14949 + Interview Questions in Maths in Class 11 Page 231 InterviewSolution

11501.	Find the component statements of the compound statement given below :"New Delhi is a big city and it is the capital of India."
Answer» Answer :Compound STATEMENT. The COMPONENT statements are. NEW Delhi is a big city. It is the CAPITAL of INDIA.

Discussion

11502.	Show that (b-a) cos C+ c (cos B- cos A)=c sin ""( A-B)/( 2)cosec ""( A+B)/(2)
Answer» ANSWER :` = C SIN ((A-B)/( 2)) COSEC ((A+B)/(2))`

Discussion

11503.	Let f: R rarr R, g: R rarr R be two functions given by f(x)=2x-3, g(x)=x^(3)+5. Then , (fog)^(-1) is equal to
Answer» `((X+7)/(2))^(1//3)` `(x- 7/2)^(1//3)` `((x-2)/(7))^(1//3)` `((x-7)/(2))^(1//3)` ANSWER :D

Discussion

11504.	If a, b, c are in A.P., then prove that : (i) b+c,c+a,a+b" are also in A.P." (ii) (1)/(bc),(1)/(ca),(1)/(ab)"are also in A.P." (iii) (a(b+c))/(bc),(b(c+a))/(ca),(c(a+b))/(ab)"are also in A.P."
Answer» SOLUTION :N/a

Discussion

11505.	Find the mean deviation about the mean for the data : 38,70,48,40,42,55,63,46,54,44
Answer» ANSWER :8.4

Discussion

11506.	If 1 is a twice repeated root of the equation ax^3 +bx^2+bx+d=0 , then
Answer» a = B= d a + b = 0 b + d = 0 a = d ANSWER :B::C::D

Discussion

11507.	Find the union of each of the following pairs of sets : A =[ a, e, i, o, u} B = {a, b, c}
Answer» Answer :`A cup B= {a, e, i, o, U} CAP {a, b, c}= {a, b, c, e, i, o, u}`

Discussion

11508.	Numbers of terms in expansion (2x+3y+4z)^(7) are 8 .
Answer» ANSWER :FALSE STATEMENT

Discussion

11509.	The range of alpha"for which the points " (alpha,alpha+2) and ((3alpha)/2,alpha^2) lie on opposite sides of the line 2x+3y-6=0
Answer» `(-OO,-2)` (0,1) `(-oo,-2)UU(0,1)` `(-oo,1)uu(2,oo)` ANSWER :C

Discussion

11510.	If lim_(yto-2)(3x^(2)ax+a+3)/(x^(2)+x-2) limit exists then a=………..
Answer» 15 -15 12 `-12` ANSWER :A

Discussion

11511.	This section contains 2 questions. Each question contains STATEMENT-I (Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Statement - 1 : The minimum value of the expression sin alpha + sin beta + sin gamma where alpha, beta , gamma are real numbers such that alpha + beta + gamma=pi, is negative because Statement - 2 : alpha, beta, gamma are angles of a triangle
Answer» STATEMENT -1 is True, Statement-2 is True, Statement -2 is a correct EXPLANATION for Statement-1 Statement-1 is True, Statement-2 is True, Statement-2 NOT a correct explanation for Statement-1. Statement-1 is True, Statement-2 is False. Statement-1 is False, Statement-2 is True. Answer :C

Discussion

11512.	Find the derivative of the following functions:2 tan x -7 sec x
Answer» ANSWER :`2 SEC^(2)x-7 sex x TANX`

Discussion

11513.	If 4 sin 27^(@) = sqrt(alpha) + sqrt(beta) then the sum of the digits in (alpha + beta - alpha beta + 2)^(4)
Answer» ANSWER :4

Discussion

11514.	Find the equation of the parabola satisfying the following condition, Vertex (0,0) passing through (2,3) and axis along x-axis.
Answer» SOLUTION :`y^2= 9/2 X`

Discussion

11515.	Which of the following is/are the value of cos[1/2cos^(-1)(cos(-(14pi)/5))]?
Answer» `COS(-(7pi)/5)` `sin((pi)/10)` `cos((2pi)/5)` `-cos((3PI)/5)` Answer :B::C::D

Discussion

11516.	Prove that cot(pi/4-theta)=(cos2theta)/(1-sin2theta) and hence find the value of Cot15^(@)
Answer» ANSWER :`sqrt5/2, -2`

Discussion

11517.	The minimum value of 2costheta+(1)/(sintheta)+sqrt(2)tan theta in (0, (pi)/(2)) is
Answer» `2+ sqrt2` `3 sqrt2` `2 SQRT3` `3 + sqrt2` Answer :B

Discussion

11518.	The range of sin^(6) x + cos^(6) x
Answer» `[-(1)/(4), (1)/(4)]` `[(1)/(4),(1)/(2)]` `[(1)/(4),1]` `[-(1)/(2), -(1)/(4)]` ANSWER :C

Discussion

11519.	Let R be the relation on Z defined by R= {(a,b): a, b in Z, a-b "is an integer"). Find the domain and range of R.
Answer» ANSWER :R is Z

Discussion

11520.	Equation of a line in the plane pi -= 2x - y + z -4=0 which is perpendicular to the line l whose equation is (x-2)/(1) = (y-2)/(-1) = (z-3)/(--2) and which passes through the point of intersection of l and pi is
Answer» `(X-2)/(1) = (y -1)/(5) = (z-1)/(-1)` `(x-1)/(3) = (y-3)/(5) = (z-5)/(-1)` `(x -2)/(2) = (y+1)/(-1) = (z+1)/(1)` `(x -2)/(2) = (y-1)/(-1) =(z-1)/(1)` ANSWER :B

Discussion

11521.	One of solution of \|y - cos a\| le xwhere x and a are values that satisfy the given equation is
Answer» `y in [ - 5, 7]` `y in [ - 7, 5]` `y in [5, 7]` `y in [- 7, - 5]` ANSWER :B

Discussion

11522.	If D is mid point of the side BC of a triangle ABC and AD is perpendicular is AC then (a^(2) - c^(2))/b^(2) =
Answer» 1 2 3 4 Answer :C

Discussion

11523.	Find the derivative of w.r.to x (x ^(3) + 6x ^(2) + 12x -13) ^(100)
Answer» ANSWER :`300 (x+2) ^(2) (x ^(3) + 6X ^(2) + 12 x - 13) ^(99)`

Discussion

11524.	11 + 103 + 1005 +…….up to n terms is…….
Answer» `(1)/(9) (10^(N)-1) + n^(2)` `(10)/(9) (10^(n)-1) + n^(2)` `(10)/(9) (10^(n)-1) + 2N` NONE of these Answer :B

Discussion

11525.	Find the mean deviationabout the median for the following data 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21.
Answer» ANSWER :5.27

Discussion

11526.	If x, y and r are positive integers, then ""^(x)C_(r)+""^(x)C_(r-1)+""^(y)C_(1)+""^(x)C_(r-2)""^(y)C_(2)+......+""^(y)C_(r)=
Answer» `(X!y!)/(R!)` `((x!y!))/(r!)` `""^(x+y)C_(r)` `""^(XY)C_(r)` ANSWER :C

Discussion

11527.	If the ordered pairs of natural numbers (a_(1), b_(1)) and (a_(2), b_(2)) are satisfying the equation are cot^(-1)8=tan^(-1)a-tan^(-1)b. Then the value of (a_(1)+b_(1)+a_(2)+b_(2))/9 is
Answer» ANSWER :8

Discussion

11528.	A = {1,{2,3}4}then{2,3} subA
Answer» ANSWER :FALSE STATEMENT

Discussion

11529.	One ofi the combinations from the fundamental physical constants is (hc)/G. The unit of this expression is
Answer» `Kg^2` `m^3` `S^(-1)` `m` SOLUTION :`Kg^2`

Discussion

11530.	The value of""^(50)C_4 +underset(r=1) overset(6)sum ""^(56-r)C_3is
Answer» ` ""^(55)C_4` ` ""^(55)C_3` ` ""^(56)C_3` ` ""^(56)C_4` ANSWER :D

Discussion

11531.	The maximm height of an arch of th cycloid x=a( theta- sin theta), y=a (1-cos theta) is
Answer» `a PI` a 2a 3a Answer :C

Discussion

11532.	Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (i) {(2,1),(5,1),(8,1),(11,1),(14,1),(17,1)} (ii) {(2,1),(4,2),(6,3),(8,4),(10,5),(12,6),(14,7)} (iii) {(1,3),(1,5),(2,5)}
Answer» ANSWER :(i) yes DOMAIN ={2,5,8,11,14,17}, Range ={1} (ii) yes, Domain ={2,4,6,8,12,14}, Range ={1,2,3,4,5,6,7} (iii) No.

Discussion

11533.	Find area at the quadrilateral ABCD with vertices A(1, 1), B(7, -3), C(12, 2) and D(7, 21).
Answer» ANSWER :132 SQ. UNIT

Discussion

11534.	For all sets A and B, (A cup B) - B = A - B.
Answer» ANSWER :R.H.S.

Discussion

11535.	If P={1,2}, form the set P xx P xx P
Answer» <P> ANSWER :`P XX P xx P= {(1, 1,1) (1,1,4)(1,4,1)(1,4,4) (4,1,1)(4,1,4) (4,4,1) (4,4,4)}`

Discussion

11536.	If bar(a)=i+j+k, bar(b)=i-j+2k and bar(c)=x""i+(x-2)j-k. If the vector bar(c) lies in the plane of bar(a) and bar(b) then x equals to
Answer» 0 1 -4 -2 Answer :D

Discussion

11537.	Therangeof cos^(2) x + sin^(4) xis
Answer» `[(1)/(2), 1]` `[1, (3)/(2)]` `[(3)/(2), 2]` `[(3)/(4), 1]` ANSWER :D

Discussion

11538.	Express each of the complex number given in the form of a+ib (1/5 + i2/5 -(4+i5/2))
Answer» ANSWER :`-19/5 - (21i)/10`

Discussion

11539.	The set of values of a for which f(x)=x^(3)-ax^(2)+48x+1 is increasing for all real values of x is
Answer» `(-12,12)` `(-OO,-12)` `(12,oo)` `(-oo,oo)` ANSWER :A

Discussion

11540.	Two cars started from a plane one moving due east and the other due north with equal speed V. Then the rate at which they were being seperated from each other is
Answer» `(SQRT(2))/(V)` `(V)/(sqrt(2))` `(1)/(sqrt(2)V)` `(1)/(sqrt(2)V)` ANSWER :D

Discussion

11541.	Which of the following sentences are statements? Give reasons for your answer: There are 35 days in a month.
Answer» ANSWER :It is a STATEMENT.

Discussion

11542.	Find the probability ofobtaining a sum 8 in a single throw of two dice.
Answer» ANSWER :`(5)/(36)`

Discussion

11543.	sec x =2
Answer» Answer :`pi/3, (5pi)/(3), 2NPI PM (pi)/(3), N in Z`

Discussion

11544.	Solve the following: x^(3) + 3=0
Answer» ANSWER :`+- SQRT(3)i`

Discussion

11545.	Find the mean and variance for the following frequency distributions in
Answer» SOLUTION : `:.` MEAN `=(sumf_(i)x_(i))/(sumf_(i))=1350/50=27` Variance `sigma^(2)=1/Nsumf_(i)(x_(i)-barx)^(2)` `=1/50xx6600=132`

Discussion

11546.	Find the mean and variance for the following frequency distributions in
Answer» Solution : Mean `BARX=(sumf_(i)x_(i))/(sumf_(i))=3210/30=107` VARIANCE `=1/N sumf_(i)(x_(i)-barx)^(2)=68280/30=2276`

Discussion

11547.	A plane is 1 km from one landmark and 2 km from another. From the planes point of view the land between them subtends an angle of 45^o. How far apart are the landmarks?
Answer» ANSWER :`SQRT[5-(2SQRT2)]KM`

Discussion

11548.	Find the angle in radian through which a pendulum swings if its length is 75 cm and the e tip describes an arc of length (i) 10 cm (ii) 15 cm (iii) 21 cm
Answer» ANSWER :`(i) (2)/(15)` (II) `1/5` (III) `7/25`

Discussion

11549.	Find the sum of all numbers between 200 and 400 which are divisible by 7?
Answer» ANSWER :8729

Discussion

11550.	If the ratio of the base radius and height of a cone is 1 : 2 and percentage error in the radius is K, then percentage error in its volume is
Answer» K 2K 3K 4K Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

Find the component statements of the compound statement given below :"New Delhi is a big city and it is the capital of India."

Show that (b-a) cos C+ c (cos B- cos A)=c sin ""( A-B)/( 2)cosec ""( A+B)/(2)

Let f: R rarr R, g: R rarr R be two functions given by f(x)=2x-3, g(x)=x^(3)+5. Then , (fog)^(-1) is equal to

If a, b, c are in A.P., then prove that : (i) b+c,c+a,a+b" are also in A.P." (ii) (1)/(bc),(1)/(ca),(1)/(ab)"are also in A.P." (iii) (a(b+c))/(bc),(b(c+a))/(ca),(c(a+b))/(ab)"are also in A.P."

Find the mean deviation about the mean for the data : 38,70,48,40,42,55,63,46,54,44

If 1 is a twice repeated root of the equation ax^3 +bx^2+bx+d=0 , then

Find the union of each of the following pairs of sets : A =[ a, e, i, o, u} B = {a, b, c}

Numbers of terms in expansion (2x+3y+4z)^(7) are 8 .

The range of alpha"for which the points " (alpha,alpha+2) and ((3alpha)/2,alpha^2) lie on opposite sides of the line 2x+3y-6=0

If lim_(yto-2)(3x^(2)ax+a+3)/(x^(2)+x-2) limit exists then a=………..

Find the derivative of the following functions:2 tan x -7 sec x

If 4 sin 27^(@) = sqrt(alpha) + sqrt(beta) then the sum of the digits in (alpha + beta - alpha beta + 2)^(4)

Find the equation of the parabola satisfying the following condition, Vertex (0,0) passing through (2,3) and axis along x-axis.

Which of the following is/are the value of cos[1/2cos^(-1)(cos(-(14pi)/5))]?

Prove that cot(pi/4-theta)=(cos2theta)/(1-sin2theta) and hence find the value of Cot15^(@)

The minimum value of 2costheta+(1)/(sintheta)+sqrt(2)tan theta in (0, (pi)/(2)) is

The range of sin^(6) x + cos^(6) x

Let R be the relation on Z defined by R= {(a,b): a, b in Z, a-b "is an integer"). Find the domain and range of R.

Equation of a line in the plane pi -= 2x - y + z -4=0 which is perpendicular to the line l whose equation is (x-2)/(1) = (y-2)/(-1) = (z-3)/(--2) and which passes through the point of intersection of l and pi is

One of solution of |y - cos a| le xwhere x and a are values that satisfy the given equation is

If D is mid point of the side BC of a triangle ABC and AD is perpendicular is AC then (a^(2) - c^(2))/b^(2) =

Find the derivative of w.r.to x (x ^(3) + 6x ^(2) + 12x -13) ^(100)

11 + 103 + 1005 +…….up to n terms is…….

Find the mean deviationabout the median for the following data 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21.

If x, y and r are positive integers, then ""^(x)C_(r)+""^(x)C_(r-1)+""^(y)C_(1)+""^(x)C_(r-2)""^(y)C_(2)+......+""^(y)C_(r)=

If the ordered pairs of natural numbers (a_(1), b_(1)) and (a_(2), b_(2)) are satisfying the equation are cot^(-1)8=tan^(-1)a-tan^(-1)b. Then the value of (a_(1)+b_(1)+a_(2)+b_(2))/9 is

A = {1,{2,3}4}then{2,3} subA

One ofi the combinations from the fundamental physical constants is (hc)/G. The unit of this expression is

The value of""^(50)C_4 +underset(r=1) overset(6)sum ""^(56-r)C_3is

The maximm height of an arch of th cycloid x=a( theta- sin theta), y=a (1-cos theta) is

Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (i) {(2,1),(5,1),(8,1),(11,1),(14,1),(17,1)} (ii) {(2,1),(4,2),(6,3),(8,4),(10,5),(12,6),(14,7)} (iii) {(1,3),(1,5),(2,5)}

Find area at the quadrilateral ABCD with vertices A(1, 1), B(7, -3), C(12, 2) and D(7, 21).

For all sets A and B, (A cup B) - B = A - B.

If P={1,2}, form the set P xx P xx P

If bar(a)=i+j+k, bar(b)=i-j+2k and bar(c)=x""i+(x-2)j-k. If the vector bar(c) lies in the plane of bar(a) and bar(b) then x equals to

Therangeof cos^(2) x + sin^(4) xis

Express each of the complex number given in the form of a+ib (1/5 + i2/5 -(4+i5/2))

The set of values of a for which f(x)=x^(3)-ax^(2)+48x+1 is increasing for all real values of x is

Two cars started from a plane one moving due east and the other due north with equal speed V. Then the rate at which they were being seperated from each other is

Which of the following sentences are statements? Give reasons for your answer: There are 35 days in a month.

Find the probability ofobtaining a sum 8 in a single throw of two dice.

sec x =2

Solve the following: x^(3) + 3=0

Find the mean and variance for the following frequency distributions in

Find the mean and variance for the following frequency distributions in

A plane is 1 km from one landmark and 2 km from another. From the planes point of view the land between them subtends an angle of 45^o. How far apart are the landmarks?

Find the angle in radian through which a pendulum swings if its length is 75 cm and the e tip describes an arc of length (i) 10 cm (ii) 15 cm (iii) 21 cm

Find the sum of all numbers between 200 and 400 which are divisible by 7?

If the ratio of the base radius and height of a cone is 1 : 2 and percentage error in the radius is K, then percentage error in its volume is