14949 + Interview Questions in Maths in Class 11 Page 166 InterviewSolution

8251.	Let a,b,c,d,e be the observations with mean m and standard deviation S. The standard deviation of the observation a + k , b+ k , c+ k, d+k, e+k is……
Answer» ANSWER :REMAIN same as 's'.

Discussion

8252.	Assertion (A): sqrt(4sin^(4)theta+sin^(2)2theta)+4cos^(2)(pi/4-theta/2)=2" then "theta in Q_(3) or Q_(4) Reason (R ): In Q_(3) & Q_(4), \|sintheta\|=-sintheta
Answer» A is true, R is true and R is CORRECT explanation of A A is true, R is true and R is not correct explanation of A A is true, R is FALSE A is false, R is true ANSWER :A

Discussion

8253.	Find the real numbers x and y if (x-yi) (3+5i) is the conjugate of -6 -24i
Answer» ANSWER :`x=3, y= -3`

Discussion

8254.	If P(alpha,beta), abgt0 " and the variable line " x/a+y/b=1 " is draw through the given point" p(alpha,beta), then the least area of triangle formed by this line and the coordinate axes is
Answer» `ALPHA,BETA` `2ALPHA,beta` `3alpha,beta` `1/2alpha,beta` ANSWER :B

Discussion

8255.	The circumcentre of the triangle formed by the pointgs (1,2,3), (3,-1,5), (4,0,-3) is
Answer» ANSWER :`(7/2,(-1)/2,1`

Discussion

8256.	Evaluate the following limits : lim_(x to 0) (sin 2x + sin 6x)/(sin 5x - sin 3x)
Answer» ANSWER :4

Discussion

8257.	The range of the function f (x) = sqrt(x - x ^(2)) is
Answer» `(0,3) ` `[0,3]` `(0,3]` `[0,3)` ANSWER :B

Discussion

8258.	The product of three increasing numbers in GP is 5832. If we add 6 to the second number and 9 to the third number, then resulting numbers form an AP. Find the numbers in GP. And 9 to thethird number, then resulting numbers form an AP. Find the numbers in GP.
Answer» ANSWER :`18,18xx(3)/(2),18xx(3)/(2)xx(3)/(2), …….(i.e.)18, 27, (81)/(2),…..`

Discussion

8259.	If sum_(i=1)^9 (x_i- 5) = 9 and sum_(i=1)^9 (x_i - 5)^2 = 45. The standard deviation of the observations x_1, x_2,………,x_9 is ………….
Answer» 9 4 2 3 Answer :B

Discussion

8260.	Write down the contrapositive of the following statements.: If it snows, then the weather will be cold.
Answer» ANSWER :does NTO SNOW.

Discussion

8261.	What is the geometric property possessed by the straight lines of each system given by (4x + 3y + 2) + k (3x + 7y) = 0
Answer» Solution :A FAMILY of lines passing through the INTERSECTION of ` 4X + 3y + 2 = 0` and `3X + 7y = 0`

Discussion

8262.	If y = sin ^(-1) ((b + a sin x )/( a +b sin x )) (a ge 0, b gt 0)
Answer» ANSWER :(ASSUMING COS X to be POSITIVE)

Discussion

8263.	Express the following expression in the form of a+ib. ((3+isqrt(5))(3-isqrt(5))/((sqrt(3) + 2i)-(sqrt(3)-isqrt(2)))
Answer» ANSWER :`0-I (7sqrt(2))/2`

Discussion

8264.	If A=Tan^(-1)((xsqrt(3))/(2k-x)) and B=Tan^(-1)((2x-k)/(ksqrt(3))) then A-B=
Answer» `(PI)/4` `(pi)/2` `(pi)/6` `(pi)/3` Answer :C

Discussion

8265.	A card is selected from a pack of 52 cards. Calculate the probability that the card is an ace of spades.
Answer» ANSWER :`(1)/(52)`

Discussion

8266.	The price index of a commodity is 99. What does it indicate about the charge in price of the commodity in current year as compared to base year?
Answer» ANSWER :MARGINAL DECREASE in PRICE of the COMMODITY

Discussion

8267.	If x, y in [0, 2 pi] ,then the total number of ordered pairs (x, y) satisfying the equation sinx cos y = 1 is
Answer» 1 2 3 4 Answer :C

Discussion

8268.	If the line (x)/(a) + (y)/(b)= 1 touches the circlex^(2) + y^(2) = 1 , " then " a^(2) + b^(2) =
Answer» 1 `a^(2) B^(2)` 0 `a + b` SOLUTION :N/A

Discussion

8269.	A non-zero vector bar(a), is parallel to the line of intersection of the plane determined by the vectors bar(i), bar(i) + bar(j) and the plane determined by the vectors bar(i)- bar(j), bar(i) + bar(k) Find the angle between bar(a) and the vector bar(i)- 2bar(j) + 2bar(k)
Answer» ANSWER :`THETA= 45^(@) or 135^(@)`

Discussion

8270.	A speaks the truth in 70% cases and B in 80% cases. The probability that they will contradict each other in describing a single event is
Answer» `0.56` `0.42` `0.4` `0.38` ANSWER :D

Discussion

8271.	3,(9)/(2),6,(15)/2 ............ Sequence has 10^(th) term a_(10) = .........
Answer» ANSWER :`33/2`

Discussion

8272.	If (sin^3theta-cos^3theta)/(sintheta-costheta)-(costheta)/(sqrt((1+cot^2theta)))-2tanthetacottheta=-1, thetain[0,2pi] then
Answer» `THETAIN(0,PI//2)-{pi//4}` `thetain(pi/2,pi)-{3PI//4}` `thetain(pi,(3pi)/2)-{5pi//4}` `thetain(0,pi)-{pi//4,pi//2}` Answer :D

Discussion

8273.	Let A= {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a,b) a, b in A,b is exactly divisible by a} (i) Write R in roster form (ii) Find the domain of R (iii) Find the range of R.
Answer» Answer :(i) R={(1,1),(1,2),(1,3),(1,4),(1,6),(2,4),(2,6),(2,2),(4,4),(6,6),(3,3),(3,6)} (II) DOMAIN of R={1,2,3,4,6} (III) Range of R={1,2,3,4,6}

Discussion

8274.	Evaluate Lt_(xto0)((a^(x)+b^(x)+c^(x))/3)^(1/x) where a,b,cinR^(+).
Answer» ANSWER :`ROOT(3)(ABC)`

Discussion

8275.	The probability of an occurrence of event A is .7 and that of the occurrence of event B is .3 and the probability of occurrence of both is .4.
Answer» ANSWER :A

Discussion

8276.	Determine the conjugate and the reciprocal of each complex number given below: 3-i
Answer» ANSWER :`3 + I, (3)/(10) + (1)/(10)i`

Discussion

8277.	Find the complex number satsifying the equation z+sqrt(2)\|(z+1)\|+i=0
Answer» ANSWER :`-2-i`

Discussion

8278.	If tan alpha is equal to the integral solution of the inequality 4x^(2)-16x+15lt0 and cos beta is equal to the slope of the bisector of the coordinate axes in the first quadrant, then sin(alpha+beta)sin(alpha-beta) is equal to
Answer» `1/5` `3/5` `2/sqrt(5)` `4/5` ANSWER :D

Discussion

8279.	Find all other trigonometric ratios:sin x = 2/5, x lies in second quadrant.
Answer» ANSWER :`COSEC x = 5/3, COS x =-4/5 , sec x =- 5/4 , TAN x=- 3/4, COT x =- 4/3`

Discussion

8280.	Check the validity of the following statements : (i) every radius of a circle is its chord. (ii) if x and y are integers such that xgty. Then -xlarry. (iii) sqrt(5) is a rational number.
Answer» SOLUTION :(i) FALSE (II) TRUE (III) False

Discussion

8281.	Find the centroid of the tetrahedron whose vertices are (2,3,-4) (-3,3,-2),(-1,4,2), (3,5,1)
Answer» ANSWER :`=((1)/(4),(15)/(4),(-3)/(4))`

Discussion

8282.	The symbolic from of negation p or qis . …. .
Answer» ANSWER :`~PVVQ`

Discussion

8283.	The ratio in which the line passing through the points (-1,2),(2,-3) divides the line segment joining the points (1,1),(5,-2) is
Answer» `7:18` INTERNALLY `7:18` EXTERNALLY `18:7` internally `18:7` externally Answer :B

Discussion

8284.	If (1+i)(1+2i)(1+3i)....(1+ni)=a+ib then 2xx5xx10xx....xx(1+n^(2))=...
Answer» `a-ib` `a^(2)+B^(2)` `a^(2)-b^(2)` `a+b` ANSWER :C

Discussion

8285.	Evaluate the following limits : Lim_(x to 0) ((1+x)^(n)-1)/x
Answer» ANSWER :N

Discussion

8286.	ABC is a triangle with angle B greater than angle C . D and E are points on BC such that AD is perpendicular to BC and AE is the bisector of angle A. Complete the relation angle DAE = 1/2 [(…..)- angle C]
Answer» `ANGLE D` `angle A` `angle B` `angle C ` ANSWER :C

Discussion

8287.	Find the mean deviation about the mean for the data in
Answer» ANSWER :11.28

Discussion

8288.	Find the mean deviation about the mean for the data in
Answer» ANSWER :157.92

Discussion

8289.	If f(x)={{:(1 ,if "x is reational"),(-1, if "x isirrational"):}thenLt_(x to 1+)(f(x)=
Answer» R `PHI` `(-1,1)` `R^(+)` ANSWER :B

Discussion

8290.	Find the mean deviation about the mean for the data in {:("x"_(i),5,10,15,20,25),("f"_(i),7,4,6,3,5):}
Answer» ANSWER :6.32

Discussion

8291.	Solve the equations: Q. 3^(2x)-10\times3^x+9=0.
Answer» ANSWER :2,0

Discussion

8292.	1+ 4x^(2)+7x^(4)+...
Answer» ANSWER :`(1)/(1-x^(2))+(3X^(2))/((1-x^(2))^(2))`

Discussion

8293.	Solve the equations: (x+1)(x+2)(x+3)(x+4)=120
Answer» ANSWER :`1-6,(-5pmisqrt(39))/(2)`

Discussion

8294.	An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn. The probability that the second ball drawn is red will be:
Answer» `(3)/(12)` `(5)/(12)` `(3)/(4)` `(1)/(2)` ANSWER :D

Discussion

8295.	Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A= { 1, 2, 3, 4}, B = { 2,4, 6, 8 } and C = { 3, 4, 5, 6 }. Find (A ∪ B)′
Answer» ANSWER :`{ 5, 7, 9 }`

Discussion

8296.	The sides of a right angled trinagles are in A.P., then they are in the ratio
Answer» `2:1:1` `2:3:5` `3:4:5` `3:1:2` ANSWER :C

Discussion

8297.	If the area of the triangle formed by the lines 3x^2-2xy-8y^2=0 and the line 2x+y-k=0 is 5sq. Units then k=
Answer» 5 6 7 8 Answer :A

Discussion

8298.	If f(x)=(g(x)+g(-x))/(2)+2/([h(x)+h(-x)]^(-1))where g and h are differentiable functions then f""^(1)(0) =
Answer» 1 0 `1/2` `3/2` ANSWER :B

Discussion

8299.	If the first term of an infinite G.P. is 1 and each term is twice the sum of the succeeding terms, then the sum of the series is
Answer» 2 `(5)/(2)` `(7)/(2)` `(3)/(2)` ANSWER :D

Discussion

8300.	The range of y such that the equation in x , ycos x = sin xhas a real solution is
Answer» [-2,2] `[-SQRT(2), sqrt(2)]` [-1,1] `[-1//2, 1//2]` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Let a,b,c,d,e be the observations with mean m and standard deviation S. The standard deviation of the observation a + k , b+ k , c+ k, d+k, e+k is……

Assertion (A): sqrt(4sin^(4)theta+sin^(2)2theta)+4cos^(2)(pi/4-theta/2)=2" then "theta in Q_(3) or Q_(4) Reason (R ): In Q_(3) & Q_(4), |sintheta|=-sintheta

Find the real numbers x and y if (x-yi) (3+5i) is the conjugate of -6 -24i

If P(alpha,beta), abgt0 " and the variable line " x/a+y/b=1 " is draw through the given point" p(alpha,beta), then the least area of triangle formed by this line and the coordinate axes is

The circumcentre of the triangle formed by the pointgs (1,2,3), (3,-1,5), (4,0,-3) is

Evaluate the following limits : lim_(x to 0) (sin 2x + sin 6x)/(sin 5x - sin 3x)

The range of the function f (x) = sqrt(x - x ^(2)) is

The product of three increasing numbers in GP is 5832. If we add 6 to the second number and 9 to the third number, then resulting numbers form an AP. Find the numbers in GP. And 9 to thethird number, then resulting numbers form an AP. Find the numbers in GP.

If sum_(i=1)^9 (x_i- 5) = 9 and sum_(i=1)^9 (x_i - 5)^2 = 45. The standard deviation of the observations x_1, x_2,………,x_9 is ………….

Write down the contrapositive of the following statements.: If it snows, then the weather will be cold.

What is the geometric property possessed by the straight lines of each system given by (4x + 3y + 2) + k (3x + 7y) = 0

If y = sin ^(-1) ((b + a sin x )/( a +b sin x )) (a ge 0, b gt 0)

Express the following expression in the form of a+ib. ((3+isqrt(5))(3-isqrt(5))/((sqrt(3) + 2i)-(sqrt(3)-isqrt(2)))

If A=Tan^(-1)((xsqrt(3))/(2k-x)) and B=Tan^(-1)((2x-k)/(ksqrt(3))) then A-B=

A card is selected from a pack of 52 cards. Calculate the probability that the card is an ace of spades.

The price index of a commodity is 99. What does it indicate about the charge in price of the commodity in current year as compared to base year?

If x, y in [0, 2 pi] ,then the total number of ordered pairs (x, y) satisfying the equation sinx cos y = 1 is

If the line (x)/(a) + (y)/(b)= 1 touches the circlex^(2) + y^(2) = 1 , " then " a^(2) + b^(2) =

A non-zero vector bar(a), is parallel to the line of intersection of the plane determined by the vectors bar(i), bar(i) + bar(j) and the plane determined by the vectors bar(i)- bar(j), bar(i) + bar(k) Find the angle between bar(a) and the vector bar(i)- 2bar(j) + 2bar(k)

A speaks the truth in 70% cases and B in 80% cases. The probability that they will contradict each other in describing a single event is

3,(9)/(2),6,(15)/2 ............ Sequence has 10^(th) term a_(10) = .........

If (sin^3theta-cos^3theta)/(sintheta-costheta)-(costheta)/(sqrt((1+cot^2theta)))-2tanthetacottheta=-1, thetain[0,2pi] then

Let A= {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a,b) a, b in A,b is exactly divisible by a} (i) Write R in roster form (ii) Find the domain of R (iii) Find the range of R.

Evaluate Lt_(xto0)((a^(x)+b^(x)+c^(x))/3)^(1/x) where a,b,cinR^(+).

The probability of an occurrence of event A is .7 and that of the occurrence of event B is .3 and the probability of occurrence of both is .4.

Determine the conjugate and the reciprocal of each complex number given below: 3-i

Find the complex number satsifying the equation z+sqrt(2)|(z+1)|+i=0

If tan alpha is equal to the integral solution of the inequality 4x^(2)-16x+15lt0 and cos beta is equal to the slope of the bisector of the coordinate axes in the first quadrant, then sin(alpha+beta)sin(alpha-beta) is equal to

Find all other trigonometric ratios:sin x = 2/5, x lies in second quadrant.

Check the validity of the following statements : (i) every radius of a circle is its chord. (ii) if x and y are integers such that xgty. Then -xlarry. (iii) sqrt(5) is a rational number.

Find the centroid of the tetrahedron whose vertices are (2,3,-4) (-3,3,-2),(-1,4,2), (3,5,1)

The symbolic from of negation p or qis . …. .

The ratio in which the line passing through the points (-1,2),(2,-3) divides the line segment joining the points (1,1),(5,-2) is

If (1+i)(1+2i)(1+3i)....(1+ni)=a+ib then 2xx5xx10xx....xx(1+n^(2))=...

Evaluate the following limits : Lim_(x to 0) ((1+x)^(n)-1)/x

ABC is a triangle with angle B greater than angle C . D and E are points on BC such that AD is perpendicular to BC and AE is the bisector of angle A. Complete the relation angle DAE = 1/2 [(…..)- angle C]

Find the mean deviation about the mean for the data in

Find the mean deviation about the mean for the data in

If f(x)={{:(1 ,if "x is reational"),(-1, if "x isirrational"):}thenLt_(x to 1+)(f(x)=

Find the mean deviation about the mean for the data in {:("x"_(i),5,10,15,20,25),("f"_(i),7,4,6,3,5):}

Solve the equations: Q. 3^(2x)-10\times3^x+9=0.

1+ 4x^(2)+7x^(4)+...

Solve the equations: (x+1)(x+2)(x+3)(x+4)=120

An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn. The probability that the second ball drawn is red will be:

Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A= { 1, 2, 3, 4}, B = { 2,4, 6, 8 } and C = { 3, 4, 5, 6 }. Find (A ∪ B)′

The sides of a right angled trinagles are in A.P., then they are in the ratio

If the area of the triangle formed by the lines 3x^2-2xy-8y^2=0 and the line 2x+y-k=0 is 5sq. Units then k=

If f(x)=(g(x)+g(-x))/(2)+2/([h(x)+h(-x)]^(-1))where g and h are differentiable functions then f""^(1)(0) =

If the first term of an infinite G.P. is 1 and each term is twice the sum of the succeeding terms, then the sum of the series is

The range of y such that the equation in x , ycos x = sin xhas a real solution is