14949 + Interview Questions in Maths in Class 11 Page 131 InterviewSolution

6501.	If vec(i), vec(j), vec(k) is an orthonomal system of vectors, vec(a) is a vector and vec(a) xx vec(i) + 2vec(a)- 5vec(j)=vec(0) then vec(a)=
Answer» `2vec(J) + VEC(K)` `2vec(j)-vec(k)` `2vec(i) + vec(j)` `2vec(i) + vec(j)` ANSWER :A

Discussion

6502.	A cubic function of x ahs maximum 10 and minimum -5//2, when x=-3 and x=2 respectively. Find the function.
Answer» ANSWER :`1/5X^3+3/(10)x^2-(18)/5x+(19)/(10)`

Discussion

6503.	If alpha, beta , gamma , deltaare the solutions of the equation tan(theta+(pi)/4)= 3 tan 3 theta , no two of which have equal tangents. The value of (1)/(tan alpha)+ (1)/(tan beta)+(1)/(tan gamma)+(1)/(tan delta) is
Answer» `-8` 8 `2//3` `1//3` ANSWER :B

Discussion

6504.	The perpendicular distance from origin to the plane passing through the points 2bari -2barj +bark, 3bari +2barj-bark, 3bari -barj-2bark is
Answer» `12/(sqrt(30))` `25/(sqrt(110))` `10/(sqrt(60))` `15/(sqrt(187))` Answer :B

Discussion

6505.	Solvecos x - sqrt3 sin x =1, 0^(@) le x le 360 ^(@).
Answer» ANSWER :`0^(@) LE X le 360^(@)`

Discussion

6506.	The orhocenter of triangle formed by the lines xy=0 and x+y=1 is
Answer» `(1/2,1/2)` `(1/3,1/3)` (0,0) `(1/4,1/4)` ANSWER :C

Discussion

6507.	root(5)(8.0125)
Answer» ANSWER :7.517

Discussion

6508.	Let f(x)=(x)/(e^(x)-1)+(x)/(2)+1, then f is
Answer» an ODD function an EVEN function both odd and even neither odd nor even Answer :B

Discussion

6509.	What universal set would you propose for each of the following : The set of circles with unit radius.
Answer» ANSWER :The SET of all the CIRCLES in the PLANE.

Discussion

6510.	For a group of 200candidates the mean and standard deviation were found to be 40 and 15 repectively . Later on it was found that the score 43 was misread as 34. Findthe correct mean and standard deviation.
Answer» ANSWER :40.045;14.995

Discussion

6511.	LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? {3, 4} ⊂A
Answer» ANSWER :as `{3,4}∈A`

Discussion

6512.	Q cup Z = Q, where Q is the set of rational numbers and Z is the set of integers.
Answer» ANSWER :1

Discussion

6513.	If 1, omega, omega^(2) are the three cube roots of unity, then simplify: (3 + 5omega + 3omega^(2))^(2) (1 + 2omega + omega^(2))
Answer» ANSWER :4

Discussion

6514.	Let f(x) = x - [x] , x in Rthen f(1/2) is
Answer» 1 0 `-1` NONE of these ANSWER :A

Discussion

6515.	Consider the numbers 1,2,3,4,5,6,7,8,9,10 . If 1 is added to each number, the variance of the numbers so obtained is ……….
Answer» 6.5 2.87 3.87 8.25 Answer :D

Discussion

6516.	Valume of parallelpiped formed by vectors veca xx vecb, vecb xx vecc and vecc xx vecais 36 sq. units.
Answer» SOLUTION :`[veca xx vecb vecb xx VECC vecc xx veca]=36` `or [veca vecb vecc]=6` ` Rightarrow` volume of terthedron FORMED by vectors. `veca,vecb and vecc is1/6 [ veca vecb vecc] =1` `[veca +vecb vecb +vecc vecc +veca] =2 [veca vecb vecc] =12` `veca-vecb,vecb-vecc and vecc-veca`are coplanar, `Rightarrow [veca-vecb vecb -veccvecc-veca]=0`

Discussion

6517.	Find the derivative with tan^(-1) ((sinx )/(1 + cos x)) with respect to tan^(-1) ((cos x)/(1 + sin x))
Answer» Answer :` THEREFORE (du)/(DV) = ((du)/(dx))/((dv)/(dx)) = ((1)/(2))/(-(1)/(2)) = (1)/(CANCEL(1))XX (-cancel2)/(1) therefore (du)/(dv) = - 1 `

Discussion

6518.	(i) Find the equation of line passing through (2,2) and makes an angle of 135^(@) from positive direction of X-axis. (ii) Find the equation of a line passing through the point (2,1) and makes an angle 'theta' from the positive direction of X-axis where cos theta=-(1)/(3).
Answer» ANSWER :`(i) x+y=4` `(II) 2sqrt(2)+y=4sqrt(2)+1`

Discussion

6519.	If A and B are mutually exclusive events, P(A) = 0.35 and P(B)= 0.45, find (i) P(A')(ii) P(B')(iii) P(AcupB) (iv) P(AcapB)(v) P(AcapB')(vi) P(A'capB')
Answer» ANSWER :(i) 0.65 (ii)0.55 (iii) 0.8 (iv) 0 (v) 0.35 (VI) 0.2

Discussion

6520.	Find the centre and radius of the circle x^(2)+y^(2)-4x-8y-45=0 ?
Answer» ANSWER :centre =(2,4)radius=`SQRT(65)` unit.

Discussion

6521.	ABCDEF is a regular hexagon. If bar(AB)=bar(a), bar(BC)=bar(b)" then "bar(CE)=
Answer» `(BAR(B)-2BAR(a))` `2(bar(a)-bar(b))` `bar(b)-bar(a)` `bar(a)-bar(b)` ANSWER :A

Discussion

6522.	If the lines 4x+3y-1=0, x-y+5=0 and kx+5y-3=0 are concurrent, then k =
Answer» 4 5 6 7 Answer :C

Discussion

6523.	If alpha, beta , gamma , deltaare the solutions of the equation tan(theta+(pi)/4)= 3 tan 3 theta , no two of which have equal tangents. The value of tan alpha tan beta tan gamma tan deltais
Answer» `-1//3` `-2` 0 none of these Answer :a

Discussion

6524.	If alpha, beta , gamma , deltaare the solutions of the equation tan(theta+(pi)/4)= 3 tan 3 theta , no two of which have equal tangents. The value of tan alpha + tan beta + tan gamma + tan deltais
Answer» `1//3` `8//3` `-8//3` 0 Answer :d

Discussion

6525.	Solve the equations: Q. x^(5)+242=(243)/(x^(5)).
Answer» ANSWER :3 or 1.

Discussion

6526.	Let R be a relation from Q to Q defined by R={(a,b): a,b in Q and a-b in Z}. Show that (i) (a,a) in R" for all " a in Q (ii) (a,b) in R implies that (b,a) inR (iii) (a,b) in R and (b,c) in R implies that (a,c) in R
Answer» ANSWER :SINCE, `a-a= 0 in Z`, if the that `(a, a) in R`

Discussion

6527.	If f and g are real functions defined by f(x)= x^(2) + 7 and g(x)= 3x + 5. Then, find each of the following f(1)-f(-2)
Answer» ANSWER :`t^(2)-4`

Discussion

6528.	If A+B+C=(pi)/2, " then " sum (cos (B+C))/(cos B cos C)=
Answer» 1 2 3 4 Answer :B

Discussion

6529.	In the space the equation by + cz + d = 0 represents a plane perpendicular to the ..... plane
Answer» YOZ ZOX XO Y `Z= K` ANSWER :A

Discussion

6530.	The set of whole numbers is a finite set .
Answer» ANSWER :F

Discussion

6531.	If sin theta + cosec theta =2 then sin^(n) theta + cosec^(n) theta =
Answer» ANSWER :`:.SIN^(N) THETA + COSEC^(n) theta = 1+1=2`

Discussion

6532.	Find lim_(xrarr0)[sqrt(1+sin^2 2x)-sqrt(1-sin^2 2x)]/(xtan2x)
Answer» ANSWER :4

Discussion

6533.	Evaluate the following limits : Lim _( x to oo) sqrt(x)(sqrt(x+c)-sqrt(x))
Answer» ANSWER :`c/2`

Discussion

6534.	Find the equation of ellipse whose distance between foci is 8 units and distance between the directrices is 18 units.
Answer» ANSWER :`(X^(2))/36+(y^(2))/20=1`

Discussion

6535.	If lamdax + 4y + 5z = 7, 4x + 4lamda y +10z - 14 = 0represent the same plane the value of lamda=
Answer» 1 2 0 3 Answer :B

Discussion

6536.	Write a short note on vector product between two vectors.
Answer» Solution : (i) The vector PRODUCT or cross product of two vectors is DEFINED as ANOTHER vector having a magnitude equal to the product of the magnitudes of two vectors and the sine of the angle between them. (ii) The direction of the product vector is perpendicular to the plane containing the two vectors, in accordance with the RIGHT hand screw rule or right hand thumb rule. (iii) Thus, if `vecA` and `vecB` are two vectors, then their vector product is written as `vec(A) xx vec(B)`is a vector`vecC`defined by ` vecC = vecA xx vecB = (AB sin theta) HATN`

Discussion

6537.	Find the points on the x-axis, whose distances from the linex/3 + y/4 = 1 are 4units.
Answer» ANSWER :`(-2, 0) " and " (8, 0)`

Discussion

6538.	If y = a log\|x\| + bx^(2) + x has extreme values at x = 2 and x = -4/3 then find a and b.
Answer» ANSWER :a = 4, B = -3/4

Discussion

6539.	The marksof seven students in intelligence and arithmetic tests are as follows : {:("Candidate",A,B,C,D,E,F,G),("Intelligence test", 30,52,60,62,45,32,41),("Arithmetic test", 41,62,70,78,53,45,57):} Calculate Karl Person's coefficient of correlation and interpret it .
Answer» ANSWER :`0.97`; a very very HIGHDEGREE POSITIVE CORRELATION

Discussion

6540.	If (baraxxbarb)xxbarc=baraxx(barbxxbarc) where bara,barb,barc are any three vectors such that bara.barbne0,barb.barcne0 then bara and barc are
Answer» Parallel Inclined at an ANGLE of `pi/3` between them Inclined at an angle of `pi/6` between them Perpendicular Answer :A

Discussion

6541.	Compute the following limits : Lt_(xto0)(1-cosx)/x^(2)
Answer» ANSWER :`1//2`

Discussion

6542.	Find the term independent of x in the expansion of (1+x+2x^(3))(3/2 x^(2)-1/(3x))^(9)
Answer» ANSWER :` :. " REQUIRED CONSTANT TERM " =17/54 `

Discussion

6543.	a cos ^(2) "" ( A) /(2)+ b cos ^(2) "" ( B)/(2)= c cos ^(2) "" ( C) /(2) =
Answer» ` s- ( R ) /( R) ` ` s + ( r ) / ( R ) ` ` s - (DELTA )/( R ) ` ` s + ( Delta )/( R) ` ANSWER :D

Discussion

6544.	Evaluate the following limits : Lim_(x to 0) (8^(x)-2^(x))/x
Answer» ANSWER :LOG 4

Discussion

6545.	Given that alpha and beta are the roots of the equation 2x^(2)-3x+4=0, find an equation whose roots are alpha+(1)/(alpha) and beta+(1)/(beta).
Answer» ANSWER :`8X^(2)-18x+13=0`.

Discussion

6546.	\|{:(1,w,w^(2)),(w,w^(2),1),(w^(2),1,w):}\| =
Answer» `-1` 1 0 2 Answer :C

Discussion

6547.	If f(x)=x^(2)/2+3x where x=2,deltax=0.05 then df=
Answer» 2.5 0.25 2.635 2.652 Answer :B

Discussion

6548.	Let f_(n)(theta) = ("cos"(theta)/(2)+ cos 2 theta + "cos" (7 theta)/(2)+....+ cos (3n - 2) (theta)/(2))/("sin"(theta)/(2) + sin 2 theta + "sin" (7 theta)/(2) +....+sin (3n - 2) (theta)/(2)). Then match the entries of column-I with their corresponding values given in column-II. {:(,"Column-I",,"Column-II"),((A),f_(3) ((3pi)/(16)),(p),2 - sqrt(3)),((B),f_(5) ((pi)/(28)),(q),sqrt(3 + 2sqrt(2))),((C),f_(7) ((pi)/(60)),(r),sqrt(2) - 1),(,,(s),2 + sqrt(3)):}
Answer» ANSWER :A - R; B - Q; C - s

Discussion

6549.	Solve sqrt(2)x^(2) +x + sqrt(2)=0
Answer» ANSWER :`(-1+- SQRT(7)i)/(2sqrt(2))`

Discussion

6550.	If the sumof the squares of the sides of a trianglesABC isequal totwice the squareof its circumdiameter, thensin ^(2) A + sin ^(2) B+ sin ^(2) C =
Answer» ` 4` `3` ` 1` `2` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

If vec(i), vec(j), vec(k) is an orthonomal system of vectors, vec(a) is a vector and vec(a) xx vec(i) + 2vec(a)- 5vec(j)=vec(0) then vec(a)=

A cubic function of x ahs maximum 10 and minimum -5//2, when x=-3 and x=2 respectively. Find the function.

If alpha, beta , gamma , deltaare the solutions of the equation tan(theta+(pi)/4)= 3 tan 3 theta , no two of which have equal tangents. The value of (1)/(tan alpha)+ (1)/(tan beta)+(1)/(tan gamma)+(1)/(tan delta) is

The perpendicular distance from origin to the plane passing through the points 2bari -2barj +bark, 3bari +2barj-bark, 3bari -barj-2bark is

Solvecos x - sqrt3 sin x =1, 0^(@) le x le 360 ^(@).

The orhocenter of triangle formed by the lines xy=0 and x+y=1 is

root(5)(8.0125)

Let f(x)=(x)/(e^(x)-1)+(x)/(2)+1, then f is

What universal set would you propose for each of the following : The set of circles with unit radius.

For a group of 200candidates the mean and standard deviation were found to be 40 and 15 repectively . Later on it was found that the score 43 was misread as 34. Findthe correct mean and standard deviation.

LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? {3, 4} ⊂A

Q cup Z = Q, where Q is the set of rational numbers and Z is the set of integers.

If 1, omega, omega^(2) are the three cube roots of unity, then simplify: (3 + 5omega + 3omega^(2))^(2) (1 + 2omega + omega^(2))

Let f(x) = x - [x] , x in Rthen f(1/2) is

Consider the numbers 1,2,3,4,5,6,7,8,9,10 . If 1 is added to each number, the variance of the numbers so obtained is ……….

Valume of parallelpiped formed by vectors veca xx vecb, vecb xx vecc and vecc xx vecais 36 sq. units.

Find the derivative with tan^(-1) ((sinx )/(1 + cos x)) with respect to tan^(-1) ((cos x)/(1 + sin x))

(i) Find the equation of line passing through (2,2) and makes an angle of 135^(@) from positive direction of X-axis. (ii) Find the equation of a line passing through the point (2,1) and makes an angle 'theta' from the positive direction of X-axis where cos theta=-(1)/(3).

If A and B are mutually exclusive events, P(A) = 0.35 and P(B)= 0.45, find (i) P(A')(ii) P(B')(iii) P(AcupB) (iv) P(AcapB)(v) P(AcapB')(vi) P(A'capB')

Find the centre and radius of the circle x^(2)+y^(2)-4x-8y-45=0 ?

ABCDEF is a regular hexagon. If bar(AB)=bar(a), bar(BC)=bar(b)" then "bar(CE)=

If the lines 4x+3y-1=0, x-y+5=0 and kx+5y-3=0 are concurrent, then k =

If alpha, beta , gamma , deltaare the solutions of the equation tan(theta+(pi)/4)= 3 tan 3 theta , no two of which have equal tangents. The value of tan alpha tan beta tan gamma tan deltais

If alpha, beta , gamma , deltaare the solutions of the equation tan(theta+(pi)/4)= 3 tan 3 theta , no two of which have equal tangents. The value of tan alpha + tan beta + tan gamma + tan deltais

Solve the equations: Q. x^(5)+242=(243)/(x^(5)).

Let R be a relation from Q to Q defined by R={(a,b): a,b in Q and a-b in Z}. Show that (i) (a,a) in R" for all " a in Q (ii) (a,b) in R implies that (b,a) inR (iii) (a,b) in R and (b,c) in R implies that (a,c) in R

If f and g are real functions defined by f(x)= x^(2) + 7 and g(x)= 3x + 5. Then, find each of the following f(1)-f(-2)

If A+B+C=(pi)/2, " then " sum (cos (B+C))/(cos B cos C)=

In the space the equation by + cz + d = 0 represents a plane perpendicular to the ..... plane

The set of whole numbers is a finite set .

If sin theta + cosec theta =2 then sin^(n) theta + cosec^(n) theta =

Find lim_(xrarr0)[sqrt(1+sin^2 2x)-sqrt(1-sin^2 2x)]/(xtan2x)

Evaluate the following limits : Lim _( x to oo) sqrt(x)(sqrt(x+c)-sqrt(x))

Find the equation of ellipse whose distance between foci is 8 units and distance between the directrices is 18 units.

If lamdax + 4y + 5z = 7, 4x + 4lamda y +10z - 14 = 0represent the same plane the value of lamda=

Write a short note on vector product between two vectors.

Find the points on the x-axis, whose distances from the linex/3 + y/4 = 1 are 4units.

If y = a log|x| + bx^(2) + x has extreme values at x = 2 and x = -4/3 then find a and b.

The marksof seven students in intelligence and arithmetic tests are as follows : {:("Candidate",A,B,C,D,E,F,G),("Intelligence test", 30,52,60,62,45,32,41),("Arithmetic test", 41,62,70,78,53,45,57):} Calculate Karl Person's coefficient of correlation and interpret it .

If (baraxxbarb)xxbarc=baraxx(barbxxbarc) where bara,barb,barc are any three vectors such that bara.barbne0,barb.barcne0 then bara and barc are

Compute the following limits : Lt_(xto0)(1-cosx)/x^(2)

Find the term independent of x in the expansion of (1+x+2x^(3))(3/2 x^(2)-1/(3x))^(9)

a cos ^(2) "" ( A) /(2)+ b cos ^(2) "" ( B)/(2)= c cos ^(2) "" ( C) /(2) =

Evaluate the following limits : Lim_(x to 0) (8^(x)-2^(x))/x

Given that alpha and beta are the roots of the equation 2x^(2)-3x+4=0, find an equation whose roots are alpha+(1)/(alpha) and beta+(1)/(beta).

|{:(1,w,w^(2)),(w,w^(2),1),(w^(2),1,w):}| =

If f(x)=x^(2)/2+3x where x=2,deltax=0.05 then df=

Solve sqrt(2)x^(2) +x + sqrt(2)=0

If the sumof the squares of the sides of a trianglesABC isequal totwice the squareof its circumdiameter, thensin ^(2) A + sin ^(2) B+ sin ^(2) C =