14949 + Interview Questions in Maths in Class 11 Page 164 InterviewSolution

8151.	The perimeter of a triangle is 16 cm. One of the sides is of length 6 cm. iF the area of the triangle is 12 sq cm, then the triangle is
Answer» Right-angled Isosceles Equilateral Scalene Answer :B

Discussion

8152.	Equation of a plane passing through the point A (3,-2,1) and perpendicular to 4bari+7barj-4bark is
Answer» `BARR.(4bari+7barj-4bark) = 6` `barr.(4bari+7barj-4bark) = (-2)/9` `barr.(4bari+7barj-4bark) = -9` `barr.(4bari+7barj-4bark) = -6` ANSWER :D

Discussion

8153.	If Tan^(-1)x+Tan^(-1)y+Tan^(-1)z=(pi)/2 and (x-y)^(2)+(y-z)^(2)+(z-x)^(2)=0 then x^(2)+y^(2)+z^(2)=
Answer» 0 4 1 None Answer :C

Discussion

8154.	The perimeter of triangle is 14 units and two of its vertices are (-3,0), (3, 0) then the locus of the 3rd vertex is
Answer» `(X^(2))/(16)+(y^(2))/(7)=1` `(x^(2))/(25)+(y^(2))/(16)=1` `(x^(2))/(7)+(y^(2))/(16)=1` `(x^(2))/(16)+(y^(2))/(25)=1` Answer :1

Discussion

8155.	A(2,3),B(1,5),C(-1,2) are three points and PA^(2)+PB^(2)=2PC^(2) then locus of P is
Answer» `10x+8y-29=0` `10x+8y+29=0` `10x-8y+29=0` `10x-8y-29=0` ANSWER :1

Discussion

8156.	The minimum value of f(x)=(2x-3)(3x-1) on [0,1] is
Answer» `12//11` `11//12` `13//12` 1 Answer :B

Discussion

8157.	Calculate mean, variance and standard deviation for the following distribution.
Answer» ANSWER :14.18

Discussion

8158.	The value of a so that the sum of the squares of roots of the equation x^2-(a-2)x-a+1=0 assume the least value is
Answer» 2 0 3 1 Answer :A

Discussion

8159.	If thed.c's (l,m,n) of two lines are related as l + m + n = 0, 2lm - mn + 2nl = 0, then the angle between the lines is
Answer» `30^(@)` `45^(@)` `90^(@)` `120^(@)` ANSWER :D

Discussion

8160.	Given two vectors veca= -hati +hatj + 2hatk and vecb =- hati - 2 hatj -hatk
Answer» Solution :a. `vecaxxvecb=\|{:(HATI,hatj,hatk),(-1,1,2),(-1,-2,-1):}\|=3hati'-3hatj+3hatk` Hence, the AREA of the triangle is `(3SQRT3)/2` b. The area of the parallelogram is `3sqrt3` C. The area of a paralleogram whose diagonals are `2 veca and 4vecb is 1/2 \|2 veca xx 4vecb\|=12sqrt3` d. VOLUME of the parallelpiped `= \|(veca xx vecb).vecc\|=sqrt(9+36+9)= 3sqrt6`

Discussion

8161.	If the functions f(x) and g(x) are continuous in [a,b] and differentiable in (a,b), then EE at lease one 'c' such that a lt c lt b and \|{:(f(a),f(b)),(g(a), g(b)):}\| =----- \|{:(f(a),f'(c)),(g(a), g'(c)):}\|
Answer» a-B a+b b-a `F'(b)-f'(a)` ANSWER :C

Discussion

8162.	(8.67 xx 99)/(1.78)
Answer» ANSWER :19.19

Discussion

8163.	If abs(sin^(-1)x)+abs(cos^(-1)x)=pi/2, then x in
Answer» R [-1, 1] [0, 1] `PHI` ANSWER :C

Discussion

8164.	Choose the correct or the most suitable answer from the given four alternatives. lim_(xrarrinfty)[(x^2 +5x +6)/(x^2 +x-6)]^x is:
Answer» `e^4` `e^2` `e^3` 1 Answer :A

Discussion

8165.	The values of f(x)=3 sin(sqrt((pi^(2))/(16)-x^(2))) lie in the inerval ________
Answer» `[0, (3)/(SQRT(2))]` `[ - (3)/(sqrt(2)), (3)/(sqrt(2))]` `(0, (3)/(sqrt(2)))` `( - (3)/(sqrt(2)), 0)` ANSWER :A

Discussion

8166.	Derive section formula in three dimensions for internal division . Also find the co-ordinates of the midpoint of the line joining the points P(x_1,y_1,z_1) and Q (x_2,y_2,z_2) ?
Answer» <P> ANSWER : Again mid point P(x,y,Z)= `[(1+5)/2+(2+6)/2,(3+7)/2] =[3,4,5]`

Discussion

8167.	If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 }, find A ∪ B ∪ C
Answer» Answer :`={1, 2, 3, 4} CUP {3, 4, 5, 6} cup {5, 6, 7, 8} = {1, 2, 3, 4, 5, 6, 7, 8}`

Discussion

8168.	If pth term of an A.P. is c and the qth term is d, what is the rth term?
Answer» ANSWER :`(C(r-q)+d(p-r))/(p-q)`

Discussion

8169.	ABC is a variable triangle such that A is (1,2), and B and C lie on the line y=x+lambda (lambda " is a variable ). Then the locus of the the orthocenter of "Detla ABC is
Answer» x+y=0 x-y=0 `x^2+y^2=4` x+y=3 Answer :D

Discussion

8170.	If sin (theta + alpha) = a and sin (theta + beta) = b,"then" cos 2 (alpha - beta) - 4ab cos (alpha - beta) =
Answer» `1 - a^(2) - B^(2)` `1 - 2A^(2) - 2B^(2)` `2 + a^(2) - b^(2)` `2 - a^(2) - b^(2)` ANSWER :B

Discussion

8171.	If f(x) = {:{(x^(alpha)logx,","xgt 0),(0,","x=0):} and Rolle' theorem is applicable to f(x) for x in [0,1] then alpha may be equal to
Answer» `-2` `-1` 0 `1//2` ANSWER :D

Discussion

8172.	Lengths of the tangents from A, B, and C to the incircle are in A.P., then
Answer» `r_(1),r_(2),r_(3)` are in H.P `r_(1),r_(2),r_(3)` are in A.P a,b,C are in A.P `coaA=(4c-3b)/(2C)` ANSWER :A::C::D

Discussion

8173.	A riangle ABC is placed so that the mid-pointof the sides are on the x,y,z axes. Lengths oftheinterceptsmade by the planecontaining the triangleon these axes are respectively alpha, beta, gamma. Coordinatesof the centroidof the triangleABC are
Answer» `(-alpha//3, beta//3, gamma//3)` `(alpha//3, -beta//3, gamma//3)` `(alpha//3, -gamma//3)` `(alpha//3, beta//3, gamma//3)` ANSWER :d

Discussion

8174.	Two sides of a triangle are given by the roots of the equation x^2-5x+6=0 and the angle between the sides is pi//2. Then the perimeter of the triangle is
Answer» ` 5+ sqrt2` ` 5+ SQRT3` ` 5 + SQRT5` `5+ SQRT7` Answer :D

Discussion

8175.	f(x) is continous and differentiable function .Given , f(x) assumes valus of the form +-sqrt(I) where I denotes set of whole numbers whenever x=a or b , otherwise f(x) assumes real values. Also , f(c)=-(3)/(2)and\|f(a)\|le\|f(b)\| The number of values that (f(a))^(2)+(f(b))^(2)+(f(c))^(2) can assume is
Answer» 4 2 3 7 Answer :A

Discussion

8176.	f(x) is continous and differentiable function .Given , f(x) assumes valus of the form +-sqrt(I) where I denotes set of whole numbers whenever x=a or b , otherwise f(x) assumes real values. Also , f(c)=-(3)/(2)and\|f(a)\|le\|f(b)\| The number of rational values that f(a) +f(b)+f(c ) can assume is /are
Answer» 4 2 3 5 Answer :C

Discussion

8177.	ax+by+cz+d=0,dne0 does not represent a plane if
Answer» `a^(2)+B^(2)+C^(2)=0` `a^(2)+b^(2)+c^(2)NE0` `a+b=0` `a+b+c=0` Answer :A

Discussion

8178.	Sin^(-1)("sin"(2pi)/3)=
Answer» `(pi)/3` `(2PI)/3` `(4PI)/3` `(5PI)/3` Answer :A

Discussion

8179.	A bag contains20 tickest with marked numbers 1 to 20 . One ticket is drawn at random . Find the probability that it will be a multiple of 2 or 5.
Answer» ANSWER :`=(3)/(5)`.

Discussion

8180.	Write the first six terms of an A.P. in whicha=x ,d = 3x +2
Answer» ANSWER :X, 4x+2, 7X +4, 10X+ 6,13x+8,16x+10

Discussion

8181.	Mean is the measure of dispersion.
Answer» ANSWER :FALSE STATEMENT

Discussion

8182.	Let vec(a)= 2vec(i) + vec(k), vec(b) = vec(i) + vec(j) + vec(k) and vec( c)= 4vec(i) -3vec(j) + 7vec(k). Determine a vector vec(r ) satisfying vec( r) xx vec(b)= vec( c) xx vec(b) and vec(r ).vec(a)= 0.
Answer» ANSWER :`-7 VEC(J) + 3vec(K)`

Discussion

8183.	If f(x) = {{:(x-5, "if" , x le 1),(4x^2-9, "if", 1 lt x lt 2),(3x+4 ,"if", x ge 2):} , then the right hand derivative of f(x) at x=2 is…........... .
Answer» 0 2 3 4 Answer :C

Discussion

8184.	If sin theta + cos theta =and sin^(3) theta + cos^(3)theta = q, then p(p^(2) - 3) =
Answer» Q 2Q `-q` `-2q` ANSWER :D

Discussion

8185.	Two vertices of a triangle have position vectors 3hati+4hatj-4hatk and 2hati+3hatj+4hatk. If the position vector of the centroid is hati+2hatj+3hatk, then the position vector of the third vertex is
Answer» `- 2hati - hatj + 9 HATK ` `- 2 HATI - hatj - 6 hatk ` `-2 hati - hatj + 6 hatk ` `2hati - hatj + 6hatk ` Answer :` - 2hati - hatj + 9 hatk `

Discussion

8186.	If the line 2x+y=k passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3:2 then k equals
Answer» `29/5` 5 6 `11/5` ANSWER :C

Discussion

8187.	Explain in detail the triangle law of addition.
Answer» Solution :(i) Let `vecA` and `vecB ` are two vectors they are inclined at angle `theta` between them. (ii) According to triangle law of vector addition, head of the vector `vecA` is connected to tail of the vector `vecB`and both are represented in adjescent side of a triangle in some order. (iii) Let `vecR`be the resultant vector, which is represented in third closing side of the triangle in opposite order. (iv) Let `alpha` be the angle MADE by the resultant vector `vecR`with vector `vecA`. (v) Thus we can write, `vecR = vecA + vecB` a) Magnitude of resultant vector (i) From `Delta ABN,` ` cos theta = (AN)/(B) , An = B cos theta"" [cos theta = (adj)/(hyp)]` ` sin theta = (BN)/(B) , BN = B sin theta "" [ sin theta = (OPP)/(hyp)]` (ii) From `DeltaOBN,`[PYTHOGORAS theoram `hyp^2 = adj^2 + opp^2`] ` OB^2= ON^2 + BN^2` `R^2 = (A+B cos theta)^2 + (B sin theta)^2` ` R^2 = A^2 + B^2 cos^2 theta + 2AB cos theta + B^2 sin^2 theta` ` R = \|vecA + vecB\| = sqrt(A^2 + B^2 + 2AB cos theta )` b) Direction of resultant vectors: From `DeltaΟΒΝ,` ` tan alpha = (BN)/(ON) = (BN)/(OA + AN)` ` tan alpha = ((Bsin theta)/(A + B cos theta))` ` alpha = tan^(-1) [(B sin theta)/(A + B cos theta)]`

Discussion

8188.	Three Letters can be posted in five letter boxes in 3^5 ways.
Answer» ANSWER :`= 5^3 =125 `

Discussion

8189.	Find all points of discontinuityof f, where f is defined by f(x)={{:(\|x\|+3," if "x le -3),(-2x," if "-3 ltx lt 3),(6x+2," if "x ge 3):}.
Answer» ANSWER :discontinous at x-3

Discussion

8190.	Evaluate the following limits. Lt_(xto0)(sinx-sin(sinx))/x^(3)
Answer» ANSWER :`1/6`

Discussion

8191.	If the equation of the plane passing through the line of intersection of the panes ax + by + cz +d=0, a _(1) x + b _(1) y + c _(1) z + d _(1) =0 and perpendicular to the XY-plane is px + py + rz + s =0 then S =
Answer» `DC _(1)-d _(1) C ` `dc _(1) + d _(1)c ` `d d _(1) + c c_(1)` `a a _(1) + B b_(1) + c c _(1)` ANSWER :A

Discussion

8192.	Let S={1, 2, 3, 4, 5, 6} and E={1, 3, 5} then E' is ……….
Answer» ANSWER :B::D

Discussion

8193.	(1)/(1.3) + (1)/(3.5) + (1)/(5.7) + …. (n-3) terms
Answer» `(N)/( n+2)` `(n+1)/( n (n+5))` `(n-3)/( 2n-5)` `(n-1)/( n (2n-3))` ANSWER :C

Discussion

8194.	If the base of an isosceles triangle is of length 2P and the length of the altitude dropped to the base is q, then the distance from the mid point of the base to the side of the triangle is
Answer» `(AH)/(SQRT(a^(2)+H^(2)))` `(ah)/(sqrt(a^(2)-h^(2)))` `(ah)/(sqrt(h^(2)-a^(2)))` `(2ah)/(sqrt(a^(2)+h^(2)))` ANSWER :A

Discussion

8195.	Ifp_1 ,p_2,p_3 are the lengthsof altitudesofDelta ABCfrom the vertices andDeltais the area ofDelta ABC " then "(1)/(p_1)+(1)/(p_2)- (1)/( p_3)=
Answer» ` (s-a)/( DELTA ) ` ` (s-c)/( Delta ) ` ` (s-B)/( Delta ) ` ` (s)/( Delta ) ` ANSWER :B

Discussion

8196.	-15 lt (3(x-2))/( 5) le 0
Answer» ANSWER :`(-23,2]`

Discussion

8197.	Evaluate the following limit : Lim_(theta to pi/4) (sin theta -cos theta)/(theta-1/4pi)
Answer» ANSWER :`SQRT(2)`

Discussion

8198.	If f(x) = {{:(3x-2, if , x ge 3),(x^(2)-2, if, -2 le x le 2), (2x+1, if , x lt -3):}, then find, (if exists) (i) f(7), (ii) f(0), (iii) f(-9), (iv) f(-4), (v) f(-2), (vi) f(-7), (vii) f(2.5), (vii) f(4)
Answer» Answer :(i) 19, (ii) `-2`, (iii) `-17`, (iv) `-7`, (V) 2, (vi) `-13`, (VII) Not defined, (viii) 10

Discussion

8199.	Find the domainand the rangeof the relation R given by R= { (x,y) : y = x+6/x, where xy in N and x lt 6 }
Answer» ANSWER :DOMAIN = {1,2,3} RANGE= {5.7}

Discussion

8200.	If a + b + c = 5 then the maximum value of ab^(3)c is……
Answer» 3 9 27 81 Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

The perimeter of a triangle is 16 cm. One of the sides is of length 6 cm. iF the area of the triangle is 12 sq cm, then the triangle is

Equation of a plane passing through the point A (3,-2,1) and perpendicular to 4bari+7barj-4bark is

If Tan^(-1)x+Tan^(-1)y+Tan^(-1)z=(pi)/2 and (x-y)^(2)+(y-z)^(2)+(z-x)^(2)=0 then x^(2)+y^(2)+z^(2)=

The perimeter of triangle is 14 units and two of its vertices are (-3,0), (3, 0) then the locus of the 3rd vertex is

A(2,3),B(1,5),C(-1,2) are three points and PA^(2)+PB^(2)=2PC^(2) then locus of P is

The minimum value of f(x)=(2x-3)(3x-1) on [0,1] is

Calculate mean, variance and standard deviation for the following distribution.

The value of a so that the sum of the squares of roots of the equation x^2-(a-2)x-a+1=0 assume the least value is

If thed.c's (l,m,n) of two lines are related as l + m + n = 0, 2lm - mn + 2nl = 0, then the angle between the lines is

Given two vectors veca= -hati +hatj + 2hatk and vecb =- hati - 2 hatj -hatk

If the functions f(x) and g(x) are continuous in [a,b] and differentiable in (a,b), then EE at lease one 'c' such that a lt c lt b and |{:(f(a),f(b)),(g(a), g(b)):}| =----- |{:(f(a),f'(c)),(g(a), g'(c)):}|

(8.67 xx 99)/(1.78)

If abs(sin^(-1)x)+abs(cos^(-1)x)=pi/2, then x in

Choose the correct or the most suitable answer from the given four alternatives. lim_(xrarrinfty)[(x^2 +5x +6)/(x^2 +x-6)]^x is:

The values of f(x)=3 sin(sqrt((pi^(2))/(16)-x^(2))) lie in the inerval ________

Derive section formula in three dimensions for internal division . Also find the co-ordinates of the midpoint of the line joining the points P(x_1,y_1,z_1) and Q (x_2,y_2,z_2) ?

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 }, find A ∪ B ∪ C

If pth term of an A.P. is c and the qth term is d, what is the rth term?

ABC is a variable triangle such that A is (1,2), and B and C lie on the line y=x+lambda (lambda " is a variable ). Then the locus of the the orthocenter of "Detla ABC is

If sin (theta + alpha) = a and sin (theta + beta) = b,"then" cos 2 (alpha - beta) - 4ab cos (alpha - beta) =

If f(x) = {:{(x^(alpha)logx,","xgt 0),(0,","x=0):} and Rolle' theorem is applicable to f(x) for x in [0,1] then alpha may be equal to

Lengths of the tangents from A, B, and C to the incircle are in A.P., then

A riangle ABC is placed so that the mid-pointof the sides are on the x,y,z axes. Lengths oftheinterceptsmade by the planecontaining the triangleon these axes are respectively alpha, beta, gamma. Coordinatesof the centroidof the triangleABC are

Two sides of a triangle are given by the roots of the equation x^2-5x+6=0 and the angle between the sides is pi//2. Then the perimeter of the triangle is

f(x) is continous and differentiable function .Given , f(x) assumes valus of the form +-sqrt(I) where I denotes set of whole numbers whenever x=a or b , otherwise f(x) assumes real values. Also , f(c)=-(3)/(2)and|f(a)|le|f(b)| The number of values that (f(a))^(2)+(f(b))^(2)+(f(c))^(2) can assume is

f(x) is continous and differentiable function .Given , f(x) assumes valus of the form +-sqrt(I) where I denotes set of whole numbers whenever x=a or b , otherwise f(x) assumes real values. Also , f(c)=-(3)/(2)and|f(a)|le|f(b)| The number of rational values that f(a) +f(b)+f(c ) can assume is /are

ax+by+cz+d=0,dne0 does not represent a plane if

Sin^(-1)("sin"(2pi)/3)=

A bag contains20 tickest with marked numbers 1 to 20 . One ticket is drawn at random . Find the probability that it will be a multiple of 2 or 5.

Write the first six terms of an A.P. in whicha=x ,d = 3x +2

Mean is the measure of dispersion.

Let vec(a)= 2vec(i) + vec(k), vec(b) = vec(i) + vec(j) + vec(k) and vec( c)= 4vec(i) -3vec(j) + 7vec(k). Determine a vector vec(r ) satisfying vec( r) xx vec(b)= vec( c) xx vec(b) and vec(r ).vec(a)= 0.

If f(x) = {{:(x-5, "if" , x le 1),(4x^2-9, "if", 1 lt x lt 2),(3x+4 ,"if", x ge 2):} , then the right hand derivative of f(x) at x=2 is…........... .

If sin theta + cos theta =and sin^(3) theta + cos^(3)theta = q, then p(p^(2) - 3) =

Two vertices of a triangle have position vectors 3hati+4hatj-4hatk and 2hati+3hatj+4hatk. If the position vector of the centroid is hati+2hatj+3hatk, then the position vector of the third vertex is

If the line 2x+y=k passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3:2 then k equals

Explain in detail the triangle law of addition.

Three Letters can be posted in five letter boxes in 3^5 ways.

Find all points of discontinuityof f, where f is defined by f(x)={{:(|x|+3," if "x le -3),(-2x," if "-3 ltx lt 3),(6x+2," if "x ge 3):}.

Evaluate the following limits. Lt_(xto0)(sinx-sin(sinx))/x^(3)

If the equation of the plane passing through the line of intersection of the panes ax + by + cz +d=0, a _(1) x + b _(1) y + c _(1) z + d _(1) =0 and perpendicular to the XY-plane is px + py + rz + s =0 then S =

Let S={1, 2, 3, 4, 5, 6} and E={1, 3, 5} then E' is ……….

(1)/(1.3) + (1)/(3.5) + (1)/(5.7) + …. (n-3) terms

If the base of an isosceles triangle is of length 2P and the length of the altitude dropped to the base is q, then the distance from the mid point of the base to the side of the triangle is

Ifp_1 ,p_2,p_3 are the lengthsof altitudesofDelta ABCfrom the vertices andDeltais the area ofDelta ABC " then "(1)/(p_1)+(1)/(p_2)- (1)/( p_3)=

-15 lt (3(x-2))/( 5) le 0

Evaluate the following limit : Lim_(theta to pi/4) (sin theta -cos theta)/(theta-1/4pi)

If f(x) = {{:(3x-2, if , x ge 3),(x^(2)-2, if, -2 le x le 2), (2x+1, if , x lt -3):}, then find, (if exists) (i) f(7), (ii) f(0), (iii) f(-9), (iv) f(-4), (v) f(-2), (vi) f(-7), (vii) f(2.5), (vii) f(4)

Find the domainand the rangeof the relation R given by R= { (x,y) : y = x+6/x, where xy in N and x lt 6 }

If a + b + c = 5 then the maximum value of ab^(3)c is……