Assignment No‐1 

Engineering graphics 

Class‐ XI 

Lettering 

Note: all dimensions are in mm. 

1. H‐8, W‐6, G‐2 (alphabets A to Z) 

2. H‐6, W‐5 G‐1 (alphabets A to Z) 

3. H‐4, W‐3 G‐0.5 (numerals 0‐9) 

 

Type of Lines 

Note: Practice each type five times 

 

      Line type                                          Use/Application 

1. Continuous thick (dark)                     Visible outlines 

2. Continuous thin (faint)          Projection, dimension, construction lines 

3. Dashed thick (dark)                              Hidden edges 

4. Chain line thin (faint)                            Centre, axis line 

5. Section plane (chain line with thick ends) 

6. Section/Hatching lines (thin & faint lines inclined at an angle of 45 with 

uniform gap of 2‐3 mm) 

 

 

 

   

 

Assignment No‐2 

Engineering graphics 

Class‐ XI 

Rectilinear Figures 

 

1. To construct an equilateral triangle with given altitude 40mm 

2. Draw a pentagon and hexagon with side 40mm by angle method 

            (Angle = 180 – 360/n) 

3. Draw a hexagon with side 30mm by circle method. 

4. Draw regular polygons from triangle to octagon with base side 40mm by 

general method. 

 

 

 

Assignment No‐3 

 

Circles and Tangents 

 

1. To inscribe a circle in a regular polygon e.g. in a pentagon with side 40mm 

2. To describe a regular hexagon around a circle of radius 20mm (angle 60) 

3. To describe a regular octagon around a circle of radius 25mm (angle 45) 

 

 

 

Assignment No‐4 

Class‐11 

   Engineering Graphics 

Curves 

 

1. Construct an ellipse with major axis = 120mm &minor axis = 80mm by 

following methods :‐ 

Arcs of circles method 

Concentric circle method 

Oblong method 

 

2. To construct a parabola when the distance of the focus from the 

directrix is 50mm. 

 

3. To construct a parabola given the base 80mm and axis = 120mm. 

 

4. To construct a cycloid, given the diameter of the generating circle 

=35mm. 

 

5. To draw an involute of a given circle of diameter 35mm. 

 

 

 

 

Assignment No‐5 

Class‐11 

   Engineering Graphics 

Projection of Points 

 

1. Draw the projections of the following points on the same ground 

line, keeping the projectors 25mm apart.  

A) In the H.P. and 20mm behind the V.P. 

B) 40mm above the H.P. and 25mm in front of V.P. 

C) In the V.P. and 40mm above the H.P. 

D) 25mm below the H.P. &25mm behind the V.P. 

E) 15mm above the H.P. and 50mm behind V.P.  

F) 40mm below the H.P. and 25mm in front of V.P. 

G) In both the H.P. and V.P.  

 

Extra Practice Questions 

 

2. A  point  is  50mm  from  both  the  reference  planes.  Draw  its 

projections in all possible positions. 

3. State the quadrants in which the following points are situated. 

a) A point P, its top view is 40mm above xy, the front view, 20mm 

below the top view 

b) A point Q, its projections coincide with each other 40mm below 

xy. 

4. A point P  is 15mm above the H.P. and 20mm  in  front of the V.P. 

Another point Q is 25mm behind the V.P. and 40mm below the H.P. 

Draw  projections  of  P&Q  keeping  the  distance  between  their 

projectors equal to 90mm. Draw straight  lines  joining  i) their top 

views & ii) their front views.  

 

Assignment No‐6 

Class‐11 

 Engineering Graphics 

Projection of Lines  

1. Draw the projections of a 75mm long straight line, in the following positions: a) (i) Parallel to both the H.P. and the V.P. and 25mm from each.      (ii)Parallel to and 30mm above the H.P. and in the V.P.      (Iii) Parallel to and 40mm in front of V.P. and in the H.P. b) (i) Perpendicular to the H.P, 20mm in front of the V.P. and it’s one end 15mm above the H.P 

     (Ii) Perpendicular to the V.P, 25mm above the H.P and its one end in the V.P. 

     (iii) Perpendicular to the H.P., in the V.P. and its one end in the H.P. 

   c) (i) Inclined at 45 to the V.P. in the H.P. & it’s one end in the V.P. 

    (ii) Inclined at 30 to the H.P.& it’s one end 20 mm above it, parallel to and 30 mm in front of V.P. 

    (iii) Inclined at 60 to the V.P. its one end 15 mm in front of it, parallel to& 25 mm above the H.P. 

2. A 100mm  long  line  is parallel  to & 40mm above  the H.P.  Its  two ends are 25mm &50m  in  front of  the V.P.  respectively. Draw  its projections &find  its inclination with the V.P. 

3. A 90 mm long line is parallel to & 25mm in front of the V.P. Its one end is in the H.P. while  the  other  is  50mm  above  the H.P. Draw  its  projections &find  its inclination with the H.P. 

Extra Practice Questions 

4) The top view of a 70mm long line measures 55mm the line is in the V.P. its one end being 25mm above the H.P. Draw its projections. 

5) The front view of a line, inclined at 30deg. to the V.P. is 65mm long. Draw the projections of the line when it is parallel to & 45mm above H.P. its one end being 30mm in front of the V.P.   

 

Assignment No‐7 

Class‐11 

   Engineering Graphics 

Projection of planes 

 

1) A regular pentagon of 25mm side has one side on the ground. Its 

plane is inclined at 45deg. to the H.P. & perpendicular to the V.P. 

Draw its projections. 

 

2) Draw the projections of a circle of 50mm diameter, having its 

plane vertical & inclined at 30deg. to the V.P. Its centre is 30mm 

above the H.P. & 20mm in front of the V.P. 

 

3) Draw the projection of a regular hexagon of 25mm side, having 

one of its sides in the H.P. & inclined at 60deg. to the V.P. & its 

surface making an angle of 45deg. with the H.P. 

 

4) A thin 30deg.‐60deg. set‐square has its longest edge of 80mm in 

the V.P. & inclined at 30deg. to the H.P. Its surface makes an 

angle of 45deg. with the V.P. Draw its projections. 

 

 

 

 

Assignment No‐8 

Class‐11 

   Engineering Graphics 

Projection of Solids 

 

1) Draw the projections of a pentagonal pyramid base 30mm edge & axis 50mm long, having its base on the H.P. & an edge of the base parallel to the V.P.  

2)  A hexagonal prism with base edge 25mm & length of axis 50mm has one of its rectangular faces parallel to the H.P. its axis is perpendicular to the V.P. & 35mm above the ground.  

3) Draw the projections of a pentagonal prism base 25mm side & axis 50mm long, resting on one of its rectangular faces on the H.P. with the axis incline d at 45deg. to the V.P. 

 

4) A hexagonal pyramid, base side 25mm & axis 50mm long has an edge of its base on the ground. its axis is inclined at 30deg. to the ground & parallel to the V.P. draw its projections.  

5) Draw the projections of a cone base 75mm diameter & axis 100mm long lying on the H.P. on one of its generators with the axis parallel to the V.P.  

 

 

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ASSIGNMENT COMPLEX NUMBERS

SUBJECT: MATHEMATICS

CLASS: XI

1. Evaluate the following

i) (−√−1)4𝑛+3

n∈ ℕ ii) 𝑖𝑛 + 𝑖𝑛+1 + 𝑖𝑛+2 + 𝑖𝑛+3 = 0 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑛𝜖ℕ

ii) (𝑖77 + 𝑖70 + 𝑖87 + 𝑖414)3

2. Express each of the following in the form a+ib

i. {(1

3+

7

3𝑖) + (4 +

1

3 𝑖) − (−

4

3+ 𝑖)}

3. Express the following in the standard form a+ib where Z= 1

1−cos 𝜃+2𝑖𝑠𝑖𝑛 𝜃

4. If (𝑎+𝑖)2

(2𝑎−𝑖)= p+iqthen show that 𝑝2 + 𝑞2 =

(𝑎2+1)2

(4 𝑎2+1)

5. Find all non zero complex nos z satisfying �̅� = 𝑖 𝑍2

6. If (1 + 𝑖)(1 + 2𝑖)(1 + 3𝑖) … … … … … . (1 + 𝑛𝑖) = (𝑥 + 𝑖𝑦)then show that

2.5.10…………………(1 + 𝑛2) = 𝑥2 + 𝑦2

7. Find the real values of x and y if (1+𝑖 )𝑥−2𝑖

3+𝑖+

(2−3𝑖) 𝑦+𝑖

3−𝑖= 𝑖

8. Evaluate the following 2𝑥3 + 2𝑥2 − 7𝑥 + 72 𝑤ℎ𝑒𝑛 𝑥 = 3−5𝑖

2

9. Find the least positive integer value of for which (1+𝑖)𝑛

(1−𝑖)𝑛−2 is a real no.

10. Find the square root of the following

i) – 11 – 60 √−1 ii) 1+ 4 √−3

11. Find the modulus and argument of the following complex numbers

i) 1+3𝑖

1−2𝑖 ii)

1−√3 𝑖

1+ √3 𝑖

12. If √𝑎 + 𝑖𝑏 = x+iy then find the value of √𝑎 − 𝑖𝑏

13. If a = cos𝜃 + 𝑖 𝑠𝑖𝑛𝜃 then show that 1+𝑎

1−𝑎= 𝑖 𝑐𝑜𝑡

𝜃

2

14. Solve the following quadratic equations

i) 𝑥2 + 𝑥 +1

√2=0 ii) √5𝑥2 + 𝑥 + √5 = 0

15. Find the real values of x and y for which the complex numbers -3 + i𝑥2𝑦 and 𝑥2 + 𝑦 + 4𝑖

are conjugate of each other.

16. If (𝑎 + 𝑖𝑏)(𝑐 + 𝑖𝑑)(𝑒 + 𝑖𝑓)(𝑔 + 𝑖ℎ) = 𝐴 + 𝑖𝐵 then prove that

(𝑎2 + 𝑏2)(𝑐2 + 𝑑2)(𝑒2 + 𝑓2)(𝑔2 + ℎ2) = 𝐴2 + 𝐵2

17. Express the following number in the form r ( cos 𝜃 + 𝑖 𝑠𝑖𝑛𝜃) where z= (1 − 𝑠𝑖𝑛𝛼) + 𝑖 𝑐𝑜𝑠𝛼

18. If a+ib = 𝑐+𝑖

𝑐−𝑖 where c is a real no then prove that 𝑎2 + 𝑏2 = 1 𝑎𝑛𝑑

𝑏

𝑎=

2𝑐

𝑐2−1

2 of 2

19. If (𝑥 + 𝑖𝑦)1/3 = a+ib then show that

i) 𝑥

𝑎+

𝑦

𝑏= 4 (𝑎2 − 𝑏2) ii)

𝑥

𝑎−

𝑦

𝑏= −2 (𝑎2 + 𝑏2)

20. Prove that 𝑥4 + 4 = (𝑥 + 1 + 𝑖)(𝑥 + 1 − 𝑖)(𝑥 − 1 + 𝑖)(𝑥 − 1 − 𝑖)

21. If (1+𝑖

1−𝑖)

3

− (1−𝑖

1+𝑖)

3

= 𝑥 + 𝑖𝑦 then find x and y

22. If (1−𝑖

1+𝑖)

100

= a+ib then find a and b

23. For a positive integer n find the value of (1 − 𝑖)𝑛 (1 −1

𝑖)

𝑛

1 of 2

ASSIGNMENT (LINEAR INEQUALITIES)

SUBJECT: MATHEMATICS

CLASS: XI

1. Solve the following linear inequality 5x- 3 when

i) x is a real no.

ii) x is an integer

iii) x is a natural no.

2. A company manufactures cassettes and its cost and revenue function for a week are

C = 300 + 3/2 x & R = 2x respectively , where x is the no. of cassettes produced

and sold in a week . find the minimum no.of cassettes must be sold for the company to

realize the profit ?

3. Find all pairs of consecutive even natural numbers , both of which are larger than 8

Such that their sum is less than 40.

4. Show that the following system of linear equations has no solution .

x+2y , 3x+4y , x and y

5. The water acidity in a pool is considered normal when the average pH reading of three

Daily measurements is between 7.2 and 7.8 . If the first two pH reading are 7.48 and

7.85 .find the range of pH value for the third reading that will result in the acidity

level being normal .

6. Solve the following inequations

7. Solve the following system of linear inequalities graphically :

12x+12y , 3x+6y , 8x+4y , x

8. Solve the following system of linear inequalities graphically :

5x+y , 2x+2y , x+4y , x

9. Solve -5

10. Solve the following linear inequality

2 of 2

11. The marks obtained by Rohit in four tests were 65 , 70 ,72 and 60 . find the minimum

marks he

Should obtain in the fifth test to have an average of atleast 70marks .

12. Show that the solution set of following system of linear inequalities is an unbounded

region 2x+y , x+2y , x

ASSIGNMENT

MATHEMATICS

CLASS XI

PERMUTAIONS AND COMBINATIONS

Q1) How many numbers divisible by 5 and lying between 4000 and 5000 can be

formed using the digits 4,5,6,7,8 if repetition is allowed ?

Q2) Find the number of diagonals and triangles formed in a decagon.

Q3) How many different numbers greater than 50000 can be formed using the

digits 0,1,2,5,9 ?

Q4) Find the number of different 6 letter arrangements that can be formed from

the letters of the word ‘DOUBLE’ so that

a) All the vowels are together

b) Vowels do not occur together

Q5) How many words with or without meaning can be formed using 2 vowels and

3 consonants from the letters of the word ‘TEACHER’ ?

Q6) How many words can be formed with the letters of the word ‘ORDINATE’ so

that vowels occupy odd places ?

Q7) There are 12 points in a plane of which 5 points are collinear. Find the

number of lines obtained by joining these points.

Q8) How many natural numbers less than 1000 can be formed from the digits 0, 1,

2, 3, 4, 5 when repetition of digits are allowed.

Q11) If all the words of the word ‘TOUGH’ are arranged in all possible ways as

listed in a dictionary. Then find the rank of the word ‘TOUGH’

Q12) In how many ways can 5 persons sit in a car,2 including the driver in the

front seat and 3 in the back seat,if 2 particular persons do not know driving?

Q13) In how many ways 4 different balls be distributed in 5 boxes so that all the

balls are not put in the same box?

Q14) In how many ways can final eleven be selected from 15 cricket players if

(i) There is no restriction

(ii) One particular player must be included

(iii) One of them,who is in bad form,must be excluded

(iv) Two of them being leg spinners, one and only one leg spinner must

be included ?

Q15) A tea party is arranged for 18 men along two sides of a long table with 9

chairs on each side.Four men wish to sit on one particular side and three on the

other side.In how many ways can they be seated?

Assignment

Relations and Functions

1. If

2,3 , 4,5 and C = 5,6A B ,

Then find

A B C

2. Let 2,3 , 4,5A B .Find the total number of relations from A into B.

3. Determine the domain and range of the relation R defined by

{ 1, 1 : {1,2,3,4,5,6}}R x x x

4. If , 1,2,3,4x y , then is , : 4f x y x y a function? Justify.

5. Draw the graph of the function 3y x and 𝑦 =1

𝑥.

6. Find the range of the function 3

.3

xf x

x

7. Let :f R R , be defined as 2 1f x x , then find the pre-image of 17 and

image of 2.2

8. If 2 3 1f x x x and 2 2f f , then find the value of .

9. Let 2,3,4,5,6A .Let R be the relation on A defined by the rule

“ y divides x ifonly and if , Ryx ”. Find R as a subset of A A .

10. Let : and g : f R R N N be two functions defined as

2 2and gf x x x x . Are they equal functions?

11. Find the domain and range of the following functions:

(i) 1- 3x

(ii) 2

3

2 x

(iii) 29 x

(iv) 1

3x

12. If f is the identity function and g is the modulus function , find , , . ,f

f g f g f gg

13. If , ,f g h are three real valued functions defined as

211, g , 2 3f x x x h x x

x , find the value of 2 f g h at 1x .

14.Draw the graph of the following function

1 3

12 1

2 i 1

)(

xif

xifx

xfx

xf

ASSIGNMENT

MATHEMATICS

CLASS XI

SEQUNCES AND SERIES

Q1) The sum of n terms of a series is n2+3n for all values of n.Find 10th term of the series.

Q2) Write 1

2+

2

3+

3

4+ − − − − − − +

𝑛

𝑛+1in sigma notation.

Q3) Find the sum of all three digit numbers which leave the remainder 2 when divided by 5.

Q4) Solve for x :

1+4+7+10+_ _ _ _ _ _ _ _ _ _ _+ x = 590

Q5) Find the sum of the A.P. a1 ,a2, a3 , _ _ _ _ a30 given that a1 +a7+ a10+a21 + a24 + a30 =540

Q6) If a+b+c≠ 0 and 𝑏+𝑐−𝑎

𝑎 ,

𝑐+𝑎−𝑏

𝑏 ,

𝑎+𝑏−𝑐

𝑐 are in A.P.,prove that

1

𝑎 ,

1

𝑏 ,

1

𝑐 are in A.P.

Q7) The digits of a three digit natural number are in A.P.and their sum is 15.The number

obtained by reversing the digits is 396 less than the original number.Find the number.

Q8) The product of first three terms of a geometric series is 1000.If 6 is added to its second

term and 7 added to third term ,then the terms become in A.P.Find the Geometric series.

Q9) A side of an equilateral triangle is 20cm long.A second equilateral triangle is inscribed in

it by joining mid-points of the sides of the first triangle.The process is continued.Find the

perimeter of the sixth inscribed triangle.

Q10) If the sum of an infinite G.P. is 15 and the sum of squares of these terms is 45.Find the

G.P.

Q11) Find the sum to n terms of the series :

13

1+

13+23

1+3+

13+23+33

1+3+5+ - - - - -- - - - - - -

Q12) IfSk=1+2+3+−−−−− +𝑘

𝑘 , find

S12

+S22 +- - - - - - - -Sn

2

ASSIGNMENT

SETS

CLASS XI

SUBJECT: MATHEMATICS

1. If A = { x : x = 4n + 1, n ≤6 , n∈ N } , B = { 3n: n≤ 8 , n 𝜖 N } then find

i. A – ( A – B )

ii. ( A U B ) – ( A ∩ B )

2. Give an example to show that if A U B and A ∩ B are given, then A and B may not be

uniquely determinable.

3. If A = { 0,{φ}} write P(A).

4. Write the set {1

2 ,

2

5 ,

3

10 ,

4

17 ,

5

26 ,

6

37 ,

7

50 ,

8

65 } in the set builder form.

5. If B = {1,2 } and A is a set such that A U B = {1,2,5,8,9}. Find A if

i. A and B are disjoint sets

ii. A is not the superset of B

iii. B is the subset of A

6. If U = { x : x is a letter in English alphabet }

A = { x : x is a vowel in English }

Find A/ and (A/ )/ .

7. Draw the Venn diagram of the following

i. A/∩ ( B U C )

ii. A/∩ ( C - B )

8. If A and B be two sets containing 3 and 6 elements respectively. Find the minimum and

maximum number of elements in A U B.

9. Two finite sets have m and n elements. The number of subsets of first set is 112 more

than the second set. Find the value of m and n.

10. A school launched an awareness programme with a team of 60 students on different

days. 25 students participated in a programme against child labour , 26 students in a

programme against drug abuse , 26 students participating in a programme against

dowry system , 9 participated against both child labour and dowry system , 11

participated against both child labour and drug abuse , 8 participated against both drug

abuse and dowry system , 3 participated in all the three programmes. Find

i. The number of students who participated in any of the programmes.

ii. The number of students who participated in exactly one programme