x,m_(1),m_(2) are the roots of the equation x^(2)+ax-1=0. For all values of a the orthocentre of the triangle lies at

If the plane 7x + 11y + 13z = 3003 meets the coordinate axes in A, B, C then the centroid of the Delta ABC is

On intersecting the plane with coordinate axes, then the areas of triangle formed on xy,yz,zx planes are 12, 4, 6 then equation of plane is

Which of the following sentences are statement? Give reason for your answer: Sun is star.

If two sides of a triangle are the roots of the equation 4x^2-(2sqrt6)x+1=0 and the included angle is 60^@, then the third side is

Find the modulus of the following using the property of modulus (3+4i) (8-6i)

Which of the following sentences are statements? Give reasons for your answer: Mathematics is a fun.

If PM is the perpendicular from P(2,3) on to the lie x+y=3 the M=

Rewrite the following statement with “if-then” in five different ways conveying the same meaning. If a natural number is odd, then its square is also odd.

The value of f(2) so that f(x)=(2^(x+2)-16)/(4^(x)-16) is continuous at x=2 is

x_1,x_2,x_3,….x_n then (x_1-barx)+(x_2-barx)+(x_n-barx)=0.

The pair of straight line x^2-3xy+2y^2=0 and x^2-3xy+2y^2+x-2=0 from a :

Find the slope of a line whose inclination is 60^(@)

If sin x + cos x = sqrt( y + (1)/(y))" for " x in [0, pi] . then

A = {3k| k in N} B = {3k -1|k in N} and C = {3k-2| k in N}. Then A , B and C are disjoint sets .

The range of f(x)=-3 cos sqrt(3x+x+x^(2)) is

If bara,barb,barcare three vectors such thatabsbara =1, absbarb = 2, absbarc =3 and bara+barb+barc = bar0 ,then bara.barb+barb.barc+barc.bara =

P is point on hyperbola 16x^(2) - 9y^(2) = 144. S_(1) and S_(2) are its foci then PS_(1) - PS_(2) = ………

Find the most general value of theta satisfying the equation tantheta=-1 and costheta=(1)/(sqrt(2)).

Consider the point A(3,2,-4) and B (9,8,-10) Find the co-ordinates of the points which divides AB internally in the ratio 2:3

Consider the point A(3,2,-4) and B (9,8,-10) Find the co-ordinates of the points which divides AB internally in the ratio 1:2

The set of all numbers a such that a^(2) + 2a, 2a + 3 " and " a^(2) + 3a + 8are the sides of a triangle is ………..

The point of intersection of the perpendiecular lines ax^(2)+3xy-2y^(2)-5x+5y+c=0 is

XOZ plane divides the join of (2,3,1 ) and (6,7,1 ) in the ratio

A vector bar(a) has components a_(1), a_(2), a_(3) in the right handed system OXYZ. If the coordinate system is rotated about z-axis through an angle pi//2, the component of bar(a) in the new system are

Differentiate (x^(2)-1)/(x^(2)+1) with respect to x:

Which term of the sequence sqrt2, (1)/(sqrt2), (1)/(2 sqrt2)……is (1)/(512 sqrt2) ?

Assume that theta is a rational multiple of pi such that cos thetais a distinct rational . The number of values of cos thetais

Solve the inequality for x:3x-7 gt 2 (x-6), 6-x gt 11 -2x

A die is rolled. Let E be the event ''die shows 4'' and F be the event ''die shows even number''. Are E and F mutually exclusive ?

A : The general solution of sin x = -1 is n pi + (-1)^(n)(3pi)/(2), n in Z R : The principal solution of sin x = 0 lies in [-pi//2, pi//2]

Show that x^(n)=1+n(1-(1)/(x))+(n(n+1))/(1.2)(1-(1)/(x))^(2)+….