14949 + Interview Questions in Maths in Class 11 Page 281 InterviewSolution

14001.	From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person can not hold more than one position?
Answer» ANSWER :56

Discussion

14002.	The point (0,5) is closer to the curve x^(2)=2y at
Answer» `(2sqrt(2),0)` `(0,0)` `(2,2)` `(1,1)` ANSWER :D

Discussion

14003.	Let f(x)={{:(((x-1)(6x-1))/(2x-1)",",ifx ne(1)/(2)),(0",",ifx=(1)/(2)):} Then at x=(1)/(2) , which of the following is/are not true ?
Answer» f has a local maxima f has a local minima f has an inflection point f has a REMOVABLE DISCONTINUITY ANSWER :A::B::D

Discussion

14004.	Write the ascending order of areas of the triangles formed with coordinate axes and the following lines (A) x+y+3=0 "" (B) x+y+1=0"" (C) 2x+y-6=0""(D) 4x+3y-12=0
Answer» A,B,C,D B,A,C,D C,A,B,D B,D,A,C Answer :D

Discussion

14005.	the rangeof cos (x+ (pi)/(6)) cos (x-(pi)/(6)) is
Answer» `[-(1)/(4),(1)/(4)]` `[-(3)/(4),(3)/(4)]` `[-(1)/(4),(3)/(4)]` `[-(1)/(2),(1)/(2)]` ANSWER :3

Discussion

14006.	Given the ellipse 36x^(2)+100y^(2)=3600, find the equations and the lengths of the focal radii drawn through the point (8, 18/5).
Answer» ANSWER :EQUATION are `x-8=0, 9x-40y+72=0`; LENGTHSOF the FOCAL RADII are `18/5, 82/5`

Discussion

14007.	Write Negation of the following statements: Christmas is celebrated on 25th December.
Answer» ANSWER :Charactmas is not a CELEBRATED on 25TH DECEMBER.

Discussion

14008.	Which term is negative for a sequence 19, 18(1)/(5), 17(2)/(5),….?
Answer» ANSWER :`25^(TH)` TERM

Discussion

14009.	If alpha=3sin^(-1)(6/11) and beta=3 cos^(-1)(4/9) where the inverse trigoometric functions take only the principal values, then the correct options (s) is (are)
Answer» `COS betagt0` `sinbetalt0` `cos(ALPHA+beta)gt0` `cos alpha LT0` ANSWER :B::C::D

Discussion

14010.	If y = tan^(-1)((2^(x))/(1 + 2^(2x + 1))) then (dy)/(dx) at x = 0 is
Answer» `1` `2` `1 N 2` `-1/10 "LOG" 2` ANSWER :D

Discussion

14011.	If A,B,C are angles of a tringle such that A is obtuse then
Answer» `tanA tanB GT1` `tan B tan C lt1` `tan C tan A GT 1` 776 Answer :B

Discussion

14012.	Find the derivative of (x-1)(x-2)
Answer» ANSWER :`2x-3`

Discussion

14013.	Identify the quantifier in the following statements and write thenegation of the statements. There exists a capital for every state in India.
Answer» ANSWER :The quantifier for the GIVEN statement is ' there exists '. It is true Negation of this statement is ~p : There exists a state in INDIA which does not have a CAPITAL.

Discussion

14014.	Identify the quantifier in the following statements and write thenegation of the statements. There exists a number which is equal to its square.
Answer» Answer :The quantifier for the given STATEMENT is 'there EXISTS' . It is TRUE . Negation or the given statement is ~p : There does not EXIST a NUMBER which is equal to its square.

Discussion

14015.	A, B and C are subset of universal set cup. If A= {2, 4, 6, 8, 12, 20}, B= {3, 6, 12, 15} and C= {5, 10, 15, 20} and cup is the set of all whole numbers, draw a Venn diagram showing the relation of cup, A, B and C.
Answer» ANSWER :`(##KPK_AIO_MAT_XI_C01_E12_025_A01##)`

Discussion

14016.	For real x, let f(x)=x^(3)+5x+1, then
Answer» F is one-one but not ONTO R f is onto R but one-one f is one-one and onto R f is neither one-one nor onto R Answer :C

Discussion

14017.	The value of 'c' in Lagrange's mean value theorem for f(x) = x^(3)-2x^(2) - x + 4 in [ 0,1 ] is
Answer» `1//3` `1//2` `2//3` 1 Answer :A

Discussion

14018.	Convert the following complex number in the polar form : ((1+i)^(13))/((1-i)^(7))
Answer» ANSWER :`8(cospi+isinpi)`

Discussion

14019.	There are two stations P,Q due north, due south of a tower of height 15 metres. The angle of depression of P and Q as seen from topa tower are cot^(-1)"" (12)/5, sin^(-1)"" (3)/5. The distance between P and Q is -------
Answer» `48` `56` `65` `25` ANSWER :B

Discussion

14020.	If the sidesof a triangleare 5, 7, 8then itsarea is
Answer» ` 10 SQRT3` ` 3sqrt(10)` ` (3)/(SQRT(10))` `( 10 )/(sqrt3)` ANSWER :A

Discussion

14021.	If A!=A^(2)=I then \|I+A\|=
Answer» 1 `-1` 0 2 Answer :C

Discussion

14022.	Let x, y, z be elementsfrom interval [0, 2 pi] satisfying the inequality ( 4 + sin 4 x) ( 2 + cot^(2) y) ( 1 + sin^(4 )z) le 12 sin ^(2) zthen
Answer» The NUMBER of ordered pairs (z, x) is 8 The number of ordered pairs (y, z) such that z = y is 2 The number of ORDEREDPAIRS (x, y) is 4 The number of ordered pairs ( y , z) is 6 Answer :A::B

Discussion

14023.	Statement I : If cos ((pi)/(3) cos 2 pi x)= sqrt(3) then the general solution of theequation is x = n pm (1)/(6), n in I Statement II : If tan P theta = tan Q theta , then the value of theta from an A.P with common difference (pi)/(P - Q) Which of the above statements are correct?
Answer» Only I Only II Both I and II neither I or II Answer :C

Discussion

14024.	A person riding a car4 sees a fallen tree in the road at a distance of 40 meters away from him. He applies breaks at the rate of 16 metres/"second"^(2). If the car was moving at a speed of 32 m/s when the break is applied, would it stop before hitting the fallen tree.
Answer» Answer :`because` The CAR stops at a DISTANCE of 8 METERS to the FALLEN TREE.

Discussion

14025.	Define greatest integer function. Write its domain and range.
Answer» ANSWER :`D_(F)=R,R_(f)=Z`

Discussion

14026.	The vertices of a triangle are A(3,4),B(-4,3),C(4,3). The altitude from A on B meets the circumcircle at (3,-4).
Answer» ANSWER :E(3,-4)

Discussion

14027.	Resolve into partial fractions(1)/((x+1)(x+2)(x+3)
Answer» ANSWER :`(1)/(2(x+3)`

Discussion

14028.	Express each of the following complex number in the form a+ib: (5-i)((1)/(8)i)
Answer» ANSWER :`(5)/(8)+0.i`

Discussion

14029.	Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Equation of horizontal and vertical line passes from point (-5,6).
Answer» ANSWER :`X + 5 = 0, y - 6 = 0`

Discussion

14030.	If the four straight lines ax+by+p=0, ax+by+q=0, cx+dy+r=0 and cx+dy+s=0 form a prallelogram. Show that the area of the parallelogram so formed is \|((p-q)(r-s))/(bc-ad)\|
Answer» ANSWER :`\|((p-q)(r-s))/(bc-ad)\|`

Discussion

14031.	Find the distance of the line 4x - y = 0from the point P (4, 1) measured along the line making an angle of 135^(@)with the positive x- axis.
Answer» ANSWER :`3sqrt2` UNITS.

Discussion

14032.	Find the vector equation and its cartesian form of the plane containing the points (2, 3, -1) ( 4, 5, 2), (3, 6, 5).
Answer» ANSWER :`[BARR.(2bari+3barj-bark)(2bari+2barj+3barKbari+3barJ+6bark]=03x-9y+4z+25=0`

Discussion

14033.	If cot^(-1)((n^(2)-10n+21.6)/(pi))gt(pi)/6, n in Nthen n can be
Answer» 3 2 4 8 Answer :A::C::D

Discussion

14034.	A wire of length l is cut into two parts which are bent respectively in the form of a square and a circle. What are the lengths of the pieces of the wire respectively so that the sum of the areas is the least.
Answer» ANSWER :`(PI L)/(pi + 4), (4L)/(pi + 4)`

Discussion

14035.	^nC_8=^nC_8 , n=…….
Answer» 17 12 13 14 Answer :A

Discussion

14036.	We wish toselect 6 persons from 8 persons, but if the person A is chosen, then B must be chosen. Then the number of ways the selection can be made is
Answer» 15 7 22 20 Answer :C

Discussion

14037.	Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (x+secx)(x-tanx)
Answer» ANSWER :`(X+secx)(1-sec^(2)x)+(x-TANX)(1+secx tanx)`

Discussion

14038.	If A+B=pi//2 thentan B+ 2 tan (A-B)=
Answer» CosA SinA SINB SinC TanA CotA Answer :C

Discussion

14039.	Write each of the statement in the form if p, then q: r: You can access the website only if you pay a subsciption fee.
Answer» ANSWER :If you ACCESS the WEBSITE, then you PAY subscription fee.

Discussion

14040.	If vec(a) + 2vec(b) + 4 vec(c )= vec(0), then vec(a) xx vec(b) + vec(b) xx vec(c )+ vec(c )xx vec(a)=
Answer» 0 `1(VEC(b) XX vec(C ))` `2(vec(b) xx vec(c ))` `7(vec(b) xx vec(c ))` Answer :D

Discussion

14041.	if sqrt(3) sin x +cosxis maximum then x=
Answer» `(PI)/(4)` `(pi)/(3)` `(2pi)/(5)` `(pi)/(2)` Answer :2

Discussion

14042.	To pass an examinations a students has to pass in each of the 3 papers. In how many ways can a students fail in the examination?
Answer» ANSWER :` 2^(3)-1 = ` WAYS

Discussion

14043.	The range of Sin^(-1)x-Cos^(-1)x is
Answer» `[(-3pi)/2,(PI)/2]` `[(-5PI)/3,(pi)/3]` `[(-3pi)/2,pi]` `[0,pi]` ANSWER :A

Discussion

14044.	Evaluate lim_(xto(pi)/(2))(tan2x)/(x-(pi)/(2))
Answer» ANSWER :2

Discussion

14045.	Find the sum of the series 3xx5+ 5xx7+ 7xx9+ .. to n terms
Answer» ANSWER :`(N(4N^(2)+18n+23))/(3)`

Discussion

14046.	If y = sqrt(a^(3x + 1) +sqrt(a^(3x + 1)+ sqrt(a^(3x +1) + ...." to "oo))) then (dy)/(dx) =
Answer» `(a^(3X + 1)."log a")/((2Y - 1))` `(3.a^(3x + 1)."log a")/((2y - 1))` `(3.a^(3x + 1)."log a")/((2y + 1))` `(a^(3x + 1)."log a")/((2y + 1))` ANSWER :B

Discussion

14047.	Find Lt_(xto0)((sinx-x+x^(3)/6)/x^(5))
Answer» ANSWER :`1/120`

Discussion

14048.	Find the mean deviation using median:
Answer» SOLUTION : Here, `N=50impliesN/2=25`

Discussion

14049.	If alpha , beta are complementary angles, sin alpha = 3//5 , thensin alpha cos beta - cos alphasin beta =
Answer» `(7)/(25)` `- (7)/(25)` `(25)/(7)` `- (25)/(7)` ANSWER :B

Discussion

14050.	The volume of a ball increases at 2pic.c//sec. The rate of increase of radius when the volume is 288pi c.cms is
Answer» 1/36 cm/sec 1/72 cm/sec 1/18 cm/sec 1/9 cm/sec Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

From a committee of 8 persons, in how many ways can we choose a chairman﻿ and a vice chairman assuming one person can not hold more than one position?﻿

The point (0,5) is closer to the curve x^(2)=2y at

Let f(x)={{:(((x-1)(6x-1))/(2x-1)",",ifx ne(1)/(2)),(0",",ifx=(1)/(2)):} Then at x=(1)/(2) , which of the following is/are not true ?

Write the ascending order of areas of the triangles formed with coordinate axes and the following lines (A) x+y+3=0 "" (B) x+y+1=0"" (C) 2x+y-6=0""(D) 4x+3y-12=0

the rangeof cos (x+ (pi)/(6)) cos (x-(pi)/(6)) is

Given the ellipse 36x^(2)+100y^(2)=3600, find the equations and the lengths of the focal radii drawn through the point (8, 18/5).

Write Negation of the following statements: Christmas is celebrated on 25th December.

Which term is negative for a sequence 19, 18(1)/(5), 17(2)/(5),….?

If alpha=3sin^(-1)(6/11) and beta=3 cos^(-1)(4/9) where the inverse trigoometric functions take only the principal values, then the correct options (s) is (are)

If y = tan^(-1)((2^(x))/(1 + 2^(2x + 1))) then (dy)/(dx) at x = 0 is

If A,B,C are angles of a tringle such that A is obtuse then

Find the derivative of (x-1)(x-2)

Identify the quantifier in the following statements and write thenegation of the statements. There exists a capital for every state in India.

Identify the quantifier in the following statements and write thenegation of the statements. There exists a number which is equal to its square.

A, B and C are subset of universal set cup. If A= {2, 4, 6, 8, 12, 20}, B= {3, 6, 12, 15} and C= {5, 10, 15, 20} and cup is the set of all whole numbers, draw a Venn diagram showing the relation of cup, A, B and C.

For real x, let f(x)=x^(3)+5x+1, then

The value of 'c' in Lagrange's mean value theorem for f(x) = x^(3)-2x^(2) - x + 4 in [ 0,1 ] is

Convert the following complex number in the polar form : ((1+i)^(13))/((1-i)^(7))

There are two stations P,Q due north, due south of a tower of height 15 metres. The angle of depression of P and Q as seen from topa tower are cot^(-1)"" (12)/5, sin^(-1)"" (3)/5. The distance between P and Q is -------

If the sidesof a triangleare 5, 7, 8then itsarea is

If A!=A^(2)=I then |I+A|=

Let x, y, z be elementsfrom interval [0, 2 pi] satisfying the inequality ( 4 + sin 4 x) ( 2 + cot^(2) y) ( 1 + sin^(4 )z) le 12 sin ^(2) zthen

Statement I : If cos ((pi)/(3) cos 2 pi x)= sqrt(3) then the general solution of theequation is x = n pm (1)/(6), n in I Statement II : If tan P theta = tan Q theta , then the value of theta from an A.P with common difference (pi)/(P - Q) Which of the above statements are correct?

A person riding a car4 sees a fallen tree in the road at a distance of 40 meters away from him. He applies breaks at the rate of 16 metres/"second"^(2). If the car was moving at a speed of 32 m/s when the break is applied, would it stop before hitting the fallen tree.

Define greatest integer function. Write its domain and range.

The vertices of a triangle are A(3,4),B(-4,3),C(4,3). The altitude from A on B meets the circumcircle at (3,-4).

Resolve into partial fractions(1)/((x+1)(x+2)(x+3)

Express each of the following complex number in the form a+ib: (5-i)((1)/(8)i)

Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Equation of horizontal and vertical line passes from point (-5,6).

If the four straight lines ax+by+p=0, ax+by+q=0, cx+dy+r=0 and cx+dy+s=0 form a prallelogram. Show that the area of the parallelogram so formed is |((p-q)(r-s))/(bc-ad)|

Find the distance of the line 4x - y = 0from the point P (4, 1) measured along the line making an angle of 135^(@)with the positive x- axis.

Find the vector equation and its cartesian form of the plane containing the points (2, 3, -1) ( 4, 5, 2), (3, 6, 5).

If cot^(-1)((n^(2)-10n+21.6)/(pi))gt(pi)/6, n in Nthen n can be

A wire of length l is cut into two parts which are bent respectively in the form of a square and a circle. What are the lengths of the pieces of the wire respectively so that the sum of the areas is the least.

^nC_8=^nC_8 , n=…….

We wish toselect 6 persons from 8 persons, but if the person A is chosen, then B must be chosen. Then the number of ways the selection can be made is

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (x+secx)(x-tanx)

If A+B=pi//2 thentan B+ 2 tan (A-B)=

Write each of the statement in the form if p, then q: r: You can access the website only if you pay a subsciption fee.

If vec(a) + 2vec(b) + 4 vec(c )= vec(0), then vec(a) xx vec(b) + vec(b) xx vec(c )+ vec(c )xx vec(a)=

if sqrt(3) sin x +cosxis maximum then x=

To pass an examinations a students has to pass in each of the 3 papers. In how many ways can a students fail in the examination?

The range of Sin^(-1)x-Cos^(-1)x is

Evaluate lim_(xto(pi)/(2))(tan2x)/(x-(pi)/(2))

Find the sum of the series 3xx5+ 5xx7+ 7xx9+ .. to n terms

If y = sqrt(a^(3x + 1) +sqrt(a^(3x + 1)+ sqrt(a^(3x +1) + ...." to "oo))) then (dy)/(dx) =

Find Lt_(xto0)((sinx-x+x^(3)/6)/x^(5))

Find the mean deviation using median:

If alpha , beta are complementary angles, sin alpha = 3//5 , thensin alpha cos beta - cos alphasin beta =

The volume of a ball increases at 2pic.c//sec. The rate of increase of radius when the volume is 288pi c.cms is

From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person can not hold more than one position?