14949 + Interview Questions in Maths in Class 11 Page 297 InterviewSolution

14801.	For all sets A, B and C, if A sub B, then A cup C sub B cup C.
Answer» ANSWER :1

Discussion

14802.	The mean of 5 observations is 4.4 and their variance is 8.24 . If three of the observations are 1,2 and 6, find the other two observations.
Answer» ANSWER :4 and 9

Discussion

14803.	If y=e^(sqrtx)+e^(-sqrtx) , then (dy)/(dx) is equal to
Answer» `(e^sqrtx-e^(-sqrtx))/(2sqrtx)` `(e^sqrtx-e^(-sqrtx))/(2X)` `1/(2sqrtx)SQRT(y^2-4)` `1/(2sqrtx)sqrt(y^2+4)` Answer :A::C

Discussion

14804.	If f : R toRis defindby f (x)= x - [x], where[x] , is the greatest integernot exceding x , then the set of discontinuous off is
Answer» `PHI` R Z N Answer :C

Discussion

14805.	Express (5-3i)^(3) in the form a+ib.
Answer» ANSWER :`-10-198i`

Discussion

14806.	The solution set of the equation (2cosx-1)(3+2cosx)=0" in "0lexle2pi is
Answer» `{(pi)/(3),(pi)/(2)}` `{(pi)/(3),(5PI)/(3)}` `{(pi)/(2),(3PI)/(2)}` `{(pi)/(2),pi}` Answer :B

Discussion

14807.	LetR = {(x, y) : x, y in R, x^(2)+y^(2) le 25} and R'={(x,y):x, y in R, y ge 4/9 x^(2)} , then find thedomain and range of R nn R'
Answer» `[-3, 3]` and `[0, 5]` `[-3, 2]` and `[1, 5]` `[-2, 2]` and `[2, 3]` `[ -1, 1]` and `[3, 5]` Answer :A

Discussion

14808.	Consider the points A(-5,6,8), B(1,8,11),C(4,2,9) and D(-2,0,6) Find AC and BD and prove that ABCD is a square also
Answer» SOLUTION :`sqrt98, sqrt98`

Discussion

14809.	Consider the fuunctionh_2( x) =f(\|g\|) and h_2( x) = \|f( g(x))\| If for h_1 (x) and h_2( x)are identical functions , then which of the following is not true?
Answer» Domain of `h_(1)(x)` and `h_(2)(x)` is `x in [2n PI (2n +1)pi], n in Z` RANGE of `h_(1)(x)` and `h_(2)(x)` is [0, 1] Period of `h_(1)(x)` and `h_(2)(x)` is `pi` NONE of these Answer :D

Discussion

14810.	When the origin is shifted to (-2,-3) and the axes are rotated through an angle 45^(0), find the transformed equation of 2x^(2)+4xy-5y^(2)+20x-22y-14 = 0.
Answer» `X^(2)-14xy-7y^(2)=2` `x^(2)-14xy-7y^(2)=4` `x^(2)-14xy+7y^(2)=2` `x^(2)+14xy+7y^(2)=2` ANSWER :A

Discussion

14811.	LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? {φ} ⊂ A
Answer» ANSWER :as `φ ⊂ A`,

Discussion

14812.	f and g are real functions defined by f(x)= 2x + 1 and g(x) =4x -7. If f(x) = g(x) then x = …. .
Answer» ANSWER :X= 4

Discussion

14813.	Differentiate (ax+b)/( ax+d) with respect to x from definition.
Answer» ANSWER :`(d)/( DX) ((AX +b)/( cx+d) ) = (ad - bc)/( (cx+d)^2)`.

Discussion

14814.	For a gt 0, if the functionf(x)=2 x^(3) - 9 a x^(2) + 12 a^(2) x + 1attains its maximum value at p and minimum value at q such that p^(2) - q then a=
Answer» 1 2 `(1)/(2)` 3 Answer :B

Discussion

14815.	If sin (pi)/(2n )+ cos""(pi)/(2n)= (sqrt(n))/(2), " where " n in z, then the number of values of n between 4 and 8 for which the equation is true is
Answer» 1 2 3 4 Answer :A

Discussion

14816.	The product of the d.r's of a line perpendicular to the plane passing through the points (4,0,0), (0,2,0) and (1,0,1) is
Answer» 6 2 0 1 Answer :B

Discussion

14817.	LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? φ ∈ A
Answer» ANSWER :as `φ ⊂ A`,

Discussion

14818.	Evaluate the following limits : Lt_(xto0)(log_(e)(1+5x))/x
Answer» ANSWER :5

Discussion

14819.	Put the equation 12y=5x+65 in the form x"cos"theta+y"sin"theta=p and indicate clearly, in a rough diagram the position of the straight line and the meaning of the constant theta and p.
Answer» ANSWER : `(-5)/(13)x+12/(13)y=5;p=5, theta=112^(@)37'` NEARLY

Discussion

14820.	Three urns containing red and white chips are as followsUrn I:6red and 4 whiteUrn II: 3 red and 5 whiteUrn III: 4 red and 6 whiteAn urn is chosen at random and chip is drawn form it.Find the probability that it is white. Find also the probability that it comes from urn II.
Answer» ANSWER :`(13/(15)`

Discussion

14821.	Write the general term in the expansion of (x^2- y)^6
Answer» ANSWER :`(-1)^R` `^6`Cundersetr.`X^(12-2r)` .`y^r`

Discussion

14822.	Show that the following sets of points are collinear and find the equation of theline passing through them a. (-5,1)(5,5)(10,7) b. (1,3)(-2,-6)(2,6)
Answer» ANSWER :a. `2x-6y+15=0` B. `3x-y=0`

Discussion

14823.	Out of 26 cards numberedfrom 1 to 26 , one card is chosen . Find the probability that it is not divisible by 4.
Answer» ANSWER :`(10)/(13)`

Discussion

14824.	Let f(x)=xsqrt(4ax-x^(2)),(agt0) . Then f(x) is
Answer» INCREASING in (0,3a), DECREASING in (3a,4a) increasing in (a,4a) , decreasing in `(5aoo)` increasing in (0,4a) NONE of these Answer :A

Discussion

14825.	Find equation of line whose sum and product of intercepts on axis are 1 and -6 respectively.
Answer» ANSWER :`2X - 3y - 6 = 0; 3X - 2y + 6 = 0`

Discussion

14826.	The mean and variance of 7 observation are 8 and 16, respectively. If five of the observation are 2,4,10,12,14 . Find the remaining two observations.
Answer» ANSWER :8 and 6

Discussion

14827.	If ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents apair of parallel lines then sqrt((g^(2)-ac)/(f^(2)-bc))=
Answer» `(a)/(B)` `SQRT((a)/(b))` `sqrt((b)/(a))` `(b)/(a)` ANSWER :B

Discussion

14828.	A function is represented parametrically by the equations x=(1+t)/(t^3),y=3/(2t^2)+2/t then (dy)/(dx) -x ((dy)/(dx))^3has the absolute value of equal to
Answer» ANSWER :A

Discussion

14829.	Find the mean and variance for each of the data :6,7,10,12,13,4,8,12
Answer» ANSWER :9.25

Discussion

14830.	If a machine cost Rs. 10000 in 2015 andRs. 15000 in 2018, then find the price relative.
Answer» SOLUTION :N/A

Discussion

14831.	Find the square root of complex number -i.
Answer» ANSWER :`(1)/(SQRT(2))(1-i)` or `(1)/(sqrt(2))(-1+i)`

Discussion

14832.	Which of the following sets can be the subset of the general solution of 1 + cos 3 x = 2 cos 2 x , (n in Z) is
Answer» `N PI + (pi)/(3)` `n pi + (pi)/(6)` `n pi - (pi)/(6)` `2 n pi` ANSWER :D

Discussion

14833.	Find (dy)/(dx) for the function (using logarithms). y= ( x ^(4) (x ^(2) + 4) ^(1//3))/( sqrt ( 4x ^(2) - 7))
Answer» ANSWER :`y [ (4)/(x) + (2x)/( 3 (x ^(2) + 4)) - (4x )/( 4x ^(2) + 7)]`

Discussion

14834.	Find the perpendicular distance between the lines y=mx+c, y=mx+d
Answer» ANSWER :`(\|c~d\|)/SQRT(1+m^(2))`

Discussion

14835.	a and b are non zero real numbers and n inN then a_(n) = a+bn represent arithmetic sequence.
Answer» ANSWER :TRUE STATEMENT

Discussion

14836.	ABCD is rectangle in which AB= 9cm , BC =6 cm . P is a point in CD such that PC=x. If AP^2+PB^2 is minimum then x=
Answer» `9/2` `3` `7/2` `(-9)/2` ANSWER :A

Discussion

14837.	If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 }, find B ∪ C
Answer» Answer :`{3, 4, 5, 6, 7, 8 }`

Discussion

14838.	The set of points of disconitunity of the function f(x)= underset(n to oo) (Lt) ((2sinx)^(2n))/(3n^(2)-(2cosx)^(2n))is
Answer» `{NPI// N in Z}` `{n pi+-pi//6//n in Z}` `{npi+-pi//2//n in Z}` `{npi+-pi//3//n in Z}` ANSWER :A

Discussion

14839.	By shifting origin at ............. Point the co - ordinates of (7,2) becomes (-1,3).
Answer» ANSWER :(8,-1)

Discussion

14840.	y=x+e^x , then (d^2x)/(dy^2) is equal to
Answer» `1/((1+e^x)^2)` `(-e^x)/((1+e^x)^2)` `(-e^x)/((1+e^x)^3)` `e^x` ANSWER :C

Discussion

14841.	R_1={(x,y)\|y=2x+7,yin R and x in [-5,5]} Then range of R_1 …...... .
Answer» ANSWER :[-317]

Discussion

14842.	If the lines x^(2)+2xy-35y^(2)-4x+44y-12=0 and 5x+lambday-8=0 ae concurrent then lambda=
Answer» 0 1 `-1` 2 Answer :D

Discussion

14843.	Consider the polynomial f(x)=1+2x+3x^(2)+4x^(3) . Let s be the sum ofall distinet real roots of f(x) and let t=\|s\| . Thefunction f(x) is
Answer» Increasing in `(-t,-(1)/(4))` and DECREASING in `(-(1)/(4),t)` Decreasing in `(-t,-(1)/(4))` and increasing in `(-(1)/(4),t)` Increasing in `(-t,t)` Decreasin g in (-t,t) ANSWER :B

Discussion

14844.	The sum of some terms of aG.P. is 315 whose first term and the common ratio are and 2,respectively. Find the last term and the number of terms.
Answer» Answer :NUMBER of TERMS =6 Last terms = 160

Discussion

14845.	The sum of all the solution is of the equation cos theta cos ((pi)/3+theta)cos ((pi)/3-theta)=1/4, theta in [0,6pi ]
Answer» `15pi` `30 PI` `(100pi)/3` `100pi` ANSWER :B

Discussion

14846.	Equation of the plane passing thrgouh the point (2,2,1) and (9,3,6), and bot to the plane 2x + 6y + 6z -1=0 is
Answer» `3X + 4y + 5z=0` `3x + 4y - 5z =9` `3x + 4y - 5z =9` `3x - 4y - 5z =9` ANSWER :B

Discussion

14847.	Which of the following statements are true and which are false? In each case give a valid reason for saying so. p: Each radius of a circle is a chord of the circle
Answer» Answer :FALSE. By DEFINITION of the CHORD, it should intersect the circle in TWO points.

Discussion

14848.	By rotating the axes at an angle alpha if (4,2) in the new system formedas (2 + sqrt(3), 1 - 2 sqrt(3)) then alpha =
Answer» `(PI)/(6)` `(pi)/(4)` `(pi)/(3)` `(pi)/(2)` Answer :C

Discussion

14849.	A line from origin meets the lines (x-2)/(1)=(y-1)/(-2)=(z+1)/(1) and (x-(8)/(3))/(2)=(y+3)/(-1)=(z-1)/(1) at P and Q respectively. Find the square of the distance between P and Q.
Answer» ANSWER :6

Discussion

14850.	If (5,6) + z = (2,-1) then z = (3,-7)
Answer» ANSWER :FALSE STATEMENT

Discussion

Explore topic-wise InterviewSolutions in .

For all sets A, B and C, if A sub B, then A cup C sub B cup C.

The mean of 5 observations is 4.4 and their variance is 8.24 . If three of the observations are 1,2 and 6, find the other two observations.

If y=e^(sqrtx)+e^(-sqrtx) , then (dy)/(dx) is equal to

If f : R toRis defindby f (x)= x - [x], where[x] , is the greatest integernot exceding x , then the set of discontinuous off is

Express (5-3i)^(3) in the form a+ib.

The solution set of the equation (2cosx-1)(3+2cosx)=0" in "0lexle2pi is

LetR = {(x, y) : x, y in R, x^(2)+y^(2) le 25} and R'={(x,y):x, y in R, y ge 4/9 x^(2)} , then find thedomain and range of R nn R'

Consider the points A(-5,6,8), B(1,8,11),C(4,2,9) and D(-2,0,6) Find AC and BD and prove that ABCD is a square also

Consider the fuunctionh_2( x) =f(|g|) and h_2( x) = |f( g(x))| If for h_1 (x) and h_2( x)are identical functions , then which of the following is not true?

When the origin is shifted to (-2,-3) and the axes are rotated through an angle 45^(0), find the transformed equation of 2x^(2)+4xy-5y^(2)+20x-22y-14 = 0.

LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? {φ} ⊂ A

f and g are real functions defined by f(x)= 2x + 1 and g(x) =4x -7. If f(x) = g(x) then x = …. .

Differentiate (ax+b)/( ax+d) with respect to x from definition.

For a gt 0, if the functionf(x)=2 x^(3) - 9 a x^(2) + 12 a^(2) x + 1attains its maximum value at p and minimum value at q such that p^(2) - q then a=

If sin (pi)/(2n )+ cos""(pi)/(2n)= (sqrt(n))/(2), " where " n in z, then the number of values of n between 4 and 8 for which the equation is true is

The product of the d.r's of a line perpendicular to the plane passing through the points (4,0,0), (0,2,0) and (1,0,1) is

LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? φ ∈ A

Evaluate the following limits : Lt_(xto0)(log_(e)(1+5x))/x

Put the equation 12y=5x+65 in the form x"cos"theta+y"sin"theta=p and indicate clearly, in a rough diagram the position of the straight line and the meaning of the constant theta and p.

Three urns containing red and white chips are as followsUrn I:6red and 4 whiteUrn II: 3 red and 5 whiteUrn III: 4 red and 6 whiteAn urn is chosen at random and chip is drawn form it.Find the probability that it is white. Find also the probability that it comes from urn II.

Write the general term in the expansion of (x^2- y)^6

Show that the following sets of points are collinear and find the equation of theline passing through them a. (-5,1)(5,5)(10,7) b. (1,3)(-2,-6)(2,6)

Out of 26 cards numberedfrom 1 to 26 , one card is chosen . Find the probability that it is not divisible by 4.

Let f(x)=xsqrt(4ax-x^(2)),(agt0) . Then f(x) is

Find equation of line whose sum and product of intercepts on axis are 1 and -6 respectively.

The mean and variance of 7 observation are 8 and 16, respectively. If five of the observation are 2,4,10,12,14 . Find the remaining two observations.

If ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents apair of parallel lines then sqrt((g^(2)-ac)/(f^(2)-bc))=

A function is represented parametrically by the equations x=(1+t)/(t^3),y=3/(2t^2)+2/t then (dy)/(dx) -x ((dy)/(dx))^3has the absolute value of equal to

Find the mean and variance for each of the data :6,7,10,12,13,4,8,12

If a machine cost Rs. 10000 in 2015 andRs. 15000 in 2018, then find the price relative.

Find the square root of complex number -i.

Which of the following sets can be the subset of the general solution of 1 + cos 3 x = 2 cos 2 x , (n in Z) is

Find (dy)/(dx) for the function (using logarithms). y= ( x ^(4) (x ^(2) + 4) ^(1//3))/( sqrt ( 4x ^(2) - 7))

Find the perpendicular distance between the lines y=mx+c, y=mx+d

a and b are non zero real numbers and n inN then a_(n) = a+bn represent arithmetic sequence.

ABCD is rectangle in which AB= 9cm , BC =6 cm . P is a point in CD such that PC=x. If AP^2+PB^2 is minimum then x=

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 } and D = { 7, 8, 9, 10 }, find B ∪ C

The set of points of disconitunity of the function f(x)= underset(n to oo) (Lt) ((2sinx)^(2n))/(3n^(2)-(2cosx)^(2n))is

By shifting origin at ............. Point the co - ordinates of (7,2) becomes (-1,3).

y=x+e^x , then (d^2x)/(dy^2) is equal to

R_1={(x,y)|y=2x+7,yin R and x in [-5,5]} Then range of R_1 …...... .

If the lines x^(2)+2xy-35y^(2)-4x+44y-12=0 and 5x+lambday-8=0 ae concurrent then lambda=

Consider the polynomial f(x)=1+2x+3x^(2)+4x^(3) . Let s be the sum ofall distinet real roots of f(x) and let t=|s| . Thefunction f(x) is

The sum of some terms of aG.P. is 315 whose first term and the common ratio are and 2,respectively. Find the last term and the number of terms.

The sum of all the solution is of the equation cos theta cos ((pi)/3+theta)cos ((pi)/3-theta)=1/4, theta in [0,6pi ]

Equation of the plane passing thrgouh the point (2,2,1) and (9,3,6), and bot to the plane 2x + 6y + 6z -1=0 is

Which of the following statements are true and which are false? In each case give a valid reason for saying so. p: Each radius of a circle is a chord of the circle

By rotating the axes at an angle alpha if (4,2) in the new system formedas (2 + sqrt(3), 1 - 2 sqrt(3)) then alpha =

A line from origin meets the lines (x-2)/(1)=(y-1)/(-2)=(z+1)/(1) and (x-(8)/(3))/(2)=(y+3)/(-1)=(z-1)/(1) at P and Q respectively. Find the square of the distance between P and Q.

If (5,6) + z = (2,-1) then z = (3,-7)