14949 + Interview Questions in Maths in Class 11 Page 160 InterviewSolution

7951.	If the angle between two lines is pi/4 and slope of one the lines is 1/2 , find the slope of the other line.
Answer» ANSWER :` m = - 1/3`

Discussion

7952.	In triangle ABC, tan A + tan B + tan C = 6 and tanA tanB = 2, then the values of tan A, tan B, tan C are, respectively:
Answer» 1,2,3 3, 2/3, 7 4,1/2, 3/2 5,2/5, 3/5 Answer :A

Discussion

7953.	If y ^(x) + x ^(y) + x ^(x) = a ^(b)then find(dy)/(dx)
Answer» ANSWER :`- ((y ^(X) LOG y + x ^(y -1) + x ^(x) + x ^(x) (log x +1)))/( y ^( x -1) x + x ^(y). log x)`

Discussion

7954.	If the period of the function f(x)= sin (sqrt([n])x) where [n] denotes the greatest integer less than or equal to n is 2pi, then
Answer» `1 le N lt 2` `1 lt n lt 2` `1 le n lt 2` `1 lt n le 2` ANSWER :A

Discussion

7955.	Find the mean deviation using meadian from the following data:
Answer» SOLUTION : Here `N=195`(ODD) MEDIAN `M=(N+1)/2` TH term `=(195+1)/2` th term `=98` th term `=50` Mean DEVIATION `=(sumf_(i)\|x_(i)-M\|)/(sumf_(i))` `=2750/195=14.10`

Discussion

7956.	If sqrt(2)cosA=cosB+cos^(3)B and sqrt(2) sinA=sinB-sin^3B then sin(A-B) =
Answer» `pm1` `pm1/(2)` `PM(1)/3` `pm(1)/(4)` Answer :C

Discussion

7957.	If bara,barb" and "bara-barb are unit vectors, then what is the angle between bara" and "barb?
Answer» ANSWER :`60^(@)`

Discussion

7958.	The radius of the circumcircle of an isosceles triangle POR is equal to PO = PR, then the angle P is
Answer» `pi//6` `pi//3` `pi//2` `2pi//3` ANSWER :D

Discussion

7959.	Write the equation of the plane parallel to the plane x+y+z=0 and passing through the point (a, b, c).
Answer» ANSWER :`x+y+z=a+b+c`

Discussion

7960.	If the lines x cos alpha + y sin alpha = P and x - sqrt(3) y+ 1 =0 are mutually perpendicular then alpha=…....
Answer» `(PI)/(2)` `(pi)/(4)` `(pi)/(3)` `(pi)/(3)` ANSWER :C

Discussion

7961.	Check whether the given sentence is a statement or not : "Open the door".
Answer» ANSWER :Not a STATEMENT

Discussion

7962.	Write down the slopes of the following lines: x x_(1)+yy_(1)=a^(2)
Answer» ANSWER : `(-x_(1))/(y_(1))`

Discussion

7963.	m,n are integers with 0ltnltm. A is the point (m,n) on the Cartesian Plane. B is the rflection of A on theline y=x. C is the reflection of B on the y-axis. D is the reflection of C on the x-axis. And E is the reflection of D on they y-axis. The area of the pentagon ABCDE is
Answer» 2M(m+n) m(m+3n) m(2m+3n) 2m(m+3n) ANSWER :B

Discussion

7964.	Write each of the following statements in the form ''if-then'' To get an A^(+) in the class, it is necessary that you do all the exercises of the book.
Answer» ANSWER :If you GET `A^(+)` in the CLASS, then you do all the EXERCISES in the BOOK.

Discussion

7965.	The planes x=pma, y=pma, z=pma form a
Answer» PARALLELOPIPED RECTANGULAR parallelopiped cube tetrahedron ANSWER :B

Discussion

7966.	If f:R rarrS, defined by f(x)=sinx-sqrt3cos x+1, is onto, then the interval of S is
Answer» `[0, 3]` `[-1, 1]` `[0, 1]` `[-1, 3]` ANSWER :D

Discussion

7967.	Find the derivative of (5x^(3)+3x-1)(x-1)
Answer» ANSWER :`20X^(3)-15X^(2)+6x-54`

Discussion

7968.	d/(dx){e^((1/2)log(1-Tanh^2x))+3^((1/2)log_(3)(coth^2x-1))}=
Answer» `(-(sinh^3x+cosh^3x))/(cosh^2xsinh^2x)` `(sinh^3x+cosh3x)/(cosh^2xsinh^2x)` `(sinh^2x+cosh^2x)/(sinh^2xcosh^2x)` `sech^2x cosh^2x` ANSWER :A

Discussion

7969.	Find the slope of the line, which makes an angle of 30^(@) with the positive direction of y-axis measured anticlockwise.
Answer» ANSWER :`- SQRT3`

Discussion

7970.	Let U = set of all triangle and X = set of all triangles whose measure of all angle is less than 60^@ then X' = ……
Answer» ANSWER :U

Discussion

7971.	Find the solution of sin x =- (1)/(2).
Answer» Answer :`X = N pi + (-1)^(n) (4pi)/(3),` where `n in Z`

Discussion

7972.	The locus of the point (sectheta+tantheta,sectheta-tantheta) where theta is parameter, is
Answer» `X^(2)+y^(2)=1` `x^(2)-y^(2)=1` `xy=1` `xy+1=0` ANSWER :3

Discussion

7973.	Let S_(n) denote the sum of the cubes of the first n natural numbers and S'_(n) denote the sum of the first n natural numbers, then underset(r=1)overset(n)Sigma ((S_(r))/(S'_(r))) equals to
Answer» `(N(n+1) (n+2))/(6)` `(n(n+1))/(2)` `(n^(2) + 3n+ 2)/(2)` NONE of these Answer :A

Discussion

7974.	There are 3 prizes to be distributed amongst 6 students. In how many ways can it be done when :(i)no student gets more than one prize.(ii)there is no restriction as to the number of prizes any student gets(iii)no student gets all the prizes ?
Answer» ANSWER :(i) 120 (ii)216 (III)210

Discussion

7975.	A card is drawn from an ordinary pack of 52 cards and a gambler betsthat, it is a spade or an ace. What are the odds against his wining this bet?
Answer» ANSWER :`9:4`.

Discussion

7976.	If the p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c respectively, prove that a(q-r)+b(r-p)+c(p-q)=0.
Answer» ANSWER :`= (0)A+(0) D = 0`

Discussion

7977.	Show that the function defined by f(x)= cos (x^2) is a continuous function.
Answer» ANSWER :there is no POINT of discontinouity

Discussion

7978.	If the straight lines 2x+3y-1=0,x+2y-1=0 and ax+by-1=0 form a triangle with origin as orthocentre then (a,b)=
Answer» (6,4) (-3,3) (-8,8) (0,7) ANSWER :C

Discussion

7979.	A point is on the X-axis. What are its y coordinate and z coordinates ?
Answer» ANSWER :y and Z COORDINATES are ZERO

Discussion

7980.	Sum of the squares of deviation from the mean of x series is136 and that of y series is 13. Sum of the product of the deviations of x and y series from their respective means is 122. Find the Pearson's coefficient of correlation.
Answer» ANSWER :0.89

Discussion

7981.	Find the coefficient of one middle term in the expansio of (1+x)^(2n).
Answer» ANSWER :`""^(2N)C_(N)`

Discussion

7982.	If the sides of a triangle ABC are 6,8,10 units, then the radius of its circumcircle is
Answer» 4 3 6 5 Answer :D

Discussion

7983.	Complete the following tables:
Answer» SOLUTION :Missing figures in the Ist row are `45^@` , `480^@` , and `-114^@33.` Missing figures in the 2ND row are `pi/7` , `7pi/3` , `pi/10`

Discussion

7984.	If f(x) is a function such that f^('')(x)+ f(x) = 0 and g(x) = (f(x))^2 + (f'(x))^2 and g(3)= 3 then g(8) =
Answer» `5` `0` `3` `8` Answer :C

Discussion

7985.	Obtain lnght of latus rectum and equation of direction of the parabola (x + 1)^(2) = 4(y + 2) by shifting origin at point (-1, -2).
Answer» ANSWER :Length of latus rectum : 4 unit EQUATION of DIRECTRIX : y + 3 = 0

Discussion

7986.	What are the points on the Y- axis whose distance from the line (x)/( 3) + (y)/( 4) =1 is 4 units.
Answer» ANSWER :`(-2, 0) " and " (8, 0)`

Discussion

7987.	Find the real constants a , b, so that the function f given by f(x)={{:(sinx,"if "xle0),(x^(2)+a,"if "0ltxlt1),(bx+3,"if "1lexle3),(-3,"if "x gt3):}is continuous on R .
Answer» ANSWER :`-2`

Discussion

7988.	Find the sum to n terms of the series 3.8 +6.11 +9.14 + ...
Answer» ANSWER :3N(n+1) (n+3)

Discussion

7989.	The period of the function f(x) =[6x + 7] + cos pi x - 6x, where [.] denotes the greatest integer function, is
Answer» 3 `2PI` 2 `PI` Answer :C

Discussion

7990.	How many three-digit numbers can be made using the digits 0, 1, 2, …, 9, if no digit is repeated ?
Answer» ANSWER :648

Discussion

7991.	sin(1//2Cot^(-1)(-3//4))=
Answer» `1//sqrt(5)` `2//sqrt(5)` `-2//sqrt(5)` `-1//sqrt(5)` ANSWER :B

Discussion

7992.	The range of 'a' so that a^2x^2+2xy+4y^2=0 represents distinct lines
Answer» `agt1/2 or ALT(-1)/2` `(-1)/2leale1/2` `(-1)/2ltalt1/2` `age1/2 or ale(-1)/2` ANSWER :C

Discussion

7993.	Multiplicative inverse of complex number z= 2 - 3i is ............
Answer» ANSWER :`(2)/13 +3/(13) i`

Discussion

7994.	The minimum value of ((A^(2)+A+1)(B^(2)+B+1)(C^(2)+C+1)(D^(2)+D+1))/(BACD) , wher A,B,C,D are positive
Answer» `3^(4)` `3^(-4)` `2^(4)` `3^(-4)` ANSWER :A

Discussion

7995.	Prove that sin^(2)5^(@) +sin^(2)10^(@) + sin^(2)15^(@)+...+sin^(2)90^(@)=(19)/(2)
Answer» 7 `8 1//2` `9 1//2` `7 1//2` ANSWER :C

Discussion

7996.	Let the sum of n, 2n, 3n terms of an A.P. be S_1, S_2 and S_3 , respectively, show that S_3 =3(S_2-S_1)
Answer» ANSWER :`S_(3)`

Discussion

7997.	If bara is a unit vector and barxis any vector such that (barx-bara).(barx+bara)= 15 " then find " absbarx.
Answer» ANSWER :4

Discussion

7998.	If f:R to R is defined as f(x+y)=f(x)+f(y) AA x,y in R and f(1) = 7, find sum_(r=1)^(n)f(r ).
Answer» `(7N)/(2)` `(7(n+1))/(2)` `7n(n+1)` `(7n(n+1))/(2)` ANSWER :D

Discussion

7999.	Find the component statements of the following and check whether they are true or not: 24 is a multiple of 2,4, and 8.
Answer» ANSWER :TRUE.

Discussion

8000.	For triangle ABC, R = 5/2 and r=1. Let I be the incenter of the triangle and D, E, and F be the feet ofthe perpendiculars from I to BC,CA and AB, respectively. The value of (IDxx IExxIF)/(IAxxIBxxIC) is equal to
Answer» `(5)/(2)` `(5)/(4)` `(1)/(10)` `(1)/(5)` ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in .

If the angle between two lines is pi/4 and slope of one the lines is 1/2 , find the slope of the other line.

In triangle ABC, tan A + tan B + tan C = 6 and tanA tanB = 2, then the values of tan A, tan B, tan C are, respectively:

If y ^(x) + x ^(y) + x ^(x) = a ^(b)then find(dy)/(dx)

If the period of the function f(x)= sin (sqrt([n])x) where [n] denotes the greatest integer less than or equal to n is 2pi, then

Find the mean deviation using meadian from the following data:

If sqrt(2)cosA=cosB+cos^(3)B and sqrt(2) sinA=sinB-sin^3B then sin(A-B) =

If bara,barb" and "bara-barb are unit vectors, then what is the angle between bara" and "barb?

The radius of the circumcircle of an isosceles triangle POR is equal to PO = PR, then the angle P is

Write the equation of the plane parallel to the plane x+y+z=0 and passing through the point (a, b, c).

If the lines x cos alpha + y sin alpha = P and x - sqrt(3) y+ 1 =0 are mutually perpendicular then alpha=…....

Check whether the given sentence is a statement or not : "Open the door".

Write down the slopes of the following lines: x x_(1)+yy_(1)=a^(2)

m,n are integers with 0ltnltm. A is the point (m,n) on the Cartesian Plane. B is the rflection of A on theline y=x. C is the reflection of B on the y-axis. D is the reflection of C on the x-axis. And E is the reflection of D on they y-axis. The area of the pentagon ABCDE is

Write each of the following statements in the form ''if-then'' To get an A^(+) in the class, it is necessary that you do all the exercises of the book.

The planes x=pma, y=pma, z=pma form a

If f:R rarrS, defined by f(x)=sinx-sqrt3cos x+1, is onto, then the interval of S is

Find the derivative of (5x^(3)+3x-1)(x-1)

d/(dx){e^((1/2)log(1-Tanh^2x))+3^((1/2)log_(3)(coth^2x-1))}=

Find the slope of the line, which makes an angle of 30^(@) with the positive direction of y-axis measured anticlockwise.

Let U = set of all triangle and X = set of all triangles whose measure of all angle is less than 60^@ then X' = ……

Find the solution of sin x =- (1)/(2).

The locus of the point (sectheta+tantheta,sectheta-tantheta) where theta is parameter, is

Let S_(n) denote the sum of the cubes of the first n natural numbers and S'_(n) denote the sum of the first n natural numbers, then underset(r=1)overset(n)Sigma ((S_(r))/(S'_(r))) equals to

There are 3 prizes to be distributed amongst 6 students. In how many ways can it be done when :(i)no student gets more than one prize.(ii)there is no restriction as to the number of prizes any student gets(iii)no student gets all the prizes ?

A card is drawn from an ordinary pack of 52 cards and a gambler betsthat, it is a spade or an ace. What are the odds against his wining this bet?

If the p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c respectively, prove that a(q-r)+b(r-p)+c(p-q)=0.

Show that the function defined by f(x)= cos (x^2) is a continuous function.

If the straight lines 2x+3y-1=0,x+2y-1=0 and ax+by-1=0 form a triangle with origin as orthocentre then (a,b)=

A point is on the X-axis. What are its y coordinate and z coordinates ?

Sum of the squares of deviation from the mean of x series is136 and that of y series is 13. Sum of the product of the deviations of x and y series from their respective means is 122. Find the Pearson's coefficient of correlation.

Find the coefficient of one middle term in the expansio of (1+x)^(2n).

If the sides of a triangle ABC are 6,8,10 units, then the radius of its circumcircle is

Complete the following tables:

If f(x) is a function such that f^('')(x)+ f(x) = 0 and g(x) = (f(x))^2 + (f'(x))^2 and g(3)= 3 then g(8) =

Obtain lnght of latus rectum and equation of direction of the parabola (x + 1)^(2) = 4(y + 2) by shifting origin at point (-1, -2).

What are the points on the Y- axis whose distance from the line (x)/( 3) + (y)/( 4) =1 is 4 units.

Find the real constants a , b, so that the function f given by f(x)={{:(sinx,"if "xle0),(x^(2)+a,"if "0ltxlt1),(bx+3,"if "1lexle3),(-3,"if "x gt3):}is continuous on R .

Find the sum to n terms of the series 3.8 +6.11 +9.14 + ...

The period of the function f(x) =[6x + 7] + cos pi x - 6x, where [.] denotes the greatest integer function, is

How many three-digit numbers can be made using the digits 0, 1, 2, …, 9, if no digit is repeated ?

sin(1//2Cot^(-1)(-3//4))=

The range of 'a' so that a^2x^2+2xy+4y^2=0 represents distinct lines

Multiplicative inverse of complex number z= 2 - 3i is ............

The minimum value of ((A^(2)+A+1)(B^(2)+B+1)(C^(2)+C+1)(D^(2)+D+1))/(BACD) , wher A,B,C,D are positive

Prove that sin^(2)5^(@) +sin^(2)10^(@) + sin^(2)15^(@)+...+sin^(2)90^(@)=(19)/(2)

Let the sum of n, 2n, 3n terms of an A.P. be S_1, S_2 and S_3 , respectively, show that S_3 =3(S_2-S_1)

If bara is a unit vector and barxis any vector such that (barx-bara).(barx+bara)= 15 " then find " absbarx.

If f:R to R is defined as f(x+y)=f(x)+f(y) AA x,y in R and f(1) = 7, find sum_(r=1)^(n)f(r ).

Find the component statements of the following and check whether they are true or not: 24 is a multiple of 2,4, and 8.

For triangle ABC, R = 5/2 and r=1. Let I be the incenter of the triangle and D, E, and F be the feet ofthe perpendiculars from I to BC,CA and AB, respectively. The value of (IDxx IExxIF)/(IAxxIBxxIC) is equal to