14949 + Interview Questions in Maths in Class 11 Page 247 InterviewSolution

12301.	Ifthe origin is the centroid of the triangle PQR with vertices P(2a,2,6)Q(-4,3b,-10) and R(8,14,2c) then find the valuesof a ,b and c
Answer» ANSWER :a=2,B=`-16/3,c=2`

Discussion

12302.	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 D – B
Answer» ANSWER :`{ 5, 10, 15 }`

Discussion

12303.	Find the number of 4 - digit numbers that can be formed by using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even ?
Answer» ANSWER :120, 48

Discussion

12304.	arg (-1) = .........
Answer» ANSWER :`PI`

Discussion

12305.	A rectanglewith one side lying along the x - axis is to be inscribed in the closedregion of the xy plane bounded by the lines y=0,y=3x, and y=30-2x . If M is the largest area of such a rectangle, then value of (2M)/(27) is ________
Answer» ANSWER :5

Discussion

12306.	If A is square matrix then A A^(T) is. . . . Matrix
Answer» symmetric skew symmetric scalar Idempotent Answer :A

Discussion

12307.	A(2, 3, 4) B(-1, 2, 3) then the lengths of projection on {:("Column-I","Column-II"),((A)"xy plane", (p) sqrt(2)),((B) "yz plane", (q) sqrt(5)),((C )"cx plane" ,(r ) sqrt(10)):}
Answer» ANSWER :A-r;B-p;C-r

Discussion

12308.	Let A={1,2} and B={3,4}. Find the number of relations from A to B.
Answer» ANSWER :16

Discussion

12309.	The value of c in Lagrange's Mean Value theorem for the function f(x) = {:{(x cos ((1)/(x)),","xcancel(=)0),(0,","x=0):} in the intervale [-1,1] is
Answer» 0 `(1)/(2)` `-(1)/(2)` not EXIST in the INTERVAL Answer :D

Discussion

12310.	If f(z)=(7-z)/(1-z^(2)) where z=1+2i, the \|f(z)\| is equal to
Answer» `(\|Z\|)/(2)` \|z\| `2\|z\|` NONE of these Answer :A

Discussion

12311.	A triangular plot has two adjacent sides 130m and 80m .the included angle between the sides is 30^o .find the cost of levelling the ground at the rate of Rs 10per sq.m.
Answer» ANSWER :Rs26000

Discussion

12312.	(cosh(x))/(1-tanh(x))+(sinh(x))/(1-coth(x))=
Answer» `sinhx+cothx` `tanhx+cothx` `sinhx+coshx` `tanhx-cothx` ANSWER :C

Discussion

12313.	Find the sum to n terms of the series : 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)+3^(2))+….
Answer» ANSWER :`(N(n+1)^(2)(ndiv2))/(12)`

Discussion

12314.	If r=x+y+z and tan^(-1)sqrt((xr)/(yz))+"tan"^(-1)sqrt((yr)/(zx))+tan^(-1)sqrt((zr)/(xy))=kpi then the value of k is
Answer» ANSWER :1

Discussion

12315.	Define the real valued function f: R -{0} to R" defined by "f(x)=1/2 x in R-{0}. Complete the Table given below using this definition. What is the domain and range of this function?
Answer» Answer :`(##KPK_AIO_MAT_XI_C02_E07_021_A01##)` Domain set and RANGE set of the each FUNCTION is the set of all non zero REAL NUMBERS

Discussion

12316.	The periodof tan ( x+ 8x+ 27 x … n ^(3 )x ) is
Answer» `(8pi)/(N^(2)(n+1)^(2))` `(4PI)/(n^(2) (n+1)^(2))` `(2PI)/( n^(2) (n+1)^(2))` `(4pi)/(n(n+1))` ANSWER :2

Discussion

12317.	If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that (1)/( p^2) = (1)/( a^2) + (1)/( b^2).
Answer» ANSWER :`(1)/( p^2) = (1)/( a^2) + (1)/( b^2)`

Discussion

12318.	IfA = {: [ ( 1,0,0) , ( 0,1,0) , ( a,b,-1)]:}show thatA^(2)isa unitmatrix .
Answer» ANSWER :`A^(2) `

Discussion

12319.	If 0^(@)lt theta lt 90^(@) and cos theta=(4)/(5) find the values of sin (270^(@)-theta)
Answer» ANSWER :`-4/5`

Discussion

12320.	Find the numbers of non-zero integral solutions of the equation \|1-i\|^(x) =2^(x)
Answer» ANSWER :`:.x=0`

Discussion

12321.	Differentiate the following w.r.t. x or t or u as the case may be: 1. (ax+ b) (cx+d)
Answer» ANSWER :`C (AX + B) + a (CX +d)`

Discussion

12322.	Let f be a function defined by f(x)={{:((tanx)/(x)",",x ne0),(1",",x=0):}Statement -I x=0 is point of minimum of f Statement II : f'(0)=0
Answer» I is FALSE and II is true BothI and II are trueand II is the CORRECT explanation of I Both I and II are true and II is not the correct ecxplanation of I I is true and IIis false Answer :C

Discussion

12323.	For two A.P.: 2, 5, 8,…..up to 50 terms and 3, 5, 7, 9,….., up to 60 terms. How many terms are same?
Answer» ANSWER :20 TERMS

Discussion

12324.	In what ratio, the line joining (-1, 1) " and " (5, 7)is divided by the line x + y = 4 ?
Answer» ANSWER :`1 : 2`

Discussion

12325.	With usual notations, in triangleABC, a cos (B-C)+b cos (C-A)+c cos(A-B) is equal to
Answer» `(ABC)/(R^(2))` `(abc)/(4R^(2))` `(4ABC)/(R^(2))` `(abc)/(2R^(2))` Answer :A

Discussion

12326.	A coin and a die are tossed . Describe the following events . A : getting a head even number ,
Answer» ANSWER :`A={H2,H4,H6}`

Discussion

12327.	If (2,3,4) is the centroid of the tetrahedron for which (2,3,-1) ,(3,0,-2),(-1,4,3) are three vertices then fourth vertex is
Answer» (4, 5, 16) (3, 2, 4) (2, 3, 4) (2, 2, 12) ANSWER :a

Discussion

12328.	Under rotation of axes through an angletheta, x cos alpha+y sin alpha=p changes toX cos beta +Y sin beta =p then
Answer» `COS beta=cos(alpha-theta)` `cos alpha=cos(beta-theta)` `2 cos alpha=cos (beta-theta)` `2 cos beta=cos(alpha-theta)` ANSWER :A

Discussion

12329.	If cos (theta - alpha) , cos theta , cos (theta + alpha )are in H.P. thencos theta .sec"" (alpha )/(2) =
Answer» 1 `+-2` `SQRT3` `+-SQRT2` ANSWER :D

Discussion

12330.	Find the value of x, if \|(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,3x-64)\|=0.
Answer» ANSWER :`x=4`

Discussion

12331.	Decide, among the following sets, which sets are subsets ofone and another: A = { x : x ∈ Rand x satisfy x^(2) – 8x + 12 =0 }, B = { 2, 4, 6 }, C = { 2, 4, 6, 8, . . . }, D = { 6 }.
Answer» ANSWER :`A ⊂B,A ⊂ C,B ⊂ C,D ⊂ A,D ⊂ B,D ⊂ C`

Discussion

12332.	Express each of the following in the form b or bi, where b is a real number (x)/(i)
Answer» ANSWER :`-XI`

Discussion

12333.	State whether each of the following statement is true or false. Justify your answer. { 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.
Answer» ANSWER :1

Discussion

12334.	Let f={(x, x^2/(1+x^(2))), x in R} be a function from R into R. Determine the range of f.
Answer» ANSWER :[0, 1)

Discussion

12335.	A cross - section ofa parabolic reflector is shown. The diameter of opening at the focus is 10 cm. Find the equation of the parabola. Find diameter of the opening at the focus is 10 cm. Find the equation of the parabola. Find diameter of the opening at 11 cm from the vertex.
Answer» ANSWER :`y^(2) = 10X, 2sqrt(110) CM`

Discussion

12336.	The point P moves such that the sum of the squares of its distances from two fixed points A(a,0),B(-a,0) is 8a^(2) the locus of P is
Answer» `x^(2)-y^(2)=a^(2)` `x^(2)+y^(2)=a^(2)` `x^(2)+y^(2)=3a^(2)` `x^(2)+y^(2)=6a^(2)` ANSWER :3

Discussion

12337.	If 1, log_(y)x, log_(z)y,-15 log_(x)z are in A.P. then the correct statement is :
Answer» `Z^(3)=X` `x^(3)=z` `z^(3)=y` NONE of these Solution :N/a

Discussion

12338.	Find the sum 1+4/5+7/(25)+(10)/(125)+ . ..
Answer» ANSWER :`35/16`

Discussion

12339.	if (2)/(5)(y)/(z)+(2)/(5)(z)/(x)+(2)/(5)(x)/(y),(2)/(5)(x)/(y)+(2)/(5) (y)/(z) are the sides of a triangle then its area is
Answer» `(4)/(25) SQRT((x)/(y)+(y)/(z)+(z)/(x))` xyz 1 `x+y+z` Answer :A

Discussion

12340.	Let A={1,2}, B={1,2,3,4}, C={5,6} and D={5,6,7,8}. Verify that (i) A xx (B cap C)=(A xx B) cap (A xx C), (ii) A xx C is a subset of B xx D
Answer» ANSWER :`A XX C, B xx D`

Discussion

12341.	2 Radian = .......... Degree.
Answer» ANSWER :`114^(@) 32' 44''`.

Discussion

12342.	The value ofunderset(x to 1)(Lt) ((x^(3)+2x^(2)+x+1)/(x^(2)+2x+3))^((1-cso(x-1))/(x-1)^(2))
Answer» E `e^(1//2)` 1 `sqrt((5)/(6))` ANSWER :D

Discussion

12343.	From the top of a hill h metre high, the angles of depressions of the top and the bottom of a pillar are alpha and beta, respectively. The height (in metres) of the pillar is
Answer» `(H(TANBETA-tanalpha))/(tanbeta)` `(h(tanalpha-tanbeta))/(tanalpha)` `(h(tanbeta+tanalpha))/(tanbeta)` `(h(tanbeta+tanalpha))/(tanalpha)` ANSWER :A

Discussion

12344.	Find the point to which the origin has to shifted to eliminate x and y terms in the equation 3(x-2)^(2)+5(y+3)^(2)=6.
Answer» ANSWER :(2, 3)

Discussion

12345.	Which of the following can not be valid assignment of probabilities for outcomes of sample Space S = {omega_(1), omega_(2), omega_(3), omega_(4), omega_(5), omega_(6), omega_(7)} Assignment omega_(1)" "omega_(2)" "omega_(3)" "omega_(4)" "omega_(5)" "omega_(6) (a) 0.1 0.01 0.05 0.03 0.01 0.2 0.6 (b) 1/7 1/7 1/7 1/7 1/7 1/7 1/7 (c) 0.1 0.2 0.3 0.4 0.5 - 0.6 - 0.7 (d) -0.1 0.2 0.3 0.4 -0.2 0.1 0.3 (e) 1/14 2/14 3/14 4/14 5/14 6/14 15/14
Answer» ANSWER :(a) YES, (B) Yes, (C) No, (d) No, (E) No.

Discussion

12346.	Solve \|(4-x,4+x,4+x),(4+x,4-x,4+x),(4+x,4+x,4-x)\|=0
Answer» ANSWER :` RARR X = 0 " or " x = - 12 `

Discussion

12347.	The sum of all five digit numbers formed with the digits 1,2,3,4,5 without repetition of digits are
Answer» 3,00,000 3,60,000 3,90,000 None of these Answer :D

Discussion

12348.	If y=log_u\|cos4x\|+\|sinx\| where u=sec2x then (dy/dx)_(x=-pi/6) is
Answer»

Discussion

12349.	Thet eccentricity of the ellipse ((x-1)^(2))/(9)+ ((y+1)^(2))/(25) =1 is
Answer» `4/5` `3/5` `5/4` `5/3` ANSWER :A

Discussion

12350.	Evaluate : (4+3sqrt(-20))^(1//2)+(4-3 sqrt(-20))^(1//2)
Answer» SOLUTION :`PM6`

Discussion

Explore topic-wise InterviewSolutions in .

Ifthe origin is the centroid of the triangle PQR with vertices P(2a,2,6)Q(-4,3b,-10) and R(8,14,2c) then find the valuesof a ,b and c

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 D – B

Find the number of 4 - digit numbers that can be formed by using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even ?

arg (-1) = .........

A rectanglewith one side lying along the x - axis is to be inscribed in the closedregion of the xy plane bounded by the lines y=0,y=3x, and y=30-2x . If M is the largest area of such a rectangle, then value of (2M)/(27) is ________

If A is square matrix then A A^(T) is. . . . Matrix

A(2, 3, 4) B(-1, 2, 3) then the lengths of projection on {:("Column-I","Column-II"),((A)"xy plane", (p) sqrt(2)),((B) "yz plane", (q) sqrt(5)),((C )"cx plane" ,(r ) sqrt(10)):}

Let A={1,2} and B={3,4}. Find the number of relations from A to B.

The value of c in Lagrange's Mean Value theorem for the function f(x) = {:{(x cos ((1)/(x)),","xcancel(=)0),(0,","x=0):} in the intervale [-1,1] is

If f(z)=(7-z)/(1-z^(2)) where z=1+2i, the |f(z)| is equal to

A triangular plot has two adjacent sides 130m and 80m .the included angle between the sides is 30^o .find the cost of levelling the ground at the rate of Rs 10per sq.m.

(cosh(x))/(1-tanh(x))+(sinh(x))/(1-coth(x))=

Find the sum to n terms of the series : 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)+3^(2))+….

If r=x+y+z and tan^(-1)sqrt((xr)/(yz))+"tan"^(-1)sqrt((yr)/(zx))+tan^(-1)sqrt((zr)/(xy))=kpi then the value of k is

Define the real valued function f: R -{0} to R" defined by "f(x)=1/2 x in R-{0}. Complete the Table given below using this definition. What is the domain and range of this function?

The periodof tan ( x+ 8x+ 27 x … n ^(3 )x ) is

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that (1)/( p^2) = (1)/( a^2) + (1)/( b^2).

IfA = {: [ ( 1,0,0) , ( 0,1,0) , ( a,b,-1)]:}show thatA^(2)isa unitmatrix .

If 0^(@)lt theta lt 90^(@) and cos theta=(4)/(5) find the values of sin (270^(@)-theta)

Find the numbers of non-zero integral solutions of the equation |1-i|^(x) =2^(x)

Differentiate the following w.r.t. x or t or u as the case may be: 1. (ax+ b) (cx+d)

Let f be a function defined by f(x)={{:((tanx)/(x)",",x ne0),(1",",x=0):}Statement -I x=0 is point of minimum of f Statement II : f'(0)=0

For two A.P.: 2, 5, 8,…..up to 50 terms and 3, 5, 7, 9,….., up to 60 terms. How many terms are same?

In what ratio, the line joining (-1, 1) " and " (5, 7)is divided by the line x + y = 4 ?

With usual notations, in triangleABC, a cos (B-C)+b cos (C-A)+c cos(A-B) is equal to

A coin and a die are tossed . Describe the following events . A : getting a head even number ,

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

Under rotation of axes through an angletheta, x cos alpha+y sin alpha=p changes toX cos beta +Y sin beta =p then

If cos (theta - alpha) , cos theta , cos (theta + alpha )are in H.P. thencos theta .sec"" (alpha )/(2) =

Find the value of x, if |(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,3x-64)|=0.

Decide, among the following sets, which sets are subsets ofone and another: A = { x : x ∈ Rand x satisfy x^(2) – 8x + 12 =0 }, B = { 2, 4, 6 }, C = { 2, 4, 6, 8, . . . }, D = { 6 }.

Express each of the following in the form b or bi, where b is a real number (x)/(i)

State whether each of the following statement is true or false. Justify your answer. { 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.

Let f={(x, x^2/(1+x^(2))), x in R} be a function from R into R. Determine the range of f.

A cross - section ofa parabolic reflector is shown. The diameter of opening at the focus is 10 cm. Find the equation of the parabola. Find diameter of the opening at the focus is 10 cm. Find the equation of the parabola. Find diameter of the opening at 11 cm from the vertex.

The point P moves such that the sum of the squares of its distances from two fixed points A(a,0),B(-a,0) is 8a^(2) the locus of P is

If 1, log_(y)x, log_(z)y,-15 log_(x)z are in A.P. then the correct statement is :

Find the sum 1+4/5+7/(25)+(10)/(125)+ . ..

if (2)/(5)(y)/(z)+(2)/(5)(z)/(x)+(2)/(5)(x)/(y),(2)/(5)(x)/(y)+(2)/(5) (y)/(z) are the sides of a triangle then its area is

Let A={1,2}, B={1,2,3,4}, C={5,6} and D={5,6,7,8}. Verify that (i) A xx (B cap C)=(A xx B) cap (A xx C), (ii) A xx C is a subset of B xx D

2 Radian = .......... Degree.

The value ofunderset(x to 1)(Lt) ((x^(3)+2x^(2)+x+1)/(x^(2)+2x+3))^((1-cso(x-1))/(x-1)^(2))

From the top of a hill h metre high, the angles of depressions of the top and the bottom of a pillar are alpha and beta, respectively. The height (in metres) of the pillar is

Find the point to which the origin has to shifted to eliminate x and y terms in the equation 3(x-2)^(2)+5(y+3)^(2)=6.

Solve |(4-x,4+x,4+x),(4+x,4-x,4+x),(4+x,4+x,4-x)|=0

The sum of all five digit numbers formed with the digits 1,2,3,4,5 without repetition of digits are

If y=log_u|cos4x|+|sinx| where u=sec2x then (dy/dx)_(x=-pi/6) is

Thet eccentricity of the ellipse ((x-1)^(2))/(9)+ ((y+1)^(2))/(25) =1 is

Evaluate : (4+3sqrt(-20))^(1//2)+(4-3 sqrt(-20))^(1//2)