14949 + Interview Questions in Maths in Class 11 Page 126 InterviewSolution

6251.	Let f(x)=[x]^(2)+[x+1]-3 where [x] le x. Then
Answer» `f(X)` is many-one and into FUN. `f(x)=0` for infinite number of values of x `f(x)=0` for onlytwo real values `f(x)` is a one-one function Answer :A::B

Discussion

6252.	Find the value ofcosec 750^(@)
Answer» ANSWER :2

Discussion

6253.	1+3+3^(2)+....+3^(n-1) =
Answer» `((3^(N)-1))/(2)` `((3^(2N)-1))/(2)` `((3^(n)+1))/(2)` `((3^(2n)+1))/(2)` Solution :Let `P (n) :1+3+3^(2)+â€¦..+3^(n-1)=(3^(n)-1)/(2)` `" If "n =1 , "the " L.H.S. =1` `R.H.S. =(3^(1)-1)/(2)=(3-1)/(2)=1` `:. ""L.H.S. =R.H.S.` Therefore the STATEMENT P (n) is true for n=1 Let P (n) be true for n=K. `:. P (k) : 1+3+3^(2) +.....+3^(k-1) =(3^(K)-1)/(2)` `P (k+1) :1+3+3^(2)+......+3^(k)` `=1+3+3^(2)+......+3^(k)` `=1+3+3^(2)+.......+3^(k-1)+3^(k)` `=(3^(k)-1)/(2) +3^(k)` `=(3^(k)-1+2.3^(k))/(2)=((1+2)3^(k)-1)/(2)` `=(3.3^(k)-1)/(2)=(3^(k+1)-1)/(2)` Then the statement P (n) is also true for n=K +1 , HENCE form the principle of MATHEMATICAL induction P (n) is true for `n in N`

Discussion

6254.	If 2x^(2)-3xy+y^(2)=0represents two sides of a triangle and lx + my + n = 0 is the third side then locus of incentre of the triangle is
Answer» `3x^2-2xy-3y^2=0` `2x^2+3xy+y^2=0` `3x^2-2xy-3y^2=0` `2x^2-3xy-2y^2=0` ANSWER :A

Discussion

6255.	Write down the slopes of the following lines: -6y-11x=0
Answer» ANSWER : `(-11)/(6)`

Discussion

6256.	If xgt0,ygt0,x+y=32 and x^6+y^6 is minimum then the numbers are
Answer» 14,18 12,20 16,16 17,15 Answer :C

Discussion

6257.	Prove that the condition that one root of ax^(2)+bx+c=0 may be the square of the other is b^(3)+a^(2)c+ac^(2)=3abc.
Answer» ANSWER :3ABC.

Discussion

6258.	If A=(-2, 3, 4), B= ( 1, 2, 3) are two points and P is the point of intersection of AB and zx-plane, then P_(x)+P_(y)+P_(z)=
Answer» 6 `-8` 8 0 Answer :C

Discussion

6259.	The point p(1,1) is translated parallel to 2x=y in the first quadrant through a unit distance. The coordinates of point in new position of p are
Answer» (2,2) `(+1/sqrt2,1+1/sqrt2)` `(-1/sqrt5,1-1/sqrt5)` `(+1/sqrt5,1+1/sqrt5)` ANSWER :B

Discussion

6260.	If the angle between line with d.cs (-(2)/(sqrt(21)), (a)/(sqrt(21)), (b)/(sqrt(21))) and other line with d.c ((3)/(sqrt(54)), (3)/(sqrt(54)), (-6)/(sqrt(54))) is 90^(0) then a pair of possible values of 'a' and 'b' respectively are
Answer» `-1, 4 ` 4, 2 4, 1 `-4, -2` ANSWER :C

Discussion

6261.	lim_(xrarr 0)(ax^3+bx^2+cx+d)/((a+1)x+b) = …… .
Answer» ANSWER :`d/b`

Discussion

6262.	A sum of Rs. 10,000 is invested at 8% p.a. compound interest? How long will it take for the total sum of money to be twice the amount invested?
Answer» SOLUTION :9.01 YEARS

Discussion

6263.	d/(dx){e^(logsqrt(1+cot^2x))}=
Answer» `"COSEC"X COT x ` `-"cosec"x cot x ` `-"cosec"^x cot x ` 0 Answer :B

Discussion

6264.	Solve the inequality2 le 3x -4le 5
Answer» ANSWER :`[2,3]`

Discussion

6265.	How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
Answer» ANSWER :40320

Discussion

6266.	If (sin(x+y))/(sin(x-y))=(a+b)/(a-b) then (tanx)/(tany) = …………
Answer» `(B)/(a)` `(a)/(b)` `AB` `a-b` ANSWER :B

Discussion

6267.	If a,x_(1), x_(2), x_(3) …..and b, y_(1), y_(2), …..form two infinite A.P's with common difference p and q respectively then the locus of P(h, k) when h=(x_(1)+x_(2)+x_(3)……+x_(n))/(n), k=(y_(1)+y_(2)+……..+y_(n))/(n) is
Answer» <P>`Q(x-a)=p(y-b)` `p(x-a)=q(y-b)` `p(x+a)=q(y+b)` `p(y+a)=q(x+b)` ANSWER :A

Discussion

6268.	The derivative of Cos ^(-1) (4x ^(3) -3x) w.r.t x is
Answer» ANSWER :`(-3)/( SQRT (1 - x ^(2)))`

Discussion

6269.	If bara, barb, barc, bard are vectors such that bard is a unit vector, the projection of bara on bard is 2 and [bara barb barc] = 3 find the value of { ( a xx b) xx (bara xx barc)} .bard
Answer» ANSWER :6

Discussion

6270.	The system of linear equations x+lamday-z=0 lamdax-y-z=0 and x+y-lamdaz=0 has non trivial solutions for
Answer» exactly THREE value of `LAMDA` INFINITELY many values of `lamda` exactly ONE value of `lamda` exactly two values of `lamda` ANSWER :A

Discussion

6271.	Equation of line passes from A(-(3)/2,(5)/2) and parallel to Y - axis is 2x - 5 = 0 .
Answer» ANSWER :FALSE STATEMENT

Discussion

6272.	Iftangent to the curve x^(2) = y - 6 at point (1,7) touches the circle x^(2) + y^(2) + 16x+ 12y + c = 0 then value of c is ………
Answer» 195 185 85 95 Answer :D

Discussion

6273.	2+3+5+6+8+9+…...2n terms =
Answer» `3N^(2) + 2N` `4N^(2) + 2n` `4n^(2)` `5n^(2) + 2n` Answer :A

Discussion

6274.	If the product of the perpendicular distances from (1, k) to the pair of lines x^(2)-4xy+y^(2)=0 is (3)/(2) units, then k=
Answer» 4 5 6 8 Answer :B

Discussion

6275.	If costheta-sintheta=1, then theta
Answer» `PI` `(3pi)/(2)` `(2PI)/(3)` `(pi)/(6)` Answer :B

Discussion

6276.	Find the sum to n terms of each of the series in 1xx2+2xx3+3xx4+4xx5+....
Answer» ANSWER :`n/3(n+1)(n+2)`

Discussion

6277.	Iftan (A-B)=7//24 , tan A=4//3 " where " A,B are acute , then A+B=
Answer» `(PI)/(5)` `(pi)/(4)` `(pi)/(3)` `(pi)/(2)` ANSWER :D

Discussion

6278.	Find the ratio in which the point R(5,-4,-6) divides the jion of the A(2,-34) and B(3,1,-2).
Answer» ANSWER :`1:2`

Discussion

6279.	lim_(xto(pi)/(2))(1-sinx)/(cosx)=……..
Answer» 1 0 -1 2 Answer :B

Discussion

6280.	When the origin is shifted to (4,-5) by the translation of axes, find the coordinates of the point (-2,4) with reference to new axes.
Answer» ANSWER :(-6,9)

Discussion

6281.	A stone is thrown vertically up and the height s reached in time t is given by s=80t-16t^2. The stone reaches the maximum height in time t =
Answer» 2 sec 2.5 sec 3 sec 3.5 sec Answer :B

Discussion

6282.	phi is null set and for given non null sets A and B,A cap(AcupB) = …..
Answer» ANSWER :`PHI`

Discussion

6283.	Four persons are selected at random out of 3 men, 2 women and 4 children. The probability that there are exactly 2 children in the selection is ....
Answer» `(10)/(21)` `(8)/(63)` `(5)/(21)` `(9)/(21)` ANSWER :A

Discussion

6284.	Find the equation of line perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 30^(@).
Answer» ANSWER :`SQRT3 X + y = 10`

Discussion

6285.	A man starts repaying a loan as first installment of Rs. 100. If he increases theinstallment by Rs 5 every month, what amount he will pay in the 30^("th")installment?
Answer» ANSWER :RS 245

Discussion

6286.	Write the converse, contradiction and contrapositive of the statement 'If x+3=9,then x=6.?
Answer» Answer :GIVEN statement ISX + 3=9 => X=6. (i) Its converse is x =6 => x+3=9,i.e.,if x =6, then x + 3 =9. Its contradiction is x =6 => x +3`!=` 9,i.e., If x=6, then x +3 != 9. Its contrapositive is x != 6 => x +3 !=9,i.e., If x != 6, then x + 3 != 9.

Discussion

6287.	Which of the following sets are finite or infinite : {x : x in Z, x lt 5}
Answer» ANSWER :it is an INFINITE SET

Discussion

6288.	Find the value of sin 750^(@)cos300^(@)+cos1470^(@)sin(-1020^(@))
Answer» ANSWER :1

Discussion

6289.	A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?
Answer» ANSWER :More than 320 LITRES but LESS than 1280 litres.

Discussion

6290.	0.2 + 0.22 + 0.222+ …. upto n terms is equal to
Answer» `((2)/(9)) - ((2)/(81) ) ( 1-10^(-N) ) ` `n- ((1)/( 9) ) (1-10^(-n) )` `((2)/( 9))[n-((1)/( 9))(1-10^(-n)) ]` `(2)/( 9) ` Answer :C

Discussion

6291.	Convert the following complex number in the polar form : 2-2i
Answer» Answer :`2 sqrt(2)("COS"(PI)/(4)+I"SIN"(-(pi)/(4)))`

Discussion

6292.	Solve the general vlaue. cot theta + tan theta = 2 cosec theta
Answer» Answer :`2N PI PM (1)/(3) pi`

Discussion

6293.	Differentiate from first principles: 12. (x^2+1)/( x)
Answer» ANSWER :`1- (1)/(x^2)`

Discussion

6294.	If (1, k) is the point of intersection of the lines given by 2x^(2)+5xy+3y^(2)+6x+7y+4=0 then k=
Answer» 1 `-1` `-2` 4 Answer :C

Discussion

6295.	Two dice are thrown. Find the probability of getting an odd number onthe first die and a multiple of 3 on the other.
Answer» ANSWER :`(11)/(36)`

Discussion

6296.	Find the value if k , if the lines joining the origin with the points of intersection of the curve2x^(2)-2xy+3y^(2)+2x-y-1=0 and the x + 2y = k are mutually perpendicular .
Answer» ANSWER :`k=+-1`

Discussion

6297.	Evaluate the following limits : Lim_(x to oo) (sqrt(3x^(2)-1)-sqrt(2x^(2)-1))/(4x+3)
Answer» ANSWER :`(SQRT(3)-sqrt(2))/4`

Discussion

6298.	Differentiate the following with respect to x.y = sinx cosx
Answer» ANSWER :`-SIN^(2)X + COS^(2)x`

Discussion

6299.	A=(cos9^(@)-sin9^(@))/(cos9^(@)+sin 9^(@)), B=(cos21^(@)+sin21^(@))/(cos21^(@)-sin21^(@)) and C=tan 20^(@)+tan 40^(@)+sqrt(3)tan20^(@)tan40^(@) then descending order is
Answer» A, B, C B, C, A C, A, B C, B, A ANSWER :B

Discussion

6300.	If sin""(pi)/18 sin""(5pi)/18 sin""(7pi)/18 =
Answer» 8 `1/8` `1//7` 6 Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

Let f(x)=[x]^(2)+[x+1]-3 where [x] le x. Then

Find the value ofcosec 750^(@)

1+3+3^(2)+....+3^(n-1) =

If 2x^(2)-3xy+y^(2)=0represents two sides of a triangle and lx + my + n = 0 is the third side then locus of incentre of the triangle is

Write down the slopes of the following lines: -6y-11x=0

If xgt0,ygt0,x+y=32 and x^6+y^6 is minimum then the numbers are

Prove that the condition that one root of ax^(2)+bx+c=0 may be the square of the other is b^(3)+a^(2)c+ac^(2)=3abc.

If A=(-2, 3, 4), B= ( 1, 2, 3) are two points and P is the point of intersection of AB and zx-plane, then P_(x)+P_(y)+P_(z)=

The point p(1,1) is translated parallel to 2x=y in the first quadrant through a unit distance. The coordinates of point in new position of p are

If the angle between line with d.cs (-(2)/(sqrt(21)), (a)/(sqrt(21)), (b)/(sqrt(21))) and other line with d.c ((3)/(sqrt(54)), (3)/(sqrt(54)), (-6)/(sqrt(54))) is 90^(0) then a pair of possible values of 'a' and 'b' respectively are

lim_(xrarr 0)(ax^3+bx^2+cx+d)/((a+1)x+b) = …… .

A sum of Rs. 10,000 is invested at 8% p.a. compound interest? How long will it take for the total sum of money to be twice the amount invested?

d/(dx){e^(logsqrt(1+cot^2x))}=

Solve the inequality2 le 3x -4le 5

How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?

If (sin(x+y))/(sin(x-y))=(a+b)/(a-b) then (tanx)/(tany) = …………

If a,x_(1), x_(2), x_(3) …..and b, y_(1), y_(2), …..form two infinite A.P's with common difference p and q respectively then the locus of P(h, k) when h=(x_(1)+x_(2)+x_(3)……+x_(n))/(n), k=(y_(1)+y_(2)+……..+y_(n))/(n) is

The derivative of Cos ^(-1) (4x ^(3) -3x) w.r.t x is

If bara, barb, barc, bard are vectors such that bard is a unit vector, the projection of bara on bard is 2 and [bara barb barc] = 3 find the value of { ( a xx b) xx (bara xx barc)} .bard

The system of linear equations x+lamday-z=0 lamdax-y-z=0 and x+y-lamdaz=0 has non trivial solutions for

Equation of line passes from A(-(3)/2,(5)/2) and parallel to Y - axis is 2x - 5 = 0 .

Iftangent to the curve x^(2) = y - 6 at point (1,7) touches the circle x^(2) + y^(2) + 16x+ 12y + c = 0 then value of c is ………

2+3+5+6+8+9+…...2n terms =

If the product of the perpendicular distances from (1, k) to the pair of lines x^(2)-4xy+y^(2)=0 is (3)/(2) units, then k=

If costheta-sintheta=1, then theta

Find the sum to n terms of each of the series in 1xx2+2xx3+3xx4+4xx5+....

Iftan (A-B)=7//24 , tan A=4//3 " where " A,B are acute , then A+B=

Find the ratio in which the point R(5,-4,-6) divides the jion of the A(2,-34) and B(3,1,-2).

lim_(xto(pi)/(2))(1-sinx)/(cosx)=……..

When the origin is shifted to (4,-5) by the translation of axes, find the coordinates of the point (-2,4) with reference to new axes.

A stone is thrown vertically up and the height s reached in time t is given by s=80t-16t^2. The stone reaches the maximum height in time t =

phi is null set and for given non null sets A and B,A cap(AcupB) = …..

Four persons are selected at random out of 3 men, 2 women and 4 children. The probability that there are exactly 2 children in the selection is ....

Find the equation of line perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 30^(@).

A man starts repaying a loan as first installment of Rs. 100. If he increases theinstallment by Rs 5 every month, what amount he will pay in the 30^("th")installment?

Write the converse, contradiction and contrapositive of the statement 'If x+3=9,then x=6.?

Which of the following sets are finite or infinite : {x : x in Z, x lt 5}

Find the value of sin 750^(@)cos300^(@)+cos1470^(@)sin(-1020^(@))

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?

0.2 + 0.22 + 0.222+ …. upto n terms is equal to

Convert the following complex number in the polar form : 2-2i

Solve the general vlaue. cot theta + tan theta = 2 cosec theta

Differentiate from first principles: 12. (x^2+1)/( x)

If (1, k) is the point of intersection of the lines given by 2x^(2)+5xy+3y^(2)+6x+7y+4=0 then k=

Two dice are thrown. Find the probability of getting an odd number onthe first die and a multiple of 3 on the other.

Find the value if k , if the lines joining the origin with the points of intersection of the curve2x^(2)-2xy+3y^(2)+2x-y-1=0 and the x + 2y = k are mutually perpendicular .

Evaluate the following limits : Lim_(x to oo) (sqrt(3x^(2)-1)-sqrt(2x^(2)-1))/(4x+3)

Differentiate the following with respect to x.y = sinx cosx

A=(cos9^(@)-sin9^(@))/(cos9^(@)+sin 9^(@)), B=(cos21^(@)+sin21^(@))/(cos21^(@)-sin21^(@)) and C=tan 20^(@)+tan 40^(@)+sqrt(3)tan20^(@)tan40^(@) then descending order is

If sin""(pi)/18 sin""(5pi)/18 sin""(7pi)/18 =