CAMBRIDGE SCHOOL NOIDA MATHS ASSIGNMENT CLASS XI TOPIC: SETS THEORY AND LINEAR INEQUALITIES

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1 CAMBRIDGE SCHOOL NOIDA MATHS ASSIGNMENT CLASS XI TOPIC: SETS THEORY AND LINEAR INEQUALITIES Q1. Taking the set of natural numbers as the universal set, write down the complement of {x: x is a natural number divisible by 3} Q. The total number of subsets of a finite set containing n elements are? Q3. For any two sets A and B, evaluate Q4. Two finite sets having m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set. Then, find the values of m and n. Q5. If A and B are two given sets, then Q6. If then find Q7. In a survey of 600 students in a school, 150 students were found to be taking tea and 5 taking coffee, 100 were taking both. find how many students were taking neither tea nor coffee. Q8. In a group of 65 people, 40 like nutrition Indian food, 10 like both Indian nutrition food and fast food. How many like only fast food? Q9. For sets A, B and C using properties of sets, prove that 1) ) Q10. If A and B are two sets containing 3 and 6 elements respectively, what can be the minimum number of elements in find also, the maximum number of elements in Q11. Let A and B be two sets. Using properties of sets prove that: 1) ) Q1. A survey shows that 76% of the Indians like oranges, whereas 6% like bananas. What percentage of Indians like both oranges and bananas? Q13. Let A and B be sets. If and for some set X, show that Q14. In a survey of 100 persons it was found that 8 read magazine A, 30 read magazine B, 4 read magazine c, 8 read magazine A and B, 10 read magazine A and C, 5 read magazines B and C and 3 read all the three magazines. Find how many read none of the three magazines. Q15. In a survey of 100 students, the number of students studying the various languages were found to be: English only 18, English but not Hindi 3, English and Sanskrit 8, English 6, Sanskrit 48, Sanskrit and Hindi 8, no language 4. Find how many students were studying Hindi.

2 Q16. Solve: when x is integer number. Q17. Solve the following system of inequations: Q18. Solve the following system of equation graphically X y 1, x + y, x + y 8. x 0, y 0 (6) Q19. A solution of 1% boric acid is to be diluted by adding a 15% boric acid solution to it. The resulting mixture is to be more than acid. If we have 640 liters of the 8% solution. How many liters of the % solution will have to be added? Q0. Solve the following system of equation graphically X+y 10, x + y 1, x y 0. x 0, y 0 Q1. Find all pairs of consecutive odd positive integers, both of which are smaller than 18, such that their sum is more than 0. Q. The cost and revenue functions of a product are given by C(x) = x and g(x) = 6x + 0 respectively, where x is the number of items produced by the manufacturer. How many items the manufacturer must sell to realize some profit? Q3. A man wants to cut three lengths from a single piece of board of length 91cm. The second length is to be 3cm longer than the shortest and third length is to be twice as long as the shortest. What are the possible lengths for the shortest board if third piece is to be at least 5cm longer than the second? Q4. A solution is to be kept between and. What is the range of the temperature in degree Celsius / fahrenheit if conversion formula is given by Q5. To receive grade A in a course one must obtain an average of 90 marks or more in five papers each of 100 marks. If shikha scored 87, 95, 9 and 94 in four papers. Find the minimum marks that she must score in last paper to get grade A in the course.

3 Maths Assignment- (Class XI) Topic: sets Section A Q-1 If A= {x: x x } then represent A in tabular form. Q- If A= {, { } } then what will be n(p (P ( A) ) ). Q-3 If in a survey 63 % of Americans like cheese whereas 76 % like apples then find the range of the Americans which will like both cheese and apples. Q-4 If n( A) =8 and n ( B )= 4 and B is a subset of A then find n( A B ). Q-5 If a N= { ax : x Є N },then the find the set 3N 7N. Section B Q-6 In a battle 70 % of the combatants lost one eye,80 % an ear,75% an arm, 85 %a leg, and x% lost all of the four limbs. What will be the minimum value of x? Explain the disadvantages of battles. Q-7 In a school 0 teachers either teach maths or physics.1 of them teach mathematics while 4 teach both the subjects. Then find the number of teachers teaching physics only. Explain how these two subjects related with each other. Q-8 If A= { a, b, c, e }, B= { a, e, i, o }, C= { a,e, i, o, u } U= AU B U C Then Evaluate (A- B) U (B- C ) U ( C-A) U (A B C ) c Q-9 For sets A,B and C using properties of sets, prove that A ( B- C)= (A B) (A C) Q-10 If A and B are two sets then prove that ( AU B) c U ( A c B) = A c. Section C Q-11 In a survey of 100 students the number of students studying the various languages were found to be: English only 18, English but not Hindi 3, English and Sanskrit 8 English 6, Sanskrit 48, Sanskrit and Hindi 8, no language 4. Find: a) How many students were studying Hindi only? b) How many students were studying English and Hindi? c) Explain importance of language in education. Q-1 A survey conveys the result that 1 persons liked product soft drink,6 liked coconut water and 9 liked milk shakes. If 14 persons liked product soft drink and coconut water; 1 persons liked product soft drink and milk shakes 14 persons liked coconut water and milk shakes and 8 liked all the three products. Find: a)how many of them liked atleast products. b)how many liked at most products. c)which drink you feel has more nutrient value? Comment.

4 Maths Assignment-1 (Class XI) Topic: Linear Inequalities Section A Represent the solution on number line: ( - 3x ) 7/4. 3 / ( x-4) 0 3. x x-3 / (x-3) /x+1> 1/x Section B 6.Solve the system of in equations : x/ (x+1) ¾ 6x / (4x-1 ) ½. 7. Evaluate x: x + 3 / ( x+5) Solve for x: x- 5 / (x +) 1 9. x+1 + x How many litres of water have to be added to 3 litres of Sikanji (Lemon water ) containing 9% sugar solution so that the resulting mixture will contain more than 11 % but less than 18% sugar content. Explain how Sikanji is good for health. Section C Solve the system of in equations graphically : x + y 10 ; x + 3 y 6; x + 4 y 8 ; x ; y x y 4; 3 y 4 x 1; x- y 4; x 0 ; y x-y 5; x + y 0 ; y- 3x -5/ ; x 0 ; y x + y 10, x y 4 x 5; y 15. y- 3x 15, x + y 0, x-y 1 5, y 0. 1.Write the additive inverse of -3i.Write the polar form of i 3.write the modulus of Maths Assignment-3 (Class XI) Topic: Complex Number 1 1 i 1 i

5 4.If arg z 1 = 30 o and z1 z z1 z, find argz. 1 i i 5. Evaluate: Re. 1 i i 6.Evaluate i n + i n+1 + i n+ + i n+3 7.Suggest the value of x and y such that (1+i)x (+i)y = -(6+y)i Section B 8, Find the square root of 5-1i. Z 9.Find all complex numbers Z for which is purely imaginary. Z 3 10.If a ib cos isin,then prove that a +b =4a-3 11.If z 1 z, prove that z 1,where z is any complex number. Section C 1.If x=3+i,find the value of x 4-4x 3 +4x +8x If x 1 (5 3 i ), then.. find.. x x 1 x 3 x 1 14.Show that the area of the triangle on the Argand Plane formed by the complex 1 numbers z, iz and z+iz is z 4 where z is a complex, Show that z Re z 15.If z z 1, ASSIGNMENT SUBJECT: MATHEMATICS TOPIC: TRIGONOMETRY CLASS: XI SECTION A 1. Find the radian measure of 15 30'.. Find the degrere measure of Evaluate : cos(-1710 o ) If sec, and, find 9sec 4cot Evaluate: cos sec cos cos Evaluate: tan15 o 7. Solve: tan x = Write the Principal solution of the equation sin x = - 1 3

6 9. If cos = 3 and θ lies in the fourth quadrant find the value of 5 cosec θ + cot θ Evaluate: sin cos ec cos SECTION B o Evaluate: sin 1. sinα + sinβ +sinγ sin(α+β+γ) = 4 sin sin sin o o Prove that sin 0 sin 40 sin80 o 8 sec8a 1 tan8a 14. Show that sec4a 1 tan A 15. Prove that cos8 cos 16.Show that sin A sin(b-c)+sinb sin(c-a)+ sin C sin(a-b)=0 17.If two circles, arcs of same length subtend angles 45 o and 60 o at the centre, find the ratio of their radii. 18. Solve: sin x + cos x = Solve: tan x + sec x = 1 0. If and are two different roots of the equation a cos x + b sin x = c, prove that a cos( ) a b b SECTION C 1. Solve: sin x 5 sin x cos x 8cos x = -. Evaluate: sin 18 o. 3. Prove that Prove that (1+cosΠ/8)1+cos3Π/8)(1=cos5Π/8)(1+cos7Π/8)=1/8 nsin cos 4. If tan,pr ove : tan( ) (1 n) tan 1 nsin 5. Prove that tan6 o. tan4 o.tan66. o tan78 o = 1 ASSIGNMENT SUBJECT: MATHEMATICS TOPIC: MATHEMATICAL INDUCTION SECTION A 1. If P(n) be a statement 10n+3 is a prime number, then prove that P(1) and P() are true but P(3) is false.. If P(n) : n 7 -n is a multiple of 7, check the validity of P() 3. If P(n) : n > n, if P(m) is true, then show that P(m+1) is also true. SECTION B

7 Prove the following by using the principal of mathematical induction n 4. a+(a+d)+(a+d)+.[a+(n-1)d] = [ a ( n 1) d ], nєn n n n (6 1), nєn (n-1) 3 = n (n -1), nєn n n 1 4n 3 3 4n n+ +1 n+1 is divisible by 133, nєn 9. 4 n -3n-1 is divisible by 9, nєn 10. x n -y n is divisible by x+y, nєn. SECTION C n times = 10 n 9 n 10, n n 7n 1. is a natural number for all, nєn nєn n +3.4 n+ +5 is divisible by 9, nєn 14. n > n, n 5, nєn n < (n+1), nєn, nєn

DELHI PUBLIC SCHOOL BLUE PRINT WEEKLY TEST CLASS XI (MATHEMATICS)

DELHI PUBLIC SCHOOL BLUE PRINT WEEKLY TEST CLASS XI (MATHEMATICS) S. N0. TYPES OF QUESTIONS NO. OF QUESTION MARKS TOTAL 1. VERY SHT ANSWER 6 1 6 2. SHT ANSWER 5 4 20 3. LONG ANSWER WITH ONE 4 6 24 VALUE