14949 + Interview Questions in Maths in Class 11 Page 209 InterviewSolution

10401.	The point of intersection of the diagonals of the rhombus formed by the lines 2x+y-5=0, x+2y+8=0, 2x+y+5=0, and x+2y-2=0 is
Answer» (2,-1) (-1,2) (1,-2) (-2,1) ANSWER :C

Discussion

10402.	LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? {1, 2, 3} ⊂A
Answer» ANSWER :INCORRECT

Discussion

10403.	Let bara and barb be non-zero, non collinear vectors. If abs(bara+barb) = abs(bara-barb) "find the angle between " bara and barb.
Answer» ANSWER :`pi/2`

Discussion

10404.	If Cos^(-1)x gt Sin^(-1)x, then x belongs to the interval
Answer» `(-INFTY, 0)` `(-1,0)` `[0,1/sqrt(2))` `[-1,1/sqrt(2))` ANSWER :D

Discussion

10405.	Find the equation of the hyperbola whose foci are (4,1), (8,1) and whose eccentricity is 2.
Answer» ANSWER :`2 (x-6) ^(2) - (y -1) ^(2) =3`

Discussion

10406.	If bara, barb lie in a plane, normal to the plane containing barc, bard then (baraxxbarb).(barcxxbard) =
Answer» 3 2 1 0 Answer :D

Discussion

10407.	Evaluate the following limits : lim_( x to 1/2) (4x^(2)-1)/(2x-1)
Answer» ANSWER :2

Discussion

10408.	If tan A + tan B=p and cot A+ cot B=q thencot (A+B)=
Answer» `(p-q)/(PQ)` `(q-p)/(pq)` `(pq)/(p+q)` `(pq)/(p-q)` ANSWER :B

Discussion

10409.	Every line of the system (1+2lambda)x+(lambda-1)y+2(1+2lambda)=0, lambda being a parameter, passes through a fixed point A. The equation of the line passing through A and parallel to the line 3x-y = 0 is
Answer» `3x-y+5=0` `-3x+y+5=0` `3x-y+6=0` `3x-y+8=0` ANSWER :C

Discussion

10410.	If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 }, find A ∪ B ∪ D
Answer» Answer :`={1, 2, 3, 4} CUP {3, 4, 5, 6}= {1, 2, 3, 4, 5, 6}`

Discussion

10411.	Prove that the sum of nth term from the beginning and nth term from the end of an A.P. is· constant.
Answer» SOLUTION :N/a

Discussion

10412.	Find the derivative of each of the following from the first principle . (i) sqrt(2x+3), (ii) sqrt(4-x) , (iii) (1)/(sqrt(x))
Answer» Solution :(i) Let `y = sqrt(2x+3)`. Let `deltay` be an increment in y, corresponding to an increment `deltax` in x. Then, `y + deltay = sqrt(2(x+deltax) + 3)` `rArr deltay = sqrt(2(x+delta) + 3) - sqrt(2x+3)` `rArr (deltay)/(deltax) = (sqrt(2(x+deltax) +3) - sqrt(2x+))/(deltax)` `rArr (dy)/(dx) = underset(deltax rarr0)("lim") (deltay)/(deltax) = underset(deltaxrarr0)("lim") (sqrt(2(x+deltax) + 3) - sqrt(2x+3))/(deltax)` `=underset(deltaxrarr0)("lim"){((sqrt(2x+2deltax + 3)- sqrt(2x+3)))/(deltax) xx ((sqrt(2x+2deltax +3) + sqrt(2x+3)))/((sqrt(2x+2deltax+3)+ sqrt(2x+3)))}` `= underset(deltaxrarr0)("lim')({(2x+2deltax+3)-(2x+3)})/(deltax.(sqrt(2x+2deltax+3) + sqrt(2x+3)))` `= underset(deltax rarr0)("lim') (2deltax)/(deltax.(sqrt(2x+2deltax+ 3)+ sqrt(2x+3)))` `= underset(deltax rarr0)("lim") (2)/((sqrt(2x+2deltax+3) + sqrt(2x+3)))` `= (2)/(2sqrt(2x+3)) = (1)/(sqrt(2x+3))`. `:. (d)/(dx) (sqrt(2x+3)) = 1/(sqrt(2x+3))` (ii)Let `y = sqrt(4-x)`. Let `deltax` be an increment in y, corresponding to an increment `deltax` in x. Then, `y + deltay = sqrt(4-(x+deltax))` `rArr (deltay)/(deltax) = sqrt(4-(x+deltax)) - sqrt(4-x)` `rArr (deltay)/(deltax) = (sqrt(4-(x+deltax) - sqrt(4-x)))/(deltax)` `rArr (dy)/(dx) = underset(deltax rarr0)("lim") (deltay)/(deltax)` `= underset(deltax rarr0)("lim") ({sqrt(4-(x+deltax)) - sqrt(4-x)})/(deltax)` ` = underset(deltax rarr0)("lim") {((sqrt(4-x-deltax))-sqrt(4-x))/(deltax)xx((sqrt(4-x-deltax)+sqrt(4-x)))/((sqrt(4-x+deltax)+sqrt(4-x)))}` `= underset(deltax rarr0) ("lim")({(4-x-deltax)- (4-x)})/(deltax(sqrt(4-x-deltax) + sqrt(4-x)))` `= underset(deltax rarr0)("lim") (-deltax)/(deltax(sqrt(4-x-deltax) + sqrt(4-x)))` `= underset(deltax rarr 0)("lim") (-1)/((sqrt(4-x-deltax ) + sqrt(4-x))) = (-1)/(2sqrt(4-x))` `:. d/(dx) (sqrt(4-x)) = (-1)/(2sqrt(4-x))` (iii) Let `y = 1/(sqrt(x))`. Let `deltay` be an increment in y. corresponding to an increment `deltax` in x. brgt Then, `y + delta y = (1)/(sqrt(x+deltax))` `rArr deltay = (1/(sqrt(x+delta)) - (1)/(sqrt(x)))` `rArr (deltay)/(deltax) = (1)/(deltax) .[(1)/(sqrt(x+deltax)) - 1/(sqrt(x))]` `rArr (dy)/(dx) = underset(deltaxrarr0)("lim") (deltay)/(deltax)` `= underset(deltax rarr0)("lim") (1)/(deltax).[(1)/(sqrt(x+deltax))- 1/(sqrt(x))]` `= underset(deltax rarr 0)("lim"){((sqrtx- sqrt(x+deltax)))/(deltax.sqrt(x+deltax).sqrt(x)) xx ((sqrt(x) + sqrt(x+ deltax)))/((sqrtx +sqrt(x+deltax)))}` `= underset(deltax rarr 0)("lim") [({x-(x+deltax)})/(deltax.sqrt(x+deltax).sqrt(x).(sqrt(x)+sqrt(x+deltax)))}` `= underset(deltax rarr 0)("lim") {(-deltax)/(sqrt(x+deltax) . sqrt(x) . (sqrt(x) + sqrt(x+deltax)))}` `= (-1)/(sqrt(x).sqrt(x).(2sqrt(x))) = (-1)/(2^(3/2))` Hence, `(d)/(dx) = (1/(sqrt(x))) = (-1)/(2x^(3//2))`.

Discussion

10413.	Value of tan 130^(@). Tan 140^(@).
Answer» 1 `-1` `0` `2` ANSWER :A

Discussion

10414.	Express 1 + i in modulus amplitude form
Answer» ANSWER :`SQRT2(COS(PI)/+isinpi/4)`

Discussion

10415.	Which of the following is correct for any two complex number z_(1) and z_(2)?
Answer» `\|z_(1)z_(2)\|=\|z_(1)\|\|z_(2)\|` `ARG(z_(1)z_(2))=arg(z_(1))*(z_(2))` `\|z_(1)+z_(2)\|=\|z_(1)\|+\|z_(2)\|` `\|z_(1)+z_(2)\|ge\|z_(1)\|+\|z_(2)\|` ANSWER :A

Discussion

10416.	Differentiate the following w.r.t. x or t or u as the case may be: 12. f(x) = (x^3 + 2x)/( x^2 +4)
Answer» ANSWER :`f'(X) = (x^4 + 10 x^2 + 8)/( (x^2 + 4)^2)`

Discussion

10417.	Let f(x) =x^n,n si being a positive integer . The value of n for which f^(1)(a+b) =f'^(1)(a)+f^(1)(b) when a , b gt 0 is
Answer» 1 2 3 4 Answer :B

Discussion

10418.	A construction company employs 2 executive engineers, Engineer I does the work for 60% of jobs of the company. Engineer 2 does the work for 40% of jobs of the company. It is known from the past experience that the probability of an error when engineer does the work is 0.03, whereas the probability of an error in the work of engineer 2 is 0.04. Suppose a serious error occurs in the work, which engineer would you guess did the work?
Answer» ANSWER :`9/17`

Discussion

10419.	If one of the lines given by ax^(2)+2hxy+by^(2)=0 passes through (2,3) and the other passes through (4, 5) then a+2h+b=0
Answer» `-1` 1 0 2 Answer :B

Discussion

10420.	Ifcot ""(A)/(2)= 30 , Cot "" (B)/(2)= 50 , Cot "" ( C)/(2)= 70then the ascending order of the sides of the triangles ABC is
Answer» a,B,C a,c,b b,a,c c,b,a Answer :D

Discussion

10421.	A card is drawn from a pack of cards . Findthe probability that it is a red ace
Answer» ANSWER :`=(1)/(26)`.

Discussion

10422.	Express the equation 3x^2+2y^2=6 of an ellipse in standard form
Answer» SOLUTION :`x^2/2+y^2/3=1`

Discussion

10423.	If the area of the triangle ABC is a^(2)-(b-c)^(2) then its circumradius R=
Answer» `((a)/(6))sin^(2)((A)/(2))` `((a)/(16))"cosec"^(2)((A)/(2))` `((b)/(16)) sin^(2)((B)/(2))` `((C)/(16)) sin^(2)((C)/(2))` ANSWER :B

Discussion

10424.	if x^n - 1 is divisible by x - k , then the least positive integralvalue of k is
Answer» 1 2 3 4 Answer :A

Discussion

10425.	Convert sin5A+sinA into product form and show that sin5A=5sinA-20sin^3A +16sin^5A
Answer» SOLUTION :2sin3Acos2A

Discussion

10426.	Letf(x) = (3)/(4)x+1 . f^(n)(x)be defined as f^(2) (x)= f(f(x)), and " for "n ge 2 f^(n+1)(x) = f(f^(n) (x)) ." if"lambda underset( n to infty ) Limf^(n)(x) .then
Answer» `lambda` is independent of x `lambda` is a LINEAR POLYNOMIAL in x the line `y= lambda` has slope 0 the line `4y=lambda` touches the unit CIRCLE center at the origin. Answer :A::C::D

Discussion

10427.	If kbara = 3barb+2barc, bara=-2barb+5barc " and if " barb and barc have opposite direction, then
Answer» `K in (-3/2,2/5)` `KIN(-3/2,1/5)` `k in (-1/2,2/3)` `k in (-2/3,1/4)` ANSWER :A

Discussion

10428.	Find modulus and argument of the complex numbers z=-1-isqrt(3)
Answer» ANSWER :`2,(-2PI)/3`

Discussion

10429.	Write the negation of the following statements: s: There exists a number x such that 0ltxlt1
Answer» ANSWER :There does not exists REAL nuber x such that `0LTXLT1`.

Discussion

10430.	Find the value of a so that f(x)={{:(ax+3,if x lt 3),(3-x +2x^(2),if x ge3):}is continuous on R is continuous on R
Answer» ANSWER :a=5

Discussion

10431.	Find the equation of the lines joining the origin to the points of intersection of x^2 + y^2 =1 and x + y = 1.
Answer» ANSWER :`90^(@)`

Discussion

10432.	Find the derivatives of the function cos ec ^(-1) (e ^(2x +1))
Answer» ANSWER :`(-2)/( SQRT(e ^(4x +2))-1)`

Discussion

10433.	The value of x for which sin[cot^(-1)(1+x)]=cos(tan^(-1)x) is :
Answer» `1//2` `1` 0 `-1//2` ANSWER :D

Discussion

10434.	Ifcot ""^(A)/(2): cot ""(B) /(2): cot "" ( C )/(2) = 1: 4: 15 , then largestangle is
Answer» ` 120 ^(@) ` ` 135 ^(@) ` ` 160 ^(@) ` ` 180 ^(@) ` ANSWER :A

Discussion

10435.	Let n(A)=4 and n(B)=5. The number of all possible many-one functions from A to B is
Answer» 625 20 120 505 Answer :D

Discussion

10436.	If the following functions functions are defined from [-1, 1] to [-1, 1], select those which are not bijective.
Answer» `sin(sin^(-1)X)` `2/pi sin^(-1)(sin x)` `(sgn(x))ln(e^(x))` `x^(3)(sgn(x))` ANSWER :B::C::D

Discussion

10437.	Minimum distance of the line 3x +4y - 50 =0 from the point lies on circle x^2+y^2=25 is ...........
Answer» 2 5 1 4 Answer :B

Discussion

10438.	The volume of the greatest cylinder which can be inscribed in a cone ofheight h and semi- vertical angle alpha is
Answer» `4000pi//3cm^(3)` `400pi//3cm^(3)` `4000pi//sqrt(3)CM^(3)` `400pi//sqrt(3)cm^(3)` ANSWER :A

Discussion

10439.	underset(n to oo)lim (1+3+6+...+n(n+1)//2)/(n^(3))=
Answer» ANSWER :`1/6`

Discussion

10440.	Verify : sin^(2)theta+cos^(2)theta=1"if "theta=30^(@),
Answer» ANSWER :1

Discussion

10441.	Solve the following equations : 4x^(2)-12x+25=0
Answer» ANSWER :`(3)/(2)+2I,(3)/(2)-2i`

Discussion

10442.	The sum of first three terms of a G.P. is 39/10 and their product is 1. Find the common ratio and the terms.
Answer» ANSWER :`r=5/2 " or " 2/5; ` TERMS are `2/5,1,5/2` or `5/2 ,1,2/5`

Discussion

10443.	Statement - 1 : The point A(1,0,7) is the mirror image of the point B(1,6,3) in the line (x)/(1)=(y-1)/(2)=(z-2)/(3) Statement -2 : The line (x)/(1)=(y-1)/(2)=(z-2)/(3) bisects the line segment joining A (1,0,7) and B(1,6,3)
Answer» Statement 1 is false, statement 2 is TRUE. Statement 1 is true, statement 2 is true, statement 2 is a CORRECT explanation for statement 1. Statement 1 is true, statement 2 is true, statement 2 is not a correct explanation for statement 1. Statement 1 is true, statement 2 is false. Answer :C

Discussion

10444.	Two dice are thrown simultaneously . Findthe probability of getting a multiple of 3 as the sum .
Answer» ANSWER :`(12)/(36),i.e,(1)/(3)`

Discussion

10445.	Find the multiplicative inverse of each of the following complex numbers when it exists. 0+0i
Answer» ANSWER :Does not EXIST

Discussion

10446.	If the axes are rotated anticlockwise through an angle 90^(@) then the equation x^(2) = 4ay is changed to the equation
Answer» `y^(2) = 4AX` `X^(2) = - 4AY` `y^(2) = - 4ax` `x^(2) = 4ay` ANSWER :A

Discussion

10447.	Find the principal value solution of sin3x-3sin2x+sinx=cos3x-3cos2x+cosx
Answer» ANSWER :`{(PI)/(4),(5PI)/(8),(9pi)/(8),(13pi)/(8)}`

Discussion

10448.	Which of the following statement is not true
Answer» `BARA.(barb+BARC)=bara.barb+bara.barc` `(baraxxbarb)xxbarc=BARAXX(barbxxbarb)` `bara.(barbxxbarc)=(baraxxbarb).barc` `baraxx(barb+barc)=baraxxbarb+baraxxbarc` Answer :B

Discussion

10449.	Find the component statements of the following compound statements: The sky is blue and the grass is green.
Answer» <P> Answer :p: The sky is blue. Q: The grass is GREEN

Discussion

10450.	A soft dringk manufacturer wants to fabrucate cylindrical cans for its products .The can is to have a volume of 34375 cu cm If r is the radius for the can to require least amount of material then 8pir^(2) is equal to
Answer» 1275 7793 1475 1575 Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

The point of intersection of the diagonals of the rhombus formed by the lines 2x+y-5=0, x+2y+8=0, 2x+y+5=0, and x+2y-2=0 is

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

Let bara and barb be non-zero, non collinear vectors. If abs(bara+barb) = abs(bara-barb) "find the angle between " bara and barb.

If Cos^(-1)x gt Sin^(-1)x, then x belongs to the interval

Find the equation of the hyperbola whose foci are (4,1), (8,1) and whose eccentricity is 2.

If bara, barb lie in a plane, normal to the plane containing barc, bard then (baraxxbarb).(barcxxbard) =

Evaluate the following limits : lim_( x to 1/2) (4x^(2)-1)/(2x-1)

If tan A + tan B=p and cot A+ cot B=q thencot (A+B)=

Every line of the system (1+2lambda)x+(lambda-1)y+2(1+2lambda)=0, lambda being a parameter, passes through a fixed point A. The equation of the line passing through A and parallel to the line 3x-y = 0 is

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 }, find A ∪ B ∪ D

Prove that the sum of nth term from the beginning and nth term from the end of an A.P. is· constant.

Find the derivative of each of the following from the first principle . (i) sqrt(2x+3), (ii) sqrt(4-x) , (iii) (1)/(sqrt(x))

Value of tan 130^(@). Tan 140^(@).

Express 1 + i in modulus amplitude form

Which of the following is correct for any two complex number z_(1) and z_(2)?

Differentiate the following w.r.t. x or t or u as the case may be: 12. f(x) = (x^3 + 2x)/( x^2 +4)

Let f(x) =x^n,n si being a positive integer . The value of n for which f^(1)(a+b) =f'^(1)(a)+f^(1)(b) when a , b gt 0 is

If one of the lines given by ax^(2)+2hxy+by^(2)=0 passes through (2,3) and the other passes through (4, 5) then a+2h+b=0

Ifcot ""(A)/(2)= 30 , Cot "" (B)/(2)= 50 , Cot "" ( C)/(2)= 70then the ascending order of the sides of the triangles ABC is

A card is drawn from a pack of cards . Findthe probability that it is a red ace

Express the equation 3x^2+2y^2=6 of an ellipse in standard form

If the area of the triangle ABC is a^(2)-(b-c)^(2) then its circumradius R=

if x^n - 1 is divisible by x - k , then the least positive integralvalue of k is

Convert sin5A+sinA into product form and show that sin5A=5sinA-20sin^3A +16sin^5A

Letf(x) = (3)/(4)x+1 . f^(n)(x)be defined as f^(2) (x)= f(f(x)), and " for "n ge 2 f^(n+1)(x) = f(f^(n) (x)) ." if"lambda underset( n to infty ) Limf^(n)(x) .then

If kbara = 3barb+2barc, bara=-2barb+5barc " and if " barb and barc have opposite direction, then

Find modulus and argument of the complex numbers z=-1-isqrt(3)

Write the negation of the following statements: s: There exists a number x such that 0ltxlt1

Find the value of a so that f(x)={{:(ax+3,if x lt 3),(3-x +2x^(2),if x ge3):}is continuous on R is continuous on R

Find the equation of the lines joining the origin to the points of intersection of x^2 + y^2 =1 and x + y = 1.

Find the derivatives of the function cos ec ^(-1) (e ^(2x +1))

The value of x for which sin[cot^(-1)(1+x)]=cos(tan^(-1)x) is :

Ifcot ""^(A)/(2): cot ""(B) /(2): cot "" ( C )/(2) = 1: 4: 15 , then largestangle is

Let n(A)=4 and n(B)=5. The number of all possible many-one functions from A to B is

If the following functions functions are defined from [-1, 1] to [-1, 1], select those which are not bijective.

Minimum distance of the line 3x +4y - 50 =0 from the point lies on circle x^2+y^2=25 is ...........

The volume of the greatest cylinder which can be inscribed in a cone ofheight h and semi- vertical angle alpha is

underset(n to oo)lim (1+3+6+...+n(n+1)//2)/(n^(3))=

Verify : sin^(2)theta+cos^(2)theta=1"if "theta=30^(@),

Solve the following equations : 4x^(2)-12x+25=0

The sum of first three terms of a G.P. is 39/10 and their product is 1. Find the common ratio and the terms.

Statement - 1 : The point A(1,0,7) is the mirror image of the point B(1,6,3) in the line (x)/(1)=(y-1)/(2)=(z-2)/(3) Statement -2 : The line (x)/(1)=(y-1)/(2)=(z-2)/(3) bisects the line segment joining A (1,0,7) and B(1,6,3)

Two dice are thrown simultaneously . Findthe probability of getting a multiple of 3 as the sum .

Find the multiplicative inverse of each of the following complex numbers when it exists. 0+0i

If the axes are rotated anticlockwise through an angle 90^(@) then the equation x^(2) = 4ay is changed to the equation

Find the principal value solution of sin3x-3sin2x+sinx=cos3x-3cos2x+cosx

Which of the following statement is not true

Find the component statements of the following compound statements: The sky is blue and the grass is green.

A soft dringk manufacturer wants to fabrucate cylindrical cans for its products .The can is to have a volume of 34375 cu cm If r is the radius for the can to require least amount of material then 8pir^(2) is equal to