14949 + Interview Questions in Maths in Class 11 Page 220 InterviewSolution

10951.	Draw the graph of the quadratic function x^(2)-4x+3 and hence find the roots of the equation x^(2)-4x+3=0. What is the minimum value of the function ?
Answer» ANSWER :ROOTS are 1,3. MINIMUM value=-1

Discussion

10952.	p^^q is valid (true) is …..
Answer» <P>p and Q are TRUE p and q are FALSE p is true and q is false p is false and q is ture Answer :A

Discussion

10953.	Radius of the circlewith centre (0,3) and passes from focus of ellipse (x^(2))/(16)+(y^2)/(9)=1 is ……
Answer» 4 3 `sqrt(12)` `(7)/(2)` ANSWER :A

Discussion

10954.	Circum circle of a Delta^("le")ABC is a circle passing through the vertices, Nine point circle is circum circle of pedal triangle and its centre N is midpoint of circum centre and ortho centre of Delta^("le")ABC then If circum circle passes through N then sum(Cos2A)=
Answer» 0 `(1)/(2)` `-1` 1 Answer :B

Discussion

10955.	Circum circle of a Delta^("le")ABC is a circle passing through the vertices, Nine point circle is circum circle of pedal triangle and its centre N is midpoint of circum centre and ortho centre of Delta^("le")ABC then If the circum circle and nine point circle cut orthogonally then sum(cos2A)=
Answer» 0 `(1)/(2)` `-1` 1 Answer :D

Discussion

10956.	Circum circle of a Delta^("le")ABC is a circle passing through the vertices, Nine point circle is circum circle of pedal triangle and its centre N is midpoint of circum centre and ortho centre of Delta^("le")ABC then If nine point circle touches circum circle then sum(Cos2A)
Answer» 0 `(1)/(2)` `-1` 1 Answer :C

Discussion

10957.	A ={1, 2, 3, 5} and B= {4, 6, 9}. Define a relation R from A to B by R= {(x, y): the difference between x and y is odd, x in A, y in B}. Write R in roster form.
Answer» ANSWER :R={(1,4),(1,6),(2,9),(3,4),(3,6),(5,4),(5,6)}

Discussion

10958.	If a and b are unit vectors and a xx b = 1, then the angle between a and b is
Answer» `PI//4` `pi//2` `pi//3` `pi` ANSWER :B

Discussion

10959.	If bara=2bari-3barj+5bark,barb=3bari-4barj+5bark and barc = 5bari - 3barj -2bark, then the volume of the parallelopiped with co-terminus edges bara+ barb, barb + barc, barc + bara is
Answer» 1 5 8 16 Answer :D

Discussion

10960.	Explain the meaning of heat and workwith suitable examples.
Answer» Solution :Meaning of heat and work : (i) When hands are RUBBED against each other the temperature of the hands increases. Some work is done on hands by RUBBING. (II) The temperature of the hands increases due to this work. Now if the hands are placed on the chin, the temperature of the chin increases. This is because the hands are at higher temperature than the chin. (iii) The temperature of hands is increased due to work and temperature of the chin is increased due to heat transfer from the hands to the chin. (iv) By doing work on the system, the temperature in the system will increase and sometimes may not. Like heat, work is also not a quantity and through the work energy is transferred to the system (v) Either the system can transfer energy to the surrounding by doing work on surrounding or the surrounding may transfer energy to the system by doing work on the system. (vi) For the transfer of energy from one body to ANOTHER body through the process of work, they need not be at different temperatures.

Discussion

10961.	Let (x, y) be such that sin^(-1)(ax)+cos^(-1)(y)+cos^(-1)(bxy)=pi//2. Match the statements in column I with statements in column II. {:("Column I", "Column II"), ("A) If a = 1 and b = 0, then (x, y)", "p) lies on the circle "x^(2)+y^(2)=1), ("B) If a = 1 and b = 1, then (x, y)", "q) lies on "(x^(2)-1)(y^(2)-1)=0), ("C) If a = 1 and b = 2, then (x, y)", "r) lies on y = x"), ("D) If a = 2 and b = 2, then (x, y)", "s) lies on "(4x^(2)-1)(y^(2)-1)=0):}
Answer» ANSWER :A-p;B-q;C-p;D-s

Discussion

10962.	The radius of a sphere is 5 cm. If an error of 0.02 cm is made in the radius then the error in its surface area is
Answer» `0.8pi` `8pi` `0.4pi` `80pi` ANSWER :A

Discussion

10963.	Find the sum of all 4-digit numbersthat can be formedusingdigits 0,2,5,7,8without repetitions ?
Answer» ANSWER :571956

Discussion

10964.	The plane parallel to YZ-plane is perpendicular to _____ .
Answer» ANSWER :X-axis

Discussion

10965.	sec h^(-1)((1)/(3)) =
Answer» `log_(E)(3+SQRT(8))` `log_(e)(3-sqrt(8))` `log_(e)(sqrt(3-sqrt(8)))` `log_(e)(sqrt(3+sqrt(8)))` ANSWER :A

Discussion

10966.	Find the value of :""^(10)C_4
Answer» ANSWER :` 210`

Discussion

10967.	if the functions f(x) and phi (x ) are continuous in [a,b] and differentiable in (a,b) , then the value of 'c' for the pair of function f (x) = sqrt(x ) , phi (x) = ( 1)/( sqrt(x)) is
Answer» `SQRT(a)` `sqrt(B)` `sqrt(AB)` `- sqrt(ab)` ANSWER :C

Discussion

10968.	List all the subsets of the set { –1, 0, 1 }.
Answer» ANSWER :`PHI, {-1}, {0}, {1}, {-1, 0}, {-1, 1}, {0, 1}" and "{-1, 0, 1}`

Discussion

10969.	Period of sin(e^( tan x) + e^( cot x) ) is
Answer» `(PI)/(2)` `pi` `(3pi)/(2)` `2pi` Answer :B

Discussion

10970.	Express each of the complex number given in the form of a+ib 3(7 + i7)+ i(7 + i7)
Answer» ANSWER :14 + 28 i

Discussion

10971.	Find the value of p for which the fucntionf(x) = ((4^(x) -1)^(3))/(sin ((x)/(p)) log_(e)(1 + (x^(2))/(3))), x ne 0 " and " f(0) = 12 (log4)^(3) , is continuous at x = 0 .
Answer» <P> Answer :From (1) & (2) , p = 4

Discussion

10972.	If (kx)/((x+2)(x-1))=(2(x-1)+1(x+2))/((x+2)(x-1)) =(3x)/(x+2)(x-1) implies kx=3ximpliesk=3
Answer» `-1/2` `-2/3` `1/2` `2/3` ANSWER :A

Discussion

10973.	sqrt(2+sqrt(2+sqrt(2+sqrt(2))))=
Answer» `"COS"(PI)/(32)` `"2 cos"(pi)/(32)` `"2 cos"(pi)/(64)` `"cos"(pi)/(64)` Answer :C

Discussion

10974.	If the position vectors of three consecutive vertices of a parallelogram are bar(i)+bar(j)+bar(k),3bar(j)+5bar(k) and 7bar(i)+9bar(j)+11bar(k), then fourth vertex is
Answer» `8BAR(i)+7bar(J)+7bar(K)` `8bar(i)-7bar(j)-7bar(k)` `7bar(i)-7bar(j)-7bar(k)` `7bar(i)-7bar(j)+8bar(k)` ANSWER :A

Discussion

10975.	Write the negation of the followng statements: p: For every positive real number x the number x-1 is also positive.
Answer» ANSWER :not POSITIVE NUMBER.

Discussion

10976.	Simplify:(9+4i) ((3)/(2)-i) (9-4i)
Answer» ANSWER :`(291)/(2)-97i`

Discussion

10977.	Evaluate the following limits : Lim_(x to 2) (x^(10) - 1024)/(x^(5) - 32)
Answer» ANSWER :64

Discussion

10978.	The value of 3 f(x ) - 2 f(1/x)=x then f^(1)(2) =
Answer» `2/7` `1/2` 2 `7/2` ANSWER :B

Discussion

10979.	Write any two applications of Bernoulli's Theorem
Answer» Solution :(a) Blowing off roofs during wind STORM. (i) In olden days, the roofs of the huts or houses were designed with a slope. (II) One important scientific reason is that as per the Bernoulli's principle, it will be safeguarded except roof during storm or cyclone. (iii) During cyclonic condition, the roof is blown off without damaging the other parts of the house. (iv) In ACCORDANCE with the Bernoulli's principle, the high wind blowing over the roof creates a low-pressure `P_1` . (v) The pressure under the roof `P_2`is greater. Therefore, this pressure difference `(P_2 - P_1)` creates an up thrust and the roof is blown off. (b) Aerofoil lift : (i) The wings of an airplane (aerofoil) are so designed that its upper SURFACE is more curved than the lower surface and the front edge is broader than the real edge. (ii) As the aircraft moves, the air moves faster above the aerofoil than at the BOTTOM. (iii) According to Bernoulli's Principle, the pressure of air below is greater than above, which creates an upthrust called the dynamic lift to the aircraft.

Discussion

10980.	Length of latus rectum of ellipse 4x^2+9y^2=1 is ............ .
Answer» ANSWER :`4/9`

Discussion

10981.	How many words can be made form the letters of the word DAUGHTER assuming that no letter is repeated ? How many words can be made from this word in which so that consonants and vowels occupy their own place ?
Answer» ANSWER :40320, 720

Discussion

10982.	Equation of line passes from (2,-3) and makes an angle pi/4 with X - axis is ..........
Answer» ANSWER :`x-y-5=0`

Discussion

10983.	If (1)/(x-4) lt 0then x gt 4.
Answer» ANSWER :FALSE STATEMENT

Discussion

10984.	P(n) : n (n+1) is even number then P(3) = .........
Answer» ANSWER :12

Discussion

10985.	If x lt -1," then "2tan^(-1)x+sin^(-1)((2x)/(1+x^(2)))=
Answer» `-PI` `pi` `-2PI` `2pi` ANSWER :A

Discussion

10986.	If the sum of first n terms of an A.P. is cn^(2) then the sum of squares of these n terms is
Answer» `(n(4n^(2)+1)C^(2))/(3)` `(n(4n^(2)-1)c^(2))/(3)` `(n(4n^(2)+1)c^(2))/(6)` ANSWER :A::B::C::D

Discussion

10987.	How many words (with or without meaning)of three distinct letters of the English aphabets are there?
Answer» ANSWER :` 15600`

Discussion

10988.	If the lines represented by the equation 3y^2-x^2+2sqrt3x-3=0 are rotated about the point (sqrt3,0) through an angle of 15^@, one is clockwise direction and other in anticlokwise direction so that they become perpendicualr, then equation of the pair of lines in the new possition is
Answer» `y^2-x^2+2sqrt3x+3=0` `y^2-x^2+2sqrt3x-3=0` `y^2-x^2-2sqrt3x+3=0` `y^2-x^2+3=0` ANSWER :B

Discussion

10989.	For sets A and B , n(A) = 20 , n(B) = 30 , n (A cup B) = 40 , n (A cap B)= 10 and n(U) = 100then n(A' cap B') = 60 .
Answer» ANSWER :FALSE STATEMENT

Discussion

10990.	A flag staff of height 10 metres is placed on the top of a tower of height 30 metres. At the top of a tower of height 40 metres, the flag staff and the tower subtend equal angles then the distance between the two towers in metres is
Answer» `10sqrt2` `20sqrt2` `30sqrt2` `40sqrt2` ANSWER :C

Discussion

10991.	Evaluate the following limits: lim_(xrarrinfty)[(x^2 -2x +1)/(x^2 -4x +3)]^x
Answer» ANSWER :`e^2`

Discussion

10992.	A rrarr2 then area of circle with radius r = ….. .
Answer» ANSWER :`4PI`

Discussion

10993.	For ninz,2sin^(2)theta=cos2theta implies theta//2 =
Answer» `2npipm(PI)/(3)` `npipm(pi)/(6)` `(NPI)/(2)pm(pi)/(12)` `npipm(pi)/(12)` Answer :C

Discussion

10994.	Smallest positive root of the equaiton sqrt(sin ( 1- x)) = sqrt( cos x )
Answer» `( 7 pi)/( 2) + (1)/(2)` ` ( 7 pi)/( 4) + (2)/(3)` `( 7 pi)/( 4) + (1)/(2)` ` (7 pi)/( 2) + (2)/(3)` ANSWER :C

Discussion

10995.	Show that the equation 8x^(2) - 24xy + 18y^(2)- 6x + 9y - 5 = 0 represents a pair of parallel straight lines and find the distance between them.
Answer» ANSWER :`(7)/(2sqrt(13))`

Discussion

10996.	n(A DeltaB) = n(A) + n(B) - 2n (A cap B)
Answer» ANSWER :TRUE STATEMENT

Discussion

10997.	The lines (x-1)/(2)=(y+1)/(3)=(z-1)/(4) and (x-3)/(1)=(y-k)/(2)=(z)/(1) intersect if K equals
Answer» `-1` `2/9` `9/2` `2/5` ANSWER :C

Discussion

10998.	If P(Acup B) = 0.7 and P(Acap B) = 0.2," then " P(A') + P(B')=
Answer» `1.8` `0.6` `1.1` `1.4` ANSWER :C

Discussion

10999.	The probability that a student will pass his examination is 0.73, the probability of the student getting a compartment is 0.13, and the probability that the student will either pass or get compartment is 0.96.
Answer» ANSWER :A

Discussion

11000.	The total number of ordered pairs (x,y) satisfying \|x\|+\|y\|=4, sin((pi)x^(2)//3)=1 is equal to
Answer» 2 3 4 6 Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

Draw the graph of the quadratic function x^(2)-4x+3 and hence find the roots of the equation x^(2)-4x+3=0. What is the minimum value of the function ?

p^^q is valid (true) is …..

Radius of the circlewith centre (0,3) and passes from focus of ellipse (x^(2))/(16)+(y^2)/(9)=1 is ……

Circum circle of a Delta^("le")ABC is a circle passing through the vertices, Nine point circle is circum circle of pedal triangle and its centre N is midpoint of circum centre and ortho centre of Delta^("le")ABC then If circum circle passes through N then sum(Cos2A)=

Circum circle of a Delta^("le")ABC is a circle passing through the vertices, Nine point circle is circum circle of pedal triangle and its centre N is midpoint of circum centre and ortho centre of Delta^("le")ABC then If the circum circle and nine point circle cut orthogonally then sum(cos2A)=

Circum circle of a Delta^("le")ABC is a circle passing through the vertices, Nine point circle is circum circle of pedal triangle and its centre N is midpoint of circum centre and ortho centre of Delta^("le")ABC then If nine point circle touches circum circle then sum(Cos2A)

A ={1, 2, 3, 5} and B= {4, 6, 9}. Define a relation R from A to B by R= {(x, y): the difference between x and y is odd, x in A, y in B}. Write R in roster form.

If a and b are unit vectors and a xx b = 1, then the angle between a and b is

If bara=2bari-3barj+5bark,barb=3bari-4barj+5bark and barc = 5bari - 3barj -2bark, then the volume of the parallelopiped with co-terminus edges bara+ barb, barb + barc, barc + bara is

Explain the meaning of heat and workwith suitable examples.

The radius of a sphere is 5 cm. If an error of 0.02 cm is made in the radius then the error in its surface area is

Find the sum of all 4-digit numbersthat can be formedusingdigits 0,2,5,7,8without repetitions ?

The plane parallel to YZ-plane is perpendicular to _____ .

sec h^(-1)((1)/(3)) =

Find the value of :""^(10)C_4

if the functions f(x) and phi (x ) are continuous in [a,b] and differentiable in (a,b) , then the value of 'c' for the pair of function f (x) = sqrt(x ) , phi (x) = ( 1)/( sqrt(x)) is

List all the subsets of the set { –1, 0, 1 }.

Period of sin(e^( tan x) + e^( cot x) ) is

Express each of the complex number given in the form of a+ib 3(7 + i7)+ i(7 + i7)

Find the value of p for which the fucntionf(x) = ((4^(x) -1)^(3))/(sin ((x)/(p)) log_(e)(1 + (x^(2))/(3))), x ne 0 " and " f(0) = 12 (log4)^(3) , is continuous at x = 0 .

If (kx)/((x+2)(x-1))=(2(x-1)+1(x+2))/((x+2)(x-1)) =(3x)/(x+2)(x-1) implies kx=3ximpliesk=3

sqrt(2+sqrt(2+sqrt(2+sqrt(2))))=

If the position vectors of three consecutive vertices of a parallelogram are bar(i)+bar(j)+bar(k),3bar(j)+5bar(k) and 7bar(i)+9bar(j)+11bar(k), then fourth vertex is

Write the negation of the followng statements: p: For every positive real number x the number x-1 is also positive.

Simplify:(9+4i) ((3)/(2)-i) (9-4i)

Evaluate the following limits : Lim_(x to 2) (x^(10) - 1024)/(x^(5) - 32)

The value of 3 f(x ) - 2 f(1/x)=x then f^(1)(2) =

Write any two applications of Bernoulli's Theorem

Length of latus rectum of ellipse 4x^2+9y^2=1 is ............ .

How many words can be made form the letters of the word DAUGHTER assuming that no letter is repeated ? How many words can be made from this word in which so that consonants and vowels occupy their own place ?

Equation of line passes from (2,-3) and makes an angle pi/4 with X - axis is ..........

If (1)/(x-4) lt 0then x gt 4.

P(n) : n (n+1) is even number then P(3) = .........

If x lt -1," then "2tan^(-1)x+sin^(-1)((2x)/(1+x^(2)))=

If the sum of first n terms of an A.P. is cn^(2) then the sum of squares of these n terms is

How many words (with or without meaning)of three distinct letters of the English aphabets are there?

If the lines represented by the equation 3y^2-x^2+2sqrt3x-3=0 are rotated about the point (sqrt3,0) through an angle of 15^@, one is clockwise direction and other in anticlokwise direction so that they become perpendicualr, then equation of the pair of lines in the new possition is

For sets A and B , n(A) = 20 , n(B) = 30 , n (A cup B) = 40 , n (A cap B)= 10 and n(U) = 100then n(A' cap B') = 60 .

A flag staff of height 10 metres is placed on the top of a tower of height 30 metres. At the top of a tower of height 40 metres, the flag staff and the tower subtend equal angles then the distance between the two towers in metres is

Evaluate the following limits: lim_(xrarrinfty)[(x^2 -2x +1)/(x^2 -4x +3)]^x

A rrarr2 then area of circle with radius r = ….. .

For ninz,2sin^(2)theta=cos2theta implies theta//2 =

Smallest positive root of the equaiton sqrt(sin ( 1- x)) = sqrt( cos x )

Show that the equation 8x^(2) - 24xy + 18y^(2)- 6x + 9y - 5 = 0 represents a pair of parallel straight lines and find the distance between them.

n(A DeltaB) = n(A) + n(B) - 2n (A cap B)

The lines (x-1)/(2)=(y+1)/(3)=(z-1)/(4) and (x-3)/(1)=(y-k)/(2)=(z)/(1) intersect if K equals

If P(Acup B) = 0.7 and P(Acap B) = 0.2," then " P(A') + P(B')=

The probability that a student will pass his examination is 0.73, the probability of the student getting a compartment is 0.13, and the probability that the student will either pass or get compartment is 0.96.

The total number of ordered pairs (x,y) satisfying |x|+|y|=4, sin((pi)x^(2)//3)=1 is equal to