14949 + Interview Questions in Maths in Class 11 Page 141 InterviewSolution

7001.	Theperiodof cot ((3-5x)/(7 )) is
Answer» `(7pi)/(5 ) ` `(5 PI)/(7)` `(7pi )/(5 )` `(14pi)/(5)` ANSWER :3

Discussion

7002.	Themaximum distance of the the normal to the ellipse (x^(2))/(9)+(y^(2))/(4)=1from its centre is
Answer» `(1)/(2)` 2 1 4 Answer :C

Discussion

7003.	cos(sin^(-1)(5/13))=
Answer» 1)`12//13` 2)`5//12` 3)`5//13` 4)`13//5` ANSWER :A

Discussion

7004.	Given that tan x = (12)/(5), cos y = (-3)/(5), and the angles x and y are in the same quadrants, calcualte without the use of tables the values of (i) sin (x + y), (ii) cos ""(y)/(2).
Answer» ANSWER :`(-1)/(SQRT5)`

Discussion

7005.	If the lines L_(1) and L_(2) " are given by " barr=(bari+2barj-bark)+t(2bari-3barj+bark) andbarr=(bari+barj+bark)+s(2bari+barj-bark) , then
Answer» `L_(1) and L_(2)` are perpendicular `L_(1) and L_(2)` are PARALLEL `(L_(1) ,L_(2))=45^(@)` `(L_(1) ,L_(2))=60^(@)` Answer :A

Discussion

7006.	What are the values of d/(dx) (cos x) and d/(dx) ( tan x)
Answer» SOLUTION :`sec^2 X `

Discussion

7007.	What is meant by periodic motion? Give any two examples .
Answer» Solution :Periodic motion : Any motion which repeats itself in a FIXED time interval is known as periodic motion. Examples : Hands in pendulum CLOCK, swing of a cradle, the revolution of the EARTH around the Sun, waxing and waning of MOON, ETC.

Discussion

7008.	7 persons can sit on round table for discussion in 7!ways.
Answer» ANSWER :FALSE STATEMENT

Discussion

7009.	If A = {x: x in W, x lt 2}, B= {x: x in N, 1 lt x lt 5} and C= {3, 5}, then findA xx (B uu C).
Answer» ANSWER :`{(0, 2), (0, 3), (0, 4), (0, 5), (1,2), (1,3), (1, 4), (1,5)}`

Discussion

7010.	If the roots of the equation x^(2)+px+7=0 are denoted by alpha and beta, and alpha^(2)+beta^(2)=22, find the possible values of p.
Answer» ANSWER :`PM6`

Discussion

7011.	Point P(x,y) satisfying the equation sin^(-1)x+cos^(-1)y+cos^(-1)(2xy)=(pi)/2 lies on
Answer» the BISECTOR of the first and third quadrant bisector of the SECOND and fourth quadrant. the rectangle FORMED by the LINES `x=+-1` and `y=+-1` a unit circle with CENTRE at the origin. Answer :D

Discussion

7012.	If cos 28^(@)+sin 28^(@)=k^(3), then cos17^(@) equal to
Answer» `K^(3)/SQRT(2)` `-k^(3)/sqrt(2)` `sqrt(2)k^(3)` `-sqrt(2)k^(3)` ANSWER :A

Discussion

7013.	A point is on thex axis whatare its y coordinates and z coordinates
Answer» ANSWER :y and Z COORDINATES are ZERO

Discussion

7014.	lim_(hrarr0)((e+h)^(ln(e+h))-e)/(h) is..........
Answer» ANSWER :B

Discussion

7015.	Given the meaning and value of the symbol in the following ""^(5) P_2
Answer» ANSWER :` 20 `

Discussion

7016.	Write two examplesfor inertia of rest
Answer» Solution :(i) PASSENGERS experience a backward push in a sudden start of BUS. (ii) Tightening of SEAT belts in a CAR when it stops quickly.

Discussion

7017.	If n men and m women are to be seated in a row so that no two women sit together . If ngtm, then show that number of ways in which they can be seated is (n!(n+1)!)/((n-m+1)!)
Answer» ANSWER :(B) 41

Discussion

7018.	Find the coefficient of x^(15) in the expansion (x-x^(2))^(10)
Answer» ANSWER :`= - 252 `

Discussion

7019.	Determine whether p,q and "If p, then q " are true or false in each case given below : 5x3=16
Answer» <P> ANSWER :`{:(p,Q,p =>q),(F,F,T):}`

Discussion

7020.	Find the value of \|{:(sqrt(13)+sqrt(3),2sqrt(5),sqrt(5)),(sqrt(15)+sqrt(26),5,sqrt(10)),(3+sqrt(65),sqrt(15),5):}\|
Answer» ANSWER :`15sqrt(2)-25sqrt(3)`

Discussion

7021.	Quadrilateral formed by xy + x + y + 1=0 and xy + 3x + 3y + 9 =0 is quadrilateral formed by
Answer» square rhombus rectangle parallelogram ANSWER :A

Discussion

7022.	(0.9876 xx (16.42)^(2))/((4.567)^(1/3))
Answer» ANSWER :160.4

Discussion

7023.	Evaluate {:("Lt"),(xrarr0):}(xtan2x-2xtanx)/((1-cos2x)^(2))
Answer» ANSWER :`1/2`

Discussion

7024.	Prove that tan225^(@)cot405^(@)+tan765^(@)cot675^(@)=0
Answer» ANSWER :RIGHT SIDE

Discussion

7025.	How many numbers of 5 digits can be formed with the digit 0,2,5,6,7 without taking any of these digit more than once.
Answer» ANSWER :` 4 XX 4 xx 3 xx 2 xx 1`

Discussion

7026.	If the angles of triangles ABC are in A.P. and b: c=sqrt3 : sqrt2" then "angle a =
Answer» ` 75 ^(@) ` ` 45 ^(@) ` ` 30 ^(@) ` ` 60 ^(@) ` ANSWER :A

Discussion

7027.	If sinA = -5/13 and pi lt lt (3pi)/(2), find the values of the following: i) sinA/2, ii) cosA/2, iii) tanA/2
Answer» SOLUTION :i) `5/sqrt(26)`, II) `-1/sqrt(26)`, III) `-5`

Discussion

7028.	If a= 3, b =4, c =5 thencos ""( A)/(2) =
Answer» `(2)/(SQRT( 10))` ` ( 1)/( sqrt( 10 ))` ` (3)/(sqrt(10)) ` ` ( 4)/(sqrt( 10 ))` Answer :C

Discussion

7029.	Examine whether the following statements are true or false: { x : x is an even natural number less than 6}⊂{ x : x is a natural number which divides 36}
Answer» ANSWER :1

Discussion

7030.	Construct truth table for~ [ p vv(~ q)]
Answer» ANSWER :I do notlike my SCHOOLAND I do notlikeclass TEACHER .

Discussion

7031.	If Lt_(xto2)(x^(2n)-1024)/(x^(n)-32)=64 then find n.
Answer» ANSWER :5

Discussion

7032.	Find the number of binary operations that can be defined on the set A={a,b,c}
Answer» ANSWER :`3^(9)`

Discussion

7033.	Find the variance and standard deviation for the following data:
Answer» ANSWER :6.77

Discussion

7034.	If a,b,c are pth, qth rth terms respectivelyy of a G.P then \|(loga, p, 1),(logb, q, 1),(logc, r, 1)\|=
Answer» LOG XYZ `(p-1)(q-1)(r-1)` pqr 0 Answer :D

Discussion

7035.	In following statement 'OR' is used in inclusive sense. "Roses are yellow or pink "
Answer» ANSWER :EXCLUSIVE SENCE

Discussion

7036.	A box is made from a piece of metal sheet 24 cms square by cutting equal small squares from each corner and traning up the edges If the volume of the boxis maximum then then the dimensions of the box are
Answer» 16,16,4 9,9,6 8,8,8 9,9,8 Answer :A

Discussion

7037.	Find the derivatives of the function sin ^(-1) sqrtx
Answer» ANSWER :`(1)/(2 SQRT (X - x ^(2)))`

Discussion

7038.	Write down the converse of following statements: If x:y=3:2 then 2x=3y
Answer» ANSWER :if `2x=3y` then `X:y=3:2`

Discussion

7039.	Find the derivative of the following functions:5 sec x+4 cos x
Answer» ANSWER :5 SEC x.tanx-4sinx

Discussion

7040.	Find lim_(xrarr0) f(x) and underset(xrarr1)f(x). f(x)={{:(2x+3,xle0),(3(x+1),xgt0):}
Answer» Solution :`f(x)={{:(2x+3,xle0),(3(x+1),xgt0):}` at x=0 LHL`=underset(xrarr0^(-))"lim"f(x)` `=underset(hrarr0)"lim"f(0-h)` Let `0-h=x ` `rArr0-hrarr0` `RARR hrarr0` `underset(hrarr0)"lim"2(0-h)+3=2(0)+3=3` RHL`=underset(xrarr0^(+))f(x)` `=underset(hrarr0)"lim"f(0+h)` `=underset(hrarr0)"lim"3(0+h+1)` `=3(0+1)=3` `because LHL=RHL=3` ` therefore underset(xrarr0)"lim"f(x)=3` at x=1 LHL`=underset(xrarr1^(1-))"lim"f(x)` `=underset(hrarr0)"lim"f(1-h)` `=underset(hrarr0)"lim"3(1-h+1)` `=3(2-0) =6` RHL`=underset(xrarr1^(+))"lim"f(x)` `=underset(hrarr0)"lim"f(1+h)` `=underset(hrarr0)"lim"3(1+h+1)` `=3(2+0)=6` `because LHL=RHL=6` `therefore underset(xrarr1)"lim"f(x)=6` Let `1+h=x` `rArr1+hrarr1` `rArr hrarr0`

Discussion

7041.	Two unbiased dice are thrown . Find the probability that the first die shows 6 ,
Answer» ANSWER :`=(1)/(6)`.

Discussion

7042.	A coin is tossed. If it shows head, we draw a ball from a bag consisting of 3 blue and 4 white balls, if it shows tail we throw a die. Describe the sample space of this experiment.
Answer» ANSWER :S = {H, TH, TTH, TTTH, TTTTH ….}.

Discussion

7043.	If bara,barb,barc are unit vectors such thatbara is perpendicular to the plane of barb,barc and the angle between barb andbarc " is " pi/3 " then find " abs(bara+barb+barc).
Answer» ANSWER :2

Discussion

7044.	Express (x+1)! interms of(x-1)!. Hence, solve the equation (x+1)! =12(x-1)!
Answer» SOLUTION :`(X+1)! =(x-1)x(x-1)!,x=3`

Discussion

7045.	Evaluate the following limits : Lim_(x to a ) (a^(x)-1)/(b^(x)-1)
Answer» ANSWER :`log_(B)a`

Discussion

7046.	Let f(x)=(x(1+a cosx)- b sin x)/(x^(3)), x ne 0 and f(0)= 1. Then values if 'a' and 'b' so that 'f' is continuos are
Answer» `(5)/(2), (3)/(2)` `(5)/(2),(-3)/(2)` `-(5)/(2),-(3)/(2)` `(1)/(2)-(3)/(2)` ANSWER :C

Discussion

7047.	If the coefficient of 2nd , 3rd and the 4th terms in the expansion of (1+x)^(n) are in AP, then the value of n is
Answer» 2 7 11 14 Answer :B

Discussion

7048.	If sin 2 theta+cos theta =0 then theta=
Answer» `2 n pi -(pi)/6, n in Z` `2npi+(pi)/3, n in Z` `(2npi)/3-(pi)/6, n in Z` `(2npi)/3+(pi)/4, n in Z` ANSWER :C

Discussion

7049.	In triangle ABC, if angle C is 90° and the area of triangle is 30 sq. units, then the minimum possible value of the hypotenuse c is equal to (in units)
Answer» `30sqrt(2)` `60sqrt(2)` `120sqrt(2)` `2sqrt(30)` ANSWER :A

Discussion

7050.	Find the derivative of the following functions: secx
Answer» ANSWER :secx.tanx

Discussion

Explore topic-wise InterviewSolutions in .

Theperiodof cot ((3-5x)/(7 )) is

Themaximum distance of the the normal to the ellipse (x^(2))/(9)+(y^(2))/(4)=1from its centre is

cos(sin^(-1)(5/13))=

Given that tan x = (12)/(5), cos y = (-3)/(5), and the angles x and y are in the same quadrants, calcualte without the use of tables the values of (i) sin (x + y), (ii) cos ""(y)/(2).

If the lines L_(1) and L_(2) " are given by " barr=(bari+2barj-bark)+t(2bari-3barj+bark) andbarr=(bari+barj+bark)+s(2bari+barj-bark) , then

What are the values of d/(dx) (cos x) and d/(dx) ( tan x)

What is meant by periodic motion? Give any two examples .

7 persons can sit on round table for discussion in 7!ways.

If A = {x: x in W, x lt 2}, B= {x: x in N, 1 lt x lt 5} and C= {3, 5}, then findA xx (B uu C).

If the roots of the equation x^(2)+px+7=0 are denoted by alpha and beta, and alpha^(2)+beta^(2)=22, find the possible values of p.

Point P(x,y) satisfying the equation sin^(-1)x+cos^(-1)y+cos^(-1)(2xy)=(pi)/2 lies on

If cos 28^(@)+sin 28^(@)=k^(3), then cos17^(@) equal to

A point is on thex axis whatare its y coordinates and z coordinates

lim_(hrarr0)((e+h)^(ln(e+h))-e)/(h) is..........

Given the meaning and value of the symbol in the following ""^(5) P_2

Write two examplesfor inertia of rest

If n men and m women are to be seated in a row so that no two women sit together . If ngtm, then show that number of ways in which they can be seated is (n!(n+1)!)/((n-m+1)!)

Find the coefficient of x^(15) in the expansion (x-x^(2))^(10)

Determine whether p,q and "If p, then q " are true or false in each case given below : 5x3=16

Find the value of |{:(sqrt(13)+sqrt(3),2sqrt(5),sqrt(5)),(sqrt(15)+sqrt(26),5,sqrt(10)),(3+sqrt(65),sqrt(15),5):}|

Quadrilateral formed by xy + x + y + 1=0 and xy + 3x + 3y + 9 =0 is quadrilateral formed by

(0.9876 xx (16.42)^(2))/((4.567)^(1/3))

Evaluate {:("Lt"),(xrarr0):}(xtan2x-2xtanx)/((1-cos2x)^(2))

Prove that tan225^(@)cot405^(@)+tan765^(@)cot675^(@)=0

How many numbers of 5 digits can be formed with the digit 0,2,5,6,7 without taking any of these digit more than once.

If the angles of triangles ABC are in A.P. and b: c=sqrt3 : sqrt2" then "angle a =

If sinA = -5/13 and pi lt lt (3pi)/(2), find the values of the following: i) sinA/2, ii) cosA/2, iii) tanA/2

If a= 3, b =4, c =5 thencos ""( A)/(2) =

Examine whether the following statements are true or false: { x : x is an even natural number less than 6}⊂{ x : x is a natural number which divides 36}

Construct truth table for~ [ p vv(~ q)]

If Lt_(xto2)(x^(2n)-1024)/(x^(n)-32)=64 then find n.

Find the number of binary operations that can be defined on the set A={a,b,c}

Find the variance and standard deviation for the following data:

If a,b,c are pth, qth rth terms respectivelyy of a G.P then |(loga, p, 1),(logb, q, 1),(logc, r, 1)|=

In following statement 'OR' is used in inclusive sense. "Roses are yellow or pink "

A box is made from a piece of metal sheet 24 cms square by cutting equal small squares from each corner and traning up the edges If the volume of the boxis maximum then then the dimensions of the box are

Find the derivatives of the function sin ^(-1) sqrtx

Write down the converse of following statements: If x:y=3:2 then 2x=3y

Find the derivative of the following functions:5 sec x+4 cos x

Find lim_(xrarr0) f(x) and underset(xrarr1)f(x). f(x)={{:(2x+3,xle0),(3(x+1),xgt0):}

Two unbiased dice are thrown . Find the probability that the first die shows 6 ,

A coin is tossed. If it shows head, we draw a ball from a bag consisting of 3 blue and 4 white balls, if it shows tail we throw a die. Describe the sample space of this experiment.

If bara,barb,barc are unit vectors such thatbara is perpendicular to the plane of barb,barc and the angle between barb andbarc " is " pi/3 " then find " abs(bara+barb+barc).

Express (x+1)! interms of(x-1)!. Hence, solve the equation (x+1)! =12(x-1)!

Evaluate the following limits : Lim_(x to a ) (a^(x)-1)/(b^(x)-1)

Let f(x)=(x(1+a cosx)- b sin x)/(x^(3)), x ne 0 and f(0)= 1. Then values if 'a' and 'b' so that 'f' is continuos are

If the coefficient of 2nd , 3rd and the 4th terms in the expansion of (1+x)^(n) are in AP, then the value of n is

If sin 2 theta+cos theta =0 then theta=

In triangle ABC, if angle C is 90° and the area of triangle is 30 sq. units, then the minimum possible value of the hypotenuse c is equal to (in units)

Find the derivative of the following functions: secx