14949 + Interview Questions in Maths in Class 11 Page 241 InterviewSolution

12001.	Reduce the equation x+2y-3z-6=0 of the plane to the normal form.
Answer» Answer :`(x)/(sqrt(14))+(2Y)/(sqrt(14))-(3z)/(sqrt(14))=(6)/(sqrt(14))`

Discussion

12002.	Show that the following equations represents a pair of parallel lines and also find the distance between them. x^(2)+2 sqrt(3)xy+3y^(2)-3x-3 sqrt(3) y-4=0
Answer» ANSWER :`(5)/(2)`

Discussion

12003.	Show that the following equations represents a pair of parallel lines and also find the distance between them. Show that the equation 8x^(2)-24xy+18y^(2)-6x+9y-5=0 represents a pair of parallel lines and find the distance between them.
Answer» ANSWER :DISTANCES `=(7)/(SQRT(52))`

Discussion

12004.	Derive an expression for the co-ordinates of points that divides the linejoining points A(x_1,y_1,z_1) andB(x_2,y_2,z_2) internally in the ratio m:n.Hence find the co-ordinates of midpoint of AB where A=(3,2,1) and B=(7,6,5).
Answer» ANSWER :`((mx_2+nx_1)/(m+n), (my_2+ny_1)/(m+n),(mz_2+nz_1)/(m+n))`.

Discussion

12005.	The product of first n odd natural numbers equals:
Answer» `.^(2N)C_(N) XX .^(n)P_(n)` `(1/2)^(n) .^(2n) C_(n) xx .^n P_(n)` `(1/4)^(n). xx .^(2n) C_(n) xx .^(2n)P_(n)` `.^(n)C_(n) xx .^(n)P_(n)` ANSWER :B

Discussion

12006.	y=log_(5)x+ 55 then dy/dx is:
Answer» `5/X` `log_(5)(x^(2)-1)` `(log_(5)e)/x` `(log_(e)5)/x`] ANSWER :C

Discussion

12007.	Evaluate Lt_(x to 0) (e^(x) -1)/(sqrt(1 + x) - 1)
Answer» ANSWER :2

Discussion

12008.	Iftan 69^(@) + tan 66^@ - tan 69^(@) tan66^@=2k , then the value of k is
Answer» -1 1 `(1)/(sqrt(3))` `(1)/(2)` ANSWER :D

Discussion

12009.	Consider the function f(x) satisfying the identityf(x) + f((x-1)/( x))= 1+ x AA x in R - {0,1}, and g(x)=2f ( x)- x+1 The number of roots of the equation g(x)= 1 is
Answer» 2 1 3 0 Answer :D

Discussion

12010.	Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Answer» ANSWER :11,14,17,20 and 23

Discussion

12011.	The solution set of sin7x+sin3x=sin2x+sin8x is (ninz)
Answer» `(NPI)/(5)` `{(2n+1)(pi)/(9)}` `{(2n+1)(pi)/(3)}` `{(2n+1)(pi)/(7)}` Answer :A

Discussion

12012.	If bara.(barb+barc) = barb.(barc+bara) = barc.(bara+barb) =0 and absbara = 3, absbarb = 4, absbarc = 5 , " then " abs(bara+barb+barc)=
Answer» 5 `5sqrt2` `5/SQRT2` `sqrt2` ANSWER :B

Discussion

12013.	Which of the following sets are finite or infinite The set of prime numbers less than 99
Answer» ANSWER :it is a FINITE SET

Discussion

12014.	If 3 cos x ne 2 sin x, then the general solution of sin^(2) x - cos 2x = 2 - sin 2x is x =
Answer» `n PI +(-1)^(n)(pi)/2, n inZ` `(NPI)/2, n inZ` `(4n+-1)(pi)/2, n inZ` `(2n-1)pi, n inZ` ANSWER :C

Discussion

12015.	Let bara ,barb,barc be non coplanar vectors and bara^(1)=(barbxxbarc)/([barabarbbarc]),barb^(1)=(barcxxbara)/([barabarbbarc]) and barc^(1)=(baraxxbarb)/([barabarbbarc]) then prove that [barabarbbarc][bara^(1)barb^(1)barc^(1)]=1
Answer» 0 1 2 3 Answer :B

Discussion

12016.	Write the negation of the following statements. s : Not all squares are rectangles.
Answer» SOLUTION :s: Not all SQUARE are RECTANGLES.

Discussion

12017.	The sum of n terms of an A.P. series is (n^(2) + 2n) for all values of n. Find the first 3 terms of the series:
Answer» ANSWER :3,5,7,

Discussion

12018.	The unit vector(s) parallel to bar(i)-3bar(j)-5bar(k) is
Answer» `+1/sqrt(35)(BAR(i)-3BAR(j)-5bar(k))` `bar(i)-3bar(j)-5bar(k)` `-1/sqrt(35)(bar(i)-3bar(j)-5bar(k))` Both 1 and 3 Answer :D

Discussion

12019.	IfA_1 , A_2 , A_3 are areas of excircles, A is the area of incircle of a triangle then (1) /( sqrt(A_1)) + (1)/( sqrt(A_2))+ ( 1)/( sqrt(A_3))=
Answer» `( 1)/(sqrtA) ` ` ( 1)/(A) ` ` ( 1)/(2sqrtA) ` ` ( 1)/(2A) ` ANSWER :A

Discussion

12020.	sqrt(3)x^(2) - sqrt(2)x + 3sqrt(3)=0
Answer» ANSWER :`(SQRT(2) +- sqrt(34)i)/(2sqrt(3))`

Discussion

12021.	Find the values of other 5 trignometric ratios cot x = 3/4,x lies in third quadrant.
Answer» ANSWER :`sin X =- 4/5, COSEC x =- 5/4, cos x =- 3/5, SEC x =- 5/3, tan x =- 4/3`

Discussion

12022.	If there in and error of (1)/(10) % in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere.
Answer» ANSWER :`3//10`

Discussion

12023.	The vector equation of the plane which is perpendicular to 2bari+3barj+6bark and at a distance of 7 units from origin is
Answer» `BARR.(2bari+3barj+6bark) =7` `barr.(2bari+3barj+6bark) =49` `barr.(2bari+3barj+6bark) =1` `barr.(2bari+3barj-6bark) =49` Answer :B

Discussion

12024.	P, Q and R are three collinear points. P and Q are (3, 4) and (7, 7) respectively, and PR =10 units. Find the coordinates of R.
Answer» ANSWER : `(11, 10) or (-5, -2)`

Discussion

12025.	If we consider only the principle values of the inverse trigonometric functions then the value of tan(cos^(-1)""1/(5sqrt(2))-sin^(-1)""4/sqrt(17)) is
Answer» `SQRT(29)/3` `29/3` `sqrt(3)/29` `3/29` ANSWER :D

Discussion

12026.	A straight line L with negative slope passes through the point (8,2) and cuts positive co-ordinate axes at the points P and Q. Find the minimum value of OP+OQ as L varies where O is the origin.
Answer» ANSWER :18

Discussion

12027.	Match each of the set on the left in the roster form with the same set on the right described in set builder form :
Answer» ANSWER :`I-C, II-A, III-D, IV-B`

Discussion

12028.	vec(a)= 2vec(i) + vec(j) -vec(k), vec(b)= -vec(i) + 2vec(j)- 4vec(k) and vec(c )= vec(i) + vec(j) + vec(k), then find (vec(a) xx vec(b)).(vec(b) xx vec(c )).
Answer» ANSWER :`-54`

Discussion

12029.	theta lt (pi)/(16), sqrt(2 + sqrt(2 + sqrt(2 + 2 cos 8 theta))) = k cos theta rArr k =
Answer» 2 4 8 16 Answer :A

Discussion

12030.	The minimum value of 64 sec theta +27 cosec theta where theta lies in (0,pi//2) is
Answer» 125 625 25 1025 Answer :A

Discussion

12031.	[(baraxxbarb)xx(baraxxbarc)].bard=k[bara barb barc] then k=
Answer» `bara.bard` `bara.barc` `bara.barb` `bara.bara` ANSWER :A

Discussion

12032.	Find the square root of the complex number 18i
Answer» ANSWER :`+- 3(1+i)`

Discussion

12033.	Are the following pari of sets equal? Give reasons A= {x : x is a positive integers solution of x^(2)-2x-15=0} B= {y : y in N, y^(2)= 25}
Answer» ANSWER :it is an EQUAL SET

Discussion

12034.	Solve the following equations and write general solutions2 Sin^(2) theta - 4 = 5 Cos theta
Answer» Answer :`2n PI PM (2PI)/(3)`

Discussion

12035.	The sum of roots of the equation cos^(-1)(cosx)=[x] (where [.] is G.I.F) is
Answer» `2pi+3` `pi+3` `pi-3` `2pi-3` ANSWER :A

Discussion

12036.	In each of the find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas. (x^(2))/(16)-(y^(2))/(9)=1
Answer» Answer :The eccentricity `E=(c )/(a)=(SQRT(17))/(4)` The latus rectum `(2b^(2))/(a)=(1)/(2)`

Discussion

12037.	The range of the function f(x)=(2+x)/(2-x), x != 2is
Answer» R `R-{-1}` `R-{1}` `R-{2}` ANSWER :B

Discussion

12038.	How many different group can be selected for playing tennis out of 4 ladies and 3 gentalemen, there being one lady and one gentleman on each side?
Answer» ANSWER :` 36`

Discussion

12039.	How many terms of G.P. 3, 3^(2), 3^(3), … are needed to give the sum 120?
Answer» ANSWER :4

Discussion

12040.	Convert each of the complex number in the polar form: sqrt(3)+i
Answer» ANSWER :`2(cospi/6+isinpi/6)`

Discussion

12041.	Statement I: The sum of the first 30 terms of the sequence1,2,4,7, 11, 16, 22, …..... is 4520 Statement II : If the successive differences of the terms of a sequence form an AP, then general term of the sequence is of the form an^(2) + bn+c.
Answer» Statement-1 is TRUE, Staternent-2 is true, Statement-2 is not a CORRECT EXPLANATION for Statement-1 Statement-1 is true, Statement-2 is FALSE. Statement-1 is false, Statement-2 is true. Statement-1 is true, Statement-2 is true, Statement-2 is correct explanation for Statement-1. Answer :C

Discussion

12042.	Show that the function f (x) = {{:( x , if x lt 1), ( 3-x , if 1 le x le 3), (x ^(2) - 4x +3, if x gt 3):} is not differentiable at 1,3.
Answer» Answer :`therefore f (X)` is DIFFERENTIABLE at `x =3`

Discussion

12043.	Discuss the continuity of the following functions : f(x) = sin x. cos x.
Answer» ANSWER :CONTINOUS

Discussion

12044.	A plane passes through the point (1,-2,3) and is parallel to the plane 2x - 2y + z=0. The distance of the point (-1, 2, 0) from the plane is
Answer» 2 3 4 5 Answer :D

Discussion

12045.	1 to 7, describe the sample space for the indicated experiment. A coin is tossed and a die is thrown.
Answer» Answer :`S={H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}`

Discussion

12046.	A sphere of radius 10 cms shrinks to radius 9.8 cms. Find approximately the decrease in volume and surface area
Answer» ANSWER :`80pi` CUBIC CM, `16pi` SQ cm

Discussion

12047.	Find the modulus of the following using the property of modulus ((2-3i)(4+5i))/((1-4i)(2-i))
Answer» ANSWER :`SQRT((533)/(85))`

Discussion

12048.	Write the first four terms of the sequence whose nth term is given (n^(2)+1)/(n)
Answer» ANSWER :`2, (5)/(2) , (10)/(3) , (17)/ (4)`

Discussion

12049.	Find the value of sin^(2)82 1/2-sin^(2)22 1/2.
Answer» ANSWER :`(3+sqrt(3))/(4)`

Discussion

12050.	The value of k(k gt 0) such that the length of the longest interval in which the function f(x)=sin^(-1)abs(sinkx)+cos^(-1)(coskappax) is constant pi/4 is/are
Answer» 8 4 12 16 Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

Reduce the equation x+2y-3z-6=0 of the plane to the normal form.

Show that the following equations represents a pair of parallel lines and also find the distance between them. x^(2)+2 sqrt(3)xy+3y^(2)-3x-3 sqrt(3) y-4=0

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

Derive an expression for the co-ordinates of points that divides the linejoining points A(x_1,y_1,z_1) andB(x_2,y_2,z_2) internally in the ratio m:n.Hence find the co-ordinates of midpoint of AB where A=(3,2,1) and B=(7,6,5).

The product of first n odd natural numbers equals:

y=log_(5)x+ 55 then dy/dx is:

Evaluate Lt_(x to 0) (e^(x) -1)/(sqrt(1 + x) - 1)

Iftan 69^(@) + tan 66^@ - tan 69^(@) tan66^@=2k , then the value of k is

Consider the function f(x) satisfying the identityf(x) + f((x-1)/( x))= 1+ x AA x in R - {0,1}, and g(x)=2f ( x)- x+1 The number of roots of the equation g(x)= 1 is

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

The solution set of sin7x+sin3x=sin2x+sin8x is (ninz)

If bara.(barb+barc) = barb.(barc+bara) = barc.(bara+barb) =0 and absbara = 3, absbarb = 4, absbarc = 5 , " then " abs(bara+barb+barc)=

Which of the following sets are finite or infinite The set of prime numbers less than 99

If 3 cos x ne 2 sin x, then the general solution of sin^(2) x - cos 2x = 2 - sin 2x is x =

Let bara ,barb,barc be non coplanar vectors and bara^(1)=(barbxxbarc)/([barabarbbarc]),barb^(1)=(barcxxbara)/([barabarbbarc]) and barc^(1)=(baraxxbarb)/([barabarbbarc]) then prove that [barabarbbarc][bara^(1)barb^(1)barc^(1)]=1

Write the negation of the following statements. s : Not all squares are rectangles.

The sum of n terms of an A.P. series is (n^(2) + 2n) for all values of n. Find the first 3 terms of the series:

The unit vector(s) parallel to bar(i)-3bar(j)-5bar(k) is

IfA_1 , A_2 , A_3 are areas of excircles, A is the area of incircle of a triangle then (1) /( sqrt(A_1)) + (1)/( sqrt(A_2))+ ( 1)/( sqrt(A_3))=

sqrt(3)x^(2) - sqrt(2)x + 3sqrt(3)=0

Find the values of other 5 trignometric ratios cot x = 3/4,x lies in third quadrant.

If there in and error of (1)/(10) % in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere.

The vector equation of the plane which is perpendicular to 2bari+3barj+6bark and at a distance of 7 units from origin is

P, Q and R are three collinear points. P and Q are (3, 4) and (7, 7) respectively, and PR =10 units. Find the coordinates of R.

If we consider only the principle values of the inverse trigonometric functions then the value of tan(cos^(-1)""1/(5sqrt(2))-sin^(-1)""4/sqrt(17)) is

A straight line L with negative slope passes through the point (8,2) and cuts positive co-ordinate axes at the points P and Q. Find the minimum value of OP+OQ as L varies where O is the origin.

Match each of the set on the left in the roster form with the same set on the right described in set builder form :

vec(a)= 2vec(i) + vec(j) -vec(k), vec(b)= -vec(i) + 2vec(j)- 4vec(k) and vec(c )= vec(i) + vec(j) + vec(k), then find (vec(a) xx vec(b)).(vec(b) xx vec(c )).

theta lt (pi)/(16), sqrt(2 + sqrt(2 + sqrt(2 + 2 cos 8 theta))) = k cos theta rArr k =

The minimum value of 64 sec theta +27 cosec theta where theta lies in (0,pi//2) is

[(baraxxbarb)xx(baraxxbarc)].bard=k[bara barb barc] then k=

Find the square root of the complex number 18i

Are the following pari of sets equal? Give reasons A= {x : x is a positive integers solution of x^(2)-2x-15=0} B= {y : y in N, y^(2)= 25}

Solve the following equations and write general solutions2 Sin^(2) theta - 4 = 5 Cos theta

The sum of roots of the equation cos^(-1)(cosx)=[x] (where [.] is G.I.F) is

In each of the find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas. (x^(2))/(16)-(y^(2))/(9)=1

The range of the function f(x)=(2+x)/(2-x), x != 2is

How many different group can be selected for playing tennis out of 4 ladies and 3 gentalemen, there being one lady and one gentleman on each side?

How many terms of G.P. 3, 3^(2), 3^(3), … are needed to give the sum 120?

Convert each of the complex number in the polar form: sqrt(3)+i

Statement I: The sum of the first 30 terms of the sequence1,2,4,7, 11, 16, 22, …..... is 4520 Statement II : If the successive differences of the terms of a sequence form an AP, then general term of the sequence is of the form an^(2) + bn+c.

Show that the function f (x) = {{:( x , if x lt 1), ( 3-x , if 1 le x le 3), (x ^(2) - 4x +3, if x gt 3):} is not differentiable at 1,3.

Discuss the continuity of the following functions : f(x) = sin x. cos x.

A plane passes through the point (1,-2,3) and is parallel to the plane 2x - 2y + z=0. The distance of the point (-1, 2, 0) from the plane is

1 to 7, describe the sample space for the indicated experiment. A coin is tossed and a die is thrown.

A sphere of radius 10 cms shrinks to radius 9.8 cms. Find approximately the decrease in volume and surface area

Find the modulus of the following using the property of modulus ((2-3i)(4+5i))/((1-4i)(2-i))

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

Find the value of sin^(2)82 1/2-sin^(2)22 1/2.

The value of k(k gt 0) such that the length of the longest interval in which the function f(x)=sin^(-1)abs(sinkx)+cos^(-1)(coskappax) is constant pi/4 is/are