Wednesday 26 December 2012

CBSE I NCERT Arithmetic Progression-X Solved Problems


1. A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top .If the top and the bottom rungs are two and a half meter apart, what is the length of the wood required for the rungs?

2. The sum of first n terms of an AP is given by Sn = 3n2 + 5n find the nth term of the AP.

3. How many terms of the ap -6,-11/2 , -5,...... are needed to give the sum -25

4. Find a, b such that 27, a, b - 6 are in A.P.

5. Find the sum of all the odd numbers between 50 and 150 divisible by 7

6. The sum of third and seventh term of an AP is 6 and their product is 8.

7. If Sn = n2p and Sm = m2p, (m not equal ton), is an A.P. prove that Sp = p3.

8.Show that the sum of (m+n)th term and (m-n)thterm of an A.Pis equal to twice the mth term.

9. If the ratio of the sums of n terms of 2 APs is n+1:3n+1, then find the ratio of the 7th terms of the AP.

10. Determine the sum of the first 30 terms of the sequence whose nth term is given by tn=2n+9/3

11. The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

12.The sum of the first and the last terms of an AP is 60,the sum of n terms of the AP is720.what is n?

13. If pth , qth and rth term of an AP are a,b,c respectively , then show that (a-b)r +(b-c)p + (c-a)q = 0

14. if (b+c)/a, (c+a)/b, (a+b)/c are in A.P. show that bc,ca,ab re in A.P.

15. The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms

Class X ARITHMETIC PROGRESSIONS (8) Periods

Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms and their application in solving daily life problems.

Wednesday 19 December 2012

11th Maths Chapter Set Theory


Class XI Maths Chapter Set Sets
1.1 Sets and their Representations
1.2 The Empty Set
1.3 Finite and Infinite Sets
1.4 Equal Sets
1.5 Subsets
1.6 Power Set
1.7 Universal Set
1.8 Venn Diagrams
1.9 Operations on Sets
1.10 Complement of a Set
The theory of sets was developed by German mathematician Georg Cantor (1845-1918). He first encountered sets while working on “problems on trigonometric series”.
A set is a well define collection of object.
Greek symbol ∈ (epsilon) is used to denote the phrase ‘belongs to’.
If ‘a’ is an element of a set A, we write a A.
If ‘b’ is not an element of a set A, we write b A and read “b does not belong to A”.
There are two methods we used to represents a set
a. Roaster or Tabular form: We use commas to separate elements of sets within braces { } without repainting elements. The order of listing elements has no relevance.
For example, the set of all even positive integers less than 5 is described in roster form as {2, 4,}.
b. Set builder form: We use this form if all the elements of a set possess a single common property which is not possessed by any element outside the set.
Example: V = {x : x is a vowel in English alphabet}
V is read as “the set of all x such that x is a vowel of the English alphabet”. In this description the braces stand for “the set of all”, the colon stands for “such that”.

The set of all natural numbers which divide 42 is written as   A= {x : x is a natural number which divides 42}
Q. Write the set {x: x is a positive integer and x2 < 40} in the roster form.
Solution:  x2 < 40 here,  x = 1, 2, 3, 4, 5, 6.(Whose square is less than 40 )
x  = {1, 2, 3, 4, 5, 6)
Q. Write the set A = {1, 4, 9, 16, 25…} in set-builder form
Ans: 1, 4, 9, 16, 25… are square of 1, 2, 3, 4, 5… respectively. Or Square of natural number
A = {x: x is the square of a natural number}
                               Or,
A = { x : x = n2  , Where n N}
Q. Write the set {1/2 ,  2/3, ¾, 4/5, 5/6, 6/7 }  in the set-builder form
Solution We see that each member in the given set has the denominator one  more than  the numerator
Also, the numerators begin from 1 and do not exceed 6.
{x : x = n/n+1 where is a natural number and 1£ n£6}

Finite and Infinite set
Let us see new set: B = { x : x is a student presently studying in both Classes X and XI }
We observe that a student cannot study simultaneously in both Classes X and XI. Thus, the set B contains no element at all. Such type of set is called Empty Set.
A set which does not contain any element is called the empty set or the null set or the void set.  The empty set is denoted by the symbol φ or { }
Let us see another new set 
A = {men living presently in your town}
here we do not know the numbers of element of this set
B= A = {1, 2, 3, 4, 5}
This set has a definite number of elements
Such type of sets ate called Infinite and Finite respectively.
Hence, A set which is empty or consists of a definite number of elements is called finite otherwise, the set is called infinite.
Note : All infinite sets cannot be described in the roster form. For example, the set of real numbers cannot be described in this form, because the elements of this set do not follow any particular pattern.
Q. State which of the following sets are finite or infinite:
(i) {x : x N and (x – 1) (x –2) = 0}
(ii) {x : x N and x2 = 4}
(iii) {x : x N and 2x –1 = 0}
(iv) {x : x N and x is prime}
(v) {x : x N and x is odd}
Solution (i) Given set = {1, 2}. Hence, it is finite.
(ii) Given set = {2}. Hence, it is finite.
(iii) Given set = φ. Hence, it is finite.
(iv) The given set is the set of all prime numbers and since set of prime numbers is infinite. Hence the given set is infinite
(v) Since there are infinite numbers of odd numbers, hence, the given set is infinite.
Equal Sets
Two set A and B are said to be equal if they have exactly the same elements and we
Q. write A = B. Otherwise, the sets are said to be unequal
Q. Find the pairs of equal sets, if any, give reasons:
A = {0}, B = {x : x > 15 and x < 5},
C = {x : x – 5 = 0 }, D = {x: x2 = 25},
E = {x : x is an integral positive root of the equation x2 – 2x –15 = 0}.
Solution:  Since 0 A and 0 does not belong to any of the sets B, C, D and E, it follows that, A ≠ B, A ≠ C, A ≠ D, A ≠ E.
Since B = φ but none of the other sets are empty. Therefore B ≠ C, B ≠ D and B ≠ E. Also C = {5} but –5 D, hence C ≠ D.
Since E = {5}, C = E. Further, D = {–5, 5} and E = {5}, we find that, D ≠ E. 
Thus, the only pair of equal sets is C and E.
Subsets
Consider the sets : X = set of all students in your school, Y = set of all students in your
class.
We note that every element of Y is also an element of X; we say that Y is a subset  of X. The fact that Y is subset of X is expressed in symbols as Y X. The symbol stands for ‘is a subset of’ or ‘is contained in’.
Definition 4 A set A is said to be a subset of a set B if every element of A is also an element of B
Class 11th and 12th Study materials

Tuesday 18 December 2012

8th Construction of Quadrilaterals CBSE Guess Paper

Chapter: Practical Geometry
Q.1 Construct a quadrilateral ABCD in which AB = 4.4 cm, BC = 4 cm, CD = 6.4 cm, DA = 3.8 cm and BD = 6.6 cm
Q.2 Construct a parallelogram PQRS such that PQ = 5.2 cm, PR = 6.8 cm and QS = 8.2 cm
Q.3 Construct a rhombus with side 6 cm and one diagonal 8 cm. Measure the other diagonal.
Q.4 Construct if possible a quadrilateral ABCD give AB = 6cm, BC = 3.7 cm, CD =5.7cm, AD = 5.5 cm and BD = 6.1 cm. If not possible then give reasons for not able to construct it.
Q.5 Construct a quadrilateral ABCD in which AB = 3.8 cm, BC = 3cm, AD = 2.3 cm, AC = 4.5 cm and BD = 3.8 cm
Q.6 Construct a quadrilateral PQRS in which QR = 4cm, RP = 5.6 cm, PS = 4.5 cm, RS = 5cm and QS = 6.5 cm.
Q.7 Construct a quadrilateral ABCD in which AB = 6 cm, BC = 4cm, CD = 4cm, <B= 95=, and <C = 900
Q.8 Construct a quadrilateral STUV where ST = 4.2 cm, TU = 3.6 cm, UV = 4.8 cm,
<T = 30= and <U = 1500
Q.9 Construct a quadrilateral ABCD in which AB = BC = 3cm, AD = 5cm , <A = 900
and < B = 1050
Q.10 Construct a quadrilateral BDEF where DE = 4.5 cm, EF = 3.5cm, FB = 6.5cm,
< F = 50= and < E = 1000

9th Construction of Triangle CBSE Guess Paper


Section - A
Q.1 With a ruler and compass which of the following angles cannot be constructed?
(a) 600 (b) 800 (c) 900 1050
Q.2 With a ruler and compass which of the following angles can be constructed?
(a) 800 (b) 900 (c) 1000 1100
Section - B
Q.3 Construct an angle of 450 at the initial point of a given ray and justify the construction.
Q.4 Construct the following angles and verify by measuring them by a protractor.
(i) 750 (ii) 1350
Section - C
Q.5 Construct Triangle PQR with base QR = 3.8 cm and <Q=750 and PQ + PR = 7.9cm
Q.6 Construct a with base Triangle PQ R  a with base QR = 3.4 cm and <R=750 and PQ - PR = 1.2cm
Q.7 Construct an equilateral triangle with sides 4cm.
Section -D
Q.8 Construct a triangle ABC in which and  < B = 600 and <C = 450 and  AB+BC+CA = 13 cm.
Q.9 Construct a right triangle whose base is 12cm and sum of its hypotenuse and other side is 18cm.
Q.10 Construct a with its perimeter = 11cm and the base angles of 750 and 300.
Answers:
Q.1 b Q.2 b
For more help Visit : JSUNIL TUTORIAL

Saturday 15 December 2012

8th(VIII)CBSE Chapter: Practical Geometry

Chapter: Practical Geometry:Constrtucton of Quadrilaterals
Q.1 Construct a quadrilateral ABCD in which AB = 4.4 cm, BC = 4 cm, CD = 6.4 cm, DA = 3.8 cm and BD = 6.6 cm
Q.2 Construct a parallelogram PQRS such that PQ = 5.2 cm, PR = 6.8 cm and QS = 8.2 cm
Q.3 Construct a rhombus with side 6 cm and one diagonal 8 cm. Measure the other diagonal.
Q.4 Construct if possible a quadrilateral ABCD give AB = 6cm, BC = 3.7 cm, CD =5.7cm, AD = 5.5 cm and BD = 6.1 cm. If not possible then give reasons for not able to construct it.
Q.5 Construct a quadrilateral ABCD in which AB = 3.8 cm, BC = 3cm, AD = 2.3 cm, AC = 4.5 cm and BD = 3.8 cm
Q.6 Construct a quadrilateral PQRS in which QR = 4cm, RP = 5.6 cm, PS = 4.5 cm, RS = 5cm and QS = 6.5 cm.
Q.7 Construct a quadrilateral ABCD in which AB = 6 cm, BC = 4cm, CD = 4cm, <B= 95=, and <C = 900
Q.8 Construct a quadrilateral STUV where ST = 4.2 cm, TU = 3.6 cm, UV = 4.8 cm,
<T = 30= and <U = 1500
Q.9 Construct a quadrilateral ABCD in which AB = BC = 3cm, AD = 5cm , <A = 900
and < B = 1050
Q.10 Construct a quadrilateral BDEF where DE = 4.5 cm, EF = 3.5cm, FB = 6.5cm,
< F = 50= and < E = 1000

Saturday 8 December 2012

8th CBSE Maths Sample Questions


1. Number by which 19602 be divided, So that the quotient is a perfect square is
(a) 2 (b) 9 (c) 3 (d) 4
Sol: (a)
2. If x + 1/x = 4, then the value of x2+1/x is
(a) 12 (b) 16   (c) 14 (d) 20
Sol: (c)
3. The sum of the powers of the prime factors in 108  192 is
(a) 5 (b) 7 (c) 8 (d) 12
Sol: (d)
4. The factors of x4 + y4 +x2y2 are
(a) (x2 + y2)(x2 + y2 - xy) (b) (x2 + y2)(x2 - y2)
(c) (x2 + y2 + xy)(x2 + y2 -xy) (d) Factorization is not possible
Sol: (c)
5. A square of maximum size is inscribed in a circle with centre O and radius r. Find area excluding area of square?
(a) r2 (p - 2)          (b) 2r2 (2 - p )  (c) p (r2 - 2)     (d) 8r2 – 8r
Sol: (a)
6. A is the father of C and D is the son of B.E is the brother of A. If C is the sister of D, how is B related to E?
(a) Daughter (b) Brother-in-law (c) Husband (d) Sister-in-law
Sol:(d)
7. The perimeter of a square is twice the perimeter of a circle and their areas are AS and AC respectively then
(a) AS> AC (b) AC > AS   (c) AS = 2AC (d) AS = AC
Sol: (a)
8. Two poles, 15 m and 30m height, stand upright in a playground. If their feet be 36m  apart. The distance between their tops is :
(a) 21 m (b) 39 m   (c) 41 m (d) 36m
Sol: (b)
9. A  44m x 11m sheet is rolled along length to form a cylinder.  Find the volume of the cylinder
(a) 773 m3   (b) 773.5 m3   (c) 775.3 m3   (d) 753.5 m3  
Sol: (b)
10.If in a quadrilateral, diagonals are equal, then it cannot be a :
(A) Square (B) Parallelogram (C) Rhombus (D) Rectangle
Sol: (c) 

Friday 7 December 2012

Class: X Subject: Mathematics Assignment: 2013 Chapter: Probability.


Picture


1. 17 cards numbered 1, 2, 3 …, 16, 17 are put in a box and mixed thoroughly. One person draws a card from the box. Find the probability that the number on the card is:
(i) Odd  (ii) Even  (iii) a Prime (iv) Divisible by 3  (v) Divisible by 3 and 2 both.

2. Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another. What is probability that both will visit the shop on      
(i) same day    (ii) different days?

3. Three coins are tossed once. Find the probability of:  (i) 3 heads   (ii) Exactly 2 heads   (iii) At least 2 heads

4. Cards marked with numbers 3 to 152 are thoroughly mixed. If one card is drawn at random, find the probability that the number on the card is: -
(i) An odd number (ii) A number less than 25  (iii) A number greater than 140    (iv) A number which is a perfect number  (v) A prime number between 10 and 40.

5. In a class, there are 18 girls & 16 boys. The class teacher wants to choose 1 pupil for class monitor. She writes the name of each pupil on a card & puts them into a basket & mixes thoroughly.
A child is asked to pick up one card from the basket. What is the probability that name written on the card is:-  (i) the name of a girl (ii) the name of a boy.

6. 1500 families with 2 children were selected randomly, and the following data were recorded:
Compute the probability of a family chosen at random, having: -
(i) 2 girls (ii)1girl (iii) no girl  Also check whether the sum of these probabilities is 1.

7. Find the Probability of getting 53 Sundays in a leap year.

8. Find the probability of getting 53 Sundays in a non-leap year.

9. A dice is thrown twice. What is the Probability of 
 (i) 5 will not come up either time?
(ii) 5 will come up at least once?   [Hint: throwing a dice twice and throwing two dice simultaneously are treated as the same  experiment.]

10.Two dice are thrown. Determine Probability of getting a multiple of 2 on the first dice and a multiple of 3 on the other.

11.Two dice are thrown simultaneously. Find the Probability of getting: - 
(i) A total of 2 (ii) A sum of 7 (iii) A sum of 6        (iv) A sum of 8 (v) Doublets of even numbers.
Number of girls in family:          2            1                         0
Number of families:                475         814                    211

12.There are 840 tickets sold in a raffle. Bhawna bought 5 tickets and Shilpy bought 4 tickets.
What is Probability that           
(a) Bhawna has a winning ticket? (b) Shilpy has a winning ticket?

13.A card is drawn from an ordinary pack and gambler bets that it is a spade or ace. What are odds against his winning the bet?

14.Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday) each is equally to visit the shop on any day as on another day. What is the Probability that both will visit the shop on :-          
(i) Same day  (ii) Consecutive days (iii) Different days.

15. Two dice are thrown simultaneously. List the sample space for this experiment.

16.In a single throw of 2 dices find the probability of getting:-
 (a) A total of 7 (ii) A total of 11 (iii) Doublets (iv)  Six as a product.

17.A box contains 19 balls bearing numbers 1, 2… 19. A ball is drawn at random from the box. What is Probability that number of the ball is:-
(i) a prime number 
(ii) divisible by 3 or 5          
(iii) neither divisible by 5 nor 10      
(iv)an even number

18.From a pack of 52 playing cards, jacks, queens, kings and aces of red colour are removed. From the remaining cards one card is drawn. Find the Probability that the card drawn is:
 (a) A black queen (b) A red card (c) A jack  (d) A diamond (e) A black card. 

10th Surface area and volume practice paper for CBSE Exam

1.Lead spheres of diameter 6cm are dropped into a cylindrical beaker containing some water and are completely submerged. If the diameter is 18cm and the water rises by 40cm, find the number of lead spheres dropped in the  water.                (Ans = 90)                                                                                                                   

2. A circus tent is cylindrical to a height of 3m and conical above it. If its diameter is 105m and the slant height of the conical portion is 53m, calculate the length of the canvas cloth 5m wide required to make the tent.(Ans = 1947m)

3.  A cone, a hemi-sphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes as well the ratio of their total surface areas  (Ans = 1:2:3, (√2 + 1):3:4)

4.  A cone of radius 10cm is divided into two parts by drawing a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of the two parts of the cone (Ans = 1:7)

5. A building is in the shape of a cylinder surmounted by a hemi-spherical vaulted dome. The internal diameter of the building is equal to the total height of the building. If the volume of air space inside the building is 880/21 m3, find the height of the crown of the vault above the floor.             (Ans = 4m)

6. An inverted cone of vertical height 12cm and radius of the base 9cm has water to a depth of 4cm. Find the area of the internal surface of the cone not in contact with water.    (Ans = 376.8cm2)

7. The mass of a spherical iron shot-put 12cm in diameter is 5kg. Find the mass of a hollowcylindrical pipe 12cm long (made of the same metal), if it’s internal and external diameters are 20cm and 22cm, respectively.                                    (Ans = 4.375kg)

For full paper: 
MATH ADDA By Guru:JSUNIL": 10th Surface area and volume practice paper for CB...: 1. A solid iron rectangular block of dimensions 4.4 m, 2.6m, and 1m is cast into a hollow cylindrical pipe of internal radius 30cm and t...

Tuesday 4 December 2012

8th Math Probability CBSE Test Paper

CBSE ADDA: 8th Math Probability CBSE Test Paper:
Work sheet: Subject – Maths, Class – VIII- Chapter:  Probability 1. A coin is tossed twice. Find the probability of getting both tails?...Read Full Post :

You may also like : Probability Test Paper Solved

Direct and Inverse Proportions -NCERT Class VIII Maths Test Paper

1. 68 boxes of contain commodity require a shelf- length of 13.6 m. How many boxes of the same commodity would occupy a shelf- length of 20.4 m?
2. 11 men can dig 6 and 3/4  m long trench in one day. How many men should be employed for digging 27m long trench of the same type in one day?
3. 120 men had food provisions for 200 days. After 5 days, 30 men die due to an epidemic. How long will the remaining food last?
4. A car can finish a certain journey in 10 hours at the speed of 48km/hr. By how much should  its speed be increased so that it may take only 8 hours to cover the same distance?
5. In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel, how long will these provisions last?    
6. A worker is paid Rs.210 for 6 days work. If his total income of the month is Rs. 875, for how many did he work? 
7. A train 400m long is running at a speed of 72km/hr. How much time does it take to cross a telegraph post?
8. A train 360m long is running at a speed of 45 km/hr. What time will it take to cross a 140m long bridge?
9.A  train 210m long took 12 seconds to pass a 90 m long tunnel. Find the speed of the train.
10. If 5 men or 7 women can earn Rs 875 per day, how much would 10 men and 5women earn per day.
11. The cost of 16packets of salt, each weighing 900 g, is Rs 84. Find the cost of 27packets of salt, each weighing 1kg.
11. If 3persons can weave 168 shawls in 14 days, how many shawls will be woven by 8 persons in 5d ays?
12. If the cost of transporting 160kgof goods for 125kmis Rs60. What will be the cost of transporting 200kg of goods for 400km?
13. 6oxen or 8cows can graze a field in 28days. How long would 9oxen and 2cows take to graze the same field?
14. 6 men working 8 hours a day, earn Rs 8400per week. What will be the earning per week of 9men who work for 6hoursa day?
15. A fort had provision for 300men for 90days. After 20days, 50men left the fort. How long would the food last at the same rate?