14949 + Interview Questions in Maths in Class 11 Page 114 InterviewSolution

5651.	P and Q are two points on the line x-y+1=0, If OP=OQ=6 thenlength of median through O is
Answer» `1//2` `1//sqrt(2)` `1` `7` ANSWER :B

Discussion

5652.	If""^nC_14=^nC_20 find the values of ""^nC_28 and ""^nC_32
Answer» SOLUTION :`^34C_28.^32C_n`

Discussion

5653.	Prove that the straight line 5x + 12 y = 9 touches the hyperbola x ^(2) - 9 y ^(2) =9 and find the point of contact.
Answer» ANSWER :`(5, (-4)/(3))`

Discussion

5654.	Exhaustive set of parameter 'a' so that sin^(-1)x-tan^(-1)x=a has a solution, is
Answer» `[-(PI)/6,(pi)/6]` `[-(pi)/4,(pi)/4]` `[-(pi)/2,(pi)/2]` `[-(pi)/12,(pi)/12]` Answer :B

Discussion

5655.	(6,6) is a point on the circle x^(2) + y^(2) - 4x - 6y - 12 = 0 by translation of origin to a certain point the translated equation is x^(2) + y^(2) = 25 the new co-ordinates of (6,6) are
Answer» (3,4) (3,2) (4,3) (6,6) ANSWER :C

Discussion

5656.	If bara =-bari+barj+2bark, barb =2bari +barj-bark, barc =-2bari+barj+3bark then the angle between 2bara-barc and bara+barb is
Answer» `pi/4` `pi/6` `pi/2` `(3PI)/4` ANSWER :B

Discussion

5657.	Evaluate lim_(xto0)f(x), where f(x)={{:((\|x\|)/(x)","xne0),(0","x=0):}
Answer» ANSWER :LIMIT does not EXIST at `X = 0`

Discussion

5658.	If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find A ∩ (B ∪ D)
Answer» ANSWER :`{ 7, 9, 11 }`

Discussion

5659.	A triangle is formed by the lines ax+by+c=0, lx+my+n=0 and px+qy+r=0. Given that the triangle is not right angled, show that the straight line (ax+by+c)/(ap+bq)=(lx+my+n)/(lp+mq) passes through the orthocentre of the triangle.
Answer» ANSWER :ORTHOCENTRE of the TRIANGLE.

Discussion

5660.	Find the ratio in which the line segment , joining the points P(2,3,4) and Q (-3,5,-4) is divided by yz plane . Also find the point of contact .
Answer» ANSWER :Directed distance from yz PLANE , RATIO 2:3 , POINT of CONTACT `(0,1/5,4/5)`Point of contact `(0, 19/5 , 4/5)`

Discussion

5661.	While dialing a telephone number, an old man forgets its last two digit. If the last two digits are distinct, then the probability that a man dials true number is ......
Answer» `(1)/(45)` `(1)/(90)` `(1)/(100)` `(1)/(2)` ANSWER :B

Discussion

5662.	Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find equation of the line.
Answer» ANSWER :`2KX + HY = 3KH`

Discussion

5663.	Find the approximations of the following sqrt(82)
Answer» ANSWER :9.056

Discussion

5664.	Graph of sin(x) function repeats its value in ......... Interval length.
Answer» ANSWER :`2PI`

Discussion

5665.	Write each of the following statements in the form if then: To get an A+ in the class, it is necessary that you do all the exercises of the book.
Answer» ANSWER :If you GET `A^(+)` in the CLASS, then you do all the EXERCISES in the BOOK.

Discussion

5666.	If a+ bi = (c + i)/(c-i), a, b , c in R, show that a^(2) + b^(2)=1 and (b)/(a)= (2c)/(c^(2)-1)
Answer» ANSWER :`(2C)/(C^(2)-1)`

Discussion

5667.	The magnitude of the projection of the vector bara=4bari-3barj+2bark on the line which makes equal angles with coordinate axes is
Answer» `SQRT2` `SQRT3` `1/sqrt3` `1/sqrt2` ANSWER :B

Discussion

5668.	Solve \|z\|+z= 2+ i, where z is a complex number
Answer» ANSWER :`Z= (3)/(4) + i`

Discussion

5669.	Find the 20^(th) percentile of the following data : {:("Height (in cm)",135,140,145,150,155,160,165,170),("No. of students",7,20,32,48,36,28,24,4):}
Answer» ANSWER :145 CM

Discussion

5670.	(1-Cot200^(@))(1-Cot25^(@)) =
Answer» 0 1 2 `(1)/(2)` ANSWER :C

Discussion

5671.	If y = e^("sin"^2 x + "sin"^4x + "sin"^6x +...+oo), then (dy)/(dx) =
Answer» `e^("TAN"^2x)` `e^("tan"^2x)"SEC"^2x` `2e^("tan"^2x) "tan"X."sec"^2x` `1` Answer :A

Discussion

5672.	If x= sin 1, y= sin 1^(@) then x gt y.
Answer» ANSWER :`SIN 1 GT sin 1^(@)`

Discussion

5673.	Find the value of : sin(75^(@))
Answer» ANSWER :`(i) (SQRT3+1)/(2SQRT2) ` (II)` 2- sqrt3`

Discussion

5674.	For sets A and B, n(A - B)= 8+2x, n(B - A)= 6x" and "n(A cap B)= x. If n(A)= n(B) then n(A cap B)="……….."
Answer» 26 50 24 none of these Answer :D

Discussion

5675.	The radius of the circle x^(2) + y^(2) -2x + 3y+k = 0 is 2 1/2 Find the value of k. Find also the equation of the diameter of the circle, which passes through the point (5,2 (1)/(2))
Answer» ANSWER :5

Discussion

5676.	The points (3,2,-4 ),( 5,4,-6 ) , (9,8,-10 )are
Answer» ISOSCELES triangle Equilateral triangle Collinear points Right ANGLED triangle Answer :C

Discussion

5677.	Let f(x) be a function such that f'(x)=log_(1//3)[log_(3)(sinx+a)]. If f(x) is decreasing for all real values of x , then
Answer» `a in (1,4)` `a in(4,OO)` `a in(2,3)` `a in (2,oo)` ANSWER :B

Discussion

5678.	Observe the following statements: Assertion(A) : If -(pi)/(2) lt theta lt (pi)/(2) and x=log_(e ) ((1+sin theta)/(cos theta)) then sinhx=tan theta Reason (R ) : For -(pi)/(2) lt theta lt (pi)/(2), the value of sec theta is positive. Then the true statementamong the following is
Answer» A is FALSE, R is false A is false, R is TRUE A is true, R is false A is true, R is true, `R RARR A` ANSWER :D

Discussion

5679.	If nP_4 : nP_5 = 1 : 2 then n = ............ .
Answer» ANSWER :6

Discussion

5680.	Findthe equationof the circlepassingthrough the points(i)(0,0), (5, 0) and(3, 3)(ii)(1, 2 ), ( 3, -4) and( 5, - 6)(iii)( 20, 3) , (19, 8) and (2, -9)Also, find the centreand radiusin each case.
Answer» Answer :(i) `x ^(2)+ y ^(2)- 5x- y= 0 `, CENTRE` ((5)/(2), (1)/(2))` and radius=` (sqrt( 26))/( 2)` (ii) ` x ^(2) + y ^(2) - 22x-4y+25 = 0`, centre` (11,2) ` and radius= 10 (III)` x ^(2)+ y ^(2) - 14 x- 6y - 111 = 0 `, centre ` (7, 3)`and radius= 13

Discussion

5681.	Let p be " I will marry her," and let q be " she is beautiful." Translate into symbolic form. If she is not beautiful, then I will not marry her.
Answer» <P> ANSWER :~Q =>~p

Discussion

5682.	The sum and product of the slopes of the lines2x^(2)-xy-y^(2)=0 are
Answer» -1,-2 2,-1 `(1)/(2),-1` `2,(1)/(2)` ANSWER :A

Discussion

5683.	P_1, P_2 are points on either of the two lines y- sqrt(3) \|x\| =2 at a distance of 5 units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from P_1, P_2 on the bisector of the angle between the given lines. Thinking Process : Here, equation y- sqrt(3) \|x\| =2 represents two different lines for x gt0 and x lt 0 and they are bisector of Y -axis. P_1 and P_2 are points at a distance 5 unit from point of intersection. The y coordinate of the foot of perpendicular on Y-axis is 2+5 cos ( 30^(@) ) .
Answer» ANSWER :`D= ( 0,2 + ( 5sqrt5)/( 2) )` OR `(0,(4+ 5 sqrt(3) )/( 2))`

Discussion

5684.	Find the domains of the following functionsf(x) = ( 1)/( sqrt( 2-x))
Answer» ANSWER :`(-oo,2)`

Discussion

5685.	If sin^(-1)(x)+sin^(-1)(2x)=(pi)/3 then x=
Answer» `3/28` `(SQRT(3))/28` `sqrt(3/28)` `3/(sqrt(28))` ANSWER :C

Discussion

5686.	The value (s) of x for which the functionf(x) = {{:(1 -x " , " x lt 1),( (1 -x)(2-x) " : " 1 le x le 2 ),( x -3 " , " x gt 2 ):} fails to be continuous is (are)
Answer» 1 2 3 All REAL NUMBERS ANSWER :B

Discussion

5687.	If alpha and beta are the roots of the equation x^(2)+x-7=0, form the equation whose roots are alpha^(2) and beta^(2).
Answer» ANSWER :`X^(2)-15x+49=0`.

Discussion

5688.	Let a, b in R be such that the function f given by f(x)= ln \|x\|+bx^(2)+ax, x ne0 has extreme values at x=-1 and x=2 Statemet-I : f has local maximum at x=-1 and x=2. Statement- II: a=(1)/(2),b=(-1)/(4)
Answer» I is FALSE and II is true BothI and II are TRUEAND II is the correct EXPLANATION of I Both I and II are true and II is not the correct ecxplanation of I I is true and IIis false Answer :C

Discussion

5689.	A line cutting off intercept -3 from the Y-axis and the tangent at angle to the X -axis is 3/5, its equation is,
Answer» `5Y- 3 x15 =0` `3Y - 5x + 15 =0` `5y-3x - 15 =0` NONE of these Answer :A

Discussion

5690.	If the vertices of a triangle are A(1,4,2), B(-2,1,2),C(2,3,-4) then find /_A,/_B,/_C.
Answer» Answer :`lfloorA=(PI)/(2),lfloorB=cos^(-1)((3)/(2sqrt(7))),lfloorC=cos^(-1)sqrt((19)/(28))`

Discussion

5691.	sin(12^(@))sin(48^(@))sin(54^(@))= ………..
Answer» `(1)/(16)` `(1)/(32)` `(1)/(8)` `(1)/(4)` ANSWER :C

Discussion

5692.	Evaluate the following limits : Lt_(xto0)e^(x)
Answer» ANSWER :`OO`

Discussion

5693.	The projection of the join of the two points (1,4,5), (6,7,2) on the line whose d.r's are (4,5,6) is
Answer» `(17)/(SQRT(77))` `(7)/(6)` 21 `(7)/(9)` ANSWER :A

Discussion

5694.	The sum of the n terms of two A.P. are in the ratio (2n-1): (4n+ 3). Find the ratio of their 25^(th) terms.
Answer» ANSWER :`97: 199`

Discussion

5695.	If f(x) = x^(2) + 2bx + 2c^(2)and g(x)= - x^(2)- 2cx + b^(2)such that min f(x)gt max g(x), then the relation between 'b' and 'c' is
Answer» no real VALUE of of b & c `0 LT c lt b sqrt(2)` `\|c\| lt \|b\| sqrt(2)` `\|c\| gt b sqrt(2)` Answer :D

Discussion

5696.	(sin(90^(@)-theta)sec(180^(@)-theta)sin(-theta))/(sin(180^(@)+theta)cot(360^(@)-theta)"cosec"(90^(@)+theta)).
Answer» ANSWER :`SIN THETA`

Discussion

5697.	In DeltaABC, " if " cos A=( sin B)/( 2 sin C) , then the triangle is
Answer» ISOSCELES RIGHT ANGLED EQUILATERAL Scalane ANSWER :A

Discussion

5698.	bari,barj,bark is a right handed system of vectors and bara=2bari-25barj+17bark,barb=-3barj+5bark,barc=4bark. If V is the volume of a tetrahedrone with edges bara,barb,barc then ([barabarbbarc])/V=
Answer» 6 1 `-1` `-6` ANSWER :D

Discussion

5699.	The word THINGSis given. Determine the number of different 6 letters words that can be formed
Answer» ANSWER :720

Discussion

5700.	Consider two eventsA and B such that P(A) = (1)/(4),P((B)/(A)) = (1)/(2),P((A)/(B)) = (1)/(4) . For eachof the folloiwngstatement , whichis ture. I. P(A//B) = (3)/(4) II. TheeventsA and Bare mutuallyexcluise. III. P(A//B) +P(A//B) =1
Answer» I only I and II I and III II and III Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

P and Q are two points on the line x-y+1=0, If OP=OQ=6 thenlength of median through O is

If""^nC_14=^nC_20 find the values of ""^nC_28 and ""^nC_32

Prove that the straight line 5x + 12 y = 9 touches the hyperbola x ^(2) - 9 y ^(2) =9 and find the point of contact.

Exhaustive set of parameter 'a' so that sin^(-1)x-tan^(-1)x=a has a solution, is

(6,6) is a point on the circle x^(2) + y^(2) - 4x - 6y - 12 = 0 by translation of origin to a certain point the translated equation is x^(2) + y^(2) = 25 the new co-ordinates of (6,6) are

If bara =-bari+barj+2bark, barb =2bari +barj-bark, barc =-2bari+barj+3bark then the angle between 2bara-barc and bara+barb is

Evaluate lim_(xto0)f(x), where f(x)={{:((|x|)/(x)","xne0),(0","x=0):}

If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find A ∩ (B ∪ D)

A triangle is formed by the lines ax+by+c=0, lx+my+n=0 and px+qy+r=0. Given that the triangle is not right angled, show that the straight line (ax+by+c)/(ap+bq)=(lx+my+n)/(lp+mq) passes through the orthocentre of the triangle.

Find the ratio in which the line segment , joining the points P(2,3,4) and Q (-3,5,-4) is divided by yz plane . Also find the point of contact .

While dialing a telephone number, an old man forgets its last two digit. If the last two digits are distinct, then the probability that a man dials true number is ......

Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find equation of﻿ the﻿ line.

Find the approximations of the following sqrt(82)

Graph of sin(x) function repeats its value in ......... Interval length.

Write each of the following statements in the form if then: To get an A+ in the class, it is necessary that you do all the exercises of the book.

If a+ bi = (c + i)/(c-i), a, b , c in R, show that a^(2) + b^(2)=1 and (b)/(a)= (2c)/(c^(2)-1)

The magnitude of the projection of the vector bara=4bari-3barj+2bark on the line which makes equal angles with coordinate axes is

Solve |z|+z= 2+ i, where z is a complex number

Find the 20^(th) percentile of the following data : {:("Height (in cm)",135,140,145,150,155,160,165,170),("No. of students",7,20,32,48,36,28,24,4):}

(1-Cot200^(@))(1-Cot25^(@)) =

If y = e^("sin"^2 x + "sin"^4x + "sin"^6x +...+oo), then (dy)/(dx) =

If x= sin 1, y= sin 1^(@) then x gt y.

Find the value of : sin(75^(@))

For sets A and B, n(A - B)= 8+2x, n(B - A)= 6x" and "n(A cap B)= x. If n(A)= n(B) then n(A cap B)="……….."

The radius of the circle x^(2) + y^(2) -2x + 3y+k = 0 is 2 1/2 Find the value of k. Find also the equation of the diameter of the circle, which passes through the point (5,2 (1)/(2))

The points (3,2,-4 ),( 5,4,-6 ) , (9,8,-10 )are

Let f(x) be a function such that f'(x)=log_(1//3)[log_(3)(sinx+a)]. If f(x) is decreasing for all real values of x , then

Observe the following statements: Assertion(A) : If -(pi)/(2) lt theta lt (pi)/(2) and x=log_(e ) ((1+sin theta)/(cos theta)) then sinhx=tan theta Reason (R ) : For -(pi)/(2) lt theta lt (pi)/(2), the value of sec theta is positive. Then the true statementamong the following is

If nP_4 : nP_5 = 1 : 2 then n = ............ .

Findthe equationof the circlepassingthrough the points(i)(0,0), (5, 0) and(3, 3)(ii)(1, 2 ), ( 3, -4) and( 5, - 6)(iii)( 20, 3) , (19, 8) and (2, -9)Also, find the centreand radiusin each case.

Let p be " I will marry her," and let q be " she is beautiful." Translate into symbolic form. If she is not beautiful, then I will not marry her.

The sum and product of the slopes of the lines2x^(2)-xy-y^(2)=0 are

Find the domains of the following functionsf(x) = ( 1)/( sqrt( 2-x))

If sin^(-1)(x)+sin^(-1)(2x)=(pi)/3 then x=

The value (s) of x for which the functionf(x) = {{:(1 -x " , " x lt 1),( (1 -x)(2-x) " : " 1 le x le 2 ),( x -3 " , " x gt 2 ):} fails to be continuous is (are)

If alpha and beta are the roots of the equation x^(2)+x-7=0, form the equation whose roots are alpha^(2) and beta^(2).

Let a, b in R be such that the function f given by f(x)= ln |x|+bx^(2)+ax, x ne0 has extreme values at x=-1 and x=2 Statemet-I : f has local maximum at x=-1 and x=2. Statement- II: a=(1)/(2),b=(-1)/(4)

A line cutting off intercept -3 from the Y-axis and the tangent at angle to the X -axis is 3/5, its equation is,

If the vertices of a triangle are A(1,4,2), B(-2,1,2),C(2,3,-4) then find /_A,/_B,/_C.

sin(12^(@))sin(48^(@))sin(54^(@))= ………..

Evaluate the following limits : Lt_(xto0)e^(x)

The projection of the join of the two points (1,4,5), (6,7,2) on the line whose d.r's are (4,5,6) is

The sum of the n terms of two A.P. are in the ratio (2n-1): (4n+ 3). Find the ratio of their 25^(th) terms.

If f(x) = x^(2) + 2bx + 2c^(2)and g(x)= - x^(2)- 2cx + b^(2)such that min f(x)gt max g(x), then the relation between 'b' and 'c' is

(sin(90^(@)-theta)sec(180^(@)-theta)sin(-theta))/(sin(180^(@)+theta)cot(360^(@)-theta)"cosec"(90^(@)+theta)).

In DeltaABC, " if " cos A=( sin B)/( 2 sin C) , then the triangle is

bari,barj,bark is a right handed system of vectors and bara=2bari-25barj+17bark,barb=-3barj+5bark,barc=4bark. If V is the volume of a tetrahedrone with edges bara,barb,barc then ([barabarbbarc])/V=

The word THINGSis given. Determine the number of different 6 letters words that can be formed

Consider two eventsA and B such that P(A) = (1)/(4),P((B)/(A)) = (1)/(2),P((A)/(B)) = (1)/(4) . For eachof the folloiwngstatement , whichis ture. I. P(A//B) = (3)/(4) II. TheeventsA and Bare mutuallyexcluise. III. P(A//B) +P(A//B) =1

Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find equation of the line.