14949 + Interview Questions in Maths in Class 11 Page 267 InterviewSolution

13301.	If f(x)=\|x+100\|+x^(2), test whether f'(100) exists.
Answer» ANSWER :F'(X) does not EXIST

Discussion

13302.	If y = sin^(2) (cot^(-1) sqrt((1 +x)/(1 - x))), " then " (dy)/(dx) =
Answer» `1` `-1` `1/2` `(-1)/2` ANSWER :D

Discussion

13303.	From a point P perpendiculars PM and PN are drawn upon x, y axes respectively. If MN passes through a fixed point (a, b) then the locus ofP is
Answer» `(X)/(a)+(y)/(B)=1` `(x)/(a)-(y)/(b)=1` `(a)/(x)+(b)/(y)=1` `(a)/(x)-(b)/(y)=1` ANSWER :3

Discussion

13304.	……..of the following is the equation of ellipse with focus (-1, 1) eccentricity (1)/(2) and equation of directrix is x - y + 3 = 0.
Answer» `7x^(2) + 2XY + 7y^(2) + 10x - 10y + 7 = 0` `7x^(2) - 2xy + 7y^(2) - 10x + 10y + 7 = 0` `7x^(2) - 2xy + 7y^(2) - 10x - 10y - 7 = 0` `7x^(2) - 2xy + 7y^(2) + 10x + 10y - 7 = 0` ANSWER :A

Discussion

13305.	Evaluate the following: (i) (2 + sqrt(5) )^(5) + (2 - sqrt(5) )^(5) (ii) ( sqrt(3) + 1)^(5) - ( sqrt(3) - 1)^(5) Hence, show in (ii), without using tables, that the value of ( sqrt(3) + 1)^(5) lies between 152 and 153.
Answer» ANSWER :(i) 1364 (II) 152

Discussion

13306.	Which of the following statements is true I : In a DeltaABC if a= R tan A then b^(2)+c^(2)=bc+a^(2) II.In a DeltaABC if a sin A= c cos B+ b cos C then the triangle is right angled
Answer» onlyI only II both I and II neither I nor II Answer :C

Discussion

13307.	The value of theta which satisfy r sin theta=3 and r=4(1+sin theta), 0 le theta le 2 pi
Answer» `(PI)/6` `(pi)/6,(5pi)/6` `(5pi)/6` `(pi)/3, (2pi)/3` Answer :B

Discussion

13308.	If A, B and C are any three sets, then A xx (B-C) is equal to
Answer» `(A xxB ) UU (A XXC)` `(A xxB) NN (A xxC)` `(A xxB)- (A xxC)` `(A xxB) -(A xxC)` ANSWER :C

Discussion

13309.	If the sum of n terms of an A.P. is 3n^2 + 5nand its m^("th")term is 164, find the value of m .
Answer» ANSWER :27

Discussion

13310.	If tan alpha, tan beta are the roots of the equation x^(2)+px+q=0then sin^(2) (alpha+ beta)+ p sin(alpha+ beta) (cos+beta) +q cos^(2)(alpha+ beta)=
Answer» 0 1 p q Answer :D

Discussion

13311.	Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces: 8 . . . A
Answer» ANSWER :`in`

Discussion

13312.	If theta is the angle between a line barr = bara+tbarb " and a plane " bara.barm = d " then " sin theta=
Answer» `(barb.barm)/(ABSBARB absbarm)` `barb.barm` `90^(@)` `45^(@)` ANSWER :A

Discussion

13313.	(sin 85^(@)-sin 25^(@))/(cos 65^(@))=
Answer» 2 `-1` 1 0 Answer :C

Discussion

13314.	Find all the points of local maxima and local minima of the function f(x) = x^(3) - 6x^(2) + 12 x - 8.
Answer» ANSWER :2

Discussion

13315.	Find the area of the triangle formed by the lines joining the vertex of the parabola x^2 = 12y to the ends of its latus rectum.
Answer» ANSWER :`18` SQ UNITS

Discussion

13316.	The perimeter of a Delta ABC is 6 times the A.M. of the sines of its angles. If the side 'a' is 1, then the angle A is
Answer» `(PI)/(6)` `(pi)/(4)` `(pi)/(3)` `(pi)/(2)` ANSWER :A

Discussion

13317.	What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of these (i) four cards are of the same suit, (ii) four cards belong to four different suits, (iii) are face cards, (iv) two are red cards and two are black cards, (v) cards are of the same colour?
Answer» Answer :(i) 2860, (II) ` 13^4`, (iii) 495, (iv) 105625, (V) 29900

Discussion

13318.	Find the sum of infinity of the G.P., (-5)/(4), (5)/(16), (-5)/(64),..
Answer» ANSWER :-1

Discussion

13319.	A line l passing through the origin is perpendicular to the line l _(1) : (3 + 1) hati + (-1 + 2 i) hatj + (4+ 2i ) hatk, -oo lt t lt oo , l _(2) : (3 + 2s ) hati + (3 + 2s ) hatj + (2 + s ) hatk, -oo lt s lt oo, Then the coordinate (s) of the point (s) on l _(2) at a distnce of sqrt17 from the point of intersection l and l _(1) is (are)
Answer» `((7)/(3),(7)/(3), (5)/(3))` `(-1,-1,0)` `(1,1,1)` `((7)/(9) , (7)/(9) , (8)/(9))` Answer :B::D

Discussion

13320.	Let f(x)=(x-1)^(4)(x-2)^(n), n in N.. Then f(x) has
Answer» a LOCAL maximum at x=1 if n is odd a local maximum at x=1 if n is even a local minimum at x=2 if n is even a local maximum at x=2 IFN is odd Answer :A::D

Discussion

13321.	If R in R : f is defined by f(x)=(x^(2)-2x+1)/(x^(2)+x+1) verify whether f is one-one or not.
Answer» ANSWER :not

Discussion

13322.	X and Z - axis together makes Y plane.
Answer» ANSWER :FALSE STATEMENT

Discussion

13323.	Let ABC be a triangle. Also, let h_(a) be the length of the altitude from A, h has a similar meaning Given a le h_(a) and b lt h_(b) Statement-1 a:b:c=1:1: sqrt(2) Statement - 2 : In any triangle, the length of an altitude does not exceed that of the corresponding median.
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 :B

Discussion

13324.	Evaluate the following limits : Lim_( x to 0) (x^(3) cos x)/( 1 - cos x)
Answer» ANSWER :2

Discussion

13325.	If there are 20 steamers plying between places A and B, in how many ways could the round trip from A be made if the return was made on :(i) the same steamer(ii)a different steamer ?
Answer» ANSWER :(i) 20(II) 380

Discussion

13326.	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): (4x+5sinx)/(3x+7cosx)
Answer» ANSWER :`(35+15x COS X+28 co x+28x SIN x-15 sinx)/((3x+7 cos x)^(2))`

Discussion

13327.	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)/(1+tanx)
Answer» ANSWER :`(1+tanx-X SEC^(2)x)/((1+tanx)^(2))`

Discussion

13328.	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): (1)/(ax^(2)+bx+c)
Answer» ANSWER :`(-(2ax+b))/((AX^(2)+bx+c)^(2))`

Discussion

13329.	An urn contains 3 white, 4 red and 5 black balls. Two balls are drawn one by the one without replacement. What is the probability that at least one ball is black?
Answer»

Discussion

13330.	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): (px+q)((r)/(x)+s)
Answer» ANSWER :`(-QR)/(X^(2))+PS`

Discussion

13331.	sin h^(-1)(2^((3)/(2))) =
Answer» `log_(e) (2+ sqrt(18))` `log_(e)(3+sqrt(8))` `log_(e)(3-sqrt(8))` `log_(e) (sqrt(8) + sqrt(27))` ANSWER :B

Discussion

13332.	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): (sinx+cosx)/(sinx-cosx)
Answer» ANSWER :`(-2)/((sinx-cosx)^(2))`

Discussion

13333.	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): 4sqrtx-2
Answer» ANSWER :`(2)/(SQRTX)`

Discussion

13334.	Eachof the digits 1,1,2,3,3and 4 is written on separate card. The sixcards are then laidout in a rowto form a 6-digit number. (i) How many distinct 6-digit numbersare there ? (ii) Howmanyof these 6-digit numbersare even ? (iii) How manyof these6-digit numbersare divisible by 4 ?
Answer» Answer :(i)180 (II) 60 (III) 30

Discussion

13335.	Write contrapositive and converse of the following statements: If Mohan work hard continuously then he is good student.
Answer» ANSWER :If Mohan WORKS hard then he is GOOD student.

Discussion

13336.	The numbers of rectangle formed by m horizontal and n vertical line are ..........
Answer» ANSWER :`((m),(2)) ((N),(2))`

Discussion

13337.	If (2sinalpha)/(1+cosalpha+sinalpha)=y, then prove that (1-cosalpha+sinalpha)/(1+sinalpha) is also equal to y.
Answer» ANSWER :y

Discussion

13338.	The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept -4. Then a possible value of k is
Answer» 1 2 -2 -4 Answer :D

Discussion

13339.	Which of the following are sets ? Justify your answer. The collection of questions in this Chapter.
Answer» ANSWER :it is a SET

Discussion

13340.	i) Show that barixx(baraxxbari)+barjxx(baraxxbarj)+barkxx(baraxxbark)=2bara ii) If barixx(barrxxbari)+barjxx(barrxxbarj)+barkxx(barrxxbark)=baraxxbarb then find barr interms of bara and barb
Answer» ANSWER :`(BARAXXBARB)/2`

Discussion

13341.	If f: [2, oo) rarr B defined by f(x)=x^(2)-4x+5 is a bijection, then B=
Answer» `[0, OO)` `[1, oo)` `[4, oo)` `[5, oo)` Answer :B

Discussion

13342.	If the line (x-1)/2=(y-2)/3=t intersects the line x+y=8 then t=
Answer» 1 2 3 4 Answer :A

Discussion

13343.	AA n in , 1+2x + 3x^(2) + ….+ n.x^(n-1) = (x in R, x ne 1)
Answer» `( 1 - ( N+1) x^(n) + n.x^(n+1) )/( ( 1-x)^2)` `((n+1)x^n)/( (1-x)^2) ` `(1- (n+1) x^n + n.x^(n+1))/( (1+x)^2)` `((n-1)x^n)/( (1+x)^2)` ANSWER :A::B

Discussion

13344.	The number of values of theta in the interval (-(pi)/2, (pi)/2) satistying the equation (sqrt(3))^(sec^(2)theta)=tan^(4) theta+2tan^(2) theta is
Answer» 2 4 0 1 Answer :A

Discussion

13345.	If a gt 1. Then the value of underset(x to oo) (Lt)(a^(sqrt(x))-a^(1//sqrt(x)))/(a^(sqrt(x))+a^(1//sqrt(x))) is
Answer» 1 0 2 None of these Answer :A

Discussion

13346.	If (l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)) are d.c's of two lines then find the value of (l_(1)m_(2)-l_(2)m_(1))^(2)+(m_(1)n_(2)-n_(1)m_(2))^(2)+(n_(1)l_(2)-n_(2)l_(1))^(2)+(l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2))^(2)
Answer» 3 2 1 4 Answer :C

Discussion

13347.	Without using tables, give the value of each of the following : cos330^(@)
Answer» ANSWER :`-SQRT(3)`

Discussion

13348.	If f : R to R such thatf(x- f(y))= f( f(y) ) +x f (y)+f(x)- 1 AA , y in Rthen f(x) is
Answer» `1+ (x^(2))/(4)` `1- (x^(2))/(2)` `1+ (x^(2))/(2)` `1-(x^(2))/(4)` Answer :B

Discussion

13349.	If 2/11 Is the probability of an event, what is the probability of the event 'not A'.
Answer» ANSWER :`9/11`

Discussion

13350.	Assertion :lim_(xrarr0)sin(1/x) =0 Reason: If f,g,h :I le Rsuch that g(x) le f(x) le h(x)for all x in a deleted neighbouhood of x_o contained in I and if lim_(xrarr0)g(x)=lim_(xrarrx_o)h(x)=l.Then lim_(xrarrx_o)f(x)=l.[sandwich theorem]
Answer» R is the BEST tool to prove A R is not enough to prove A A is not true both A and R are incorrect Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

If f(x)=|x+100|+x^(2), test whether f'(100) exists.

If y = sin^(2) (cot^(-1) sqrt((1 +x)/(1 - x))), " then " (dy)/(dx) =

From a point P perpendiculars PM and PN are drawn upon x, y axes respectively. If MN passes through a fixed point (a, b) then the locus ofP is

……..of the following is the equation of ellipse with focus (-1, 1) eccentricity (1)/(2) and equation of directrix is x - y + 3 = 0.

Evaluate the following: (i) (2 + sqrt(5) )^(5) + (2 - sqrt(5) )^(5) (ii) ( sqrt(3) + 1)^(5) - ( sqrt(3) - 1)^(5) Hence, show in (ii), without using tables, that the value of ( sqrt(3) + 1)^(5) lies between 152 and 153.

Which of the following statements is true I : In a DeltaABC if a= R tan A then b^(2)+c^(2)=bc+a^(2) II.In a DeltaABC if a sin A= c cos B+ b cos C then the triangle is right angled

The value of theta which satisfy r sin theta=3 and r=4(1+sin theta), 0 le theta le 2 pi

If A, B and C are any three sets, then A xx (B-C) is equal to

If the sum of n terms of an A.P. is 3n^2 + 5nand its m^("th")term is 164, find the value of m .

If tan alpha, tan beta are the roots of the equation x^(2)+px+q=0then sin^(2) (alpha+ beta)+ p sin(alpha+ beta) (cos+beta) +q cos^(2)(alpha+ beta)=

Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces: 8 . . . A

If theta is the angle between a line barr = bara+tbarb " and a plane " bara.barm = d " then " sin theta=

(sin 85^(@)-sin 25^(@))/(cos 65^(@))=

Find all the points of local maxima and local minima of the function f(x) = x^(3) - 6x^(2) + 12 x - 8.

Find the area of the triangle formed by the lines joining the vertex of the parabola x^2 = 12y to the ends of its latus rectum.

The perimeter of a Delta ABC is 6 times the A.M. of the sines of its angles. If the side 'a' is 1, then the angle A is

Find the sum of infinity of the G.P., (-5)/(4), (5)/(16), (-5)/(64),..

Let f(x)=(x-1)^(4)(x-2)^(n), n in N.. Then f(x) has

If R in R : f is defined by f(x)=(x^(2)-2x+1)/(x^(2)+x+1) verify whether f is one-one or not.

X and Z - axis together makes Y plane.

Let ABC be a triangle. Also, let h_(a) be the length of the altitude from A, h has a similar meaning Given a le h_(a) and b lt h_(b) Statement-1 a:b:c=1:1: sqrt(2) Statement - 2 : In any triangle, the length of an altitude does not exceed that of the corresponding median.

Evaluate the following limits : Lim_( x to 0) (x^(3) cos x)/( 1 - cos x)

If there are 20 steamers plying between places A and B, in how many ways could the round trip from A be made if the return was made on :(i) the same steamer(ii)a different steamer ?

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): (4x+5sinx)/(3x+7cosx)

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)/(1+tanx)

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): (1)/(ax^(2)+bx+c)

An urn contains 3 white, 4 red and 5 black balls. Two balls are drawn one by the one without replacement. What is the probability that at least one ball is black?

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): (px+q)((r)/(x)+s)

sin h^(-1)(2^((3)/(2))) =

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): (sinx+cosx)/(sinx-cosx)

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): 4sqrtx-2

Eachof the digits 1,1,2,3,3and 4 is written on separate card. The sixcards are then laidout in a rowto form a 6-digit number. (i) How many distinct 6-digit numbersare there ? (ii) Howmanyof these 6-digit numbersare even ? (iii) How manyof these6-digit numbersare divisible by 4 ?

Write contrapositive and converse of the following statements: If Mohan work hard continuously then he is good student.

The numbers of rectangle formed by m horizontal and n vertical line are ..........

If (2sinalpha)/(1+cosalpha+sinalpha)=y, then prove that (1-cosalpha+sinalpha)/(1+sinalpha) is also equal to y.

The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept -4. Then a possible value of k is

Which of the following are sets ? Justify your answer. The collection of questions in this Chapter.

i) Show that barixx(baraxxbari)+barjxx(baraxxbarj)+barkxx(baraxxbark)=2bara ii) If barixx(barrxxbari)+barjxx(barrxxbarj)+barkxx(barrxxbark)=baraxxbarb then find barr interms of bara and barb

If f: [2, oo) rarr B defined by f(x)=x^(2)-4x+5 is a bijection, then B=

If the line (x-1)/2=(y-2)/3=t intersects the line x+y=8 then t=

AA n in , 1+2x + 3x^(2) + ….+ n.x^(n-1) = (x in R, x ne 1)

The number of values of theta in the interval (-(pi)/2, (pi)/2) satistying the equation (sqrt(3))^(sec^(2)theta)=tan^(4) theta+2tan^(2) theta is

If a gt 1. Then the value of underset(x to oo) (Lt)(a^(sqrt(x))-a^(1//sqrt(x)))/(a^(sqrt(x))+a^(1//sqrt(x))) is

If (l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)) are d.c's of two lines then find the value of (l_(1)m_(2)-l_(2)m_(1))^(2)+(m_(1)n_(2)-n_(1)m_(2))^(2)+(n_(1)l_(2)-n_(2)l_(1))^(2)+(l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2))^(2)

Without using tables, give the value of each of the following : cos330^(@)

If f : R to R such thatf(x- f(y))= f( f(y) ) +x f (y)+f(x)- 1 AA , y in Rthen f(x) is

If 2/11 Is the probability of an event, what is the probability of the event 'not A'.

Assertion :lim_(xrarr0)sin(1/x) =0 Reason: If f,g,h :I le Rsuch that g(x) le f(x) le h(x)for all x in a deleted neighbouhood of x_o contained in I and if lim_(xrarr0)g(x)=lim_(xrarrx_o)h(x)=l.Then lim_(xrarrx_o)f(x)=l.[sandwich theorem]