81279 + Interview Questions in Mathematics QA in Mathematics

1.	8. An article is marked 20% above cost price. The shopkeeper allows discof 12%gain or loss percent.ong Answer Questions:
Answer»

Discussion

2.	(d) AB is the diameter of a circle whose centre is O. IF A (5,3) and O (4.2) then the coordinate of the point B(1.3) (ii) (2.3) (i) (3, 1) (iv) (3,2)
Answer» hy bro where are you from boloooooo option (ii) is the correct answer IV) (3.2) is the correct answer 2) is the right answer of the following 2) is the right answer of the following option 2 is the correct answer of the given question

2.

(d) AB is the diameter of a circle whose centre is O. IF A (5,3) and O (4.2) then the coordinate of the point B(1.3) (ii) (2.3) (i) (3, 1) (iv) (3,2)

Answer»

hy bro where are you from boloooooo

option (ii) is the correct answer

IV) (3.2) is the correct answer

2) is the right answer of the following

option 2 is the correct answer of the given question

Discussion

3.	linexy1. Find the area of the region bounded by the curve y' - 4c and the line x
Answer»

Discussion

4.	4. Find the angle which a line perpendicular to the linex-y+1 = 0 makes with the positive direction of the x-axis.
Answer»

Discussion

5.	Subtraction5x=10x-100
Answer» 10x-5x=1005x=100x=100/5x=20

Discussion

6.	Subtraction of z from y.
Answer» Equation will be y - z

6.

Subtraction of z from y.

Answer»

Equation will be

y - z

Discussion

7.	P Passing throg
Answer» as passes from (0,0), hence c=0thus equation becomesy=mx Thankw

7.

P Passing throg

Answer»

as passes from (0,0), hence c=0thus equation becomesy=mx

Thankw

Discussion

8.	5. Tangents are drawn to r? + y2 = 1 from any arbitrary point Pon the line 2x + y-4 = 0. The corresponding chord ofcontact passes through a fixed point whose coordinate is :(a) (1/4,1/2)(b) (1/2,1) (C) (1/2,1/4)(d) (1,1/2)13 -
Answer»

Discussion

9.	Show that one and only one of n, n + 2, n +4 is divisible by 3
Answer» Sol :We applied Euclid Division algorithm on n and 3.a = bq +r on putting a = n and b = 3n = 3q +r , 0<r<3i.e n = 3q -------- (1),n = 3q +1 --------- (2), n = 3q +2 -----------(3)n = 3q is divisible by 3or n +2 = 3q +1+2 = 3q +3 also divisible by 3or n +4 = 3q + 2 +4 = 3q + 6 is also divisible by 3Hence n, n+2 , n+4 are divisible by 3.

Discussion

10.	Show that one and only one of n,n+2,n+4 is divisible by 3
Answer» Solution: let n be any positive integer and b=3n =3q+rwhere q is the quotient and r is the remainder0_ <r<3so the remainders may be 0,1 and 2so n may be in the form of 3q, 3q=1,3q+2 CASE-1 IF N=3qn+4=3q+4n+2=3q+2here n is only divisible by 3 CASE 2if n = 3q+1n+4=3q+5n+2=3q=3here only n+2 is divisible by 3 CASE 3IF n=3q+2n+2=3q+4n+4=3q+2+4=3q+6here only n+4 is divisible by 3 HENCE IT IS JUSTIFIED THAT ONE AND ONLY ONE AMONG n,n+2,n+4 IS DIVISIBLE BY 3 IN EACH CASE

10.

Show that one and only one of n,n+2,n+4 is divisible by 3

Answer»

Solution:

let n be any positive integer and b=3n =3q+rwhere q is the quotient and r is the remainder0_ <r<3so the remainders may be 0,1 and 2so n may be in the form of 3q, 3q=1,3q+2

CASE-1

IF N=3qn+4=3q+4n+2=3q+2here n is only divisible by 3

CASE 2if n = 3q+1n+4=3q+5n+2=3q=3here only n+2 is divisible by 3

CASE 3IF n=3q+2n+2=3q+4n+4=3q+2+4=3q+6here only n+4 is divisible by 3

HENCE IT IS JUSTIFIED THAT ONE AND ONLY ONE AMONG n,n+2,n+4 IS DIVISIBLE BY 3 IN EACH CASE

Discussion

11.	. Show that one and only one out of n, n + 2, n + 4 is divisible by 3, where 'n' isany positive integer.
Answer»

Discussion

12.	Show that one and only one out of n,n+1,n+4 is divisible by 3 where n is any in positive integer
Answer» let n be any positive integer and b=3n =3q+rwhere q is the quotient and r is the remainder0_ <r<3so the remainders may be 0,1 and 2so n may be in the form of 3q, 3q=1,3q+2 CASE-1 IF N=3qn+4=3q+4n+2=3q+2here n is only divisible by 3 CASE 2if n = 3q+1n+4=3q+5n+2=3q=3here only n+2 is divisible by 3 CASE 3IF n=3q+2n+2=3q+4n+4=3q+2+4=3q+6here only n+4 is divisible by 3 HENCE IT IS JUSTIFIED THAT ONE AND ONLY ONE AMONG n,n+2,n+4 IS DIVISIBLE BY 3 IN EACH CASE

12.

Show that one and only one out of n,n+1,n+4 is divisible by 3 where n is any in positive integer

Answer»

let n be any positive integer and b=3n =3q+rwhere q is the quotient and r is the remainder0_ <r<3so the remainders may be 0,1 and 2so n may be in the form of 3q, 3q=1,3q+2

CASE-1

IF N=3qn+4=3q+4n+2=3q+2here n is only divisible by 3

CASE 2if n = 3q+1n+4=3q+5n+2=3q=3here only n+2 is divisible by 3

CASE 3IF n=3q+2n+2=3q+4n+4=3q+2+4=3q+6here only n+4 is divisible by 3

HENCE IT IS JUSTIFIED THAT ONE AND ONLY ONE AMONG n,n+2,n+4 IS DIVISIBLE BY 3 IN EACH CASE

Discussion

13.	Show that one and only one out of n, n+2, n+4 is divisible by 3 , where n is any positive integer
Answer» Every integer can be represented in the form of n, n+1,n+2; where n is also an integer. n+4 can also be represented by n+1. Out of every three consecutive integers, only 1 number is divisible by 3. So, out of three consecutive numbers n, n+4, n+2, only one is divisible by 3. Please hit the like button

13.

Show that one and only one out of n, n+2, n+4 is divisible by 3 , where n is any positive integer

Answer»

Every integer can be represented in the form of n, n+1,n+2; where n is also an integer.

n+4 can also be represented by n+1.

Out of every three consecutive integers, only 1 number is divisible by 3. So, out of three consecutive numbers n, n+4, n+2, only one is divisible by 3.

Please hit the like button

Discussion

14.	Show that one and only one out of n, n +2 or n +4 is divisible by 3, where n is anypositive integer
Answer» thanks

Discussion

15.	5. Show that one and only one out of n, n+2, n + 4 is divisible by 3, wheren is any positive integer.
Answer» let n be any positive integer and b=3n =3q+rwhere q is the quotient and r is the remainder0_ <r<3so the remainders may be 0,1 and 2so n may be in the form of 3q, 3q=1,3q+2 CASE-1 IF N=3qn+4=3q+4n+2=3q+2here n is only divisible by 3 CASE 2if n = 3q+1n+4=3q+5n+2=3q=3here only n+2 is divisible by 3 CASE 3IF n=3q+2n+2=3q+4n+4=3q+2+4=3q+6here only n+4 is divisible by 3

15.

5. Show that one and only one out of n, n+2, n + 4 is divisible by 3, wheren is any positive integer.

Answer»

let n be any positive integer and b=3n =3q+rwhere q is the quotient and r is the remainder0_ <r<3so the remainders may be 0,1 and 2so n may be in the form of 3q, 3q=1,3q+2

CASE-1

IF N=3qn+4=3q+4n+2=3q+2here n is only divisible by 3

CASE 2if n = 3q+1n+4=3q+5n+2=3q=3here only n+2 is divisible by 3

CASE 3IF n=3q+2n+2=3q+4n+4=3q+2+4=3q+6here only n+4 is divisible by 3

Discussion

16.	17, The cartesian equations of a line are 3x +16y -2 1-z. Find the fixed point throgCBSE2004which it passes, its direction ratios and also its vector equation.
Answer»

Discussion

17.	\begin{array} { l } { \text { Solve: } } \\ { \text { 1. } 3 - x = 9 } \end{array}
Answer» 3 - x = 9subtract 3 on both sides-x = 9 - 3 - x = 6multiply -1 on both sidesx = -6 thnx

17.

\begin{array} { l } { \text { Solve: } } \\ { \text { 1. } 3 - x = 9 } \end{array}

Answer»

3 - x = 9subtract 3 on both sides-x = 9 - 3 - x = 6multiply -1 on both sidesx = -6

thnx

Discussion

18.	Find the area of the smallest portion of the circlex^2+y^2=4 cut off by the line x + y 2
Answer»

Discussion

19.	16.) Find the cartesian and vector equations of a line which passes through the point (1,2,3)y+3and is parallel to the line-x-22-53[CBSE 2004=-
Answer»

Discussion

20.	(0, (a) find the area of the region in the first quadrant enclosed by x-axis, line x- By and the circleINCERT4
Answer»

Discussion

21.	. Find the area of the region in thefirst quadrant enclosed by -axis, line x-3yand the circlexy4.
Answer»

Discussion

22.	6.Find the area of the region in the first quadrant enclosed by x-axis, linex-3)and the circle x2+y2 4.
Answer»

Discussion

23.	1. Draw different pairs of circles. How many poindoestseach pair have in common? What is the maxnumber of common points?Consider the following pair of circlesAns.
Answer»

Discussion

24.	Using integration, find the area of the region bounded by the parabola y-4x and the linex=4.
Answer»

Discussion

25.	65. What is the reflection of thepoint (- 1, 3) in the line x--4?
Answer» Line x=-4 is a straight line parallel to y-axis and at a distance of 4units in negative direction of x- axis. Point (-1,3) is 3 unit away from given line x=-4. therefore distance of imagefrom the line is also 3 units. Thus distance of image from y-axis = 3+3+1=7 Units in negative direction of x - axis. Thus reflection of point (-1,3) in the line x=-4 is (-7,3) , Answer.

25.

65. What is the reflection of thepoint (- 1, 3) in the line x--4?

Answer»

Line x=-4 is a straight line parallel to y-axis and at a distance of 4units in negative direction of x- axis.

Point (-1,3) is 3 unit away from given line x=-4.

therefore distance of imagefrom the line is

also 3 units.

Thus distance of image from y-axis = 3+3+1=7

Units in negative direction of x - axis.

Thus reflection of point (-1,3) in the line x=-4

is (-7,3) , Answer.

Discussion

26.	l Solve the following pair of hearEquation: =0;-a's
Answer»

Discussion

27.	Find two rational numbers between 3 and 4.
Answer» 3.1,3.2,3.3,3.4,3.5,3.6,3.7,3.8,3.9 just multiple it so u get the answers

27.

Find two rational numbers between 3 and 4.

Answer»

3.1,3.2,3.3,3.4,3.5,3.6,3.7,3.8,3.9

just multiple it so u get the answers

Discussion

28.	4. Find two rational numbers between -3 and -2.
Answer»

Discussion

29.	2. The place far away from the National Highway(NH13) Bagalkot or Badami
Answer» Badami caves are further away from national highway.

Discussion

30.	PARI-A1.Which of the following is the formula for the volume of the sphere?b)arc)Tráº»
Answer» it's (d) for volume of sphere d is volume of sphere 4/3πr^3 gole ka aayatan hota h d is the correct answer the answer of your question is option d it's d) .is the volume of sphere volume of the sphere is 4/3πr^3 गोले का आयतन=4/3πr³ होता है गोले का आयतन =4/3πr³ होता है (d) is volume of sphere and correct answer. D is the best answer The correct answer d (d) is volume of sphere and right answer d is right answer because this formula is volume of sphere d is correct answer formula of volume of sphere is 4/3πr^3 (d) is correct answer (d) is the right formula for finding the volume of sphere d) is the volume of sphere D is correct answer. D is the correct answer sphere formula is 4/3πr^3 it's (d) for volume of sphere its right answer volume of sphere = 4/3 πr³ option d is the volume of sphere option D is correct can be apply at any sphere (a) option is the correct answer (d) is the correct answer of the given question (d) is the answer of this question d is the answer of this question d is the volume of sphere the answer isd. 4Πr² 3 no.d is correct........ option d is right answer (d) is a right answer d) option is answer of given question answer = d) 4/3πr³. Ans d volume of sphere Ans d volume of sphere Ans b volume of hemispher It's (d) for volume of sphere (d) is correct answer 4/3πr^3 is volume of sphere The answer is the option D answer is : volume sphere is 4/3 πr^3 D is the volume of the sphere d is right answer 4/3 πr³ the formula for the volume of the sphere is 2/3πr^3 option D is the right answer (d) is the correct answer d)is the volume of sphere d is the right answer

30.

PARI-A1.Which of the following is the formula for the volume of the sphere?b)arc)Tráº»

Answer»

it's (d) for volume of sphere

d is volume of sphere

4/3πr^3 gole ka aayatan hota h

d is the correct answer

the answer of your question is option d

it's d) .is the volume of sphere

volume of the sphere is 4/3πr^3

गोले का आयतन=4/3πr³ होता है

गोले का आयतन =4/3πr³ होता है

(d) is volume of sphere and correct answer.

D is the best answer

The correct answer d

(d) is volume of sphere and right answer

d is right answer because this formula is volume of sphere

d is correct answer formula of volume of sphere is 4/3πr^3

(d) is correct answer

(d) is the right formula for finding the volume of sphere

d) is the volume of sphere

D is correct answer.

D is the correct answer

sphere formula is 4/3πr^3

it's (d) for volume of sphere

its right answer

volume of sphere = 4/3 πr³

option d is the volume of sphere

option D is correct can be apply at any sphere

(a) option is the correct answer

(d) is the correct answer of the given question

(d) is the answer of this question

d is the answer of this question

d is the volume of sphere

the answer isd. 4Πr² 3

no.d is correct........

option d is right answer

(d) is a right answer

d) option is answer of given question

answer = d) 4/3πr³.

Ans d volume of sphere

Ans b volume of hemispher

It's (d) for volume of sphere

(d) is correct answer

4/3πr^3 is volume of sphere

The answer is the option D

answer is : volume sphere is 4/3 πr^3

D is the volume of the sphere

d is right answer 4/3 πr³

the formula for the volume of the sphere is 2/3πr^3

option D is the right answer

(d) is the correct answer

d)is the volume of sphere

d is the right answer

Discussion

31.	1. Name the lines given in fig. 3.14.Fi
Answer» i)PQ is line segment as it has two end points.

Discussion

32.	3.Find two numbels Wius scu4. Find two consecutive positive integers, sum of whose squares is 365.
Answer» let the no. be x and x+1 then we have x²+(x+1)²=365 2x²+2x-364=0 x²+x-182=0 x²+14x-13x-182=0 (x+14)(x-13)=0 That gives x=13 Avoiding negative value one number is 13 and other one 14.

Discussion

33.	2.other HieIn2
Answer»

Discussion

34.	Find the total surface area of a hollow cylinder open at both ends,if its length is 28 cm, external radius is 7cm and thickness is 1 cm.
Answer»

Discussion

35.	The total surface area of a hollow cylinder which is open from both sides is4620 sq.cm, area of base ring is 115.5 cm? and height 7 cm. Find the thicknessof the cylinder.
Answer»

Discussion

36.	The total surface area of a hollow cylinder which is open from both sides is4620 sq.cm, area of base ring is 115.5 cm2 and height 7 cm. Find the thicknessof the cylinder.Maths Axis-8
Answer»

Discussion

37.	a. Find the Taylor's seriesl T II DOWUIseriĂŠs 8I lgA l pub. If U = tan-1(x' + y 3prove that xy o0 -sin 2U by using Euler's theorem. (07x+y11 0
Answer»

Discussion

38.	OULCIJ uungle 15 100 . Find itsIn a 4ABC, if AB = AC and ZB = 65°, find ZC and ZA.han isoscolo u
Answer» GivenAB=ACThusAngle C = angle B because angles opposite to equal sides are equal so angle C = 65°angle A = angle A + angle B + angle C= 180 ° angle sum property of triangle angle A+ 65° + 65° = 180°angle A = 180 - 130 angle A = 50°

38.

OULCIJ uungle 15 100 . Find itsIn a 4ABC, if AB = AC and ZB = 65°, find ZC and ZA.han isoscolo u

Answer»

GivenAB=ACThusAngle C = angle B

because angles opposite to equal sides are equal

so angle C = 65°angle A = angle A + angle B + angle C= 180 °

angle sum property of triangle

angle A+ 65° + 65° = 180°angle A = 180 - 130 angle A = 50°

Discussion

39.	5CBSE 2012C],6) If A(-2, 1, 2) and B(2,-1,,6) are two given points, find a unit vector in thedirection of AB
Answer»

Discussion

40.	nd the slope of the line joining the two given pointsFi(4,-8) and (5,-2)
Answer»

Discussion

41.	(3)A (2,3), B (-2,5) are given points. Find the equationof locus ofpoint P, such that PA-2 PB.
Answer»

Discussion

42.	(5) A (3.)and B-(4,-5) are given points.,-3) are given points.Find the equation of locus of point P, such thatAP2+ Bp2-50.
Answer» Thanks

Discussion

43.	1. Examine the continuity of the following functions atthe given points :(1) f(x)_er_p2r2, for x + 0)at x = 0.=1,for x=0
Answer» is the correct answer

Discussion

44.	Question numbers 25 to 34 carry four-marks each. HMas eash25. By Euclid division algorithm, show that square of any positive integer is of the for3n or 3n + 1alue nfk will the pair of equations have no solution ?
Answer»

Discussion

45.	8. The profit ofValue BasedQuestiona shop isthe share3210. If 2 of it belongs to A, 1 to B and the remaining to c, wof each? What values can be depicted by the shop with the business?
Answer»

Discussion

46.	15. A hollow cyilindrical 15 cm long pipe is made of iron and its external diameter is 8 cm.The volume of iron used in making the pipe is 330 cm3. What is the thickness of the22pipe? [ Use Ď=]
Answer»

Discussion

47.	15An iron pipe 20 cm long has external diameter equalto25 cm. Ifthe thickness of the pipe is lan findthe whole surface of the pipe.
Answer» Solution:- Height of pipe = 20 cmExternal diameter = 25 cmExternal radius = 25/2 = 12.5 cmInternal diameter = 25 - (1 + 1)= 23 cmInternal radius = 23/2 = 11.5 cm Let the external radius be R and the internal radius be r.Total surface area of the pipe = 2πh(R + r) + 2π(R² - r²)⇒ 222/720(12.5 + 11.5) + 222/7{(12.5)² - (11.5²)⇒ (44480)/7 + (4424)/7⇒ 21120/7 + 1056/7⇒ 22176/7= 3168 cm²So, the total surface area of the pipe is 3168 square cm.

47.

15An iron pipe 20 cm long has external diameter equalto25 cm. Ifthe thickness of the pipe is lan findthe whole surface of the pipe.

Answer»

Solution:-

Height of pipe = 20 cmExternal diameter = 25 cmExternal radius = 25/2 = 12.5 cmInternal diameter = 25 - (1 + 1)= 23 cmInternal radius = 23/2 = 11.5 cm

Let the external radius be R and the internal radius be r.Total surface area of the pipe = 2πh(R + r) + 2π(R² - r²)⇒ 2*22/7*20(12.5 + 11.5) + 2*22/7*{(12.5)² - (11.5²)⇒ (44*480)/7 + (44*24)/7⇒ 21120/7 + 1056/7⇒ 22176/7= 3168 cm²So, the total surface area of the pipe is 3168 square cm.

Discussion

48.	An iron pipe 20 cm long has exterior diameterequal to 25 cm. If the thickness of the pipe is1 cm, find the whole surface area of the pipe.
Answer»

Discussion

49.	An iron pipe 20 cm long has external diameter equalto 25 cm. If the thickness of the pipe is 1 cm, findthe whole surface of the pipe.
Answer» Solution:- Height of pipe = 20 cmExternal diameter = 25 cmExternal radius = 25/2 = 12.5 cmInternal diameter = 25 - (1 + 1)= 23 cmInternal radius = 23/2 = 11.5 cm Let the external radius be R and the internal radius be r.Total surface area of the pipe = 2πh(R + r) + 2π(R² - r²)⇒ 222/720(12.5 + 11.5) + 222/7{(12.5)² - (11.5²)⇒ (44480)/7 + (4424)/7⇒ 21120/7 + 1056/7⇒ 22176/7= 3168 cm²So, the total surface area of the pipe is 3168 square cm Please like the solution 👍 ✔️

49.

An iron pipe 20 cm long has external diameter equalto 25 cm. If the thickness of the pipe is 1 cm, findthe whole surface of the pipe.

Answer»

Solution:-

Height of pipe = 20 cmExternal diameter = 25 cmExternal radius = 25/2 = 12.5 cmInternal diameter = 25 - (1 + 1)= 23 cmInternal radius = 23/2 = 11.5 cm

Let the external radius be R and the internal radius be r.Total surface area of the pipe = 2πh(R + r) + 2π(R² - r²)⇒ 2*22/7*20(12.5 + 11.5) + 2*22/7*{(12.5)² - (11.5²)⇒ (44*480)/7 + (44*24)/7⇒ 21120/7 + 1056/7⇒ 22176/7= 3168 cm²So, the total surface area of the pipe is 3168 square cm

Please like the solution 👍 ✔️

Discussion

50.	(iv)a +b+abc(i)(a)× (2a22)× (4e®)(ii)( xy)(iii) (ypq3) × (M)(iv) x x x
Answer» 3 i)(2×4)×(a^(2+22+26)) =8a^50 iii)-4p^4 q^4

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

8. An article is marked 20% above cost price. The shopkeeper allows discof 12%gain or loss percent.ong Answer Questions:

(d) AB is the diameter of a circle whose centre is O. IF A (5,3) and O (4.2) then the coordinate of the point B(1.3) (ii) (2.3) (i) (3, 1) (iv) (3,2)

linexy1. Find the area of the region bounded by the curve y' - 4c and the line x

4. Find the angle which a line perpendicular to the linex-y+1 = 0 makes with the positive direction of the x-axis.

Subtraction5x=10x-100

Subtraction of z from y.

P Passing throg

5. Tangents are drawn to r? + y2 = 1 from any arbitrary point Pon the line 2x + y-4 = 0. The corresponding chord ofcontact passes through a fixed point whose coordinate is :(a) (1/4,1/2)(b) (1/2,1) (C) (1/2,1/4)(d) (1,1/2)13 -

Show that one and only one of n, n + 2, n +4 is divisible by 3

Show that one and only one of n,n+2,n+4 is divisible by 3

. Show that one and only one out of n, n + 2, n + 4 is divisible by 3, where 'n' isany positive integer.

Show that one and only one out of n,n+1,n+4 is divisible by 3 where n is any in positive integer

Show that one and only one out of n, n+2, n+4 is divisible by 3 , where n is any positive integer

Show that one and only one out of n, n +2 or n +4 is divisible by 3, where n is anypositive integer

5. Show that one and only one out of n, n+2, n + 4 is divisible by 3, wheren is any positive integer.

17, The cartesian equations of a line are 3x +16y -2 1-z. Find the fixed point throgCBSE2004which it passes, its direction ratios and also its vector equation.

\begin{array} { l } { \text { Solve: } } \\ { \text { 1. } 3 - x = 9 } \end{array}

Find the area of the smallest portion of the circlex^2+y^2=4 cut off by the line x + y 2

16.) Find the cartesian and vector equations of a line which passes through the point (1,2,3)y+3and is parallel to the line-x-22-53[CBSE 2004=-

(0, (a) find the area of the region in the first quadrant enclosed by x-axis, line x- By and the circleINCERT4

. Find the area of the region in thefirst quadrant enclosed by -axis, line x-3yand the circlexy4.

6.Find the area of the region in the first quadrant enclosed by x-axis, linex-3)and the circle x2+y2 4.

1. Draw different pairs of circles. How many poindoestseach pair have in common? What is the maxnumber of common points?Consider the following pair of circlesAns.

Using integration, find the area of the region bounded by the parabola y-4x and the linex=4.

65. What is the reflection of thepoint (- 1, 3) in the line x--4?

l Solve the following pair of hearEquation: =0;-a's

Find two rational numbers between 3 and 4.

4. Find two rational numbers between -3 and -2.

2. The place far away from the National Highway(NH13) Bagalkot or Badami

PARI-A1.Which of the following is the formula for the volume of the sphere?b)arc)Tráº»

1. Name the lines given in fig. 3.14.Fi

3.Find two numbels Wius scu4. Find two consecutive positive integers, sum of whose squares is 365.

2.other HieIn2

Find the total surface area of a hollow cylinder open at both ends,if its length is 28 cm, external radius is 7cm and thickness is 1 cm.

The total surface area of a hollow cylinder which is open from both sides is4620 sq.cm, area of base ring is 115.5 cm? and height 7 cm. Find the thicknessof the cylinder.

The total surface area of a hollow cylinder which is open from both sides is4620 sq.cm, area of base ring is 115.5 cm2 and height 7 cm. Find the thicknessof the cylinder.Maths Axis-8

a. Find the Taylor's seriesl T II DOWUIseriĂŠs 8I lgA l pub. If U = tan-1(x' + y 3prove that xy o0 -sin 2U by using Euler's theorem. (07x+y11 0

OULCIJ uungle 15 100 . Find itsIn a 4ABC, if AB = AC and ZB = 65°, find ZC and ZA.han isoscolo u

5CBSE 2012C],6) If A(-2, 1, 2) and B(2,-1,,6) are two given points, find a unit vector in thedirection of AB

nd the slope of the line joining the two given pointsFi(4,-8) and (5,-2)

(3)A (2,3), B (-2,5) are given points. Find the equationof locus ofpoint P, such that PA-2 PB.

(5) A (3.)and B-(4,-5) are given points.,-3) are given points.Find the equation of locus of point P, such thatAP2+ Bp2-50.

1. Examine the continuity of the following functions atthe given points :(1) f(x)_er_p2r2, for x + 0)at x = 0.=1,for x=0

Question numbers 25 to 34 carry four-marks each. HMas eash25. By Euclid division algorithm, show that square of any positive integer is of the for3n or 3n + 1alue nfk will the pair of equations have no solution ?

8. The profit ofValue BasedQuestiona shop isthe share3210. If 2 of it belongs to A, 1 to B and the remaining to c, wof each? What values can be depicted by the shop with the business?

15. A hollow cyilindrical 15 cm long pipe is made of iron and its external diameter is 8 cm.The volume of iron used in making the pipe is 330 cm3. What is the thickness of the22pipe? [ Use Ď=]

15An iron pipe 20 cm long has external diameter equalto25 cm. Ifthe thickness of the pipe is lan findthe whole surface of the pipe.

An iron pipe 20 cm long has exterior diameterequal to 25 cm. If the thickness of the pipe is1 cm, find the whole surface area of the pipe.

An iron pipe 20 cm long has external diameter equalto 25 cm. If the thickness of the pipe is 1 cm, findthe whole surface of the pipe.

(iv)a +b+abc(i)(a)× (2a22)× (4e®)(ii)( xy)(iii) (ypq3) × (M)(iv) x x x

15. A hollow cyilindrical 15 cm long pipe is made of iron and its external diameter is 8 cm.The volume of iron used in making the pipe is 330 cm3. What is the thickness of the22pipe? [ Use Ď=]