14949 + Interview Questions in Maths in Class 11 Page 16 InterviewSolution

751.	Which of the following is not an equivalence relation on z?
Answer» ARB `hArr a+B` is an EVEN INTEGER aRb <=> a-bis an even integer `aRb hArr a lt b` `aRb hArr a= b` Answer :A::B

Discussion

752.	Let f : R to R be defined by f (x + y) = f (x) - f (y) + 2xy + 1 AA x, y in R . If f (x) is differentiable every where and f '(0) =1, find f '(x).
Answer» ANSWER :`2X - 1`

Discussion

753.	Values of x and y satisfying the equation sin^(7)y=\|x^(2)-x^(2)-9x+9\|+\|x^(3)-x^(2)-4x+4\|+sec^(2)2y+cos^(4)y are
Answer» `x=1,y=npi, N in I` `x=1, y=2npi+(pi)/2, n in I` `x=1, y=2n pi , n INI` `x=1, y=n pi +(pi)/2, n in I` ANSWER :B

Discussion

754.	Find equation of the line perpendicular to the linex - 7y + 5 = 0and having x intercept 3.
Answer» ANSWER :`y + 7X = 21`

Discussion

755.	A closed cylinder of given volume will have least surface area when the the ratio of its height and base radius is
Answer» `2 : 1` `1 : 2` `2 :3` `3 :2` ANSWER :A

Discussion

756.	If sintheta+cosectheta=2, then sin^(2)theta+cosec^(2)theta is equal to
Answer» 1 4 2 None of these Answer :C

Discussion

757.	If p_(1), p_(2), p_(3) are respectively the perpendiculars from the vertices of Delta ABC to the opposite sides, then (i) 1/p_(1) + 1/p_(2) + 1/p_(3) =
Answer» `1/r` `1/r_(1)` `1/r_(2)` `1/r_(3)` ANSWER :A

Discussion

758.	If P_(1),P_(2),P_(3) are altitudes of a DeltaABC then show that (1)/(P_(1))+(1)/(P_(2))-(1)/(P_(3))=(1)/(r_(3))
Answer» `1/r` `1/r_(1)` `1/r_(2)` `1/r_(3)` ANSWER :D

Discussion

759.	If p_(1), p_(2), p_(3) are respectively the perpendiculars from the vertices of Delta ABC to the opposite sides, then (cos A)/p_(1)+ (cos B)/p_(2) + (cos C)/p_(3) =
Answer» `1/r` `1/R` `1/r_(1)` `1/r_(3)` ANSWER :B

Discussion

760.	If p_(1), p_(2), p_(3) are respectively the perpendiculars from the vertices of Delta ABC to the opposite sides, then p_(1) , p_(2), p_(3) =
Answer» `(ABC)/(8 R^(2))` `(a^(2)B^(2)C^(2))/(8 R^(2))` `(a^(2)b^(2)c^(2))/(8 R^(3))` `(a^(3)b^(3)c^(3))/(8 R^(3))` ANSWER :C

Discussion

761.	Determine the angle between the lines whose equation are 2x-y+3=0 and x+y-2=0.
Answer» Answer : `"TAN"^(-1)(3)=71^(@)34'`

Discussion

762.	If tan x = n tan y, nin R' then the maximum value of sec^(2)(x-y) is equal to
Answer» `((N+1)^(2))/(2N)` `((n+1)^(2))/(n)` `((n+1)^(2))/(2)` `((n+1)^(2))/(4N)` ANSWER :D

Discussion

763.	If x^(2)+2hxy+y^(2)=0 represents the equation of pair of straight lines through origin and which makes an angle alpha with the linex+y=0 then h =
Answer» `COS 2ALPHA` `TAN 2alpha` `sin2alpha` `sec2alpha` ANSWER :D

Discussion

764.	lim_(xto oo)(sinx)/(x) is
Answer» ANSWER :`(##SUR_MAT_XI_V02_S_MQP_02_E01_025_S01##)`

Discussion

765.	Find the value of n: (i) .^(n)C_(10)=^(n)C_(16) (ii) .^(5)C_(n) =^(15)C_(n+3) (iii) .^(10)C_(n) =^(10)C_(n+2) (iv) .^(23)C_(3n) =.^(25)C_(n+1) (v) .^(n)C_(r) =.^(n)C_(r-2)
Answer» Answer :(i) `n - 26` (ii) `n = 6` (iii) `n = 4` (iv) `n = 6` (V) `n = 2R - 2`

Discussion

766.	What is the general form of the points which lie on X-axis?
Answer» ANSWER :`0+ib,B in R`.

Discussion

767.	If x sin a + y sin 2a + z sin 3a = sin 4 a, x sin b + y sin 2b + z sin 3b = sin 4b, x sin c + y sin 2c + z sin 3c = sin 4c. Then the roots of the equation t^(3) - ((z)/(2))t^(2) - ((y+z)/(4)) t+((z-x)/(8))=0, a, b, c ne n pi, are
Answer» sin a, sin b, sin c cos a, cos b, cos c sin 2A, sin 2B, sin 2C cos 2a, cos 2b, cos 2c ANSWER :B

Discussion

768.	If (2 sin theta )/(1+ cos theta + sin theta )=x,find the value of (1- cos theta + sin theta )/(1+ sin theta )
Answer» <P>p `1//p` `2//p` `-p` ANSWER :A

Discussion

769.	A staright line x/(a)-y/(b)=1 passes through the point (8, 6) and cuts off a triangle of area 12 units from the axes of co-ordinates.Find the equations of the straight line.
Answer» Answer : `X/(4)-y/(6)=1 and x/(8)-y/(3)=-1`

Discussion

770.	If x=(3at)/(1+t^2),y=(3at^2)/(1+t^2) then (dy)/(dx)=
Answer» `(2T)/(1-t^2)` `(2t)/(t^2-1)` `2t(t^2-1)` `-2t(t^2-1)` ANSWER :A

Discussion

771.	Find the value of n such that ""^(n)P_(5)=42.""^(n)P_(3),ngt4.
Answer» ANSWER :10

Discussion

772.	Solve the equations: 4^(x)-3^(x-(1)/(2))=3^(x+(1)/(2))-2^(2x-1).
Answer» ANSWER :`(3)/(2)`.

Discussion

773.	Find the values of and p, if the equation x cos thita+ y sin theta = p is the normal form of the line sqrt3x + y + 2 = 0 .
Answer» ANSWER :`(7 PI)/6, 1`

Discussion

774.	If the slope of the line (x/a+y/b-1)+k(x/b+y/a-1)=0 is -1, then the value of kis
Answer» `-1` `1` 0 2 Answer :B

Discussion

775.	cos^(2) 36^(@) + cos^(2) 72^(@)=
Answer» `1//4` `2//4` `3//4` 1 Answer :C

Discussion

776.	Calculate the index number for the year 2005 with 2000 as the base year by weighted aggregate method from the following data:
Answer» ANSWER :`=144.69`.

Discussion

777.	(i) How many words can be formed with the letters of the word 'FAILURE', if A and F are always together? (ii) In how many ways can 6 question papers be arranged if the best and worst papers are always together?
Answer» ANSWER :(i) 1440 (II) 240

Discussion

778.	Let A={x in R: x != 0, -4 le x le 4} and f: A rarr R is defined by f(x)=(\|x\|)/(x) for x in A. Then the range of f is
Answer» `{1, -1}` `{ X : 0 le x le 4}` `{1}` `{ x : -4 le x le 0}` ANSWER :A

Discussion

779.	Write the following relation in roster from R= {(x,y): x in A, yin B. Y is divisible by x}where A= {5, 6,7, 8} B= {10, 12, 15, 16, 18}
Answer» ANSWER :R= {(5, 10), (5, 15), (6, 12), (6, 18), (8, 16)}

Discussion

780.	There are 100 bolts and 50 nuts in a box, out of which 50% bolts and 50% nuts are defective. Two items are drawn at random from the box, find the probability that both are either bolts or defective.
Answer» SOLUTION :N/a

Discussion

781.	A bag containstickets numbered 1 to 20. Twoticketsare drawnat random, Find theprobability that sumof the two numberson the tickets is even .
Answer» ANSWER :`9/19 APPROX 0.47`

Discussion

782.	Consider three planes 2x + py + 6z = 8x + 2y + qz = 5 and x + y + 3z =4 The plnaes have infinite points common among them if
Answer» <P>`p = 2,Q in 3` ` p in 2,q in 3` `p ne 2,q = 3` `p = 2,q = 3` ANSWER :B

Discussion

783.	sin(Cot^(-1)(cos(Tan^(-1)x)))=
Answer» 0 1 `1/(SQRT(3))` `sqrt(2/3)` ANSWER :D

Discussion

784.	Find the distance between the directrices of th ellipse (x^(2))/(36) + (y^(2))/(20) = 1.
Answer» ANSWER :`E = (2)/(3)`

Discussion

785.	Fill in the blanks of the following Multiplicative inverser of 1+I is ......
Answer» ANSWER :`(1)/(2)(1-i)`

Discussion

786.	sum (a^(2) sin ( B- C ))/( sin B+ sin C) =
Answer» `0` ` 1` ` (1)/(2) ` `2` ANSWER :A

Discussion

787.	Area of the parallelogram formed by the lines y=mx,y=mx+1, y=nx and y=nx+1 equals. (in sq units)
Answer» `(ABS(m+n))/((m-n)^2)` `1/abs(m-n)` `1/abs(m+n)^2` `1/abs(m-n)^2` ANSWER :B

Discussion

788.	Let R = {(1, 3), (2, 2), (3, 2)} and S = {(2, 1), (3, 2), (2, 3)} be two relations on set A = {(1, 2, 3)}. Then, SoR is equal
Answer» ANSWER :FALSE STATEMENT

Discussion

789.	Find the specified term of the expression in each of the following binomials: (iii) Middle term of (2 x - (1)/(y) )^(8).
Answer» ANSWER :`(1120x^4)/(y^4)`

Discussion

790.	The triangle formed by the pair of line 3x^2+48xy+23y^2=0 and the line 3x-2y+4=0 is
Answer» EQUILATERAL Isosceles Right angled Scalane Answer :A

Discussion

791.	If y = sin (log _(e) x) then (x ^(2) (d ^(2) y)/(dx ^(2)) +x (dy )/(dx)=
Answer» `2` `1` `0` `-1` ANSWER :C

Discussion

792.	Perpendicular distance from origin to line 3x + 4y + 10 = 0 is .........
Answer» `-2` `(2)/(5)` `(1)/(5)` `2` ANSWER :D

Discussion

793.	P is a variable point which moves such that 3PA =2PB. If A(-2,2,3) and B=(13,-3,13) prove that P satisfies the equation. x^(2)+y^(2)+z^(2)+28x-12y+10z-247=0
Answer» 16 26 36 -26 Answer :B

Discussion

794.	Solve inequality-3 le 4 - (3x)/(-5) le 2
Answer» ANSWER :`[-4,2]`

Discussion

795.	Evaluate the following limits : Lim_( xto 1) (sqrt((x^(2)-1))+sqrt((x-1)))/(sqrt((x^(2)-1)))
Answer» ANSWER :`1- 1/(SQRT(2))`

Discussion

796.	Find the sum of the intercepts cut by the axes on the lines x+y=a,x+y=ar,x+y=ar^(2), ……….where a!=0 and r=1/2
Answer» ANSWER :`2sqrt(2)a`

Discussion

797.	If A=[(i,0,0),(0,i,0),(0,0,i)] then for ninN,A^(4n+1)=
Answer» `[(1,0,0),(0,1,0),(0,0,1)]` `[(-1,0,0),(0,-1,0),(0,0,-1)]` `[(i,0,0),(0,i,0),(0,0,i)]` `[(-i,0,0),(0,-i,0),(0,0,-i)]` ANSWER :C

Discussion

798.	(y^(2))/(16)-(x^(2))/(49)=1
Answer» Answer :(i) 8 units, 14 units (ii) `A(0,-4),B(0,4)` (iii) `F_(1)(0,-sqrt(65)),F_(2) (0,sqrt(65))` (iv) `e=(sqrt(65))/(4)` (V) `24(1)/(2)` units

Discussion

799.	Let f : R rarr R be a differentiable function satisfying f(x+y)=f(x) + f(y) +x^2y+xy^2 for all real number x and y . If lim_(x rarr 0)(f(x))/x = 1, then The value of f'(3) is
Answer» 8 10 12 18 Answer :B

Discussion

800.	Let f : R rarr R be a differentiable function satisfying f(x+y)=f(x) + f(y) +x^2y+xy^2 for all real number x and y . If lim_(x rarr 0)(f(x))/x = 1, then The value of f(9) is
Answer» 240 356 252 730 Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

Which of the following is not an equivalence relation on z?

Let f : R to R be defined by f (x + y) = f (x) - f (y) + 2xy + 1 AA x, y in R . If f (x) is differentiable every where and f '(0) =1, find f '(x).

Values of x and y satisfying the equation sin^(7)y=|x^(2)-x^(2)-9x+9|+|x^(3)-x^(2)-4x+4|+sec^(2)2y+cos^(4)y are

Find equation of the line perpendicular to the linex - 7y + 5 = 0and having x intercept 3.

A closed cylinder of given volume will have least surface area when the the ratio of its height and base radius is

If sintheta+cosectheta=2, then sin^(2)theta+cosec^(2)theta is equal to

If p_(1), p_(2), p_(3) are respectively the perpendiculars from the vertices of Delta ABC to the opposite sides, then (i) 1/p_(1) + 1/p_(2) + 1/p_(3) =

If P_(1),P_(2),P_(3) are altitudes of a DeltaABC then show that (1)/(P_(1))+(1)/(P_(2))-(1)/(P_(3))=(1)/(r_(3))

If p_(1), p_(2), p_(3) are respectively the perpendiculars from the vertices of Delta ABC to the opposite sides, then (cos A)/p_(1)+ (cos B)/p_(2) + (cos C)/p_(3) =

If p_(1), p_(2), p_(3) are respectively the perpendiculars from the vertices of Delta ABC to the opposite sides, then p_(1) , p_(2), p_(3) =

Determine the angle between the lines whose equation are 2x-y+3=0 and x+y-2=0.

If tan x = n tan y, nin R' then the maximum value of sec^(2)(x-y) is equal to

If x^(2)+2hxy+y^(2)=0 represents the equation of pair of straight lines through origin and which makes an angle alpha with the linex+y=0 then h =

lim_(xto oo)(sinx)/(x) is

Find the value of n: (i) .^(n)C_(10)=^(n)C_(16) (ii) .^(5)C_(n) =^(15)C_(n+3) (iii) .^(10)C_(n) =^(10)C_(n+2) (iv) .^(23)C_(3n) =.^(25)C_(n+1) (v) .^(n)C_(r) =.^(n)C_(r-2)

What is the general form of the points which lie on X-axis?

If x sin a + y sin 2a + z sin 3a = sin 4 a, x sin b + y sin 2b + z sin 3b = sin 4b, x sin c + y sin 2c + z sin 3c = sin 4c. Then the roots of the equation t^(3) - ((z)/(2))t^(2) - ((y+z)/(4)) t+((z-x)/(8))=0, a, b, c ne n pi, are

If (2 sin theta )/(1+ cos theta + sin theta )=x,find the value of (1- cos theta + sin theta )/(1+ sin theta )

A staright line x/(a)-y/(b)=1 passes through the point (8, 6) and cuts off a triangle of area 12 units from the axes of co-ordinates.Find the equations of the straight line.

If x=(3at)/(1+t^2),y=(3at^2)/(1+t^2) then (dy)/(dx)=

Find the value of n such that ""^(n)P_(5)=42.""^(n)P_(3),ngt4.

Solve the equations: 4^(x)-3^(x-(1)/(2))=3^(x+(1)/(2))-2^(2x-1).

Find the values of and p, if the equation x cos thita+ y sin theta = p is the normal form of the line sqrt3x + y + 2 = 0 .

If the slope of the line (x/a+y/b-1)+k(x/b+y/a-1)=0 is -1, then the value of kis

cos^(2) 36^(@) + cos^(2) 72^(@)=

Calculate the index number for the year 2005 with 2000 as the base year by weighted aggregate method from the following data:

(i) How many words can be formed with the letters of the word 'FAILURE', if A and F are always together? (ii) In how many ways can 6 question papers be arranged if the best and worst papers are always together?

Let A={x in R: x != 0, -4 le x le 4} and f: A rarr R is defined by f(x)=(|x|)/(x) for x in A. Then the range of f is

Write the following relation in roster from R= {(x,y): x in A, yin B. Y is divisible by x}where A= {5, 6,7, 8} B= {10, 12, 15, 16, 18}

There are 100 bolts and 50 nuts in a box, out of which 50% bolts and 50% nuts are defective. Two items are drawn at random from the box, find the probability that both are either bolts or defective.

A bag containstickets numbered 1 to 20. Twoticketsare drawnat random, Find theprobability that sumof the two numberson the tickets is even .

Consider three planes 2x + py + 6z = 8x + 2y + qz = 5 and x + y + 3z =4 The plnaes have infinite points common among them if

sin(Cot^(-1)(cos(Tan^(-1)x)))=

Find the distance between the directrices of th ellipse (x^(2))/(36) + (y^(2))/(20) = 1.

Fill in the blanks of the following Multiplicative inverser of 1+I is ......

sum (a^(2) sin ( B- C ))/( sin B+ sin C) =

Area of the parallelogram formed by the lines y=mx,y=mx+1, y=nx and y=nx+1 equals. (in sq units)

Let R = {(1, 3), (2, 2), (3, 2)} and S = {(2, 1), (3, 2), (2, 3)} be two relations on set A = {(1, 2, 3)}. Then, SoR is equal

Find the specified term of the expression in each of the following binomials: (iii) Middle term of (2 x - (1)/(y) )^(8).

The triangle formed by the pair of line 3x^2+48xy+23y^2=0 and the line 3x-2y+4=0 is

If y = sin (log _(e) x) then (x ^(2) (d ^(2) y)/(dx ^(2)) +x (dy )/(dx)=

Perpendicular distance from origin to line 3x + 4y + 10 = 0 is .........

P is a variable point which moves such that 3PA =2PB. If A(-2,2,3) and B=(13,-3,13) prove that P satisfies the equation. x^(2)+y^(2)+z^(2)+28x-12y+10z-247=0

Solve inequality-3 le 4 - (3x)/(-5) le 2

Evaluate the following limits : Lim_( xto 1) (sqrt((x^(2)-1))+sqrt((x-1)))/(sqrt((x^(2)-1)))

Find the sum of the intercepts cut by the axes on the lines x+y=a,x+y=ar,x+y=ar^(2), ……….where a!=0 and r=1/2

If A=[(i,0,0),(0,i,0),(0,0,i)] then for ninN,A^(4n+1)=

(y^(2))/(16)-(x^(2))/(49)=1

Let f : R rarr R be a differentiable function satisfying f(x+y)=f(x) + f(y) +x^2y+xy^2 for all real number x and y . If lim_(x rarr 0)(f(x))/x = 1, then The value of f'(3) is

Let f : R rarr R be a differentiable function satisfying f(x+y)=f(x) + f(y) +x^2y+xy^2 for all real number x and y . If lim_(x rarr 0)(f(x))/x = 1, then The value of f(9) is