14949 + Interview Questions in Maths in Class 11 Page 69 InterviewSolution

3401.	Let A=[a_(ij)]_(mxxn) be a matrix such that a_(ij)=1 for all I,j. Then ,
Answer» RANK (A) GT 1 rank (A) = 1 rank (A) = m rank (A) = n Answer :B

Discussion

3402.	If a card is drawn from a deck of 52 cards, then find the probability of getting a king or a heart or a red card.
Answer» ANSWER :`(7)/(13)`

Discussion

3403.	Find the mean deviation about median for the following data:
Answer» Solution : Here `n=50impliesN/2=50/2=25` `:.` Median class is 20-30. Now `l_(1)=20, l_(2)=30, C=14, f=14` and median `M=l_(1)+((N/2-C)xx(l_(2)-l_(1)))/f` `M=20+((25-14)xx10)/14` `=20+7.85` `=27.85` Now MEAN deviation `=(sumf_(i)d_(i))/(sumf_(i))` `=517.1/50` `=10.342`

Discussion

3404.	Differentiate w.r.t 'x' f(x) = (sqrt(x^(2)+1)+sqrt(x^(2)-1))/(sqrt(x^(2)+1)-sqrt(x^(2)-1))
Answer» Answer :`f' (X) = 2 [ x + (x^(3))/(sqrt(x^(4)-1))] `

Discussion

3405.	Show thatcot(Sin^-1sqrt(13/17))=sin(Tan^-1""2/3).
Answer» `-2/(SQRT(13))` `0` `2/(sqrt(13))` `2/(3sqrt(13))` ANSWER :B

Discussion

3406.	Find the derivative of f(x) =(x+1)/(x)
Answer» ANSWER :`-(1)/(X^(2))`

Discussion

3407.	Evaluate the following limits : Lt_(xto6)(e^(x)-e^(6))/(x-6)
Answer» ANSWER :`E^(6)`

Discussion

3408.	What loci do the equation rpresent in space? y =0, z=0
Answer» ANSWER :`Z =0`

Discussion

3409.	Solve the inequation x lt - 3 graphically
Answer» Solution :We know that the graph of `x= -3` is a straight line AB drawn parallel to the y - axis at a distance ofunits to the left of the y- axis. CLEALY , the point (0,0) does not satisfy the inequation `,x lt -3 ` So we shade that part of the plane divided by AB which does not CONTAIN O(0,0) excluding AB. The SHADED Part of the plane is the solution set of `x lt -3 ` as shown above.

Discussion

3410.	If f(x) = (x+2)/( x-2) for all x ne 2, find f' (-2).
Answer» ANSWER :`- (1)/(4)`

Discussion

3411.	Find real contans, a b so that the function 'f' given by f(x)={{:(sinx , if, x le0),(x^(2)+a, if, 0 lt x lt 1),(bx+3,if, 1 le x le 3),(-3,if,x gt 3):} is continuous on R.
Answer» ANSWER :`a=0, b=-2`

Discussion

3412.	If "Sec"^(-1)x/a-"Sec"^(-1)x/b="Sec"^(-1)b-Sec^(-1)a then x=
Answer» `AB` `SQRT(ab)` `(a+b)/2` `(2AB)/(a+b)` ANSWER :A

Discussion

3413.	A=tan 15^(0)+cot15^(0),B= tan 22(1^(0))/(2)+cot 22(1^(0))/(2) and C= sin 54^(0)-sin 18^(0) then the ascending order of A,B C is
Answer» A,B,C B,C,A C,A,B C,B,A Answer :D

Discussion

3414.	Find 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
Answer» ANSWER :3072

Discussion

3415.	Find the distance between P(x_(1), y_(1) ) and Q(x_(2) , y_(2) ) when (i) PQ is parallel to the Y-axis (ii) PQ is parallel to the X- axis.
Answer» ANSWER :`\|x_1 - x_2\|`

Discussion

3416.	If ""^nC_10= ""^nC_12 then find ""^23C_n.
Answer» ANSWER :23

Discussion

3417.	Find the domain and the range of the functions f(x) = 1/(2x-1)
Answer» SOLUTION :DOMAIN =`R -[1/2]` RANGE = R -[0]

Discussion

3418.	If a particle moves along a line by S = sqrt(1 + t) then its acceleration is proportional to _______ of its velocity at the instant.
Answer» square cube double triple Answer :B

Discussion

3419.	If omega is complex cube root of 1 then S.T [(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega)]=0
Answer» ANSWER :`=0`

Discussion

3420.	Obtain equation of ellipse satisfying given conditions Eccentricity e = (1)/(2) semi major axis of length = 4, Major axis is X- axis.
Answer» ANSWER :`3X^(2) + 4Y^(2) = 48`

Discussion

3421.	A value of c for which the conclusion of Mean Value Theorem holds for the function f(x) = log_(e )x on the interval [1, 3] is
Answer» `log_(E ) 3` `2 log_(3) e ` `1//2 log _(e) 3` ` log_(3) e ` Answer :B

Discussion

3422.	cos theta + cos 2 theta + cos 3 theta + …. + cos { (n-1) theta}+ cos n theta=
Answer» `(cos { (1)/(2) (N+1) THETA} . Sin((ntheta)/( 2) ))/( sin((theta)/(2)) )` `(cos (n+1) theta)/( sin ((theta)/( 2)) )` `( cos ( ((n-1) theta)/(2) ) sin ( ( n theta)/( 2) ) )/( sin"" ( theta)/( 2) )` `(sin ( (n theta)/( 2) ).cos{ (n+1) theta})/( sin ((theta)/( 2) ) )` Answer :A

Discussion

3423.	Find the equation of a line which makes a triangle of area 96sqrt(3) square from co-ordinate axes and the perpendicular drawn from origin to this line makes an angle 60^(@) from X-axis.
Answer» ANSWER :`x+ysqrt(3)=+-24`

Discussion

3424.	The valuetan^(-1)[sqrt((a-b)/(a+b))"tan"(theta)/2] is equal to
Answer» `COS^(-1)((a cos THETA +B)/(a+b cos theta))` `cos^(-1)((a+b cos theta)/(a cos theta+b))` `cos^(-1)((a cos theta)/(a+b cos theta))` `cos^(-1)((b cos theta)/(a cos theta+b))` ANSWER :A

Discussion

3425.	Find the slope and inclination of the line through each pair of the following points: (10, 4) and (-2, -2)
Answer» ANSWER : `1/(2), 26^(@)34'`

Discussion

3426.	OPQR is a square and M,N are the middle points of sides PQ and QR respectively then the ratio of the area of the square and the triangle OMN is
Answer» `4:1` `2:1` `8:3` `4:3` ANSWER :C

Discussion

3427.	Let P(-1,0), Q(0,0) and R(3,3sqrt(3)) be three points. The equation of the bisector of the angle PQR is
Answer» `(sqrt3//2)X+y=0` `x+sqrt3y=0` `sqrt3x+y=0` `x+(sqrt3//2)y=0` ANSWER :B

Discussion

3428.	Find the derivative of the function from first principle x ^(2)
Answer» ANSWER :`2X`

Discussion

3429.	In the tetrahedrom ABCD, A=(1,2,-3) and G=(-3,4,5) is cntroid of tetrahedron. If P is the centroid of triangle BCD then AP=
Answer» `(4sqrt21)/3` `(8sqrt21)/3` `4sqrt21` `(sqrt21)/3` ANSWER :B

Discussion

3430.	Write the converse, inverse and contrapositive of the following statements. you will be strong only if you drink your milk.
Answer» ANSWER :Converse : If you drink your MILK, then YOUARE strong. Inverse : If you are strong, then you do not drink your milk. Contrapositive : IFYOU do not drink your milk, then you are not strong.

Discussion

3431.	If Cos ^(-1) (( x ^(2) - y ^(2))/(x ^(2) + y ^(2)))=k (a constnat), then (dy)/(dx) =
Answer» `-x/y` `-y/x` `y/x` `x/y` ANSWER :C

Discussion

3432.	Find Lt_(xtooo)(x^(2)+5x+2)/(2x^(2)-5x+1)
Answer» ANSWER :`1/2`

Discussion

3433.	Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 – 24x – 18x^(2)
Answer» ANSWER :MAXIMUM PROFIT = 31

Discussion

3434.	Find the mean, variance and standard deviation for first six odd natural numbers.
Answer» ANSWER :MEAN = 6, VARIANCE = 11.67 and SD = 3.41

Discussion

3435.	If a:b: c=1:2:3 then the lines represented by ax^(2)+bxy+cy^(2)=0 are
Answer» real imaginary COINCIDENT PERPENDICULAR ANSWER :B

Discussion

3436.	Find real theta such that (3+2isintheta)/(1-2isintheta) is purely real.
Answer» ANSWER :`theta=npi, N in Z`.

Discussion

3437.	The value of sin ^(2) 12 ^(@) + sin ^(2) 12 ^(@) + sin ^(2) 39^(@) + sin ^(2) 48^(@) - sin ^(2) 9^(@) - sin ^(2) 18^(@)is "______"
Answer» ANSWER :1

Discussion

3438.	lim _ (xto 0) ( sin (x^(2) ) )/( x)
Answer» ANSWER :` ( PI )/( 180) `

Discussion

3439.	If bara, barb, barc form a left handed orthogonal system and bara. bara= 4, barb . barb = 9, barc . barc = 16 then [barabarbbarc] =
Answer» 24 `-24` 12 `-12` ANSWER :B

Discussion

3440.	Consider the expansion of (x+a)^n If these are 112,7 and 1/4 respectively, find x, a, n
Answer» SOLUTION :`x=8,x=4,a=1/2`]

Discussion

3441.	If sec alpha and "cosec" alphaare the roots of x^(2)-px+q=0 then
Answer» `p^(2)=Q(q-2)` `p^(2)=q(q+2)` `p^(2)+q^(2)=2q` `p^(2)+q^(2)=1` Answer :B

Discussion

3442.	The value of cot^(-1)(2+sqrt(3)) is
Answer» `(pi)/12` `(pi)/15` `(pi)/5` `(3PI)/10` Answer :A

Discussion

3443.	The minimum andmaximum valuesof cos theta+ 2 sqrt(2) sin thetais
Answer» `3,3` `3,-3` `[-3,3]` `[0,3]` ANSWER :1

Discussion

3444.	If (tanx-tany)^(2),(tany-tanz)^(2) and (tanz-tanx)^(2) are in A.P then tanx - tany, tany-tanz, tanz-tanx are in (A) A.P. (B) G.P. (C) H.P. (D) A.G.P
Answer» A.P G.P H.P A.G.P Answer :C

Discussion

3445.	The most general value of theta which satisfies both the equations tan theta = - 1 and cos theta = (1)/(sqrt(2)) is
Answer» `n PI + (7 pi)/(4), n in Z` `2N pi + (7 pi)/(4), n in Z` `n pi + (-1)^(n)(7 pi)/(4), n in Z` `(7 n pi)/( 4), n in Z` ANSWER :B

Discussion

3446.	State whether word or is used in following statement is Exclusive or Inclusive. Pizza is serve with cold drink or cold cofee.
Answer» ANSWER :EXCLUSIVE SENCE

Discussion

3447.	For the equation 1-2x-x^(2)=tan^(2)(x+y)+cot^(2)(x+y)
Answer» exactly one value of x EXISTS exactly TWO VALUES of x exists `y=-1+npi+pi/4, n in Z` `y=1+npi+pi//4, n in Z` ANSWER :A::D

Discussion

3448.	The condition that the equation ax^(2) + 2hxy + by^(2) + 2gx + 2fy +c=0 can take the form ax^(2) - 2hxy + by^(2)=0, when shifting the origi is
Answer» Answer :`abc + 2fgh - AF^(2) - bg^(2) - CH^(2) = 0`

Discussion

3449.	Number of point of discontinuity off(x) = (1)/(x - [x]) is
Answer» 0 2 3 `OO` ANSWER :D

Discussion

3450.	It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible ?
Answer» ANSWER :2880

Discussion

Explore topic-wise InterviewSolutions in .

Let A=[a_(ij)]_(mxxn) be a matrix such that a_(ij)=1 for all I,j. Then ,

If a card is drawn from a deck of 52 cards, then find the probability of getting a king or a heart or a red card.

Find the mean deviation about median for the following data:

Differentiate w.r.t 'x' f(x) = (sqrt(x^(2)+1)+sqrt(x^(2)-1))/(sqrt(x^(2)+1)-sqrt(x^(2)-1))

Show thatcot(Sin^-1sqrt(13/17))=sin(Tan^-1""2/3).

Find the derivative of f(x) =(x+1)/(x)

Evaluate the following limits : Lt_(xto6)(e^(x)-e^(6))/(x-6)

What loci do the equation rpresent in space? y =0, z=0

Solve the inequation x lt - 3 graphically

If f(x) = (x+2)/( x-2) for all x ne 2, find f' (-2).

Find real contans, a b so that the function 'f' given by f(x)={{:(sinx , if, x le0),(x^(2)+a, if, 0 lt x lt 1),(bx+3,if, 1 le x le 3),(-3,if,x gt 3):} is continuous on R.

If "Sec"^(-1)x/a-"Sec"^(-1)x/b="Sec"^(-1)b-Sec^(-1)a then x=

A=tan 15^(0)+cot15^(0),B= tan 22(1^(0))/(2)+cot 22(1^(0))/(2) and C= sin 54^(0)-sin 18^(0) then the ascending order of A,B C is

Find 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.

Find the distance between P(x_(1), y_(1) ) and Q(x_(2) , y_(2) ) when (i) PQ is parallel to the Y-axis (ii) PQ is parallel to the X- axis.

If ""^nC_10= ""^nC_12 then find ""^23C_n.

Find the domain and the range of the functions f(x) = 1/(2x-1)

If a particle moves along a line by S = sqrt(1 + t) then its acceleration is proportional to _______ of its velocity at the instant.

If omega is complex cube root of 1 then S.T [(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega)]=0

Obtain equation of ellipse satisfying given conditions Eccentricity e = (1)/(2) semi major axis of length = 4, Major axis is X- axis.

A value of c for which the conclusion of Mean Value Theorem holds for the function f(x) = log_(e )x on the interval [1, 3] is

cos theta + cos 2 theta + cos 3 theta + …. + cos { (n-1) theta}+ cos n theta=

Find the equation of a line which makes a triangle of area 96sqrt(3) square from co-ordinate axes and the perpendicular drawn from origin to this line makes an angle 60^(@) from X-axis.

The valuetan^(-1)[sqrt((a-b)/(a+b))"tan"(theta)/2] is equal to

Find the slope and inclination of the line through each pair of the following points: (10, 4) and (-2, -2)

OPQR is a square and M,N are the middle points of sides PQ and QR respectively then the ratio of the area of the square and the triangle OMN is

Let P(-1,0), Q(0,0) and R(3,3sqrt(3)) be three points. The equation of the bisector of the angle PQR is

Find the derivative of the function from first principle x ^(2)

In the tetrahedrom ABCD, A=(1,2,-3) and G=(-3,4,5) is cntroid of tetrahedron. If P is the centroid of triangle BCD then AP=

Write the converse, inverse and contrapositive of the following statements. you will be strong only if you drink your milk.

If Cos ^(-1) (( x ^(2) - y ^(2))/(x ^(2) + y ^(2)))=k (a constnat), then (dy)/(dx) =

Find Lt_(xtooo)(x^(2)+5x+2)/(2x^(2)-5x+1)

Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 – 24x – 18x^(2)

Find the mean, variance and standard deviation for first six odd natural numbers.

If a:b: c=1:2:3 then the lines represented by ax^(2)+bxy+cy^(2)=0 are

Find real theta such that (3+2isintheta)/(1-2isintheta) is purely real.

The value of sin ^(2) 12 ^(@) + sin ^(2) 12 ^(@) + sin ^(2) 39^(@) + sin ^(2) 48^(@) - sin ^(2) 9^(@) - sin ^(2) 18^(@)is "______"

lim _ (xto 0) ( sin (x^(2) ) )/( x)

If bara, barb, barc form a left handed orthogonal system and bara. bara= 4, barb . barb = 9, barc . barc = 16 then [barabarbbarc] =

Consider the expansion of (x+a)^n If these are 112,7 and 1/4 respectively, find x, a, n

If sec alpha and "cosec" alphaare the roots of x^(2)-px+q=0 then

The value of cot^(-1)(2+sqrt(3)) is

The minimum andmaximum valuesof cos theta+ 2 sqrt(2) sin thetais

If (tanx-tany)^(2),(tany-tanz)^(2) and (tanz-tanx)^(2) are in A.P then tanx - tany, tany-tanz, tanz-tanx are in (A) A.P. (B) G.P. (C) H.P. (D) A.G.P

The most general value of theta which satisfies both the equations tan theta = - 1 and cos theta = (1)/(sqrt(2)) is

State whether word or is used in following statement is Exclusive or Inclusive. Pizza is serve with cold drink or cold cofee.

For the equation 1-2x-x^(2)=tan^(2)(x+y)+cot^(2)(x+y)

The condition that the equation ax^(2) + 2hxy + by^(2) + 2gx + 2fy +c=0 can take the form ax^(2) - 2hxy + by^(2)=0, when shifting the origi is

Number of point of discontinuity off(x) = (1)/(x - [x]) is

It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible ?