14949 + Interview Questions in Maths in Class 11 Page 31 InterviewSolution

1501.	(baraxxbari)xxbari +(baraxxbarj)xxbarj+(baraxxbark)xxbark=
Answer» `BARA` `-bara` `2bara` `-2bara` ANSWER :D

Discussion

1502.	The volume of metallic hallow sphere is constant. If the order radius is increasint at thed rate of V cm/sec. Then the rate at which the inner radius increasing when the radii are a+d,a is
Answer» `(V(a+d)^(2))/(a^(2))` `(V(a+d))/(a)` V(a+d) a+d Answer :A

Discussion

1503.	If f(x)={{:(ax^(2)-b",", -1 lt x lt 1), (1/abs(x)",", "elsewhere"):} is differentiable at x=1, then
Answer» `a=1/2, b=(-3)/2` `a=(-1)/2, b=3/2` `a=-1/2, b=-3/2` `a=1/2, b=3/2` Answer :C

Discussion

1504.	If xy(y-x)=16 then y has a minimum value when x=
Answer» 1 3 2 4 Answer :C

Discussion

1505.	(d)/(dx)(sinx^(@))=…….
Answer» `COS X^(@)` `-SINX^(@)` `(PI)/(180)cosx^(@)` 0 Answer :C

Discussion

1506.	If 3sintheta=2costheta then the value of sin2theta is …………..
Answer» `(12)/(13)` `(5)/(13)` `(4)/(5)` `(3)/(5)` ANSWER :A

Discussion

1507.	If a ne b and a^(2)=5a-3,b^(2)=5b-3, then form that equation whose roots are a/b and b/a.
Answer» ANSWER :`3X^(2)-19x+3=0`.

Discussion

1508.	A is a fixed point on the circumference of a circle with centre 'O' and radius 'r', A particle starts at A and moves on the circumference with an 4 radian/sec. If PM is perpendicualar to OA and algle POM = pi//3, then the rate at which of DeltaPOM decreases is
Answer» `(R^(2))/(2)` sq.cms/sec `r` cms/sec `(3R^(2))/(2)` sq.cms/sec `2R^(2)` sq.cms/sec Answer :B

Discussion

1509.	The range of the function f(x)=\|x-1\|+\|x-2\|,-1 le x le 3, is
Answer» `[1, 3]` `[1, 5]` `[3, 5]` `[2, 5]` Answer :B

Discussion

1510.	If tanA=(1-cosB)/(sinB), then tan2A = …………
Answer» ANSWER :`TANB`

Discussion

1511.	If O=(0,0,0), A=(1,2,1), B=(2,1,3), C = (1,1,2) and OABC is a tetrahedron. Find the angle between the faces OAB and ABC.
Answer» ANSWER :`COS^(-1)((19)/(35))`

Discussion

1512.	A coin and a die are tossed . Describe the following events . D : getting a head or a tail.
Answer» ANSWER :`D=[H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}`

Discussion

1513.	Let P(n) : n(n+1)(n+2) is divisible by 6. Determine whether the statement is true or false, when n=3 and n=5. Justify your answer.
Answer» SOLUTION :TRUE, True

Discussion

1514.	Change the following complex numbers into polar form -4+4 sqrt3i
Answer» ANSWER :`8("cos"(2pi)/(3)+ i "SIN"(2pi)/(3))`

Discussion

1515.	Show that the followiing system of equations is consistent and solve it completely. x+y+z=3," "2x+2y-z=3," "x+y-z=1
Answer» ANSWER :`K in R` is the SOLUTION SET

Discussion

1516.	Solve the general vlaue. 2 cos theta + cos 3 theta =0
Answer» Answer :`( 2N + 1) (pi)/(2) , N pi pm (pi)/(3)`

Discussion

1517.	If R+r=r_(3) then C=
Answer» `90^(@)` `60^(@)` `45^(@)` `120^(@)` Answer :B

Discussion

1518.	If secx=sqrt(2) and x does not lie in the 1^(st) quadrant, find the value of (1+tanx+" cosec "x)/(1+cot x-" cosec "x).
Answer» ANSWER :`-1`

Discussion

1519.	If Sin theta+ Sin^(2) theta=1 and cos a cos^(12) theta+ b cos ^(12) theta+ b cos^(10) theta+ c cos^(8) theta+d cos^(6)-1 theta= then (b+c)/(a+d)
Answer» 1 2 `-2` 3 Answer :D

Discussion

1520.	Match the following from List - I to List - II \|{:("List - I","-List - II"),("(I) "\|{:(3421,3422),(3423,3424):}\|=,"(a) 3"),("(II) "\|{:(11,12,13),(12,13,14),(13,14,15):}\|=,"(b) 0"),("(III) If the matrix "[(8,-6,2),(-6,7,-4),(2,-4,lamda)]" is singular then "lamda" is","(c) -2"),("(IV) if "\|{:(a,b,0),(0,a,b),(b,0,a):}\|=0", then the real value of "a/b" is","(d) -1"):}
Answer» c,B,a,d c,b,d,a b,c,a,d b,c,d,a Answer :A

Discussion

1521.	From a point on the level ground , theangel of elevation of the top of a pole is 30^(@). On moving 20 meters nearer, the angle of elevation is 45^(@). Then the height of the pole, in meters, is
Answer» `10(sqrt3-1)m` `10(sqrt3+1)m` 15 20 Answer :B

Discussion

1522.	Differentiate the following functions w.r.t. x: x sin x
Answer» ANSWER :`X COS x + SINX `

Discussion

1523.	From 0 to …… when r increases, ""^nC_r also increases.
Answer» n n -1 `n/2` `[N/2]` ANSWER :D

Discussion

1524.	Find the general value oftheta in sec theta - cosec theta = (4)/(3)
Answer» Answer :`1/2 [N PI + (-1) ^(n) SIN ^(-1) "" (3)/(4)]`

Discussion

1525.	Let baralpha=abari+bbarj+cbark,barbeta=bbari+cbarj+abark and bargamma=cbari+abarj+bbark be three coplaner vectors with baralphanebarbetanebargamma and barr=bari+barj+bark then ~r is perpendicular to
Answer» `BARALPHA` `barbeta` `BARGAMMA` `baralpha,barbeta,bargamma` ANSWER :C

Discussion

1526.	Evaluate the following limits : Lim_(x to 0 ) ( sin 5x - sin 3x )/(sin x )
Answer» ANSWER :2

Discussion

1527.	If ( x - a) cos theta + ysin theta =(x - a) cos phi + ysinphi =a and tan (phi//2) =2b then
Answer» `y^2 = 2ax -(1-b^2)X^2` `TAN""(PI)/2=1/(x) (y+bx)` `y^2 = 2BX -(1-a^2)x^2` `tan""(phi)/2 =1/x(y-bx)` Answer :A::B::D

Discussion

1528.	In the triangle with vertices at a(6,3),B(-6,3),C(-6,-3), the median through A meets BC an P, the line AC meets the x-axis at Q, while R and S respectively denote the ortocentre and centroid of the triangle. Then the correct matching of the coordinates of points in List I to List II is
Answer» `{:(i""II""iii""iv),(D""A""E""C):}` `{:(i""ii""iii""iv),(D""B""E""C):}` `{:(i""ii""iii""iv),(D""A""F""C):}` `{:(i""ii""iii""iv),(B""A""F""C):}` ANSWER :C

Discussion

1529.	Write the conjugate of sqrt(-25) (7+ sqrt(-576))
Answer» ANSWER :`-35i-120`

Discussion

1530.	Let bar(a)= bar(i) + 2bar(j) + 3bar(k), bar(b)= - bar(i) + 2bar(j) + 3bar(k), bar( c)= 3 bar(i) + bar(j) and bar(d) is a non-zero vector perpendicular to both bar(a) and bar(b). If the angle between bar(c ) and bar(d) is theta, then find cos theta.
Answer» ANSWER :`+- (3)/(sqrt130)`

Discussion

1531.	If H is the orthocentre of triangle ABC, R = circumradius and P=AH+BH+CH, then
Answer» <P>`P=2(R+r)` max.of P is 3R min. of P is 3R P=2(R-r) ANSWER :A::B

Discussion

1532.	Find the vertex, co-ordinates of focus, axis , directrix and latus rectum of the following parabolas. (i) y^(2)-6x-4y-11=0 (ii) (x+2)^(2)=2(y+3) (iii) y^(2)=4(x+1) (iv) (y+3)^(2)=4(x-1) (v) x^(2)=2x+2y (vi) 4y^(2)-6x-8y-5=0
Answer» Answer :(i) Vertex `(-(5)/(2),2)`, focus, (-1,2), axis y2=0, equation of directrix x+4=0, latus rectum = (ii) Vertex (-2,-3), focus `(-2,-(5)/(2))`, axis x+2=0, equation of directrix 2y+7=0, latus rectum = 2 (III) Vertex (-1,0), focus (0,0) axis y=0, equation of directrix x+2=0, latus rectum = 2 (iv) Vertex (1,-3), focus (2,-3), axis y+3=0, equation of directrix x=0, latus rectum = 4 (V) Vertex `(1,-(1)/(2))`, focus (1,0), axis x-1=0, equation of directrix y+1=0, latus rectum = 2 (vi) Vertex `(-(3)/(2),1)`, focus `(-(9)/(8),1)`, axis y-1=0, equation of `x=-(15)/(8)`, latus rectum `=(3)/(2)`

Discussion

1533.	If f: R rarr Ris defined by f(x)= [x/5] for x in R, where [y] denotes the greatest integer not exceding y, then {f(x):\|x\| lt 71}=
Answer» `{-14, -13, ............,0,........,13,14}` `{-14, -13,.......,0,.......,14,15}` `{-15, -14, ........,0,.........,14, 15}` `{-15, -14,......,0,......13,14}` ANSWER :D

Discussion

1534.	The smallest positive value of x (in radians) satifying the equation log_(cosx)((sqrt(3))/2sinx)=2+log_(cosx)(tanx), is
Answer» `(PI)/12` `(pi)/6` `(pi)/4` `(pi)/3` Answer :B

Discussion

1535.	The profit function P (x) of a company selling x items is given by P(x) = -x^(3) + 9x^(2) - 15x - 13 where x represents units in thousands. Find the absolute maximum profit if the company can manufacture a maximum of 6000 units.
Answer» ANSWER :12

Discussion

1536.	Find the slope of a line whose inclination is 135^(@)
Answer» ANSWER : `-1`

Discussion

1537.	((2n)!)/( 2^(2n) (n!) ^2 ) le
Answer» `(1)/( SQRT(3n+1))` `(1) /( sqrt(3n+2) )` `(1)/( sqrt(3n+4))` `(1)/( sqrt(3n+5))` ANSWER :A

Discussion

1538.	A number x is chosen at random from the first 100 natural numbers. Let A be the event of numbers which satisfies ((x-15)(x-55))/(x-20),then P(A) is:
Answer» `0.41` `0.51` `0.61` `0.69` ANSWER :B

Discussion

1539.	Write thi negation of each of the following statements in two different ways. (i) Africa is a continent. (ii) sqrt(5) is rational. (iii) All integers are rational numbers. (iv) Some prime numbers are odd numbers. (v) Everyone in Germany speaks German.
Answer» SOLUTION :Given below are the REQUIRED negations: (i) Africa is not a continent. Or, It is false that Africa is a continent. (ii) `sqrt(5)` is not rational. Or, It is false that `sqrt(5)` is rational. (iii) There exists an integer which is not a rational number. Or, It is false that all integers are rational numbers. (iv) No prime number is an odd number. Or, It is false that some prime numbers are odd numbers. (V) At LEAST ONE person in Germany does not speak German. Or, It is false that everyone in Germany speaks German.

Discussion

1540.	The polar form of - 3 is
Answer» `(cospi+isinpi)` `pm3(cospi+isinpi)` `3(cospi+isinpi)` `-3(cospi+isinpi)` Solution :Let-3 = `R(COSTHETA +isintheta)` `therefore""rcos theta=-3 and rsintheta=0` Now, `r^(2)cos^(2)theta+r^(2)sin^(2)theta=(- 3)^(2)+0=9` `RARR" "r^(2)(cos^(2)theta+sin^(2)theta)=9` `rArr""r^(2)=9" "rArrr= 3` Now, `{:("Now,",costheta=-1,,rArrtheta=pi),(and,sintheta=0 ,,rArr the ta= PIOR 2pi):}}rArr theta=pi` Therefore, `-3=3(cospi+isinpi)`

Discussion

1541.	The vertices of a DeltaABC are A(1, 1), B(7, 3) and C(3, 6). State the slopr ofthe altitude toAB
Answer» ANSWER :-3

Discussion

1542.	Find the mean and variance for each of the data in Question:
Answer» Solution : LET assumed mean `A=20` Mean `=A+(sumf_(i)d_(i))/(sumf_(i))=20+(-40)/40=20-1=19` VARIANCE `sigma^(2)=1/(N^(2))[Nsumf_(i)d_(i)^(2)-(sumf_(i)d_(i))^(2)]` `=1/(40^(2))[40xx1776-(-40)^(2)]` `=44.4 =1=43.4`

Discussion

1543.	Find the mean and variance for each of the data in Question:
Answer» Solution : Let ASSUMED mean `A=100` Mean `=A+(sumf_(i)d_(i))/(sumf_(i))` `=100+0/22` `=100+0=100` Variance `sigma^(2)=1/(N^(2))[Nsumf_(i)d_(i)^(2)-(sumf_(i)d_(i))^(2)]` `=1/(22)^(2)[22xX640-0]` `=29.09`

Discussion

1544.	Verify : "cosec "alpha=1+cot^(2)alpha" if "alpha=(pi)/(3).
Answer» ANSWER :RIGHT SIDE

Discussion

1545.	If 0 le x le1 and theta=Sin^(-1) x +Cos^(-1) x-Tan^(-1)x then
Answer» `THETA LE pi//2` `pi//4 le theta le pi//2` `theta GE pi//4` `theta=pi//4` ANSWER :B

Discussion

1546.	If cosA=3/4, then 32 sin, A/2 sin, (5A)/2= (A) sqrt(11) (B) -sqrt(11) (C) 11 (D) -11
Answer» `SQRT7` `-sqrt7` 7 `-7` ANSWER :B

Discussion

1547.	If A=1/3[(1,2,2),(2,1,-2),(x,-2,y)] such that A A^(T)=A^(T)A=I, find (x,y).
Answer» ANSWER :(2,1)

Discussion

1548.	Compute the following limits. Lt_(xtooo)(2x^(2)-x+3)/(x^(2)-2x+3)
Answer» ANSWER :2

Discussion

1549.	Insert 3 geometric means between 16 and 256.
Answer» ANSWER :32, 64,128

Discussion

1550.	Differentiate from first principles: 6. (2x+3)/( 3x+2)
Answer» ANSWER :`(-5)/( (3X +2)^2)`

Discussion

Explore topic-wise InterviewSolutions in .

(baraxxbari)xxbari +(baraxxbarj)xxbarj+(baraxxbark)xxbark=

The volume of metallic hallow sphere is constant. If the order radius is increasint at thed rate of V cm/sec. Then the rate at which the inner radius increasing when the radii are a+d,a is

If f(x)={{:(ax^(2)-b",", -1 lt x lt 1), (1/abs(x)",", "elsewhere"):} is differentiable at x=1, then

If xy(y-x)=16 then y has a minimum value when x=

(d)/(dx)(sinx^(@))=…….

If 3sintheta=2costheta then the value of sin2theta is …………..

If a ne b and a^(2)=5a-3,b^(2)=5b-3, then form that equation whose roots are a/b and b/a.

A is a fixed point on the circumference of a circle with centre 'O' and radius 'r', A particle starts at A and moves on the circumference with an 4 radian/sec. If PM is perpendicualar to OA and algle POM = pi//3, then the rate at which of DeltaPOM decreases is

The range of the function f(x)=|x-1|+|x-2|,-1 le x le 3, is

If tanA=(1-cosB)/(sinB), then tan2A = …………

If O=(0,0,0), A=(1,2,1), B=(2,1,3), C = (1,1,2) and OABC is a tetrahedron. Find the angle between the faces OAB and ABC.

A coin and a die are tossed . Describe the following events . D : getting a head or a tail.

Let P(n) : n(n+1)(n+2) is divisible by 6. Determine whether the statement is true or false, when n=3 and n=5. Justify your answer.

Change the following complex numbers into polar form -4+4 sqrt3i

Show that the followiing system of equations is consistent and solve it completely. x+y+z=3," "2x+2y-z=3," "x+y-z=1

Solve the general vlaue. 2 cos theta + cos 3 theta =0

If R+r=r_(3) then C=

If secx=sqrt(2) and x does not lie in the 1^(st) quadrant, find the value of (1+tanx+" cosec "x)/(1+cot x-" cosec "x).

If Sin theta+ Sin^(2) theta=1 and cos a cos^(12) theta+ b cos ^(12) theta+ b cos^(10) theta+ c cos^(8) theta+d cos^(6)-1 theta= then (b+c)/(a+d)

From a point on the level ground , theangel of elevation of the top of a pole is 30^(@). On moving 20 meters nearer, the angle of elevation is 45^(@). Then the height of the pole, in meters, is

Differentiate the following functions w.r.t. x: x sin x

From 0 to …… when r increases, ""^nC_r also increases.

Find the general value oftheta in sec theta - cosec theta = (4)/(3)

Let baralpha=abari+bbarj+cbark,barbeta=bbari+cbarj+abark and bargamma=cbari+abarj+bbark be three coplaner vectors with baralphanebarbetanebargamma and barr=bari+barj+bark then ~r is perpendicular to

Evaluate the following limits : Lim_(x to 0 ) ( sin 5x - sin 3x )/(sin x )

If ( x - a) cos theta + ysin theta =(x - a) cos phi + ysinphi =a and tan (phi//2) =2b then

In the triangle with vertices at a(6,3),B(-6,3),C(-6,-3), the median through A meets BC an P, the line AC meets the x-axis at Q, while R and S respectively denote the ortocentre and centroid of the triangle. Then the correct matching of the coordinates of points in List I to List II is

Write the conjugate of sqrt(-25) (7+ sqrt(-576))

Let bar(a)= bar(i) + 2bar(j) + 3bar(k), bar(b)= - bar(i) + 2bar(j) + 3bar(k), bar( c)= 3 bar(i) + bar(j) and bar(d) is a non-zero vector perpendicular to both bar(a) and bar(b). If the angle between bar(c ) and bar(d) is theta, then find cos theta.

If H is the orthocentre of triangle ABC, R = circumradius and P=AH+BH+CH, then

Find the vertex, co-ordinates of focus, axis , directrix and latus rectum of the following parabolas. (i) y^(2)-6x-4y-11=0 (ii) (x+2)^(2)=2(y+3) (iii) y^(2)=4(x+1) (iv) (y+3)^(2)=4(x-1) (v) x^(2)=2x+2y (vi) 4y^(2)-6x-8y-5=0

If f: R rarr Ris defined by f(x)= [x/5] for x in R, where [y] denotes the greatest integer not exceding y, then {f(x):|x| lt 71}=

The smallest positive value of x (in radians) satifying the equation log_(cosx)((sqrt(3))/2sinx)=2+log_(cosx)(tanx), is

The profit function P (x) of a company selling x items is given by P(x) = -x^(3) + 9x^(2) - 15x - 13 where x represents units in thousands. Find the absolute maximum profit if the company can manufacture a maximum of 6000 units.

Find the slope of a line whose inclination is 135^(@)

((2n)!)/( 2^(2n) (n!) ^2 ) le

A number x is chosen at random from the first 100 natural numbers. Let A be the event of numbers which satisfies ((x-15)(x-55))/(x-20),then P(A) is:

Write thi negation of each of the following statements in two different ways. (i) Africa is a continent. (ii) sqrt(5) is rational. (iii) All integers are rational numbers. (iv) Some prime numbers are odd numbers. (v) Everyone in Germany speaks German.

The polar form of - 3 is

The vertices of a DeltaABC are A(1, 1), B(7, 3) and C(3, 6). State the slopr ofthe altitude toAB

Find the mean and variance for each of the data in Question:

Find the mean and variance for each of the data in Question:

Verify : "cosec "alpha=1+cot^(2)alpha" if "alpha=(pi)/(3).

If 0 le x le1 and theta=Sin^(-1) x +Cos^(-1) x-Tan^(-1)x then

If cosA=3/4, then 32 sin, A/2 sin, (5A)/2= (A) sqrt(11) (B) -sqrt(11) (C) 11 (D) -11

If A=1/3[(1,2,2),(2,1,-2),(x,-2,y)] such that A A^(T)=A^(T)A=I, find (x,y).

Compute the following limits. Lt_(xtooo)(2x^(2)-x+3)/(x^(2)-2x+3)

Insert 3 geometric means between 16 and 256.

Differentiate from first principles: 6. (2x+3)/( 3x+2)