14949 + Interview Questions in Maths in Class 11 Page 116 InterviewSolution

5751.	Find the eccentricity of the ellipse whose latus rectum is (i) half its major axis, (ii) half its minor axis.
Answer» ANSWER :(i) `1/SQRT(2)"(II) "1/2""sqrt(3)`

Discussion

5752.	…..... Is the line passes from point (1,2)and perpendicular to the line x+y+7=0.
Answer» `x+y+3=0` `x-y+1=0` `y-x+1=0` `2x-y=0` ANSWER :B

Discussion

5753.	If p is false and q is true, Write the truth valueof statements in column A.
Answer» SOLUTION :F,F,T,T]

Discussion

5754.	Show that the sum of (m + n)^(th)and (m – n)^(th)terms of an A.P. is equal to twice the m^(th)term.
Answer» ANSWER :`2 a_(N)`

Discussion

5755.	If u and v are unit vectors and theta is the acute angle between them, then 2u xx 3v is a unit vector for
Answer» EXACTLY TWO VALUES of `THETA` More than two values of `theta` No value of `theta` Exactly one value of `theta` ANSWER :D

Discussion

5756.	Find the equation of ellipse whose eccentricity is 2/3, focus is at (3,0) and vertex is at (1,0). Alsofind the coordinates of other focus.
Answer» ANSWER :`((x-7)^(2))/36+(y^(2))/20=1;` FOCUS (11,0)

Discussion

5757.	(coshx-sinhx)^(n)=
Answer» coshnx-sinhnx 2cosh(NX) 2sinh(nx) COSH(nx) + SINH(nx) ANSWER :A

Discussion

5758.	If A xx B={(,(p,q),(p,r)),(,(m,q),(m,r)):}}, find A and B.
Answer» <P> ANSWER :A= {p, m}, B= {Q, R}

Discussion

5759.	2 sin^(2) beta + 4 cos( alpha+ beta) sin alpha sin beta + cos ( 2 alpha + 2 beta )=
Answer» `sin2alpha` `COS2ALPHA` `TAN2ALPHA` `cot2alpha` ANSWER :B

Discussion

5760.	A card is drawn from a pack of cards . Findthe probability that it is not a spade and
Answer» ANSWER :`=(3)/(4)`

Discussion

5761.	How many different words can be formed by using all the letters of the word ZERO withoutrepetition ? What is the rank of the word ZERO in a dictionary ?
Answer» ANSWER :on PLACE at 24, 24

Discussion

5762.	(a)/(x^(4))-(b)/(x^(2))+cos x
Answer» ANSWER :`(-4a)/(X^(5))+(2B)/(x^(3))-sin x`

Discussion

5763.	Write the contrapositive of the following statement: if a triangle is equilateral,it is isosceles.
Answer» ANSWER :If TRIANGLE is EQUILATERAL then it is ISOSCELES triangle.

Discussion

5764.	Is the given relation a function? Give reason for your answer. g= {(x,(1)/(x))\|x " is a positive integer"}
Answer» ANSWER :It is FUNCTION

Discussion

5765.	Find the slope of a line parallelto a line whose slope is (i) -3(ii) 1/(2)(iii) 2.3(iv) 0
Answer» ANSWER :The same for each PART

Discussion

5766.	Write the first four terms of the sequence whose nth term is given (2n+1)/(2n-1)
Answer» Answer :`3 ,(5)/(8) , (7)/(5) , (9)/(7)`

Discussion

5767.	Compute a price index for the following by using price relative method.
Answer» ANSWER :`157.625`

Discussion

5768.	Compute a price index for the following by using price relative method.
Answer» ANSWER :`159.33`

Discussion

5769.	A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i) 3 (ii) 12.
Answer» ANSWER :12 (i) 1 (II) 1

Discussion

5770.	The mean and variance of 5 observations are respectively 4.4 and 8.24. If three observation are 1,2 and 4 then find the remaining two observations.
Answer» SOLUTION :NA

Discussion

5771.	If 4x + i(3x-y) =3+ i(-6), where x and y are real numbers, then find the values of x and y.
Answer» ANSWER :`x=3/4`, and `y=33/4`

Discussion

5772.	Find the bisector of the acute angle between the lines : 3x+4y=11 and 12x-5y=2
Answer» ANSWER : `11x+3y-17=0`

Discussion

5773.	Solve : tan x + secx = 1 (-180^(@) le x le 180^(@))
Answer» ANSWER :`{-pi/2,0}`

Discussion

5774.	If (cot^(-1)x)^(2)-7(cot^(-1)x)+10 gt 0, then x lies in the interval
Answer» (cot5, COT2) `(-INFTY, cot5) CUP (cot2, infty)` `(-infty, cot5)` `(cot2, infty)` ANSWER :D

Discussion

5775.	If bara = -bari+2barj+3bark, barb = bari -2barj+bark, barc = 4bari-3barj-2bark and bara +lambda barb " is perpendicular to " barc, " then " lambda =
Answer» 1 2 3 4 Answer :B

Discussion

5776.	Find the probabilityof product of a perfect square when 2 dice are thrown together.
Answer» ANSWER :`(8)/(36),i.e.,(2)/(9)`

Discussion

5777.	Number of solutions of equation 2 sin (x)/(2) cos ^(2) x - 2 sin "" (x)/(2) sin ^(2) x = cos^(2) x - sin ^(2) x " for " x in [0, 4 pi]
Answer» 6 8 10 12 Answer :A

Discussion

5778.	Simplify the following (3i) (4i)
Answer» ANSWER :`-12`

Discussion

5779.	Numbers of observation of the data is n (where n is even) then median will be average of (n/2)^(th) and (n/2+1)^(th) observation.
Answer» ANSWER :TRUE STATEMENT

Discussion

5780.	Show that the geatest interger function f(x) =[x] is not differentiable at any interger?
Answer» ANSWER :`F^(`)(N)` does not EXIST.

Discussion

5781.	Consider the statement P(n):1+3+3^2+...+3^(n-1)=(3^n-1)/2.Show that P(1) is true
Answer» ANSWER :T

Discussion

5782.	Find the value of if x^(3) - 3x + a = 0 has three real distinct roots.
Answer» ANSWER :`-2 LT a lt 2`

Discussion

5783.	Write down the equation of the straight line cuttting off intercepts a and b from the axes where a = 5, b= -6
Answer» ANSWER : `6x-5y-30=0`

Discussion

5784.	If L, M are the feet of the perpendiculars from (2, 4, 5) to the xy-plane and yz-plane respectively, then find the distance LM.
Answer» ANSWER :`SQRT(29)`

Discussion

5785.	Solve the equation for0 le x le 2pi. sin x cos x =0
Answer» Answer :`0, (pi)/(2) ,pi, (3PI)/(2), 2PI`

Discussion

5786.	Evaluate the following limits : Lim_(x to 1/2)(4x^(2)-1)/(2x-1)
Answer» ANSWER :2

Discussion

5787.	The point (2,-1,3) is the centroid of the triangle formed by the points A(3,-5,2), B(-7,4,5) and C, then the coordinate of C are
Answer» (9,2,-2) (10,-2,2) (2,1,-3) (8,1,9) ANSWER :B

Discussion

5788.	Ifx = log ( y + sqrt(y^2 -1)) then y =
Answer» tan hx COT hx SIN hx COS hx ANSWER :D

Discussion

5789.	Find the derivative of the following functions from first principle (-x)^(-1)
Answer» ANSWER :`(1)/(X^(2))`

Discussion

5790.	Assertion (A):f(x) = (sin {[ x] pi})/(1 + x^(2)) here [x] denotes greastest integer function, is continuous on R Reason (R) : Every constant function is continuous on R
Answer» Both (A) and (R) are true and (R)is the CORRECT explanation of (A) Both (A) and (R)are true and (R)is not the correct explanation of (A) (A) is true but (R) is FALSE (A) is false but (R) is TURE ANSWER :A

Discussion

5791.	Solve the equation ((1+i) x-2i)/(3+i)+ ((2-3i )y + i)/(3-i)=i,x y in R, i= sqrt(-1)
Answer» ANSWER :`x=3, y= -1`

Discussion

5792.	Reduce the following equations in intercept form and find their intercepts on axis. (iii) 3y+2=0
Answer» ANSWER :`(0.x)/(-2) + (y)/( (-2)/( 3) ) = 1`

Discussion

5793.	If in a triangle the side a and the angle A remain constant, while other elements are changed slightly then
Answer» `deltabsinB+deltacsinC=0` `deltabcosB+deltac cosC=0` `deltabsecB+deltacsecC=0` `DELTAB cosecB+deltac COSEC C=0 Answer :C

Discussion

5794.	Find the derivative of the x^(3)-27
Answer» ANSWER :`3X^(2)`

Discussion

5795.	Slope of line passes from point A(3,-2) and B(3,-7) is zero .
Answer» ANSWER :FALSE STATEMENT

Discussion

5796.	Minimum value of f(x)=(x-1)^(2)+(x-2)^(2)+..+(x-10)^(2)occurs at x=
Answer» 7 6 4 5.5 Answer :D

Discussion

5797.	Passing through the points (-1, 1) " and " (2, - 4).
Answer» ANSWER :`5X - y + 20 = 0 `

Discussion

5798.	Cos^(2)(pi/4-theta/2)-sin^(2)(pi/4-theta/2)=
Answer» `COSTHETA` `SINTHETA` `"cos"theta/2` `"sin"theta/2` Answer :B

Discussion

5799.	Semivertical angle of a cone of given total surface area of maximum volume value is
Answer» `TAN^(-1)((1)/(3))` `Sin^(-1)((1)/(3))` `Cos^(-1) (SQRT(2))` `Tan^(-1)(sqrt(2))` ANSWER :B

Discussion

5800.	Choose the correctoption for the following lim_(xrarrinfty) [sqrt(x^2 +4)+5]/[sqrt(x^2 +4)+3]
Answer» `9/4` `3/2` `2/3` `4/9` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Find the eccentricity of the ellipse whose latus rectum is (i) half its major axis, (ii) half its minor axis.

…..... Is the line passes from point (1,2)and perpendicular to the line x+y+7=0.

If p is false and q is true, Write the truth valueof statements in column A.

Show that the sum of (m + n)^(th)and (m – n)^(th)terms of an A.P. is equal to twice the m^(th)term.

If u and v are unit vectors and theta is the acute angle between them, then 2u xx 3v is a unit vector for

Find the equation of ellipse whose eccentricity is 2/3, focus is at (3,0) and vertex is at (1,0). Alsofind the coordinates of other focus.

(coshx-sinhx)^(n)=

If A xx B={(,(p,q),(p,r)),(,(m,q),(m,r)):}}, find A and B.

2 sin^(2) beta + 4 cos( alpha+ beta) sin alpha sin beta + cos ( 2 alpha + 2 beta )=

A card is drawn from a pack of cards . Findthe probability that it is not a spade and

How many different words can be formed by using all the letters of the word ZERO withoutrepetition ? What is the rank of the word ZERO in a dictionary ?

(a)/(x^(4))-(b)/(x^(2))+cos x

Write the contrapositive of the following statement: if a triangle is equilateral,it is isosceles.

Is the given relation a function? Give reason for your answer. g= {(x,(1)/(x))|x " is a positive integer"}

Find the slope of a line parallelto a line whose slope is (i) -3(ii) 1/(2)(iii) 2.3(iv) 0

Write the first four terms of the sequence whose nth term is given (2n+1)/(2n-1)

Compute a price index for the following by using price relative method.

Compute a price index for the following by using price relative method.

A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i) 3 (ii) 12.

The mean and variance of 5 observations are respectively 4.4 and 8.24. If three observation are 1,2 and 4 then find the remaining two observations.

If 4x + i(3x-y) =3+ i(-6), where x and y are real numbers, then find the values of x and y.

Find the bisector of the acute angle between the lines : 3x+4y=11 and 12x-5y=2

Solve : tan x + secx = 1 (-180^(@) le x le 180^(@))

If (cot^(-1)x)^(2)-7(cot^(-1)x)+10 gt 0, then x lies in the interval

If bara = -bari+2barj+3bark, barb = bari -2barj+bark, barc = 4bari-3barj-2bark and bara +lambda barb " is perpendicular to " barc, " then " lambda =

Find the probabilityof product of a perfect square when 2 dice are thrown together.

Number of solutions of equation 2 sin (x)/(2) cos ^(2) x - 2 sin "" (x)/(2) sin ^(2) x = cos^(2) x - sin ^(2) x " for " x in [0, 4 pi]

Simplify the following (3i) (4i)

Numbers of observation of the data is n (where n is even) then median will be average of (n/2)^(th) and (n/2+1)^(th) observation.

Show that the geatest interger function f(x) =[x] is not differentiable at any interger?

Consider the statement P(n):1+3+3^2+...+3^(n-1)=(3^n-1)/2.Show that P(1) is true

Find the value of if x^(3) - 3x + a = 0 has three real distinct roots.

Write down the equation of the straight line cuttting off intercepts a and b from the axes where a = 5, b= -6

If L, M are the feet of the perpendiculars from (2, 4, 5) to the xy-plane and yz-plane respectively, then find the distance LM.

Solve the equation for0 le x le 2pi. sin x cos x =0

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

The point (2,-1,3) is the centroid of the triangle formed by the points A(3,-5,2), B(-7,4,5) and C, then the coordinate of C are

Ifx = log ( y + sqrt(y^2 -1)) then y =

Find the derivative of the following functions from first principle (-x)^(-1)

Assertion (A):f(x) = (sin {[ x] pi})/(1 + x^(2)) here [x] denotes greastest integer function, is continuous on R Reason (R) : Every constant function is continuous on R

Solve the equation ((1+i) x-2i)/(3+i)+ ((2-3i )y + i)/(3-i)=i,x y in R, i= sqrt(-1)

Reduce the following equations in intercept form and find their intercepts on axis. (iii) 3y+2=0

If in a triangle the side a and the angle A remain constant, while other elements are changed slightly then

Find the derivative of the x^(3)-27

Slope of line passes from point A(3,-2) and B(3,-7) is zero .

Minimum value of f(x)=(x-1)^(2)+(x-2)^(2)+..+(x-10)^(2)occurs at x=

Passing through the points (-1, 1) " and " (2, - 4).

Cos^(2)(pi/4-theta/2)-sin^(2)(pi/4-theta/2)=

Semivertical angle of a cone of given total surface area of maximum volume value is

Choose the correctoption for the following lim_(xrarrinfty) [sqrt(x^2 +4)+5]/[sqrt(x^2 +4)+3]