14949 + Interview Questions in Maths in Class 11 Page 200 InterviewSolution

9951.	Find a positive value of m for which the coefficient of x^(2) in the expansion of (1+x)^(m) is 6.
Answer» ANSWER :m = 4

Discussion

9952.	Find the second derivative of the function ( y" or (d ^(2) y)/(dx ^(2))), y=sin ^(4) x
Answer» ANSWER :`2 (COS 2X - cos 4X)`

Discussion

9953.	Let F_(1) be the set of parallelograms, F_(2) the set of rectangles, F_(3) the set of rhombuses, F_(4) the set of squares and F_(5) the set of trapeziums in a plane. Then, F_(1) may be equal to
Answer» `F_(2) cap F_(3)` `F_(3) cap F_(4)` `F_(2) cup F_(5)` `F_(1) cup F_(2) cup F_(3) cup F_(4)` Answer :D

Discussion

9954.	Find the centre and radius of the circle which passes through lie points (7,5), (6, - 2), (-1 , -1 )
Answer» ANSWER :(3,2);5

Discussion

9955.	If A= {x : x is a natural number}, B= {x : x is an even natural number}, C= {x : x is an odd natural number}, D= {x : x is a prime number} then find the following sets. A cap C
Answer» ANSWER :`C= {1, 3, 5, 7, 9,…..,……}`

Discussion

9956.	If A = {x : x is a natural number },B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number }, find B ∩ C
Answer» ANSWER :`= PHI`

Discussion

9957.	If A = {x : x is a natural number },B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number }, find A ∩ D
Answer» ANSWER :`D= {2, 3, 5, 7, 11,….,……}`

Discussion

9958.	Find the value or values of m for which m( hati + hatj + hatk)ia a unit vector .
Answer» ANSWER :` therefore m SQRT(3) = pm 1 RARR m = pm (1)/(sqrt(3))`

Discussion

9959.	If A = {x : x is a natural number },B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number }, find B ∩ D
Answer» ANSWER :`= {2}`

Discussion

9960.	If A = {x : x is a natural number },B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number }, find C ∩ D
Answer» Answer :`D= {2, 3, 5, 7, 11,….,…..}- {2}`

Discussion

9961.	Using binomial theorem ,Evaluateeach of the following (102)^(5)
Answer» ANSWER :`11040808032`

Discussion

9962.	Find the square roots of the following : 7-24i
Answer» ANSWER :`+-(4-3i)`

Discussion

9963.	Show that if A ⊂ B, then C – B ⊂ C – A.
Answer» ANSWER :`THEREFORE (C - B) SUB (C - A)`

Discussion

9964.	If y =x/(a + x/(b+ x/(a + x/(b + ....+ "to " oo)))) then (dy)/(dx)=
Answer» `1/(a(2Y+ B))` `b/(a(2y + b))` `1/(AB(2y + b))` `(ab)/((2y + b))` ANSWER :B

Discussion

9965.	If (2, 1, 3), (3, 2, 5), (1, 2, 4) are the mid points of the sides BC, CA, AB of DeltaABC respectively, then the vertex A is
Answer» (2, 3, 6) (0, 2, 2) (4, 1, 4) (2, 5, 4) ANSWER :a

Discussion

9966.	If tanA=(1)/(2)andtanB=(1)/(3), then tan(2A+B) is equal to
Answer» 1 2 3 4 Answer :C

Discussion

9967.	If tan theta + tan(60^(@)+theta)+tan (120^(@)+theta)=3, then theta =
Answer» `(NPI)/(3)+(pi)/(12)` `npi+(pi)/(4)` `2NPI` `npi` ANSWER :A

Discussion

9968.	Check whether the following probabilities P(A) and P(B) consistently defined (i) P(A) = 0.5,P(B) = 0.7, P(A nn B) = 0.6 (ii) P(A) = 0.5, P(B) = 0.4, P(A uu B) = 0.8
Answer» <P> ANSWER :(i) No BECOME `P(A nn B)` must be less than or equal to `P(A)` and `P(B)`, (ii) Yes.

Discussion

9969.	Of how many terms is ,(55)/(72)the sum of the series (2)/(9) -(1)/(3)+(1)/(2)- .... ?
Answer» ANSWER :5

Discussion

9970.	Find all points of discontinuityof f, where f is defined by f(x)={{:(x^(3)-3," if "x le2),(x^(2)+1," if "x gt 2):}
Answer» ANSWER :no POINT of DISCONTINUITY

Discussion

9971.	Maximumvalueof 1+ 8 sin^(2) x^(2) cos^(2)x^(2) is
Answer» 3 -1 -8 9 Answer :1

Discussion

9972.	Find the equation of line which is at Perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 30^(@).
Answer» ANSWER :`SQRT3 X + y = 10`

Discussion

9973.	Refer to question 6 above, state true or false : (give reason for your answer) A', B', C are mutually exclusive and exhaustive.
Answer» ANSWER :`:.` GIVEN STATEMENT is FALSE.

Discussion

9974.	Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n)= 3n+1
Answer» ANSWER :`4,7,10,13,16`

Discussion

9975.	What is the number of terms in the expansion of each of the following? (ii) (5a+7b)^(3)
Answer» ANSWER :9

Discussion

9976.	If ea n de 'the eccentricities of a hyperbola and itsconjugate, prove that 1/(e^2)+1/(e '^2)=1.
Answer» ANSWER :`(a ^(2) + B ^(2))/(a ^(2) + b ^(2)) = 1.`

Discussion

9977.	The angle of elevation of the top of the tower is 45^(@) on walking up a slope inclinde at an angle of 30^(@) to the horizontal a distance20 meters, the angle of elevation of top of tower is observed to be 60^(@). The height of the tower is
Answer» ` 5 SQRT2 ` ` 7 sqrt2` ` 4 sqrt2` ` 5` ANSWER :A

Discussion

9978.	A straight line passes through the points A(2, -3,-1) and B(8, -1,2). Find the coordinates of the points on this line at a distance of 7 units from A.
Answer» ANSWER :(8,-1,2), (-4,-5,-4)

Discussion

9979.	If d/(dx)(x+\|x\|).\|x\|=4xwhere x gt 0
Answer» ANSWER :TRUE STATEMENT

Discussion

9980.	If chance of A , winning a certain race be (1)/(6) and the chance of B winning it is (1)/(3) , what is the chance that neither should win ?
Answer» ANSWER :`(1)/(2)`

Discussion

9981.	The ratio in which the line segment joining the points whose position vectors are 2 hati - 4 hatj - 7 hatk and - 3 hati + 5 hatj - 8 hatk is divided by the plane whose equation isvec r.(hati -2 hatj + 3hatk) =13 is
Answer» `13:12` INTERNALLY `12:25` EXTERNALLY `13:25` internally `37:25` internally ANSWER :B

Discussion

9982.	If sin^(-1)(x-(x^(2))/2+(x^(3))/4-……oo) +cos^(-1)(x^(2)-(x^(4))/2+(x^(6))/4-……..oo)=(pi)/2 and 0ltxltsqrt(2) then x=
Answer» `1//2` 1 `-1//2` -1 Answer :B

Discussion

9983.	Draw the graphs of the following : y = \| x-1 \| in [ 0,2 ]
Answer»

Discussion

9984.	p and q are given statements then contra positive of pvee~(prArr~q) is ….. .
Answer» <P> ANSWER :`~p^^(qvvr)`

Discussion

9985.	Which of the follwoing setof values of x satisfies the equation 2 ^((2 sin^(2)x - 3 sin x + 1))+2 ^((2 - 2 sin^(2) x + 3 sin x ))=9
Answer» `x=npi+-(PI)/6, N in I` `x = n pi +-(pi)/3, n in I` `x = n pi , n in I` `x=2n pi +(pi)/2, n in I` ANSWER :A::D

Discussion

9986.	Write the additive inverse of the following 3- 4i
Answer» ANSWER :`-3+4i`

Discussion

9987.	Prove that (i)" sin" 80^(@)"cos" 20^(@) - " cos"80^(@) " sin " 20^(@)=(sqrt(3))/(2) (ii)"cos " 45^(@)" cos"15^(@)-" sin" 45^(@)" sin "15^(@) = (1)/(2) (iii)" cos" 75^(@)" cos"15^(@)+ " sin"75^(@)" sin" 15^(2)= (1)/(2) (iv)"sin" 40^(@)" cos" 20^(@) " + cos" 40^(@)" sin " 20^(@)=(sqrt(3))/(2) (v) " cos"130^(@)" cos" 40^(@) l + " sin"130^(@) " sin" 40^(@) =0
Answer»

Discussion

9988.	If A={1,2,3,4} and B={3,4,5,6} find n(AuuB)xx(AnnB)xx(ADeltaB).
Answer» ANSWER :48

Discussion

9989.	When angle of rotation of axesis Tan^(-1) 2 the transformed equation of 4xy - 3x^(2) = a^(2)is
Answer» `2XY + a^(2) = 0` `xy - a^(2) = 0` `x^(2) - 4y^(2) = a^(2)` `x^(2) - 2Y^(2) = a^(2)` Answer :C

Discussion

9990.	A die is throw. Describe the following events : A: The number on die is less than 7. B: The number on die is multiple of 3. C : The number on die is greater than 4. D: The number on die is smaller than 2. Also find AnnC,BuuC,D'uuC'.
Answer» ANSWER :`A={1,2,3,4,5,6}` `B={3,6}, C={5,6}, D={1}` `ANNC={5,6}BUUC={3,5,6}` `D'uuC'={1,2,3,4,5,6}`

Discussion

9991.	Find three numbers a, b, c between 2 and 18 such that: (i) their sum is 25, and (ii) the numbers 2, a, b are consecutive terms of an arithmetic progression, and (iii) the numbers b, c, 18 are consecutive terms of a geometric progression.
Answer» ANSWER :a=5 , b=8, c=12

Discussion

9992.	If alpha, beta are different values of x satisfying a cos x + b sin x = c then tan ((alpha + beta)/(2))=
Answer» a + B a - b a/b b/a Answer :D

Discussion

9993.	If A = (1, 2, 3) and B(3, 5, 7) and P,Q are the points on AB such that AP = PQ = QB, then the mid point of PQ is
Answer» (2, 3, 5) `(2, (7)/(2), 5) ` `(2, 4, 5)` `(4, 7, 0)` Answer :b

Discussion

9994.	Write the solution set of the equation x^(2)+x-2=0in roster form.
Answer» ANSWER :`{1,-2}`

Discussion

9995.	The minimum value of a^(Cos^(2)x)+a^(Sin^(2)x)AA(a gt 0) is
Answer» 2A `SQRT(2)a` `2sqrt(a)` `sqrt(a)` ANSWER :C

Discussion

9996.	If 5a+5b+20c=t, then the value of t for which the line ax+by+c-1=0 always passes thorugh a fixed point is
Answer» 0 20 30 none of these Answer :C

Discussion

9997.	If the origin of a coordinate system is shifted to (-sqrt(2), sqrt(2)) and the then the coordinate system rotated anticlockwise through an angle 45^(0) , the point P(1, -1) in the original system has new coordinates
Answer» `(SQRT(2), - 2sqrt(2))` `(0, - 2 sqrt(2))` `(0, - 2 - sqrt(2))` `(0, - 2 + sqrt(2))` ANSWER :C

Discussion

9998.	Function f(x)=x^3-27x+5 is monotonically increasing when
Answer» `xlt-3` `XGT3` `xle-3` `\|x\|gt3` ANSWER :D

Discussion

9999.	IfC (2n,3) : C ( n,2)=12: 1find n,
Answer» ANSWER :` 5`

Discussion

10000.	Given P(x)=x^(4)+ax^(3)+bx^(2)+cx +d such that x=0 is the only real root of P'(x)==0. If P(-1) lt P(1), then in the interval [-1,1]
Answer» P(-1) is the minimumand P(1) is the MAXIMUM of P P(-1) is not minimumand P(1) is the maximum of P P(-1) isminimumand P(1) is not the maximum of P NEITHER P(-1) is the minimum nor P(1) is the maximum of P ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Find a positive value of m for which the coefficient of x^(2) in the expansion of (1+x)^(m) is 6.

Find the second derivative of the function ( y" or (d ^(2) y)/(dx ^(2))), y=sin ^(4) x

Let F_(1) be the set of parallelograms, F_(2) the set of rectangles, F_(3) the set of rhombuses, F_(4) the set of squares and F_(5) the set of trapeziums in a plane. Then, F_(1) may be equal to

Find the centre and radius of the circle which passes through lie points (7,5), (6, - 2), (-1 , -1 )

If A= {x : x is a natural number}, B= {x : x is an even natural number}, C= {x : x is an odd natural number}, D= {x : x is a prime number} then find the following sets. A cap C

If A = {x : x is a natural number },B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number }, find B ∩ C

If A = {x : x is a natural number },B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number }, find A ∩ D

Find the value or values of m for which m( hati + hatj + hatk)ia a unit vector .

If A = {x : x is a natural number },B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number }, find B ∩ D

If A = {x : x is a natural number },B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number }, find C ∩ D

Using binomial theorem ,Evaluateeach of the following (102)^(5)

Find the square roots of the following : 7-24i

Show that if A ⊂ B, then C – B ⊂ C – A.

If y =x/(a + x/(b+ x/(a + x/(b + ....+ "to " oo)))) then (dy)/(dx)=

If (2, 1, 3), (3, 2, 5), (1, 2, 4) are the mid points of the sides BC, CA, AB of DeltaABC respectively, then the vertex A is

If tanA=(1)/(2)andtanB=(1)/(3), then tan(2A+B) is equal to

If tan theta + tan(60^(@)+theta)+tan (120^(@)+theta)=3, then theta =

Check whether the following probabilities P(A) and P(B) consistently defined (i) P(A) = 0.5,P(B) = 0.7, P(A nn B) = 0.6 (ii) P(A) = 0.5, P(B) = 0.4, P(A uu B) = 0.8

Of how many terms is ,(55)/(72)the sum of the series (2)/(9) -(1)/(3)+(1)/(2)- .... ?

Find all points of discontinuityof f, where f is defined by f(x)={{:(x^(3)-3," if "x le2),(x^(2)+1," if "x gt 2):}

Maximumvalueof 1+ 8 sin^(2) x^(2) cos^(2)x^(2) is

Find the equation of line which is at Perpendicular distance from the origin is 5 units and the angle made by the﻿ perpendicular﻿ with the positive x-axis is 30^(@).﻿

Refer to question 6 above, state true or false : (give reason for your answer) A', B', C are mutually exclusive and exhaustive.

Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n)= 3n+1

What is the number of terms in the expansion of each of the following? (ii) (5a+7b)^(3)

If ea n de 'the eccentricities of a hyperbola and itsconjugate, prove that 1/(e^2)+1/(e '^2)=1.

The angle of elevation of the top of the tower is 45^(@) on walking up a slope inclinde at an angle of 30^(@) to the horizontal a distance20 meters, the angle of elevation of top of tower is observed to be 60^(@). The height of the tower is

A straight line passes through the points A(2, -3,-1) and B(8, -1,2). Find the coordinates of the points on this line at a distance of 7 units from A.

If d/(dx)(x+|x|).|x|=4xwhere x gt 0

If chance of A , winning a certain race be (1)/(6) and the chance of B winning it is (1)/(3) , what is the chance that neither should win ?

The ratio in which the line segment joining the points whose position vectors are 2 hati - 4 hatj - 7 hatk and - 3 hati + 5 hatj - 8 hatk is divided by the plane whose equation isvec r.(hati -2 hatj + 3hatk) =13 is

If sin^(-1)(x-(x^(2))/2+(x^(3))/4-……oo) +cos^(-1)(x^(2)-(x^(4))/2+(x^(6))/4-……..oo)=(pi)/2 and 0ltxltsqrt(2) then x=

Draw the graphs of the following : y = | x-1 | in [ 0,2 ]

p and q are given statements then contra positive of pvee~(prArr~q) is ….. .

Which of the follwoing setof values of x satisfies the equation 2 ^((2 sin^(2)x - 3 sin x + 1))+2 ^((2 - 2 sin^(2) x + 3 sin x ))=9

Write the additive inverse of the following 3- 4i

If A={1,2,3,4} and B={3,4,5,6} find n(AuuB)xx(AnnB)xx(ADeltaB).

When angle of rotation of axesis Tan^(-1) 2 the transformed equation of 4xy - 3x^(2) = a^(2)is

A die is throw. Describe the following events : A: The number on die is less than 7. B: The number on die is multiple of 3. C : The number on die is greater than 4. D: The number on die is smaller than 2. Also find AnnC,BuuC,D'uuC'.

Find three numbers a, b, c between 2 and 18 such that: (i) their sum is 25, and (ii) the numbers 2, a, b are consecutive terms of an arithmetic progression, and (iii) the numbers b, c, 18 are consecutive terms of a geometric progression.

If alpha, beta are different values of x satisfying a cos x + b sin x = c then tan ((alpha + beta)/(2))=

If A = (1, 2, 3) and B(3, 5, 7) and P,Q are the points on AB such that AP = PQ = QB, then the mid point of PQ is

Write the solution set of the equation x^(2)+x-2=0in roster form.

The minimum value of a^(Cos^(2)x)+a^(Sin^(2)x)AA(a gt 0) is

If 5a+5b+20c=t, then the value of t for which the line ax+by+c-1=0 always passes thorugh a fixed point is

If the origin of a coordinate system is shifted to (-sqrt(2), sqrt(2)) and the then the coordinate system rotated anticlockwise through an angle 45^(0) , the point P(1, -1) in the original system has new coordinates

Function f(x)=x^3-27x+5 is monotonically increasing when

IfC (2n,3) : C ( n,2)=12: 1find n,

Given P(x)=x^(4)+ax^(3)+bx^(2)+cx +d such that x=0 is the only real root of P'(x)==0. If P(-1) lt P(1), then in the interval [-1,1]

Find the equation of line which is at Perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 30^(@).