14949 + Interview Questions in Maths in Class 11 Page 211 InterviewSolution

10501.	If the centroid of the tetrahedron is (0,-1,5/2) and three vertices are (-2,3,4), (3,-4,2),(2,-5,1) then the fourth vertex is
Answer» (-3,2,3) (1,0,5) (0,-1,5) (5,-1,0) ANSWER :A

Discussion

10502.	If f(x) is a function that is odd and even simultaneously then f(3)-f(2) is
Answer» 1 -1 0 2 Answer :C

Discussion

10503.	If bara, barb, barc are three non-coplanar vectors represented by concurrent edges of a parallelopiped of volume 4 cu. units then (bara+barb).(barbxxbarc)+(barb+barc).(barcxxbara)+(barcxxbara).(baraxxbarb)=
Answer» 12 4 `pm12` 0 Answer :C

Discussion

10504.	The sum of the hypotenuse and a side of a right angled triangle is constant . If the area of the triangle is maximum then the angle between the hypotenuse and the given side is
Answer» `(PI)/(2)` `(pi)/(4)` `(pi)/(3)` `(pi)/(6)` ANSWER :C

Discussion

10505.	If the coefficients of (r-5)^th and (2r - 1)^th terms in the expansion of (1 + x)^34 are equal, find r.
Answer» ANSWER :R = 14

Discussion

10506.	If sin^(2)x-2sinx-1=0 has exactly four different solutions in x in [0, npi] then value /values of n is /are (n in N)
Answer» 5 3 4 6 Answer :A::C

Discussion

10507.	Arc of length 15pi subtends an angle (3pi)/4 at centre then radius r = .........cm
Answer» ANSWER :20 CM

Discussion

10508.	The weights of coffee in 70 jars is shown in the following table: Dtermine variance and standard deviation of the above distribution.
Answer» ANSWER :1.1655

Discussion

10509.	If the planes 3x+4y+mz-26=0, 4x-3y-z-1=0 are perpendicular, then m =
Answer» 0 1 2 -1 Answer :A

Discussion

10510.	The torque about the point 2i + j - K of a force represented by 4i + k acting through the point (I - j + 2k) is
Answer» `2vec(i) + 13vec(J) + 8vec(K)` `-2vec(i) + 13vec(j) + 8vec(k)` `2vec(i) + 13vec(j) -8vec(k)` `VEC(i) + vec(j) + 2vec(k)` ANSWER :B

Discussion

10511.	If A and B be two sets containing 3 and 6 elements respectively. What can be the minimum number of elements in A cup B? Find also, the maximum number of elements in A cup B.
Answer» ANSWER :`= 6, 9`

Discussion

10512.	Equation of the acute angular bisector of the planes 2x-y-2z-6=0,3x+2y-6z-12=0 is
Answer» `5x-13y+4z-6=0` `23x-y-32z-6=0` `23x-y-32z-78=0` `5x-13y+4z-78=0` ANSWER :C

Discussion

10513.	If y = 1 +x +(x^2)/(2!)+x^3/(3!)+....+ x^n(n!)then (dy)/(dx) is equal to
Answer» y `y + x^N/(n!)` `y - (x^n)/(n!)` `y - 1 - (x^n)/(n!)` ANSWER :C

Discussion

10514.	Statement-I : The maximum value of (logx)/x" in "0ltxltoo" is "2/e Statement-II : y=x^3+1/x^3 is an increasing function in the interval 0ltxlt1 Which of the above statement is true
Answer» only I only II both I,II neither I nor II Answer :D

Discussion

10515.	If A is a skew symmetric matrix of order n and C is a column matrix of ordernxx1,thenC^(T)ACis
Answer» an identity MATRIX of ORDER N an identity matrix of order 1 a zero matrix of order 1 an identity matrix of order 2 Answer :A::D

Discussion

10516.	From the top of the hill h meers high the angles of depressinons of the top and the bottom of a pillar are alpha and beta respectively. The height ( in meters ) of pillar is
Answer» `(H(TANBETA-tanalpha))/(tanbeta)` `(h(tanalpha-tanbeta))/(tanalpha)` `(h(tanbeta+tanalpha))/(tanbeta)` `(h(tanbeta+tanalpha))/(tanalpha)` ANSWER :A

Discussion

10517.	If z lies on x-axis number, then
Answer» `\|z^(2)\| GT \|z\|` `\|z^(2)\| gt \|z\|^(2)` `\|z^(2)\|LT \|z\|^(2)` `\|z^(2)\|GE \|z\|^(2)` Answer :B

Discussion

10518.	Find the derivatives of the function sin ^(-1) (cos x )
Answer» ANSWER :`-1`

Discussion

10519.	A wire of length 'a' is cut into two parts which are bent in the form a square and a circle. Show that the least value of the sum of the areas so formed is (a^2)/(4(pi+4)).
Answer» `(a^(2))/(pi+4)` `(a^(2))/(2(pi+4))` `(a^(2))/(3(pi+4))` `(a^(4))/(4(pi+4))` ANSWER :D

Discussion

10520.	If A+B+C= pi and (sin 2 A + sin 2B + sin 2 C)/(sin A + sin B + sin C ) = lamda sin ((A)/(2)) sin ((B)/(2)) sin ((C )/(2)) , then the value of lamdamust be
Answer» ANSWER :8

Discussion

10521.	Express each of the following in the form b or bi, where b is a real number 3i.2
Answer» ANSWER :6I

Discussion

10522.	O is the origin, P(2,3,4) and Q(1,k,1) are points such that bar(OP)botbar(OQ). Find k.
Answer» ANSWER :-2

Discussion

10523.	The point P is the foot of the perpendicular from A(0, t) to the line whose equation is y=tx. Determine the area of DeltaOAP, where O is the origin.
Answer» ANSWER :`1/(2)((t^(3))/(1+t^(2)))sq.units`

Discussion

10524.	If sin(270^(@) - x) = cos 292^(@), then find x in (0, 360^(@))
Answer» `240^(@),120^(@)` `248^(@),112^(@)` `225^(@),115^(@)` `225^(@),135^(@)` Answer :B

Discussion

10525.	The radius and height of a cone are measured as 6 cm and 12 cm respectively and there is an error of 0.06 cm in both the measurements. The approximate ewrror in the volume of the cone is
Answer» `410pisqrt2` CUBIC CM `60pi` cubic cm `3.6pi` cubic cm `320pisqrt2` cubic cm ANSWER :C

Discussion

10526.	If baraxx(barbxxbarc)=(baraxxbarb)xxc' then which of the following is incorrect ?
Answer» `BARCXXBARA=~0` `(barcxxbara)xxbarb=bar0` `(barcxxbara).barb=bar0` `barc.bara=0` ANSWER :D

Discussion

10527.	If x-iy = sqrt((a+ib)/(c-id)), prove that (x^(2) + y^(2))^(2) = (a^(2) + b^(2))/(c^(2) + d^(2))
Answer» ANSWER :`(a^(2)+B^(2))/(C^(2)+d^(2))`

Discussion

10528.	The sum of inradius and circumradius of incircle and circumcircle of a regualr polygon of side n is
Answer» `a/4 COT. PI/(2N)` `a cot. pi/n` `a/2 cot. pi/(2n)` `a cot . pi/(2n)` ANSWER :C

Discussion

10529.	Evaluate the following limits : Lim_(x to 0 ) (1- cos ax)/(" x sin 3x")
Answer» ANSWER :`(a^(2))/6`

Discussion

10530.	If in DeltaABC, A=B0C=60^(@) then (b-c)/(b+c)=
Answer» 1 `(1)/(2)` `(1)/(3)` `(1)/(4)` ANSWER :C

Discussion

10531.	The orthocentre of triangle formed by (acosalpha,asin alpha), (acosbeta,asinbeta),(acosgamma,asingamma) is
Answer» `(SUM(-acosalpha)-acosalpha)` `(sum acosalpha,SUMA SIN ALPHA)` `(sum(-acosalpha),sum(-asinalpha)` `(sum(-acosalpha),sum(-asinalpha)` ANSWER :A

Discussion

10532.	Differentiate the following functions w.r.t. x: cos 3x
Answer» ANSWER :`-3 SIN 3X`

Discussion

10533.	Expand (1-x+x^2)^4
Answer» SOLUTION :`1-4x+10x^2-16x^3+19x^4-16x^5+10x^6-4x^7+x^8]`

Discussion

10534.	From a rectangularsheet of dimension 30 cm xx 80 cm, four equal squares of side x cm. are removed at the corners, and the sieds are then turned up so as to form an open rectangular box. Find the value of x, so that the volume of the box is the greatest.
Answer» ANSWER :`X = (20)/(3)CM`

Discussion

10535.	If f(3)=2 thenlim_(xrarr2)f(x^2-1) = …........
Answer» ANSWER :2

Discussion

10536.	Solve: x^2+x/sqrt3+1=0
Answer» ANSWER :`(-1pmisqrt11)/2SQRT3`

Discussion

10537.	Find the principal argument of (1+i sqrt(3))^(2).
Answer» ANSWER :`(2PI)/(3)`

Discussion

10538.	Find equation of circle whose end points of diameter are centres of the circle x^(2) + y^(2) + 6x - 14y - 1 =0 and x^(2) + y^(2) - 4x + 10y - 2 = 0.
Answer» `X^(2) + y^(2) + x - 2y - 41 = 0` `x^(2) + y^(2) + x + 2y + 41 = 0` `x^(2) + y^(2) - x - 2y - 41 = 0` `x^(2) + y^(2) - x - 2y - 41 = 0` Answer :A

Discussion

10539.	If f: R to R defined by f(x) =(e^(x^(2)) -e^(-x^(2)))/(e^(x^(2)) +e^(-x^(3))), then f is
Answer» One-one but not onto. neither one-one nor onto many-one but onto one-one but not onto Answer :B

Discussion

10540.	sqrt(2)* " cosec " 20^(@) sec 20^(@)=
Answer» 2 `2 sin 20^(@) "cosec" 40^(@)` 4 `4 sin 45^(@) "cosec" 40^(@)` Answer :D

Discussion

10541.	If cot theta + cosec theta = sqrt(3) then theta =
Answer» `2 N pi + (pi)/( 2) , n in Z` `2 n pi + (pi)/( 3) , n in Z` `2 n pi + (pi)/( 3) , n in Z` `2 npi + (pi)/( 4) , n in Z` Answer :B

Discussion

10542.	If bara,barb,barc are coplanar vectors then (baraxxbarb)xx(barbxxbarc)+(barbxxbarc)xx(barcxxbara)+(barcxxbara)xx(baraxxbarb)=
Answer» `BAR0` `[BARABARBBARC]` `[barabarbbarc](bara+barbbarc)` `bara+barb+barc` ANSWER :A

Discussion

10543.	Find the value of f(0) so thatf(x) = (1)/(x) - (2)/(e^(2x) -1) , x ne 0 is continuous at x = 0 .
Answer» ANSWER :1

Discussion

10544.	If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find C – A
Answer» Answer :`{ 2, 4, 8, 10, 14, 16 }`

Discussion

10545.	sin 47^(@) - sin 25^(@) + sin 61^(@) - sin 11^(@) =
Answer» `sin 7^(@)` `cos 7^(@)` `sin 14^(@)` `cos 14 ^(@)` Answer :B

Discussion

10546.	Evaluate the following limits in Exercises lim_(xto0)(sinax+bx)/(ax+sinbx)a,b,a+bne0
Answer» ANSWER :`(a+b)/(a+b)=1`

Discussion

10547.	The sum of the coefficient in the expansion (1+x-3x^(2))^(4331) is ………
Answer» 1 `-1` 0 `2^(4330)` ANSWER :B

Discussion

10548.	If there is an error of 0.02 sq. cm is made in calculating the area of a circle. If the radius is 5cm, then the percentage error in the circumference of the circle is
Answer» `(0.4)/(PI)` `(0.04)/(pi)` `(4)/(pi)` `(0.004)/(pi)` ANSWER :B

Discussion

10549.	The minimum value of the function f(x)=(sinx)/(sqrt(1-cos^(2)x))+(cosx)/(sqrt(1-sin^(2)x))+(tanx)/(sqrt(sec^(2)x-1))+(cotx)/(sqrt(cosec^(2)x-1)) whenever it is defined is
Answer» 4 -2 0 -4 Answer :B

Discussion

10550.	Interval form of the set { x in R \| -1 le x lt 7 }is given by (-1, 7] .
Answer» ANSWER :FALSE STATEMENT

Discussion

Explore topic-wise InterviewSolutions in .

If the centroid of the tetrahedron is (0,-1,5/2) and three vertices are (-2,3,4), (3,-4,2),(2,-5,1) then the fourth vertex is

If f(x) is a function that is odd and even simultaneously then f(3)-f(2) is

If bara, barb, barc are three non-coplanar vectors represented by concurrent edges of a parallelopiped of volume 4 cu. units then (bara+barb).(barbxxbarc)+(barb+barc).(barcxxbara)+(barcxxbara).(baraxxbarb)=

The sum of the hypotenuse and a side of a right angled triangle is constant . If the area of the triangle is maximum then the angle between the hypotenuse and the given side is

If the coefficients of (r-5)^th and (2r - 1)^th terms in the expansion of (1 + x)^34 are equal, find r.

If sin^(2)x-2sinx-1=0 has exactly four different solutions in x in [0, npi] then value /values of n is /are (n in N)

Arc of length 15pi subtends an angle (3pi)/4 at centre then radius r = .........cm

The weights of coffee in 70 jars is shown in the following table: Dtermine variance and standard deviation of the above distribution.

If the planes 3x+4y+mz-26=0, 4x-3y-z-1=0 are perpendicular, then m =

The torque about the point 2i + j - K of a force represented by 4i + k acting through the point (I - j + 2k) is

If A and B be two sets containing 3 and 6 elements respectively. What can be the minimum number of elements in A cup B? Find also, the maximum number of elements in A cup B.

Equation of the acute angular bisector of the planes 2x-y-2z-6=0,3x+2y-6z-12=0 is

If y = 1 +x +(x^2)/(2!)+x^3/(3!)+....+ x^n(n!)then (dy)/(dx) is equal to

Statement-I : The maximum value of (logx)/x" in "0ltxltoo" is "2/e Statement-II : y=x^3+1/x^3 is an increasing function in the interval 0ltxlt1 Which of the above statement is true

If A is a skew symmetric matrix of order n and C is a column matrix of ordernxx1,thenC^(T)ACis

From the top of the hill h meers high the angles of depressinons of the top and the bottom of a pillar are alpha and beta respectively. The height ( in meters ) of pillar is

If z lies on x-axis number, then

Find the derivatives of the function sin ^(-1) (cos x )

A wire of length 'a' is cut into two parts which are bent in the form a square and a circle. Show that the least value of the sum of the areas so formed is (a^2)/(4(pi+4)).

If A+B+C= pi and (sin 2 A + sin 2B + sin 2 C)/(sin A + sin B + sin C ) = lamda sin ((A)/(2)) sin ((B)/(2)) sin ((C )/(2)) , then the value of lamdamust be

Express each of the following in the form b or bi, where b is a real number 3i.2

O is the origin, P(2,3,4) and Q(1,k,1) are points such that bar(OP)botbar(OQ). Find k.

The point P is the foot of the perpendicular from A(0, t) to the line whose equation is y=tx. Determine the area of DeltaOAP, where O is the origin.

If sin(270^(@) - x) = cos 292^(@), then find x in (0, 360^(@))

The radius and height of a cone are measured as 6 cm and 12 cm respectively and there is an error of 0.06 cm in both the measurements. The approximate ewrror in the volume of the cone is

If baraxx(barbxxbarc)=(baraxxbarb)xxc' then which of the following is incorrect ?

If x-iy = sqrt((a+ib)/(c-id)), prove that (x^(2) + y^(2))^(2) = (a^(2) + b^(2))/(c^(2) + d^(2))

The sum of inradius and circumradius of incircle and circumcircle of a regualr polygon of side n is

Evaluate the following limits : Lim_(x to 0 ) (1- cos ax)/(" x sin 3x")

If in DeltaABC, A=B0C=60^(@) then (b-c)/(b+c)=

The orthocentre of triangle formed by (acosalpha,asin alpha), (acosbeta,asinbeta),(acosgamma,asingamma) is

Differentiate the following functions w.r.t. x: cos 3x

Expand (1-x+x^2)^4

From a rectangularsheet of dimension 30 cm xx 80 cm, four equal squares of side x cm. are removed at the corners, and the sieds are then turned up so as to form an open rectangular box. Find the value of x, so that the volume of the box is the greatest.

If f(3)=2 thenlim_(xrarr2)f(x^2-1) = …........

Solve: x^2+x/sqrt3+1=0

Find the principal argument of (1+i sqrt(3))^(2).

Find equation of circle whose end points of diameter are centres of the circle x^(2) + y^(2) + 6x - 14y - 1 =0 and x^(2) + y^(2) - 4x + 10y - 2 = 0.

If f: R to R defined by f(x) =(e^(x^(2)) -e^(-x^(2)))/(e^(x^(2)) +e^(-x^(3))), then f is

sqrt(2)* " cosec " 20^(@) sec 20^(@)=

If cot theta + cosec theta = sqrt(3) then theta =

If bara,barb,barc are coplanar vectors then (baraxxbarb)xx(barbxxbarc)+(barbxxbarc)xx(barcxxbara)+(barcxxbara)xx(baraxxbarb)=

Find the value of f(0) so thatf(x) = (1)/(x) - (2)/(e^(2x) -1) , x ne 0 is continuous at x = 0 .

If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 }, C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }, find C – A

sin 47^(@) - sin 25^(@) + sin 61^(@) - sin 11^(@) =

Evaluate the following limits in Exercises lim_(xto0)(sinax+bx)/(ax+sinbx)a,b,a+bne0

The sum of the coefficient in the expansion (1+x-3x^(2))^(4331) is ………

If there is an error of 0.02 sq. cm is made in calculating the area of a circle. If the radius is 5cm, then the percentage error in the circumference of the circle is

The minimum value of the function f(x)=(sinx)/(sqrt(1-cos^(2)x))+(cosx)/(sqrt(1-sin^(2)x))+(tanx)/(sqrt(sec^(2)x-1))+(cotx)/(sqrt(cosec^(2)x-1)) whenever it is defined is

Interval form of the set { x in R | -1 le x lt 7 }is given by (-1, 7] .