14949 + Interview Questions in Maths in Class 11 Page 165 InterviewSolution

8201.	Find the coordinates of the foot of perpendicular from the point (-1,3) to the line 3x-4y-16=0.
Answer» ANSWER :Required foot of PERPENDICULAR `= ((68)/(25), (-49)/( 25))`

Discussion

8202.	Bag A contains 4 green and 3 red balls andbag B contains 4 red and 3 green balls. Onebag is taken at random and a ball is drawn andnoted it is green. The probability that it comes from bag Bis
Answer» `(2)/(7)` `(2)/(3)` `(3)/(7)` `(1)/(3)` ANSWER :C

Discussion

8203.	If tan(picostheta)=cot(pisintheta), then cos(theta-(pi)/(4))=(1)/(2sqrt(2)).
Answer» ANSWER :TRUE

Discussion

8204.	A person has 6 friends . He invites one or more then one friends. For dinner in ….. Ways.
Answer» 61 63 18 24 Answer :B

Discussion

8205.	If A gt 0 , B gt 0 and A+B = (pi)/(6), then the minimum value of tan A+ tan B is
Answer» `SQRT(3) + sqrt(2)` `2 - sqrt(3)` `4 - 2 sqrt(3)` `(2)/( sqrt(3) )` Answer :C

Discussion

8206.	Check whether the following pair of statements are negation of each other. Give reasons for your answer: (i) x+y=y+xis true for every real numbers x and y. (ii) There exists real number x and y for which x+y=y+x
Answer» ANSWER :is not STATEMENT.

Discussion

8207.	If (1-p) is a root of the quadratic equation x^(2)+px+(1-p)=0, then its roots are (a) 0,-1 (b) -1,1 (c) 0,1 (d) -1,2
Answer» ANSWER :(a)

Discussion

8208.	If A={-3,-2,-1,0,1,2,3} and f:A to Z is a function which of the following : (i) Range of f (ii) Pre-image of 5 (iii) Pre-image of 0
Answer» ANSWER :(i) {0.-3, -4 , 5 ,12} `""` (ii) 2 `""` (iii) {-3,1}

Discussion

8209.	Find the derivative of 99x at x = l00.
Answer» ANSWER :99

Discussion

8210.	A point is moving along the cubical parabola 12y = x^(3). Therate of ordinate is less than the rate of abscissa when
Answer» `x LT -2 or x GT 2` `x = PM2` `-2 lt x lt 2` `x = pm4` Answer :C

Discussion

8211.	If P(AcupB)=P(AcapB) for any two events A and B, then ………..
Answer» <P>`P(A)=P(B)` `P(A)gtP(B)` `P(A)leP(B)` NONE of these ANSWER :A

Discussion

8212.	The vector area of the rectangle whose adjacent sides are p vec(i), q vec(j) is
Answer» pq `pq VEC(k)` 1 or 2 `((pq)/(2))vec(k)` ANSWER :B

Discussion

8213.	Find the sum of the following series up to n terms: 5+55+555+......
Answer» ANSWER :`50/81(10^n-1)-(5N)/9`

Discussion

8214.	The mean and variance of six observations are 8 and 16 respectively. If each observation is multiplied by 3, find the new mean and new variance of the resulting observations.
Answer» SOLUTION :Let the given observations `x_(1), x_(2), x_(3), x_(4), x_(5), x_(6).` Then, mean `=8 rArr (1)/(6)(x_(1)+x_(2)+x_(3)+x_(4)+x_(5)+x_(6))=8` `rArr" "x_(1)+x_(2)+x_(3)+x_(4)+x_(5)+x_(6)=48."(i)"` Also, variance =16 `rArr" "(1)/(6)(x_(1)^(2)+x_(2)^(2)+x_(3)^(2)+x_(4)^(2)+x_(5)^(2)+x_(6)^(2))-8^(2)=16" "[because sigma^(2)=(Sigmax_(i)^(2))/(n)-(barx)^(2)]` `rArr" "x_(1)^(2)+x_(2)^(2)+x_(3)^(2)+x_(4)^(2)+x_(5)^(2)+x_(6)^(2)=480."...(ii)"` When each observation is multiplied by 3, then new observations are `3x_(1), 3x_(2), 3x_(3), 3x_(4), 3x_(5) and 3x_(6).` `THEREFORE" new mean "=(1)/(6)(3x_(1)+3x_(2)+3x_(4)+3x_(5)+3x_(6))` `=(3)/(6)(x_(1)+x_(2)+x_(3)+x_(4)+x_(5)+x_(6))=((1)/(2)xx48)=24" [using (i)]"` `therefore" new variance "((3x_(1))^(2)+(3x_(2))^(2)+(3x_(3))^(2)+(3x_(4))^(2)+(3x_(5))^(2)+(3x_(6))^(2))/(6)-(24)^(2)` `=(9)/(6)(x_(1)^(2)+x_(2)^(2)+x_(3)^(2)+x_(4)^(2)+x_(5)^(2)+x_(6)^(2))-576` `=((9)/(6)xx480)-576=(720-576)=144" [using (ii)]".` Hence, new mean = 24 and new variance `= 144.`

Discussion

8215.	One corner of a rectangle of width one unit is folded over so as to reach the opposite edge of the sheet. Show that minimum length of the crease is (3sqrt(3))/(4).
Answer» ANSWER :`(3sqrt(3))/(4)`

Discussion

8216.	Which of the following are sets ? Justify your answer. A collection of novels written by the writer Munshi Prem Chand.
Answer» ANSWER :it is a SET

Discussion

8217.	A= {1, 2, 3, 4, 5}, B= {4, 5, 6, 7, 8}, C= {7, 8, 9, 10, 11}, D= {10, 11, 12, 13, 14}. Find the following sets. (A cup D)cap (B cup C)
Answer» ANSWER :`{4, 5}`

Discussion

8218.	Find theperiod of (i)\| tanx\| cos2 x (ii)2 sin^(4) x+ 3 cos ^(4) x (ii) \| sin x\|+ \| cos x\|
Answer» ANSWER :`PI`

Discussion

8219.	If a function is represented parametrically by the equations x=(1+log_(e)t)/(t^2),y =(3+2log_et)/(t) , then which of the following statement are true ?
Answer» `y''(x-2xy')=y` `yy'=2x(y')^2+1` `xy'=2y(y')^2+2` `y''(y-4xy')=(y')^2` ANSWER :B::D

Discussion

8220.	Write the first six terms of an A.P. in whicha= 7 (1)/(2) , d= 1 (1)/(2)
Answer» ANSWER :`7 (1)/(2) ,9, 10 (1)/(2), 12,13 (1)/(2) ,15 `

Discussion

8221.	Evaluate the following limits in lim_(xrarrpi)(sin(pi-x))/(pi(pi-x))
Answer» ANSWER :`(1)/(PI)`

Discussion

8222.	The vector bara lies in the plane of barb, barc then
Answer» `a.(barbxxc=0` `a.(barbxxc)=1` `BARA.(BARBXXBARC)=-1` `bara.(barbxxbarc)=2` ANSWER :A

Discussion

8223.	If barp=(3,-1,5), barq = (1,2,-3).A vectorbarr is such that it is perpendicular to Z-axis and satisfies the conditions barr.barp = 9barr.barq= -4,then barr =
Answer» (-2,3,0) (2,-3,0) (2,-3,1) (3,-2,4) ANSWER :B

Discussion

8224.	Find the slope of the lines : (c) Passing through the points (3, - 2) and (3, 4),
Answer» ANSWER :`(6)/(0)`, which is not DEFINED.

Discussion

8225.	Rewrite each of the following statements in the form of conditional statements: The unit digit of an integer is 0 or 5 if it is divisible by 5.
Answer» ANSWER :If an INTEGER is divisible by 5 then its UNIT DIGITS are 0 or 5.

Discussion

8226.	Theequation of a tangent to the parabola y^2=""8x""i s""y""=""x""+""2. The point on this line from which theother tangent to the parabola is perpendicular to the given tangent is(1) (-1,""1)(2) (0,""2)(3) (2,""4)(4) (-2,""0)
Answer» ANSWER :`=10+7x^((-1)/(2) ) + (7)/(2) X^((-3)/(2))`.

Discussion

8227.	Find n if ""^(n-1)P_(3):""^(n)P_(4)=1:9.
Answer» ANSWER :9

Discussion

8228.	Solve \|3x-4\| = 5
Answer» ANSWER :`{3,-(1)/(3)}`

Discussion

8229.	If x,y,z are in A.P. then the value of \|{:(a+2,a+3,a+3x),(a+3,a+4,a+2y),(a+4,a+5,a+2z):}\|=
Answer» 1 0 2a a Answer :B

Discussion

8230.	The minimum vlaue of expresson sin alpha +sin beta + sin gamma where alpha, beta, gamma are positive real numbers
Answer» 0 `-3` NEGATIVE Possitive ANSWER :D

Discussion

8231.	I : Every strictlyy monotonic function is one one. II : The function f:R^(+)rarrR defined by f(x)=5+x^(2) is one one .
Answer» only IIS true only II is true both I & II are true neither I nor II are true Answer :C

Discussion

8232.	Find the equation of a circle which touches both the axes and the line 3x - 4y + 8 = 0 and lies in the third quadrant.
Answer» ANSWER :`therefore 9x^(2) + 9y^(2) - 24x - 24y + 16 = 0` is the required equation of the circle.

Discussion

8233.	If sqrt(3) cos theta + sin theta = sqrt(2) , " then " theta =
Answer» `n pi + (-1)^(n) pi // 4 + pi // 6, n in Z` `2 n pi pm pi//4 + pi // 6, n in Z` `n pi + pi//6, n in Z` `2 n pi pm pi // 6, n in Z` ANSWER :B

Discussion

8234.	Find the 18^(th) and 25^(th) terms of the sequence defined by a_(n)={{:(n(n+2)", if n is even natural number"),((4n)/(n^(2)+1)",if n is odd natural number"):}
Answer» ANSWER :`=(50)/(313)`

Discussion

8235.	If ((1+i)^(2))/(2-i)=x+iy then find the value of x+y.
Answer» ANSWER :`(2)/(5)`

Discussion

8236.	Show that the lines x+2=0,y-1=0 and 2x+3y+1=0 are concurrent.
Answer» ANSWER :HENCE the THREE LINES are CONCURRENT.

Discussion

8237.	Let f(x)=(x^(2)+1)/([x]).1lexle3.9. [.] denotes the greatest integer function Then
Answer» f(x)is monotonically DECREASING in [1,3.9] f(x) is monotonically INCREASING in [1,3.9] the GREATEST value of f(x) is `(1)/(3)xx16.21` the LEAST value of f(x)is 2. Answer :C::D

Discussion

8238.	cos6^(@) cos42^(@) cos66^(@) cos78^(@) =
Answer» `1//2` `1//4` `1//8` `1//16` ANSWER :D

Discussion

8239.	If p: Number of factors of 20 are 5. q: 2 is even prime number. Then validity of p implies q and validity of contrapositive statement is ……….
Answer» T,T F,F T,F F,T Answer :D

Discussion

8240.	Find the value of (10.2)^6+(9.8)^6
Answer» SOLUTION :2012004.800128]

Discussion

8241.	f(x)= tan. x/2 sec x + tan. (x)/(2^(2))sec. x/2 + tan. (x)/(2^(3))sec. (x)/(2^(2))+.....+tan. (x)/(2^(n)) sec. (x)/(2^(n-1)) and g(x)+tan ((x)/(2^(n))) where x in (- pi/2, pi/2) and n in N then
Answer» g(X) is an EVEN function g(x) is an ODD function g(x) is NEITHER even nor odd g(x) is both even and odd Answer :B

Discussion

8242.	Find the equation of hyperbola with foci at the points (-3,5) and (5,5) and length of latus rectum =2sqrt(8) units.
Answer» ANSWER :`(x-1)^(2)-(y-5)^(2)=8`

Discussion

8243.	If e^(sinh^(-1)(tan theta))=k then show that k=sec theta +tan theta
Answer» `SEC THETA` `TAN theta` `sec theta+tan theta` `sec theta-tan theta` ANSWER :C

Discussion

8244.	One side and are vertex of the equilateral triangle is 2x+2y-5=0 and (1,2) respectively. Find equation of other sides.
Answer» Answer :`(2 + SQRT(3) ) x - y-sqrt(3) =0` `( 2- sqrt(3) ) x - y+ sqrt(3) = 0`

Discussion

8245.	Consider the statement ''all prime number are both even and odd''Write the component statements of the given statement.
Answer» SOLUTION :All PRIME NUMBER are EVEN ,All prime number are ODD

Discussion

8246.	Let ABC be triangle with angle=45^(@). Let P the point on sude BC with PB=3 and PC=5, if O is circumcentre of triangle ABC, then length OP is
Answer» `sqrt(18)` `sqrt(17)` `sqrt(19)` `sqrt(15)` ANSWER :B

Discussion

8247.	Express each of the complex number given in the form of a+ib (1/5 + i2/5 -(4+I 5/2))
Answer» ANSWER :`-19/5 - (21i)/10`

Discussion

8248.	A point on the parabola y^2=18x at which the ordinate increases at twice the rate of the abscissa is
Answer» (2,4) (9/8,9/2) (-9/8,9/2) (2,-4_ Answer :B

Discussion

8249.	The rank of [(1,-1,1,1),(-1,1,1,2),(1,1,-1,3)] is
Answer» 4 3 2 1 Answer :B

Discussion

8250.	y = log(sinx+cosx) show thatdy/dx= tan(Pi/4-x).
Answer» ANSWER :`dy/dx= TAN(Pi/4-x)`

Discussion

Explore topic-wise InterviewSolutions in .

Find the coordinates of the foot of perpendicular from the point (-1,3) to the line 3x-4y-16=0.

Bag A contains 4 green and 3 red balls andbag B contains 4 red and 3 green balls. Onebag is taken at random and a ball is drawn andnoted it is green. The probability that it comes from bag Bis

If tan(picostheta)=cot(pisintheta), then cos(theta-(pi)/(4))=(1)/(2sqrt(2)).

A person has 6 friends . He invites one or more then one friends. For dinner in ….. Ways.

If A gt 0 , B gt 0 and A+B = (pi)/(6), then the minimum value of tan A+ tan B is

Check whether the following pair of statements are negation of each other. Give reasons for your answer: (i) x+y=y+xis true for every real numbers x and y. (ii) There exists real number x and y for which x+y=y+x

If (1-p) is a root of the quadratic equation x^(2)+px+(1-p)=0, then its roots are (a) 0,-1 (b) -1,1 (c) 0,1 (d) -1,2

If A={-3,-2,-1,0,1,2,3} and f:A to Z is a function which of the following : (i) Range of f (ii) Pre-image of 5 (iii) Pre-image of 0

Find the derivative of 99x at x = l00.

A point is moving along the cubical parabola 12y = x^(3). Therate of ordinate is less than the rate of abscissa when

If P(AcupB)=P(AcapB) for any two events A and B, then ………..

The vector area of the rectangle whose adjacent sides are p vec(i), q vec(j) is

Find the sum of the following series up to n terms: 5+55+555+......

The mean and variance of six observations are 8 and 16 respectively. If each observation is multiplied by 3, find the new mean and new variance of the resulting observations.

One corner of a rectangle of width one unit is folded over so as to reach the opposite edge of the sheet. Show that minimum length of the crease is (3sqrt(3))/(4).

Which of the following are sets ? Justify your answer. A collection of novels written by the writer Munshi Prem Chand.

A= {1, 2, 3, 4, 5}, B= {4, 5, 6, 7, 8}, C= {7, 8, 9, 10, 11}, D= {10, 11, 12, 13, 14}. Find the following sets. (A cup D)cap (B cup C)

Find theperiod of (i)| tanx| cos2 x (ii)2 sin^(4) x+ 3 cos ^(4) x (ii) | sin x|+ | cos x|

If a function is represented parametrically by the equations x=(1+log_(e)t)/(t^2),y =(3+2log_et)/(t) , then which of the following statement are true ?

Write the first six terms of an A.P. in whicha= 7 (1)/(2) , d= 1 (1)/(2)

Evaluate the following limits in lim_(xrarrpi)(sin(pi-x))/(pi(pi-x))

The vector bara lies in the plane of barb, barc then

If barp=(3,-1,5), barq = (1,2,-3).A vectorbarr is such that it is perpendicular to Z-axis and satisfies the conditions barr.barp = 9barr.barq= -4,then barr =

Find the slope of the lines : (c) Passing through the points (3, - 2) and (3, 4),

Rewrite each of the following statements in the form of conditional statements: The unit digit of an integer is 0 or 5 if it is divisible by 5.

Theequation of a tangent to the parabola y^2=""8x""i s""y""=""x""+""2. The point on this line from which theother tangent to the parabola is perpendicular to the given tangent is(1) (-1,""1)(2) (0,""2)(3) (2,""4)(4) (-2,""0)

Find n if ""^(n-1)P_(3):""^(n)P_(4)=1:9.

Solve |3x-4| = 5

If x,y,z are in A.P. then the value of |{:(a+2,a+3,a+3x),(a+3,a+4,a+2y),(a+4,a+5,a+2z):}|=

The minimum vlaue of expresson sin alpha +sin beta + sin gamma where alpha, beta, gamma are positive real numbers

I : Every strictlyy monotonic function is one one. II : The function f:R^(+)rarrR defined by f(x)=5+x^(2) is one one .

Find the equation of a circle which touches both the axes and the line 3x - 4y + 8 = 0 and lies in the third quadrant.

If sqrt(3) cos theta + sin theta = sqrt(2) , " then " theta =

Find the 18^(th) and 25^(th) terms of the sequence defined by a_(n)={{:(n(n+2)", if n is even natural number"),((4n)/(n^(2)+1)",if n is odd natural number"):}

If ((1+i)^(2))/(2-i)=x+iy then find the value of x+y.

Show that the lines x+2=0,y-1=0 and 2x+3y+1=0 are concurrent.

Let f(x)=(x^(2)+1)/([x]).1lexle3.9. [.] denotes the greatest integer function Then

cos6^(@) cos42^(@) cos66^(@) cos78^(@) =

If p: Number of factors of 20 are 5. q: 2 is even prime number. Then validity of p implies q and validity of contrapositive statement is ……….

Find the value of (10.2)^6+(9.8)^6

f(x)= tan. x/2 sec x + tan. (x)/(2^(2))sec. x/2 + tan. (x)/(2^(3))sec. (x)/(2^(2))+.....+tan. (x)/(2^(n)) sec. (x)/(2^(n-1)) and g(x)+tan ((x)/(2^(n))) where x in (- pi/2, pi/2) and n in N then

Find the equation of hyperbola with foci at the points (-3,5) and (5,5) and length of latus rectum =2sqrt(8) units.

If e^(sinh^(-1)(tan theta))=k then show that k=sec theta +tan theta

One side and are vertex of the equilateral triangle is 2x+2y-5=0 and (1,2) respectively. Find equation of other sides.

Consider the statement ''all prime number are both even and odd''Write the component statements of the given statement.

Let ABC be triangle with angle=45^(@). Let P the point on sude BC with PB=3 and PC=5, if O is circumcentre of triangle ABC, then length OP is

Express each of the complex number given in the form of a+ib (1/5 + i2/5 -(4+I 5/2))

A point on the parabola y^2=18x at which the ordinate increases at twice the rate of the abscissa is

The rank of [(1,-1,1,1),(-1,1,1,2),(1,1,-1,3)] is

y = log(sinx+cosx) show thatdy/dx= tan(Pi/4-x).