14949 + Interview Questions in Maths in Class 11 Page 223 InterviewSolution

11101.	The minimum and maximum values of cos x + 3 sqrt2 sin ( x+ (pi)/(4) )+6 are
Answer» `1,11` `11,-1` `6,5` `5,6` ANSWER :A

Discussion

11102.	1 to 7, describe the sample space for the indicated experiment. One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.
Answer» Answer :`S={R1,R2,R3,R4,R5,R6,W1,W2,W3,W4,W5,W6,B1,B2,B3,B4,B5,B6}`

Discussion

11103.	If in a geometric progression consisting of positive terms, each term equals the sum of the next two terms, then the common ratio of this progression equals
Answer» `SQRT(5)` `(1)/(2) (sqrt(5)-1)` `(1)/(2) (1- sqrt(5))` `(1)/(2) sqrt(5)` ANSWER :B

Discussion

11104.	lim_(x to 0)(x tan 2x-2 x tanx)/((1-cos2x)^(2))=
Answer» 2 `-2` `(1)/(2)` `(-1)/(2)` ANSWER :C

Discussion

11105.	Find the sum of n terms of each of the following 2.1 + 5.3 + 8.5 + ……..
Answer» ANSWER :`(N)/(2) (4N^(2) + n-1)`

Discussion

11106.	Evaluate the following limits. Lt_(xto0)(sin^(-1)x+tan^(-1)x)/x
Answer» ANSWER :2

Discussion

11107.	If R_(2)= {(x,y)\|x and y are integers and x^(2) + y^(2)= 64}is a relation, then find the value of R_(2).
Answer» ANSWER :`{(0, 8), (0, -8), (8,0), (-8, 0)}`

Discussion

11108.	sin 180^(@) sin 70^(@) + sin 16^(@) sin 36^(@)=
Answer» `SIN 54^(@) sin 34^(@)` `sin 54^(@) COS 34^(@)` `cos 54^(@) sin 34^(@)` `cos 54^(@) cos 34^(@)` ANSWER :A

Discussion

11109.	Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
Answer» ANSWER :`X+2y-6=0 and 2 x +y-6=0`.

Discussion

11110.	Find the sum to n terms of the series whose n^("th")term is n (n+3).
Answer» ANSWER :`(N(n+1)(n+ 5))/(3)`

Discussion

11111.	Kavita draws a card from a pack of cards . What is the probability that she drawsa heart
Answer» ANSWER :`(1)/(4)`

Discussion

11112.	The mean and standard deviation of marks obtained by 50 students of a class in three subjects. Mathematics, Physics and Chemistry are given below. Which of thethreesubjectshowsthehighestvariabilityin marksandwhichshowsthelowest ?
Answer» ANSWER :HEIGHT CHEMISTRY and LOWEST MATHEMATICS

Discussion

11113.	If x, y, z be respectively the p^(th), q^(th) and r^(th) terms of a G.P. show that x^(q-r), y^(r-p), z^(p-q)=1
Answer» ANSWER :1

Discussion

11114.	Assertion (A) : The maximum value of log_(1//3)(x^2-4x+5) is 0 Reason (R ) : If xgt0 and 0ltalt1 then log_ax is a decreasing function
Answer» Both (A) and (R) are true and R is correct explaination of A Both A and R are true and R is not the correct explanation of A (A) is true (R) false (A) is false but (R) is true ANSWER :B

Discussion

11115.	If x lt 90^(@) and sin(x + 28^(@)) = cos(3x - 78^(@)), then find x
Answer» ANSWER :`8^(@), 35^(@)`

Discussion

11116.	Consider the system of equations sin x cos 2y=(a^(2)-1)^(2)+1,cosxsin2y=a+1 The number of values of y in [0,2pi] when the system has solution for permissible values of a, is
Answer» 2 3 4 5 Answer :D

Discussion

11117.	(1+tan h (x//2))/(1-tan h(x//2)) =
Answer» `E^(-X)` `e^(x)` `2E^(x//2)` `2e^(-x//2)` ANSWER :B

Discussion

11118.	f(x)= {((2^(x + 2)-16)/(4^(x)-16)",",x ne 2),(k",",x=2):}f(x) is continuous at x=2 then find k
Answer» ANSWER :`-8`

Discussion

11119.	The value of of cosec 10^(@) + cosec 50^(@) -cosec 70^(@) is "_______"
Answer» ANSWER :6

Discussion

11120.	Following Vann diagram show the probabilities of three events. Find the following probabilities. (i) P(E_(2))(ii) P(E_(2)nnE_(3)) (iii) P(E_(1)uuE_(2))(iv) P(E_(1)nnE_(2)')
Answer» ANSWER :(i) 0.39 (II) 0.19 (III) 0.31 (IV) 0.12

Discussion

11121.	The angles of a triangle are in the ratio 3:5:10. Then the ratio of the smallest side to the greatest side is
Answer» ` 1 : sin 10 ^(@) ` ` 1: 2 sin 10 ^(@) ` ` 1 : cos 10 ^(@)` ` 1 : 2 cos 10 ^(@) ` ANSWER :D

Discussion

11122.	1 to 7, describe the sample space for the indicated experiment. A coin is tossed four times.
Answer» Answer :{HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT}

Discussion

11123.	LetA = {x : x^(2) - 5x+6 = 0 } , B = { 2,4} = {4,5} thenA xx (B cap C) is
Answer» `{(2,4),(3,4)}` `{(4,2),(4,3)}` `{(2,4),(3,4),(4,4)}` `{(2,2),(3,3),(4,4),(5,2)}` ANSWER :A

Discussion

11124.	A set P contains n elements. Two subsets A and B of P are chosen independently. Statement-1 : Probability that A cap B= A " is " (3//4)^(n) Statement-2 : Probability that A cup B= P " is " (1//2)^(n).
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 is 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

11125.	ABC is a right triangle with right angle at B, AC = 2. BC = 1 and BD is perpendicular to AC. The area of the rectangle with BD as one of its diagonal is
Answer» `(16)/(SQRT(3))` `(16)/(3)` `(16)/(3sqrt(3))` `(3sqrt(3))/(16)` ANSWER :D

Discussion

11126.	For a differntiable function , define D^()f(x) = L t_(h to 0) (f^2(x + h) - f^2(x))/(h) where f'(x) = (f(x))^2 for example, D^()f(x) = 2x if f(x) = x, D^()f(x) = 2 sin x cos xif f(x) = sin xD^()f(x) = 2e^(2x) if f(x) = e^(x) If f(x) = sin x, g(x) = cos x then D^(**)(fog)
Answer» `-SIN X sin (2 cos x)` `-sin (cos x) SINX` `-sin^2 (cos x) sin x` `-sin(cos x) sin^2 x` ANSWER :A

Discussion

11127.	A+B + C = 2S implies sin S + sin (S -A) + sin (S - B) - sin (S - C) =
Answer» `4COS""(A)/(2) .cos ""(B)/(2) .cos""(C )/(2)` `4cos ""(A)/(2).cos""(B)/(2) .sin""(C )/(2)` `4 cos ""(A)/(2).sin""(B)/(2) .cos ""(C )/(2)` `4 sin "" (A)/(2) .sin ""(B)(2) .sin""(C )/(2)` ANSWER :B

Discussion

11128.	Find the derivative with respect to x of the following: (i) x - (1)/( x)
Answer» ANSWER :`1+ (1)/(x^2)`

Discussion

11129.	Convert the complex number (-16)/(1+isqrt(3)) into polar form.
Answer» Answer :`8(COS (2pi)/3 + I sin(2pi)/3)`

Discussion

11130.	Find the equation of t he straight line through the given point P and having the given slope m if P(-1, -5), m=(-6)/(11)
Answer» ANSWER : `6x+11y+61=0`

Discussion

11131.	Find the equation of t he straight line through the given point P and having the given slope m if P(-4, 7), m=-sqrt(3)
Answer» ANSWER : `SQRT(3)x+y=7-4sqrt(3)`

Discussion

11132.	Show that (1+ cos. (pi)/(8))(1+cos. (3pi)/(8))(1+ cos. (5pi)/(8))(1+ cos .(7pi)/(8))=(1)/(8)
Answer» `1/2` `1/4` `1/8` `1/16` ANSWER :C

Discussion

11133.	Shortest distance between the lines (x-1)/(1) = (y-1)/(1) = (z-1)/(1) and (x-2)/(1) = (y-3)/(1) = (z-4)/(1) is equal to
Answer» `SQRT14` `SQRT7` `SQRT2` `2sqrt7` ANSWER :C

Discussion

11134.	For a differntiable function , define D^()f(x) = L t_(h to 0) (f^2(x + h) - f^2(x))/(h) where f'(x) = (f(x))^2 for example, D^()f(x) = 2x if f(x) = x, D^()f(x) = 2 sin x cos xif f(x) = sin xD^()f(x) = 2e^(2x) if f(x) = e^(x) If f(x) = tan x and g(x) = log xthe D^(**)(fg) (1) =
Answer» `TAN 1` `(tan 1)^2` `0` `2(tan 1)^2` ANSWER :C

Discussion

11135.	A man has 6 friends . In how many ways ways may be invite one or more of them to dinner?
Answer» ANSWER :` ""^(6)C_6`

Discussion

11136.	If 20 sin^(2) alpha+21 cos alpha-24=0 where (7pi)/(4) lt alpha lt 2pi then cot alpha//2=
Answer» `-3` 2 3 `-2` ANSWER :A

Discussion

11137.	The motion of a particle alongstraight line is given by v^(2) = u^(2) + 90s. If the particle starts from rest, then the acceleration is
Answer» 15 unit/`SEC^(2)` 30units/`sec^(2)` 45 UNITS/ `sec^(2)` 75 units/`sec^(2)` ANSWER :C

Discussion

11138.	Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y) : y=2x, y in N},
Answer» Answer :Domain of R is N, co-domain N and RANGE is EVEN NATURAL NUMBERS. Yes, it is RELATION.

Discussion

11139.	If A and B are subsets of the universal set cup, then show that, A sub B iff A cup B = B
Answer» ANSWER :`A SUB B HARR A CUP B = B`

Discussion

11140.	contrapositive of (pveeq)rArr r
Answer» ANSWER :`~p^^~q`

Discussion

11141.	Two vertice of a triangle are (3,-2) and (-6,1). Then its third vertexis
Answer» (1,6) (-1,6) (1,-6) (-1,-6) ANSWER :B

Discussion

11142.	If from the top of a tower of 60 metre heigh, the angles of depression of the top and floor of a house are alpha and beta respectively and if the height of the house is (60sin(beta-alpha))/(x), then x=
Answer» `SINALPHASINBETA` `cosalphacosbeta` `sinalphacosbeta` `COSALPHASINBETA` ANSWER :D

Discussion

11143.	Length of the conjugate axis of 12x^2-3y^(2)=-36 is .........
Answer» ANSWER :`2SQRT3`

Discussion

11144.	Let A (4, 7, 8), B (2, 3, 4) and C (2, 5, 7) be the position vectors of the vertices of a triangle ABC. The length of the internal bisector of the angle at A is
Answer» `(1)/(8) SQRT(170)` `(3)/(8) sqrt(170)` `(5)/(8) sqrt(170)` `(7)/(8) sqrt(170)` ANSWER :b

Discussion

11145.	A bag contains 2 white marbles , 4 blue marbels , and 6 red marbles . A marble is drawn at random from the bag . What is the probability that it is red ?
Answer» ANSWER :`(1)/(2)`

Discussion

11146.	A bag contains 2 white marbles , 4 blue marbels , and 6 red marbles . A marble is drawn at random from the bag . What is the probability that it is blue ?
Answer» ANSWER :`(1)/(3)`

Discussion

11147.	If ((2n),(3))div((n),(2))=12 then n = .......
Answer» ANSWER :5

Discussion

11148.	A bag contains 2 white marbles , 4 blue marbels , and 6 red marbles . A marble is drawn at random from the bag . What is the probability that it is white ?
Answer» ANSWER :`(1)/(6)`

Discussion

11149.	A bag contains 2 white marbles , 4 blue marbels , and 6 red marbles . A marble is drawn at random from the bag . What is the probability that it is not blue ?
Answer» ANSWER :`(2)/(3)`

Discussion

11150.	If f(x)= cos x,0 le x le ( pi )/( 2), then the real number 'c' of the mean value theorem is
Answer» `( pi )/( 6)` `( pi )/( 4)` `sin^(-1) ((2)/( pi ))` `cos ^(-1)((2)/( pi ))` Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

The minimum and maximum values of cos x + 3 sqrt2 sin ( x+ (pi)/(4) )+6 are

1 to 7, describe the sample space for the indicated experiment. One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.

If in a geometric progression consisting of positive terms, each term equals the sum of the next two terms, then the common ratio of this progression equals

lim_(x to 0)(x tan 2x-2 x tanx)/((1-cos2x)^(2))=

Find the sum of n terms of each of the following 2.1 + 5.3 + 8.5 + ……..

Evaluate the following limits. Lt_(xto0)(sin^(-1)x+tan^(-1)x)/x

If R_(2)= {(x,y)|x and y are integers and x^(2) + y^(2)= 64}is a relation, then find the value of R_(2).

sin 180^(@) sin 70^(@) + sin 16^(@) sin 36^(@)=

Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

Find the sum to n terms of the series whose n^("th")term is n (n+3).

Kavita draws a card from a pack of cards . What is the probability that she drawsa heart

The mean and standard deviation of marks obtained by 50 students of a class in three subjects. Mathematics, Physics and Chemistry are given below. Which of thethreesubjectshowsthehighestvariabilityin marksandwhichshowsthelowest ?

If x, y, z be respectively the p^(th), q^(th) and r^(th) terms of a G.P. show that x^(q-r), y^(r-p), z^(p-q)=1

Assertion (A) : The maximum value of log_(1//3)(x^2-4x+5) is 0 Reason (R ) : If xgt0 and 0ltalt1 then log_ax is a decreasing function

If x lt 90^(@) and sin(x + 28^(@)) = cos(3x - 78^(@)), then find x

Consider the system of equations sin x cos 2y=(a^(2)-1)^(2)+1,cosxsin2y=a+1 The number of values of y in [0,2pi] when the system has solution for permissible values of a, is

(1+tan h (x//2))/(1-tan h(x//2)) =

f(x)= {((2^(x + 2)-16)/(4^(x)-16)",",x ne 2),(k",",x=2):}f(x) is continuous at x=2 then find k

The value of of cosec 10^(@) + cosec 50^(@) -cosec 70^(@) is "_______"

Following Vann diagram show the probabilities of three events. Find the following probabilities. (i) P(E_(2))(ii) P(E_(2)nnE_(3)) (iii) P(E_(1)uuE_(2))(iv) P(E_(1)nnE_(2)')

The angles of a triangle are in the ratio 3:5:10. Then the ratio of the smallest side to the greatest side is

1 to 7, describe the sample space for the indicated experiment. A coin is tossed four times.

LetA = {x : x^(2) - 5x+6 = 0 } , B = { 2,4} = {4,5} thenA xx (B cap C) is

A set P contains n elements. Two subsets A and B of P are chosen independently. Statement-1 : Probability that A cap B= A " is " (3//4)^(n) Statement-2 : Probability that A cup B= P " is " (1//2)^(n).

ABC is a right triangle with right angle at B, AC = 2. BC = 1 and BD is perpendicular to AC. The area of the rectangle with BD as one of its diagonal is

For a differntiable function , define D^(**)f(x) = L t_(h to 0) (f^2(x + h) - f^2(x))/(h) where f'(x) = (f(x))^2 for example, D^(**)f(x) = 2x if f(x) = x, D^(**)f(x) = 2 sin x cos xif f(x) = sin xD^(**)f(x) = 2e^(2x) if f(x) = e^(x) If f(x) = sin x, g(x) = cos x then D^(**)(fog)

A+B + C = 2S implies sin S + sin (S -A) + sin (S - B) - sin (S - C) =

Find the derivative with respect to x of the following: (i) x - (1)/( x)

Convert the complex number (-16)/(1+isqrt(3)) into polar form.

Find the equation of t he straight line through the given point P and having the given slope m if P(-1, -5), m=(-6)/(11)

Find the equation of t he straight line through the given point P and having the given slope m if P(-4, 7), m=-sqrt(3)

Show that (1+ cos. (pi)/(8))(1+cos. (3pi)/(8))(1+ cos. (5pi)/(8))(1+ cos .(7pi)/(8))=(1)/(8)

Shortest distance between the lines (x-1)/(1) = (y-1)/(1) = (z-1)/(1) and (x-2)/(1) = (y-3)/(1) = (z-4)/(1) is equal to

For a differntiable function , define D^(**)f(x) = L t_(h to 0) (f^2(x + h) - f^2(x))/(h) where f'(x) = (f(x))^2 for example, D^(**)f(x) = 2x if f(x) = x, D^(**)f(x) = 2 sin x cos xif f(x) = sin xD^(**)f(x) = 2e^(2x) if f(x) = e^(x) If f(x) = tan x and g(x) = log xthe D^(**)(fg) (1) =

A man has 6 friends . In how many ways ways may be invite one or more of them to dinner?

If 20 sin^(2) alpha+21 cos alpha-24=0 where (7pi)/(4) lt alpha lt 2pi then cot alpha//2=

The motion of a particle alongstraight line is given by v^(2) = u^(2) + 90s. If the particle starts from rest, then the acceleration is

Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y) : y=2x, y in N},

If A and B are subsets of the universal set cup, then show that, A sub B iff A cup B = B

contrapositive of (pveeq)rArr r

Two vertice of a triangle are (3,-2) and (-6,1). Then its third vertexis

If from the top of a tower of 60 metre heigh, the angles of depression of the top and floor of a house are alpha and beta respectively and if the height of the house is (60sin(beta-alpha))/(x), then x=

Length of the conjugate axis of 12x^2-3y^(2)=-36 is .........

Let A (4, 7, 8), B (2, 3, 4) and C (2, 5, 7) be the position vectors of the vertices of a triangle ABC. The length of the internal bisector of the angle at A is

A bag contains 2 white marbles , 4 blue marbels , and 6 red marbles . A marble is drawn at random from the bag . What is the probability that it is red ?

A bag contains 2 white marbles , 4 blue marbels , and 6 red marbles . A marble is drawn at random from the bag . What is the probability that it is blue ?

If ((2n),(3))div((n),(2))=12 then n = .......

A bag contains 2 white marbles , 4 blue marbels , and 6 red marbles . A marble is drawn at random from the bag . What is the probability that it is white ?

A bag contains 2 white marbles , 4 blue marbels , and 6 red marbles . A marble is drawn at random from the bag . What is the probability that it is not blue ?

If f(x)= cos x,0 le x le ( pi )/( 2), then the real number 'c' of the mean value theorem is

For a differntiable function , define D^()f(x) = L t_(h to 0) (f^2(x + h) - f^2(x))/(h) where f'(x) = (f(x))^2 for example, D^()f(x) = 2x if f(x) = x, D^()f(x) = 2 sin x cos xif f(x) = sin xD^()f(x) = 2e^(2x) if f(x) = e^(x) If f(x) = sin x, g(x) = cos x then D^(**)(fog)

For a differntiable function , define D^()f(x) = L t_(h to 0) (f^2(x + h) - f^2(x))/(h) where f'(x) = (f(x))^2 for example, D^()f(x) = 2x if f(x) = x, D^()f(x) = 2 sin x cos xif f(x) = sin xD^()f(x) = 2e^(2x) if f(x) = e^(x) If f(x) = tan x and g(x) = log xthe D^(**)(fg) (1) =