14949 + Interview Questions in Maths in Class 11 Page 248 InterviewSolution

12351.	Find the ratio in which the xz-plane divides the line joining A(-2, 3, 4) and B(1, 2, 3).
Answer» ANSWER :`-3:2`

Discussion

12352.	The shortest distance between the lines whose equations are barr = t ( bari + barj + bark ), barr = bark + s(bari - bar2j + 3bark) is
Answer» 3 `3/(sqrt(38))` `sqrt(3/14)` `2/(sqrt(13))` Answer :B

Discussion

12353.	State and prove Binomial theorem for all the integers.
Answer» <P> ANSWER :`=P(m+1) ` is TRUE.

Discussion

12354.	sec x = (13)/(5), x lies in fourth quadrant.
Answer» Answer :`sin =- (12)/(13) , cosec X =- (13)/( 12), COS x = (5)/(13), TAN x =- (12)/(5), cot x =- (5)/(12)`

Discussion

12355.	Let ABC be triangle having o and I as its circumcenter and incentre, respectively. If R and r are the circumradius and the inradius, respectively, then (OI)^(2) = ...... Further and also the triangle AIO is a right angle triangle if and only if a, b, c are in ......
Answer» `R^(2) - 2Rr, A.P` `R^(2) - 2Rr, G.P.` `R^(2) + 2Rr, A.P.` `R^(2) + 2Rr + G.P.` ANSWER :a

Discussion

12356.	Differentiate f(x)=e^(2-3x) by using 1stprinciple.
Answer» ANSWER :`-3E^(2-3x)`

Discussion

12357.	Given that barc is in the plane of bara, barb and bard is not iri the plane of bara, barb then (baraxx barb) xx (barc xx bard) =
Answer» in the plane of a, B but not in the plane of `barc, BARD` parallel to `bara` parallel to `barc` parallel to `BARB` Answer :C

Discussion

12358.	If xtan^(2) 120^(@) + 4 cos^(2) 150^(@) = 9 then x =
Answer» 3 1 2 4 Answer :A

Discussion

12359.	2Cos^(-1)x=Sin^(-1)(2xsqrt(1-x^(2))) is valid for
Answer» `-1lexle1` `0LEXLE1` `0lexle1/(SQRT(2))` `1/(sqrt(2))lexle1` ANSWER :D

Discussion

12360.	Evaluate Lt_(xto0)(((1+x)^(1/x)-e+(ex)/2)/(x^(2)))
Answer» `(E)/(2)` `(11e)/(8)` `(11e)/(24)` e Answer :C

Discussion

12361.	f(x) = 3 cos x + 4 sin x + 8 has minimum value 19.
Answer» ANSWER :FALSE STATEMENT

Discussion

12362.	sum (a)/( s-a)(tan ""(B)/(2) - tan ""(C )/(2)) =
Answer» `- (1)/(2) ` ` -1` ` 1` `0 ` ANSWER :D

Discussion

12363.	Use the second derivative test to find local extrema of the function f(x) = -x^(3) + 12 x^(2) - 5 on R.
Answer» Answer :Local MINIMUM X = -5, local maximum= 251

Discussion

12364.	Find the separate equation of the following pair of straight lines 2x^(2)-xy-3y^(2)-6x+19y-20=0
Answer» Answer :`2X - 3Y + 4 = 0` `X + y - 5 = 0`.

Discussion

12365.	If alpha and betaare two distinet roots of the equation x^(2)-x+1=0 then alpha^(101)+beta^(107)=....
Answer» `-1` 0 1 2 Answer :A

Discussion

12366.	Convert 40^(@),20' into radian measure.
Answer» ANSWER :`(121pi)/(540)` RADIAN

Discussion

12367.	Show that (2,-3) lies in the origin side of 2x+3y+7=0
Answer» ANSWER :SIDE of the LINE

Discussion

12368.	Reduce (1/(1-4i) -2/(1+i))((3-4i)/(5+i)) to the standard form.
Answer» ANSWER :`(307)/(42)+(599)/(442)`

Discussion

12369.	Evaluate the following limits : Lt_(xtooo)((x+6)/(x+1))^(x+4)
Answer» ANSWER :`E^(5)`

Discussion

12370.	Evaluate the following limits : Lim_(x to 0) (e^(ax)-1)/(sin x)
Answer» ANSWER :a

Discussion

12371.	Match the following :{:(,"List - I",,"List - II"),((1),cot((pi)/(4)+theta).cot((pi)/(4)-theta),(a),0),((2),sin(45^(@)+theta)-cos(45^(@)-theta),(b),tan 56^(@)),((3),(cos11^(@)+sin11^(@))/(cos11^(@)-sin11^(@)),(c ),(sqrt(3))/(2)),((4),sin^(2)75^(@)-sin^(2)15^(@),(d),1):}
Answer» 1-d, 2-a, 3-b, 4-c 1-a, 2-b, 3-c, 4-d 1-c, 2-b, 3-d, 4-c 1-b, 2-c, 3-a, 4-d Answer :A

Discussion

12372.	If alpha, beta,gamma are acute angles and cos theta = sin beta//sin alpha, cosphi=singamma/sinalpha and cos(theta-phi) = sin beta sin gamma then the value of tan^(2)alpha - tan^(2)beta - tan^(2)gamma is equal to:
Answer» `-1` 0 1 2 Answer :B

Discussion

12373.	If cot^(2)x =cot(x-y) cot(x-z), then cot(2x) is equal to (where x ne +-pi/4)
Answer» `(cotx + coty)/2` `(cot y + cotz)/2` `(cotx + cotz)/2` `(cotx - cot Z)/2` ANSWER :B

Discussion

12374.	Find out which of the following sentences are statements and which are not. Justify your answer .
Answer» SOLUTION :

Discussion

12375.	If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.
Answer» ANSWER :Focus is at the MID - POINT of the GIVEN diameter.

Discussion

12376.	{x inR: cos2x+2cos^(2)x=2} =
Answer» `{2npi+(pi)/(3),ninz}` `{npipm(pi)/(3),ninz}` `{npipm(pi)/(6),ninz}` `{2npi+(pi)/(6),ninz}` ANSWER :C

Discussion

12377.	If alpha, beta , gamma, deltaare the four solutions of the equations tan (theta + (pi)/( 4)) = 3 tan 3 theta . No two of whichhave equal tangents , then the value of tan alpha + tan beta + tan gamma + tan delta =
Answer» 1 0 `-1` 4 Answer :B

Discussion

12378.	Find the condition that one of the roots ofax^(2) + bx+c may beQ (ii) thrice the other
Answer» ANSWER :`3B^(2) = 16ac`

Discussion

12379.	If asin^(2)x+bcos^(2)x=c, bsin^(2) y+a cos^(2) y = d and a tan x = btan y then (a^(2))/(b^(2)) =
Answer» `((a-d)(c-a))/((b-c)(d-b))` `((b-c)(b-d))/((a-c)(a-d))` `((b-c)(d-b))/((a-d)(c-a))` `((d-a)(c-a))/((b-c)(d-b))` ANSWER :A

Discussion

12380.	Find the derivative of x^(4) + y^(4) - a^(2) xy = 0 w.r.to x
Answer» ANSWER :`(a ^(2) y- 4X ^(3))/(4y ^(3) - a ^(2) x)`

Discussion

12381.	Differentiate the following with respect to x.y = tan^(-1)x + log(x+5) + cosx/x
Answer» ANSWER :`1/(1+x^(2)) + 1/x+5 -{XSINX + cosx/x^(2)}`

Discussion

12382.	The set of all points of conitnuous of fofof, where f(x) sgn (x) is
Answer» R-{0} `R-{1-,0,1}` `R-{1-1}` `{-1,0,1}` ANSWER :A

Discussion

12383.	Evaluate the following limits : Lim_( xto2) (x^(3)-8)/(x-2)
Answer» ANSWER :12

Discussion

12384.	A man wants to cut three lengths from a single piece of cloth of length 91 cm. The second length is to be 3 cm longer than the shortest andthe third length is to be twice as long as the shortest. What are the possible lengths of the shortest piece of cloth if the third piece is to at least 5 cm longer than the second.
Answer» SOLUTION :LET the LENGTH of the shortest PIECE be x cm. Then, second length `=(x+3)` cm and third length `= 2x ` cm. `thereforex +(x+3)+2xle91]and 2xge(x+3)+5` `rArr 4x+3le91 and2xgex+8` `rArr 4x le91-3and 2x-xge8` `rArr 4x le88 and x ge8` `rArrx le22 and x GE 8` `rArrx le22 and x ge 8` Hence, the length of the shortest piece is to be greater than or equalto 8 but less than to 22.

Discussion

12385.	If the angle between a line and plane is theta then the angle between the line and normal of the plane is
Answer» `2THETA` `90-THETA` 0 `theta` ANSWER :B

Discussion

12386.	For set A if n(A^4)=81then n(A)=………
Answer» ANSWER :3

Discussion

12387.	Find the distanceof the point P(-4,3,5) from coordinate axes.
Answer» ANSWER :Distance from x-axis ` = SQRT(34)` units, y-axis `=sqrt(41)` units and z-axis = 5 units

Discussion

12388.	A mirror and a source of light are situated at the origin O and at a pointon vec(OX) respectivrly. A ray of light from the sorce strikes the mirror and is reflected. If (1,-1,1) are direction ratios of the normal to the plane, find the D.C's of the reflected ray.
Answer» ANSWER :`(-(1)/(3),-(2)/(3),(2)/(3))`

Discussion

12389.	The mid-points of the sides of a triangle are (1, 5, -1),(0,4,-2) and (2, 3, 4). Find its vertices.
Answer» ANSWER :`(1,2,3), (3,4,5)`

Discussion

12390.	Write the following sets in roster form : B= {x : x in Z, x^(2) lt 20}
Answer» ANSWER :`B= {-4, -3, -2, -1, 0, 1, 2, 3, 4}`

Discussion

12391.	Find the sum of all numbers between 200 and 400 which are divisible by 7.
Answer» ANSWER :8729

Discussion

12392.	Ifa cos ^(2)"" (C )/(2)+c cos ^(2) "" (A)/(2)= (3b)/( 2 ) " then " a,b,care in
Answer» A.G.P. H.P. G.P. A.P. Answer :D

Discussion

12393.	Sum the series : (1+x)+(1+x+x^(2))+(1+x+x^(2)+x^(3))+…… up to n terms
Answer» ANSWER :`=(1)/(1-X)[N-(x^(2)(1-x^(n)))/(1-x)]`

Discussion

12394.	Iftan alpha , tan betaare the roots of the equationx^(2) + px+q=0(p ne 0) then
Answer» 0 1 p q Answer :D

Discussion

12395.	{:(,"Column-I",,"Column-II"),((A),cos 20^(0) + cos 80^(0) - sqrt(3) "cos" 50^(0),(p),-1),((B),cos 0^(0) + "cos" (pi)/(7) + "cos" (2pi)/(7) + "cos" (4pi)/(7) + "cos" (5pi)/(7) + "cos" (6 pi)/(7),(q),-(3)/(4)),((C),cos 20^(0) + cos 40^(0) + cos 60^(0) - 4 cos 10^(0) "cos" 20^(0)"cos" 30^(0),(r),1),((D),"cos" 20^(0) cos 100^(0) + cos 100^(0) "cos" 140^(0) - cos 140^(0) "cos" 200^(0),(s),0):}
Answer» <P> ANSWER :A - s; B - R; C - p; D - Q

Discussion

12396.	A committee of two persons is selected from two men and two women. What is the probability that the committee will have (a) no man? (b) one man? (c) two men?
Answer» ANSWER :` = 1/6`

Discussion

12397.	Let D, E and F be the feet of altitudes from the vertices of acute -angled triangle ABC to the sides BC, AC and AB respectively. Triangle DEF is defined as the pedal triangle ABC. (R and rare circumradius and inradius of triangle of trangle ABC, respectivley) Consider the following statements: (i)orthicentre of the triangle ABC is incentre of the triangle DEF (ii) A,B,C are excentres of triangle DEF
Answer» only (i) is true only (II) is true both (i) and (ii) are true both (i) and (ii) are false Answer :C

Discussion

12398.	Let D, E and F be the feet of altitudes from the vertices of acute -angled triangle ABC to the sides BC, AC and AB respectively. Triangle DEF is defined as the pedal triangle ABC. (R and rare circumradius and inradius of triangle of trangle ABC, respectivley) Circumradius of a pedal triangle of triangle ABC is
Answer» `R//2` `r//2` `R//4` `r//4` ANSWER :A

Discussion

12399.	Let D, E and F be the feet of altitudes from the vertices of acute -angled triangle ABC to the sides BC, AC and AB respectively. Triangle DEF is defined as the pedal triangle ABC. (R and r are circumradius and inradius of triangle of trangle ABC, respectivley) If X,Y,Z are the sides of a pedal triangle, then x + y + z is equal to
Answer» `DELTAR//2` `Delta//2R` `DeltaR` NONE of these Answer :D

Discussion

12400.	Let A be a finite set. The number of relations on A where A has 3 elements are :(i) 9(ii) 6(iii) 256(iv) 512
Answer» 9 6 256 512 Answer :D

Discussion

Explore topic-wise InterviewSolutions in .

Find the ratio in which the xz-plane divides the line joining A(-2, 3, 4) and B(1, 2, 3).

The shortest distance between the lines whose equations are barr = t ( bari + barj + bark ), barr = bark + s(bari - bar2j + 3bark) is

State and prove Binomial theorem for all the integers.

sec x = (13)/(5), x lies in fourth quadrant.

Let ABC be triangle having o and I as its circumcenter and incentre, respectively. If R and r are the circumradius and the inradius, respectively, then (OI)^(2) = ...... Further and also the triangle AIO is a right angle triangle if and only if a, b, c are in ......

Differentiate f(x)=e^(2-3x) by using 1stprinciple.

Given that barc is in the plane of bara, barb and bard is not iri the plane of bara, barb then (baraxx barb) xx (barc xx bard) =

If xtan^(2) 120^(@) + 4 cos^(2) 150^(@) = 9 then x =

2Cos^(-1)x=Sin^(-1)(2xsqrt(1-x^(2))) is valid for

Evaluate Lt_(xto0)(((1+x)^(1/x)-e+(ex)/2)/(x^(2)))

f(x) = 3 cos x + 4 sin x + 8 has minimum value 19.

sum (a)/( s-a)(tan ""(B)/(2) - tan ""(C )/(2)) =

Use the second derivative test to find local extrema of the function f(x) = -x^(3) + 12 x^(2) - 5 on R.

Find the separate equation of the following pair of straight lines 2x^(2)-xy-3y^(2)-6x+19y-20=0

If alpha and betaare two distinet roots of the equation x^(2)-x+1=0 then alpha^(101)+beta^(107)=....

Convert 40^(@),20' into radian measure.

Show that (2,-3) lies in the origin side of 2x+3y+7=0

Reduce (1/(1-4i) -2/(1+i))((3-4i)/(5+i)) to the standard form.

Evaluate the following limits : Lt_(xtooo)((x+6)/(x+1))^(x+4)

Evaluate the following limits : Lim_(x to 0) (e^(ax)-1)/(sin x)

Match the following :{:(,"List - I",,"List - II"),((1),cot((pi)/(4)+theta).cot((pi)/(4)-theta),(a),0),((2),sin(45^(@)+theta)-cos(45^(@)-theta),(b),tan 56^(@)),((3),(cos11^(@)+sin11^(@))/(cos11^(@)-sin11^(@)),(c ),(sqrt(3))/(2)),((4),sin^(2)75^(@)-sin^(2)15^(@),(d),1):}

If alpha, beta,gamma are acute angles and cos theta = sin beta//sin alpha, cosphi=singamma/sinalpha and cos(theta-phi) = sin beta sin gamma then the value of tan^(2)alpha - tan^(2)beta - tan^(2)gamma is equal to:

If cot^(2)x =cot(x-y) cot(x-z), then cot(2x) is equal to (where x ne +-pi/4)

Find out which of the following sentences are statements and which are not. Justify your answer .

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

{x inR: cos2x+2cos^(2)x=2} =

If alpha, beta , gamma, deltaare the four solutions of the equations tan (theta + (pi)/( 4)) = 3 tan 3 theta . No two of whichhave equal tangents , then the value of tan alpha + tan beta + tan gamma + tan delta =

Find the condition that one of the roots ofax^(2) + bx+c may beQ (ii) thrice the other

If asin^(2)x+bcos^(2)x=c, bsin^(2) y+a cos^(2) y = d and a tan x = btan y then (a^(2))/(b^(2)) =

Find the derivative of x^(4) + y^(4) - a^(2) xy = 0 w.r.to x

Differentiate the following with respect to x.y = tan^(-1)x + log(x+5) + cosx/x

The set of all points of conitnuous of fofof, where f(x) sgn (x) is

Evaluate the following limits : Lim_( xto2) (x^(3)-8)/(x-2)

If the angle between a line and plane is theta then the angle between the line and normal of the plane is

For set A if n(A^4)=81then n(A)=………

Find the distanceof the point P(-4,3,5) from coordinate axes.

A mirror and a source of light are situated at the origin O and at a pointon vec(OX) respectivrly. A ray of light from the sorce strikes the mirror and is reflected. If (1,-1,1) are direction ratios of the normal to the plane, find the D.C's of the reflected ray.

The mid-points of the sides of a triangle are (1, 5, -1),(0,4,-2) and (2, 3, 4). Find its vertices.

Write the following sets in roster form : B= {x : x in Z, x^(2) lt 20}

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Ifa cos ^(2)"" (C )/(2)+c cos ^(2) "" (A)/(2)= (3b)/( 2 ) " then " a,b,care in

Sum the series : (1+x)+(1+x+x^(2))+(1+x+x^(2)+x^(3))+…… up to n terms

Iftan alpha , tan betaare the roots of the equationx^(2) + px+q=0(p ne 0) then

A committee of two persons is selected from two men and two women. What is the probability that the committee will have (a) no man? (b) one man? (c) two men?

Let A be a finite set. The number of relations on A where A has 3 elements are :(i) 9(ii) 6(iii) 256(iv) 512