14949 + Interview Questions in Maths in Class 11 Page 146 InterviewSolution

7251.	If tan(cos^(-1)x)=sin^(-1)(sec^(-1)sqrt(5)) then x=
Answer» `SQRT(5/3)` `(sqrt(5))/3` `sqrt(5/2)` `(sqrt(5))/2` ANSWER :B

Discussion

7252.	If without repetition of the numbers, four digit numbers are formed with the number 0, 2,3, and 5, then find the probability of such number being divisible by 5.
Answer» ANSWER :`5/9`

Discussion

7253.	Compute : (7!)/(5!)
Answer» ANSWER :42

Discussion

7254.	Solve the following equations and write general solutions 3 sin^(4) x + cos^(4)x = 1
Answer» ANSWER :`{N pi} CUP {n pi PM (pi)/(6)}`

Discussion

7255.	Equation of diameter of circle(x -5) (x - 7) (y -1) = 0 , parallel to co-ordinate axes , are
Answer» ` x^(2) + y^(2) pm 16x pm 16Y + 8 = 0 ` `x^(2) + y^(2) pm 8x pm 8y + 16 = 0 ` `x^(2) + y^(2) pm 8x pm 8y + 16 = 0 ` `x^(2) + y^(2) pm 4x pm 4y + 8 = 0 ` SOLUTION :N/A

Discussion

7256.	Differentiate w.r.t x:f(x)=(sinx+sin((pi)/2-x))^(2)
Answer» ANSWER :`2cos2x`

Discussion

7257.	Let p be " I will marry her," and let q be " she is beautiful." Translate into symbolic form. If she is beautiful, then I will marry her.
Answer» <P> ANSWER :Q => p

Discussion

7258.	Let p be " I will marry her," and let q be " she is beautiful." Translate into symbolic form. If she is beautiful, then I will not marry her.
Answer» <P> ANSWER :Q => ~p

Discussion

7259.	sin 2 ………… sin 5
Answer» `GT` `LT` = `LE` ANSWER :A

Discussion

7260.	Define (i) f(x)=(1+x)/(1-x)^(1//5x)is continuous at x = 0.
Answer» ANSWER :`E^(2//5)`

Discussion

7261.	The maximum slope of the curve y=-x^3+3x^2+9x-27 is
Answer» 1 12 6 2 Answer :B

Discussion

7262.	Theperiodof f(x )= cos 3x + sinsqrt(3) x is
Answer» not defined `(2PI)/(3)` `(2pi)/(SQRT(3))` `2sqrt(3pi)` Answer :1

Discussion

7263.	The vector abar(i)+b""bar(j)+cbar(k) is a bisector of the angle between the vectors bar(i)+bar(j) and bar(j)+bar(k) if
Answer» a = B a = C a + b = c `a=b=c` ANSWER :B

Discussion

7264.	Let a sample space be S = {omega_(1), omega_(2),....,omega_(6)}. Which of the following assingments of probabilities to each outcomes are valid? Outcomes omega_(1)" "omega_(2)" "omega_(3)" "omega_(4)" "omega_(5)" "omega_(6) (a) 1/6 1/6 1/6 1/6 1/6 1/6 (b) 1 0 0 0 0 0 (c) 1/8 2/3 1/3 1/3 - 1/4 - 1/3 (d) 1/12 1/12 1/6 1/6 1/6 3/2 (e) 0.6 0.6 0.6 0.6 0.6 0.6.
Answer» ANSWER :` 1/2`

Discussion

7265.	The table given below shows the number of visitors (in hundreds) to a certain exhibition over a period of two weeks: Calculate 6-day moving averages and illustrate these and original information on the same graph using the some scales.
Answer» ANSWER :TREND VALUES are 161,162.25,159.75,157.92,157.42,155.84,156.34,160.83

Discussion

7266.	The sides of a triangle are three consecutive numbers and its largest angle is twice the smallest one. Find the sides of the triangle.
Answer» ANSWER :The SIDES are 4, 5 and 6

Discussion

7267.	Write the negation of the following statements.Find the truth value (b)
Answer» SOLUTION :The TRUTH VALUE is F]

Discussion

7268.	If sqrt(y - sqrt(y - sqrt(y ....oo))) = sqrt(x + sqrt(x + sqrt(x ....oo))) then (dy)/(dx) is equalto
Answer» `(y - X + 1)/(y - x - 1)` `(y - x)/(y + x)` `(x + y + 1)/(y - x)` `(y - x + 1)/(y + x)` ANSWER :A

Discussion

7269.	Find equation of line L whose length of perpendicular from origin is 2 unit with slope (5)/(12).
Answer» ANSWER :`12X + 5Y pm26 = 0`

Discussion

7270.	Consider two funtions f(x) = {:{( [x], -2le x le -1 ),(\|x\|+1, -1 lt xle 2 ):} and g(x) ={:{( [x]. -pi le x lt 0 ),(Sinx0le xle pi ):}where [.]denotes the greatestfunctions The number of integral points in the range of g(f(x)) is
Answer» 2 4 3 5 Answer :B

Discussion

7271.	Length of the tangent. Prove that the length t o f the tangent from the point P (x_(1), y(1)) to the circle x^(2)div y^(2) div2gx div2fydivc = 0 is given by t=sqrt(x_(1)^(2)+y_(1)^(2)+2gx_(1)+2fy_(1)+c) Hence, find the length of the tangent (i)to the circle x^(2) + y^(2) -2x-3y-1 = 0 from the origin, (2,5) (ii) to the circle x^(2)+y^(2)-6x+18y+4=-0 from the origin (iii) to the circle 3x^(2) +3y^(2)- 7x - 6y = 12 from the point (6, -7) (iv) to the circle x^(2) + y^(2) - 4 y - 5 = 0 from the point (4, 5).
Answer» ANSWER :4

Discussion

7272.	Consider two funtions f(x) = {:{( [x], -2le x le -1 ),(\|x\|+1, -1 lt xle 2 ):} and g(x) ={:{( [x]. -pi le x lt 0 ),( Sinx, 0le xle pi ):}where [.]denotes the greatestfunctions The exhaustive domain of g(f(x)) is
Answer» [0,2 ] [-2, 0] [-2, 2] [-1, 2] ANSWER :C

Discussion

7273.	Consider two funtions f(x) = {:{( [x], -2le x le -1 ),(\|x\|+1, -1 lt xle 2 ):} and g(x) ={:{( [x]. -pi le x lt 0 ),(Sinx0le xle pi ):}where [.]denotes the greatestfunctions The range of g(f(x))is
Answer» [ sin 3 sin 1] `[sin 3, 1] UU {-2, -1, 0}` `[sin 3, 1] uu {-2 , -1 }` `[sin 1, 1]` Answer :C

Discussion

7274.	Solution set of x ge 3 and x le 5, x in Ris [3,5]
Answer» ANSWER :TRUE STATEMENT

Discussion

7275.	Lt_(x to 0)(sinx)^(tanx)=
Answer» ANSWER :1

Discussion

7276.	Let bara, barb, barc be three vectors having magnitudes 1,1,2 respectively. If baraxx(baraxxbarc)+barb =bar0 then the angle between bara and barc is
Answer» `pi/3` `pi/6` `pi/4` `pi/2` ANSWER :B

Discussion

7277.	Write the following complex numbers in the polar form : 1- i
Answer» ANSWER :`SQRT(2) (COS -pi/4 + I SIN -pi/4)`

Discussion

7278.	Find the derivative of (x^(n)-a^(n))/(x-a) for some constant a.
Answer» Answer :`(nx^(N)-anx^(n-1)X^(n)+a^(n))/((x-a)^(2))`

Discussion

7279.	sin^4""(pi)/16+sin^4""(3pi)/16+sin^4""(5pi)/16+sin^4""(7pi)/16=
Answer» 1 `1//2` `3//2` 2 Answer :C

Discussion

7280.	The negation of the statement The product of 3 and 4 is 9 is
Answer» It is FALSE that the PRODUCT of 3 and 4 is 9. The product of 3 and 4 is 12. The product of 3 and 4 is not 12. It is false that the product of 3 and 4 is not 9. Answer :A::C::D

Discussion

7281.	intsqrt((4-x)/(4+x))dx
Answer» `SIN^(-1)((x)/(4))+sqrt(16-x^(2))+C` `sin^(-1)((x)/(4))-sqrt(16-x^(2))+c` `sin^(-1)4x+sqrt(16-x)+c` `sin^(-1)4x-sqrt(16-x^(2))+c` Answer :B

Discussion

7282.	Find the number of terms in the expansion of the following : (x+y/x)^(7)
Answer» ANSWER :8

Discussion

7283.	If0 lt x lt pi/2 then solve cot^2x-(sqrt3+1)cotx+sqrt3=0
Answer» ANSWER :`(PI)/(6), (pi)/(4)`

Discussion

7284.	Solve the equations: sqrt((x)/(1-x))+sqrt((1-x)/(x))=(13)/(6).
Answer» ANSWER :`(4)/(13),(9)/(13)`

Discussion

7285.	Locus of the image of the point (2,3) in the line (2x-3y+4)+k(x-2y+3)=0, k in R, is a
Answer» STAIGHT line PARALEL to x-axis straight line parallelto y-axis circle of radius `sqrt2` circle of radius 3 Answer :B

Discussion

7286.	Transform the equation 3x+4y+12=0 in to normal form.
Answer» ANSWER :`4x-3y+L; l in R`

Discussion

7287.	Find the equation of lines passing through origin and perpendicular to the pair of lines. 2x^(2)+5xy+2y^(2)+10x+5y=0
Answer» ANSWER :`2X^(2)=5xy+2y^(2)=0`

Discussion

7288.	Find the slope of a line perpendicular to the line whose slope is 5.
Answer» ANSWER : `(-1)/(5)`

Discussion

7289.	Write each sentence in the " If ................Then " form. Freezing water expands.
Answer» ANSWER :If WATERIS FREEZING, then it EXPANDS.

Discussion

7290.	-12 lt 4 - (3x)/(-5) le 2
Answer» ANSWER :`((-80)/(3), (-10)/(3)]`

Discussion

7291.	Find the mean and variance for each of the data in First n natural numbers
Answer» ANSWER :`(N+1)/(2),(n^(2)-1)/(12)`

Discussion

7292.	From the following data, using mean, calculate mean deviation and the coefficient of mean deviation. 21, 23, 25, 28, 30, 32, 38, 39, 46, 48
Answer» ANSWER :M.D = 7.8, COEFFT. of M.D = 0.24

Discussion

7293.	If the angle betweent he lines joining the end points of minor axis of an ellipse with its foci is pi/2, then the eccentricity of the ellipse is
Answer» `1/2` `(1)/(sqrt2)` `(SQRT3)/(2)` `(1)/(2SQRT2)` Answer :B

Discussion

7294.	The value of tan1^(@) tan2^(@) tan 3^(@)…..tan89^(@) is
Answer» 0 1 `(1)/(2)` Not defined Answer :B

Discussion

7295.	Third term and sixth term of geometric sequence is 24 and 192 respectively then r = 34.
Answer» ANSWER :FALSE STATEMENT

Discussion

7296.	Write the relation R= {(x,x^3): x is a prime number less than 10) in roster form.
Answer» ANSWER :R={(2,8),(,3,27),(,5,125),(7,343)}

Discussion

7297.	An electric current is measured by a tangent galvonometer, the current being proportional to the tangent to the angle of deflection. If the deflection is read as 45^(@) and an error of 1% is made in reading it, the percentage error in the current is
Answer» `PI` `pi//2` `pi//4` `pi//3` ANSWER :B

Discussion

7298.	Usingthe mathematical induction , showthat forany naturalnumber n, 1/( 2.5)+ 1/(5.8) + 1/( 8.11)+ …+ 1/(( 3n-1) (3n+2)) = n /(6n + 4)
Answer» ANSWER :N

Discussion

7299.	A straight line through the origin O meets the parallel lines 4+2y=9, 2x+y+6=0 at the points P and Q respectively. Then find the ratio at which O divides segment bar(PQ).
Answer» ANSWER :`3:4`

Discussion

7300.	cos9^@ - sin9^@ =
Answer» `-(SQRT(5-sqrt5))/2` `(5+sqrt5)/4` `1/2sqrt(5-sqrt5)` `sqrt(5-sqrt5)` ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in .

If tan(cos^(-1)x)=sin^(-1)(sec^(-1)sqrt(5)) then x=

If without repetition of the numbers, four digit numbers are formed with the number 0, 2,3, and 5, then find the probability of such number being divisible by 5.

Compute : (7!)/(5!)

Solve the following equations and write general solutions 3 sin^(4) x + cos^(4)x = 1

Equation of diameter of circle(x -5) (x - 7) (y -1) = 0 , parallel to co-ordinate axes , are

Differentiate w.r.t x:f(x)=(sinx+sin((pi)/2-x))^(2)

Let p be " I will marry her," and let q be " she is beautiful." Translate into symbolic form. If she is beautiful, then I will marry her.

Let p be " I will marry her," and let q be " she is beautiful." Translate into symbolic form. If she is beautiful, then I will not marry her.

sin 2 ………… sin 5

Define (i) f(x)=(1+x)/(1-x)^(1//5x)is continuous at x = 0.

The maximum slope of the curve y=-x^3+3x^2+9x-27 is

Theperiodof f(x )= cos 3x + sinsqrt(3) x is

The vector abar(i)+b""bar(j)+cbar(k) is a bisector of the angle between the vectors bar(i)+bar(j) and bar(j)+bar(k) if

The table given below shows the number of visitors (in hundreds) to a certain exhibition over a period of two weeks: Calculate 6-day moving averages and illustrate these and original information on the same graph using the some scales.

The sides of a triangle are three consecutive numbers and its largest angle is twice the smallest one. Find the sides of the triangle.

Write the negation of the following statements.Find the truth value (b)

If sqrt(y - sqrt(y - sqrt(y ....oo))) = sqrt(x + sqrt(x + sqrt(x ....oo))) then (dy)/(dx) is equalto

Find equation of line L whose length of perpendicular from origin is 2 unit with slope (5)/(12).

Consider two funtions f(x) = {:{( [x], -2le x le -1 ),(|x|+1, -1 lt xle 2 ):} and g(x) ={:{( [x]. -pi le x lt 0 ),(Sinx0le xle pi ):}where [.]denotes the greatestfunctions The number of integral points in the range of g(f(x)) is

Consider two funtions f(x) = {:{( [x], -2le x le -1 ),(|x|+1, -1 lt xle 2 ):} and g(x) ={:{( [x]. -pi le x lt 0 ),( Sinx, 0le xle pi ):}where [.]denotes the greatestfunctions The exhaustive domain of g(f(x)) is

Consider two funtions f(x) = {:{( [x], -2le x le -1 ),(|x|+1, -1 lt xle 2 ):} and g(x) ={:{( [x]. -pi le x lt 0 ),(Sinx0le xle pi ):}where [.]denotes the greatestfunctions The range of g(f(x))is

Solution set of x ge 3 and x le 5, x in Ris [3,5]

Lt_(x to 0)(sinx)^(tanx)=

Let bara, barb, barc be three vectors having magnitudes 1,1,2 respectively. If baraxx(baraxxbarc)+barb =bar0 then the angle between bara and barc is

Write the following complex numbers in the polar form : 1- i

Find the derivative of (x^(n)-a^(n))/(x-a) for some constant a.

sin^4""(pi)/16+sin^4""(3pi)/16+sin^4""(5pi)/16+sin^4""(7pi)/16=

The negation of the statement The product of 3 and 4 is 9 is

intsqrt((4-x)/(4+x))dx

Find the number of terms in the expansion of the following : (x+y/x)^(7)

If0 lt x lt pi/2 then solve cot^2x-(sqrt3+1)cotx+sqrt3=0

Solve the equations: sqrt((x)/(1-x))+sqrt((1-x)/(x))=(13)/(6).

Locus of the image of the point (2,3) in the line (2x-3y+4)+k(x-2y+3)=0, k in R, is a

Transform the equation 3x+4y+12=0 in to normal form.

Find the equation of lines passing through origin and perpendicular to the pair of lines. 2x^(2)+5xy+2y^(2)+10x+5y=0

Find the slope of a line perpendicular to the line whose slope is 5.

Write each sentence in the " If ................Then " form. Freezing water expands.

-12 lt 4 - (3x)/(-5) le 2

Find the mean and variance for each of the data in First n natural numbers

From the following data, using mean, calculate mean deviation and the coefficient of mean deviation. 21, 23, 25, 28, 30, 32, 38, 39, 46, 48

If the angle betweent he lines joining the end points of minor axis of an ellipse with its foci is pi/2, then the eccentricity of the ellipse is

The value of tan1^(@) tan2^(@) tan 3^(@)…..tan89^(@) is

Third term and sixth term of geometric sequence is 24 and 192 respectively then r = 34.

Write the relation R= {(x,x^3): x is a prime number less than 10) in roster form.

An electric current is measured by a tangent galvonometer, the current being proportional to the tangent to the angle of deflection. If the deflection is read as 45^(@) and an error of 1% is made in reading it, the percentage error in the current is

Usingthe mathematical induction , showthat forany naturalnumber n, 1/( 2.5)+ 1/(5.8) + 1/( 8.11)+ …+ 1/(( 3n-1) (3n+2)) = n /(6n + 4)

A straight line through the origin O meets the parallel lines 4+2y=9, 2x+y+6=0 at the points P and Q respectively. Then find the ratio at which O divides segment bar(PQ).

cos9^@ - sin9^@ =