14949 + Interview Questions in Maths in Class 11 Page 184 InterviewSolution

9151.	Using mathematical induction, the numbers a_(n)'s are defined by, a_(0) =1, a_(n+1) = 3n^(2) + n+a_(n) ( n ge 0). Then a_(n) =
Answer» `n^(3) + n^(2) +1` `n^(3) - n^(2) +1` `n^(3) - n^(2)` `n^(3) + n^(2)` ANSWER :B

Discussion

9152.	Choose the incorrect pair :
Answer» ` sin x "" x in R ` ` cos x "" x in R ` `LOG x "" x GT 0 ` `E^(-x) "" x gt 0 ` Answer :Hint: ` e^(-x) ` can be DEFINED in ` RR(4)e^(-x) ;x gt 0 `

Discussion

9153.	If the X liney=m,x , r = 1,2,3 cut off equal intercepts on transversal line x+y=1 , then 1+m_1 ,1+m_2 , 1+m_3 are in
Answer» A.P G.P H.P A.G..P Answer :C

Discussion

9154.	If tan theta = n tan phi then the maximum value of tan^(2)(theta-phi) is equal to
Answer» `((N+1)^(2) )/( 2N)` `((n+1)^(2) )/( n)` `((n+1)^(2) )/(2)` `((n+1)^2)/( 4N)` ANSWER :D

Discussion

9155.	To find the sum sin^(2)""(2pi)/7 + sin^(2)""(4pi)/7 + sin^(2)""(8pi)/7 , we follow the following method . Put 7 theta = 2npi, where n is any integer . Then sin 4theta = sin (2npi - 3 theta)=-sin3 theta .......(i) This means that sin theta that takes the values 0,pm sin(2pi//7),pmsin(4pi//7), and pm sin(8pi//7) From Eq . (i) we now get 2 sin 2theta cos 2 theta = 4sin^(3) theta" or " 4 sin theta sin theta cos theta (1-2 sin^(2) theta)=(4sin^2theta - 3) sin theta Rejecting the value sin theta = 0we get 4 cos theta(1-2sin^2 theta)=4 sin^2 theta-3 or 16 cos^2 theta (1 - 2 sin^(2) theta)^(2) = (4 sin^(2) theta -3)^(2) " or " 16 ( 1- sin^(2) theta) (1-4sin^(2) theta+4sin^(4)theta)= 16 sin^(4) theta- 24 sin^(2) theta + 9 or 64 sin^(6) theta - 112 sin^(4) theta - 56 sin^(2) theta - 7 =0 , and this is cubic in sin^2 theta with the roots sin^(2)((2pi)/7) , sin^(2)((4pi)/7) and sin^(2)((8pi)/7) The sum of these roots in sin^(2)""(2pi)/7 + sin^(2)""(4pi)/7 + sin^(2)""(8pi)/7 = 112/64 = 7/4 . The value of (tan^2""(pi)/7+tan^2""(2pi)/7+tan^2""(3pi)/7)/(cot^2""(pi)/7+cot^2""(2pi)/7+cot^2""(3pi)/7)is
Answer» 7 `35/3` `21/5` NONE of these Answer :C

Discussion

9156.	The principal solution of sintheta=-(1)/(2) is
Answer» `-(pi)/(4)` `-(pi)/(6)` `-(pi)/(3)` `(7pi)/(6)` ANSWER :B

Discussion

9157.	A and B are not singleton sets. n(A xx B)= 21. If A sub B" then "n(B)="……….".
Answer» ANSWER :`N(A)= 3, n(B)=5`

Discussion

9158.	IfP(x) =ax^3+bx^2+cx+d and P(0) = 4, P^(1)(0) = 3,P^(11)(0)=4,P^(111)(0) = 6then arrange the values of a , b , c , d inthe descending order of their values
Answer» a, B,C,d a,b,d,c d, c , b, a b , a , c ,d ANSWER :C

Discussion

9159.	Iftan theta + tan ( theta + (pi)/(3))+ tan ( theta + (2pi)/(3))=3 , then which of the following is equal to 1 ?
Answer» `theta = (4 N + 1) (pi)/( 3), n in Z` `theta = (4 n + 1) (pi)/(2) , n in Z` `theta = (4 +n + 1) (pi)/(4), n INZ` `theta = ( 4 n + 1) (pi)/(12), n in Z` Answer :D

Discussion

9160.	A flag staff of the height (a-b) stands on the top of a tower subtends the same angle at the point on the horizontal plalne through thefoot of the tower which are at distant a and b from the tower. The height of the tower is
Answer» B a+b a a-b Answer :B

Discussion

9161.	If tan 20^@ =p , " then " (tan 160^@ - tan 110^(@))/(1+ tan 160^(@) tan 110^(@))=
Answer» `(2P)/(1+P^(2))` `(1-P^(2))/(2P)` `(1-P^(2))/(2p)` `(2P)/(1-P^(2))` ANSWER :B

Discussion

9162.	Prove that sin ""(pi)/(9) sin ""(2pi)/(9) sin ""( 3pi)/(9) sin ""(4pi)/(9) = (3)/(16).
Answer» ANSWER :`3/16`

Discussion

9163.	(d)/(dx) {cos ^(2) [Tan ^(-1) (sin Cot ^(-1)) ]}=
Answer» `2/((x^2 + 2)^2)` `(2X)/((x^2+ 2)^2)` `(x^2 + 1)/(x^2 + 2)` `(-2x)/((x^2- 1)^2)` ANSWER :B

Discussion

9164.	One side of an equilateral triangle is the line 5y=12x=3andits centroid is at (2,-1) , find the length of aside of the triangle .
Answer» ANSWER :`4sqrt(3)` UNIT

Discussion

9165.	The base of a triangle lies along the line x=a and is of length a. The area of the triangle is a^2. The locus of the third vertex is
Answer» x+a = 0 x = 0 2x- a = 0 x-a = 0 Answer :A

Discussion

9166.	Solve :y = sin x + cos x
Answer» ANSWER :` = COS X - SIN x ` .

Discussion

9167.	If 2A is not an integral multiple of pi, then show that i) cot A+tan A=2"cosec " 2A ii) cot A-tan A=2 cot2A and deduce the values of tan52 1^(@)/2 and tan37 1^(@)/2
Answer» ANSWER :`:. tan 52 (1^(0))/2 = sqrt(6) +sqrt(4) - sqrt(3) - sqrt(2)`

Discussion

9168.	Find the modulus and amplitude of (2 + 3i)/(3+2i)
Answer» ANSWER :`"TAN"^(-1) (5)/(12)`

Discussion

9169.	Which of the following sets are finite or infinite The set of positive integers greater than 100
Answer» ANSWER :it is an INFINITE SET

Discussion

9170.	A function f : R rarr R defined by f(x) = x^(2). Determine (i) range of f (ii). {x: f(x) = 4} (iii). {y: f(y) = –1}
Answer» ANSWER :{-2, 2}

Discussion

9171.	Find the middle terms in the expansions of (3 - x^3/6^7)
Answer» Answer :` :. `The REQUIRED middle TERMS are `(-105x^(9))/8AND 35/48 X^(12)`

Discussion

9172.	Find the value of a and b: (a+2, 4)= (5, 2a + b)
Answer» ANSWER :a=3, B= -2

Discussion

9173.	In the sum to infinity of the series 3+(3+x) (1)/(4) + (3+2x)(1)/(4^(2))+ ..... "is" (44)/(9) find x.
Answer» ANSWER :x=2

Discussion

9174.	Find the 7^(th) term in the expansion of (3x - (2y)/3)^(10)
Answer» ANSWER :`(4480)/3 X^(4)y^(6)`

Discussion

9175.	Assertion (A) : A and B are given points in a space. Then locus of P such that angleAPB=90^(0) is a spherewith AB as diameter. Reason(R ) : The angle in a semisphere is as right angle
Answer» Both A and R are TRUE and R is the CORRECT EXPLANATION of A Both A and R are true but R is not the correct explanation of A A is true but R is FALSE A is false but R is true Answer :a

Discussion

9176.	Compare the following statements : p, only if q.
Answer» ANSWER :All FIVE STATEMENTS are EQUIVALENTS, i.e.,all are different ways of saying. "If p, then Q."

Discussion

9177.	If the pair of lines 3x^(2)+14xy+8y^(2)=0 and 2x^(2)+5xy-12y^(2)=0 have a common line then angle between other two lines is
Answer» `pi//2` `pi//6` `pi//4` `pi//3` ANSWER :A

Discussion

9178.	Evalute : 4 ! -3 !
Answer» ANSWER :`= 6 X 3 = 18`

Discussion

9179.	Prove that the radii of the circles x^(2)+y^(2)=1,x^(2)+y^(2)-2x-4y-11=0andx^(2)+y^(2)-4x-6y-243=0 are in G.P.
Answer»

Discussion

9180.	If the lines barr=bara+lamda(barbxxbarc) and barr=barb+mu(barcxxbara) intersect each other then the condition is
Answer» `bara.barb=bara.barc` `barb.barc=barb.bara` `barc.bara=barc.barb` None Answer :C

Discussion

9181.	If 0^(@)lt theta lt 90^(@) and cos theta=(4)/(5) find the values of tan(360^(@)-theta)
Answer» ANSWER :`-3/4`

Discussion

9182.	Which term of the following sequences: sqrt3, 3, 3 sqrt3,…. Is 729?
Answer» ANSWER :`12^(TH)`

Discussion

9183.	If x ne (npi)/2, n in I and (cosx)^(sin^(2)x-3sinx+2)=1, then find the general solutions of x.
Answer» SOLUTION :As `x ne (npi)/2 rArr COSX ne 0,1,-1` So, `(cosx)^(sin^(2)x-3sinx+2) = 1 rArr sin^(2)x-3sinx+2=0` `therefore (sinx-2)(sinx-1)=0 rArr sinx=1,2` Where `sinx=2` is not POSSIBLE and `sinx=2` is not possible and `sinx=1` which is also not possible as `x ne (npi)/(2)` `therefore` no general solutions is possible. Ans.

Discussion

9184.	If y=(sqrt(x)+1/sqrt(x)).(sqrt(x)-1/sqrt(x)) then dy/dx = ….. .
Answer» ANSWER :`(x^2+1)/x^2`

Discussion

9185.	In an examination, there are three multiple choice questions and each question has four choices. Number of ways in which a student can fail to get all answers correct, is
Answer» ANSWER :`2^(100)`

Discussion

9186.	Find the sum of: 18 terms of 57 + 49 + 41 + .....,
Answer» ANSWER :198

Discussion

9187.	Sin[2Cos^(-1){Cot(2tan^(-1)x)}]=0 Find x
Answer» `pm1` `1PM SQRT(2)` `-1pmsqrt(2)` `pmsqrt(2)` Answer :A::B::C

Discussion

9188.	If X= {1, 2, 3}, if n represents any member of X, write the following sets containing numbers represented by n- 1
Answer» ANSWER :`= {0, 1, 2}`

Discussion

9189.	If X= {1, 2, 3}, if n represents any member of X, write the following sets containing numbers represented by 4n
Answer» ANSWER :`= {4, 8, 12}`

Discussion

9190.	If X= {1, 2, 3}, if n represents any member of X, write the following sets containing numbers represented by n"/"2
Answer» ANSWER :`= {(1)/(2), 1, (3)/(2)}`

Discussion

9191.	If X= {1, 2, 3}, if n represents any member of X, write the following sets containing numbers represented by n+6
Answer» ANSWER :`= {7, 8, 9}`

Discussion

9192.	Match the following sets for all sets A, B and C.
Answer» ANSWER :`I-B, II-C, III-A, IV-F, V-D, VI-E`

Discussion

9193.	If the mid points of the sides of a triangle AB, BC and CA are D(1, 2, -3), E(3, 0, 1)and F(-1,1,-4), then find the centroid of the triangle.
Answer» SOLUTION :N/A

Discussion

9194.	Find the angle between the straight lines represented by 2x^(2)+5xy+2y^(2)-5x-7y+3=0
Answer» ANSWER :`COS^(-1)((4)/(5))`

Discussion

9195.	Ellipse x^2/(25)+y^2/(9) =1 is symmetric about Y - axis.
Answer» ANSWER :FALSE STATEMENT

Discussion

9196.	If A=(2,3), B=(-2-5), C=(-4,6) and if P is a point on BC such that AP bisects the angle A, then find P.
Answer» ANSWER :`(-(22)/(7),(9)/(7))`

Discussion

9197.	Find the derivative of (x-a)(x-b) for some constants a and b
Answer» ANSWER :`2x-a-b`

Discussion

9198.	If (3,2,-1),(4,1,1) and (6,2,5) are three vertices and (4,2,2) is the centroid of a tetrahedro, find the fourth vertex to that tetrahedron.
Answer» ANSWER :3, 3, 3

Discussion

9199.	A(0,b) , B(0,0) and C(a,0) are verticies of Delta ABC. If the medians bar(AD) and bar(BE) are mutually perpendicular then …... of the following is true.
Answer» `a= (B)/(2)` `b= (a)/(2)` `ab=1` `a= PM SQRT(2) b` ANSWER :D

Discussion

9200.	Consider the complex number z_1 = 3+i and z_2 = 1+i .What is the conjugate of z_2?
Answer» ANSWER :1 - i

Discussion

Explore topic-wise InterviewSolutions in .

Using mathematical induction, the numbers a_(n)'s are defined by, a_(0) =1, a_(n+1) = 3n^(2) + n+a_(n) ( n ge 0). Then a_(n) =

Choose the incorrect pair :

If the X liney=m,x , r = 1,2,3 cut off equal intercepts on transversal line x+y=1 , then 1+m_1 ,1+m_2 , 1+m_3 are in

If tan theta = n tan phi then the maximum value of tan^(2)(theta-phi) is equal to

The principal solution of sintheta=-(1)/(2) is

A and B are not singleton sets. n(A xx B)= 21. If A sub B" then "n(B)="……….".

IfP(x) =ax^3+bx^2+cx+d and P(0) = 4, P^(1)(0) = 3,P^(11)(0)=4,P^(111)(0) = 6then arrange the values of a , b , c , d inthe descending order of their values

Iftan theta + tan ( theta + (pi)/(3))+ tan ( theta + (2pi)/(3))=3 , then which of the following is equal to 1 ?

A flag staff of the height (a-b) stands on the top of a tower subtends the same angle at the point on the horizontal plalne through thefoot of the tower which are at distant a and b from the tower. The height of the tower is

If tan 20^@ =p , " then " (tan 160^@ - tan 110^(@))/(1+ tan 160^(@) tan 110^(@))=

Prove that sin ""(pi)/(9) sin ""(2pi)/(9) sin ""( 3pi)/(9) sin ""(4pi)/(9) = (3)/(16).

(d)/(dx) {cos ^(2) [Tan ^(-1) (sin Cot ^(-1)) ]}=

One side of an equilateral triangle is the line 5y=12x=3andits centroid is at (2,-1) , find the length of aside of the triangle .

The base of a triangle lies along the line x=a and is of length a. The area of the triangle is a^2. The locus of the third vertex is

Solve :y = sin x + cos x

If 2A is not an integral multiple of pi, then show that i) cot A+tan A=2"cosec " 2A ii) cot A-tan A=2 cot2A and deduce the values of tan52 1^(@)/2 and tan37 1^(@)/2

Find the modulus and amplitude of (2 + 3i)/(3+2i)

Which of the following sets are finite or infinite The set of positive integers greater than 100

A function f : R rarr R defined by f(x) = x^(2). Determine (i) range of f (ii). {x: f(x) = 4} (iii). {y: f(y) = –1}

Find the middle terms in the expansions of (3 - x^3/6^7)

Find the value of a and b: (a+2, 4)= (5, 2a + b)

In the sum to infinity of the series 3+(3+x) (1)/(4) + (3+2x)(1)/(4^(2))+ ..... "is" (44)/(9) find x.

Find the 7^(th) term in the expansion of (3x - (2y)/3)^(10)

Assertion (A) : A and B are given points in a space. Then locus of P such that angleAPB=90^(0) is a spherewith AB as diameter. Reason(R ) : The angle in a semisphere is as right angle

Compare the following statements : p, only if q.

If the pair of lines 3x^(2)+14xy+8y^(2)=0 and 2x^(2)+5xy-12y^(2)=0 have a common line then angle between other two lines is

Evalute : 4 ! -3 !

Prove that the radii of the circles x^(2)+y^(2)=1,x^(2)+y^(2)-2x-4y-11=0andx^(2)+y^(2)-4x-6y-243=0 are in G.P.

If the lines barr=bara+lamda(barbxxbarc) and barr=barb+mu(barcxxbara) intersect each other then the condition is

If 0^(@)lt theta lt 90^(@) and cos theta=(4)/(5) find the values of tan(360^(@)-theta)

Which term of the following sequences: sqrt3, 3, 3 sqrt3,…. Is 729?

If x ne (npi)/2, n in I and (cosx)^(sin^(2)x-3sinx+2)=1, then find the general solutions of x.

If y=(sqrt(x)+1/sqrt(x)).(sqrt(x)-1/sqrt(x)) then dy/dx = ….. .

In an examination, there are three multiple choice questions and each question has four choices. Number of ways in which a student can fail to get all answers correct, is

Find the sum of: 18 terms of 57 + 49 + 41 + .....,

Sin[2Cos^(-1){Cot(2tan^(-1)x)}]=0 Find x

If X= {1, 2, 3}, if n represents any member of X, write the following sets containing numbers represented by n- 1

If X= {1, 2, 3}, if n represents any member of X, write the following sets containing numbers represented by 4n

If X= {1, 2, 3}, if n represents any member of X, write the following sets containing numbers represented by n"/"2

If X= {1, 2, 3}, if n represents any member of X, write the following sets containing numbers represented by n+6

Match the following sets for all sets A, B and C.

If the mid points of the sides of a triangle AB, BC and CA are D(1, 2, -3), E(3, 0, 1)and F(-1,1,-4), then find the centroid of the triangle.

Find the angle between the straight lines represented by 2x^(2)+5xy+2y^(2)-5x-7y+3=0

Ellipse x^2/(25)+y^2/(9) =1 is symmetric about Y - axis.

If A=(2,3), B=(-2-5), C=(-4,6) and if P is a point on BC such that AP bisects the angle A, then find P.

Find the derivative of (x-a)(x-b) for some constants a and b

If (3,2,-1),(4,1,1) and (6,2,5) are three vertices and (4,2,2) is the centroid of a tetrahedro, find the fourth vertex to that tetrahedron.

A(0,b) , B(0,0) and C(a,0) are verticies of Delta ABC. If the medians bar(AD) and bar(BE) are mutually perpendicular then …... of the following is true.

Consider the complex number z_1 = 3+i and z_2 = 1+i .What is the conjugate of z_2?