OMTEX CLASSES

ALGEBRA SSC

ARITHMETIC PROGRESSION

EX. NO. 1.1

1. For each of the sequence, find the next four terms.

(i) 1, 2, 4, 7, 11, ..... (1 mark)

(ii) 3, 9, 27, 81, ..... (1 mark)

(iii) 1, 3, 7, 15, 31, .... (1 mark)

(iv) 192, – 96, 48, – 24, .... (1 mark)

(vi) 0.1, 0.01, 0.001, 0.0001, .... (1 mark)

(vii) 2, 5, 8, 11, .... (1 mark)

(viii) – 25, – 23, – 21, – 19, ..... (1 mark)

(ix) 2, 4, 8, 16, ...

(x) 1/2, 1/6, 1/18, 1/54

2. Find the first five terms of the following sequences, whose nth terms are given.

(i) tn = 4n – 3 (1 mark)

(ii) tn = 2n – 5 (1 mark)

(iii) tn = n + 2 (1 mark)

(iv) tn = n2 – 2n (1 mark)

(v) tn = n3 (1 mark)

(vi) tn = 1/(n+1)

3. Find the first three terms of the sequences for which Sn is given below:

(i) Sn = n2(n + 1) (2 marks)

(ii) Sn = [n2(n+1)

2]/4 (2 marks)

(iii) Sn = [n(n+1)(2n+1)]/6 (2 marks)

EXERCISE - 1.2

1. Which of the following lists of numbers are Arithmetic Progressions? Justify.

(i) 1, 3, 6, 10, ..... (1 mark)

(ii) 3, 5, 7, 9, 11, ..... (1 mark)

(iii) 1, 4, 7, 10, .... (1 mark)

(iv) 3, 6, 12, 24, .... (1 mark)

(v) 22, 26, 28, 31, ... (1 mark)

(vi) 0.5, 2, 3.5, 5, ... (1 mark)

(vii) 4, 3, 2, 1, .... (1 mark)

(viii) – 10, – 13, – 16,– 19, ..... (1 mark)

2. Write the first five terms of the following Arithmetic Progressions where, the common difference ‘d’ and

the first term ‘a’ are given :

(i) a = 2, d = 2.5 (1mark)

(ii) a = 10, d = – 3 (1mark)

(iii) a = 4, d = 0 (1mark)

(iv) a = 5, d = 2 (1mark)

(v) a = 3, d = 4 (1mark)

(vi) a = 6, d = 6 (1mark)

EXERCISE - 1.3

1. Findthe twenty fifth term of the A. P. : 12, 16, 20, 24, .....

2. Findthe eighteenth term of the A. P. : 1, 7, 13, 19, .....

3. Find tn for an Arithmetic Progression where t3 = 22, t17 = – 20.

4. Foran A. P. if t4 = 12, and d = – 10, then find its general term.

5. Given the following sequence, determine whether it is arithmetic or not. If itis an Arithmetic Progression,

find its general term : – 5, 2, 9, 16, 23, 30,.....

6. Given the following sequence, determine if it is arithmetic or not. If it is anArithmetic Progression, find its

general term. 5, 2, – 2, – 6, – 11, .....

7. How many three digit natural numbers are divisible by 4 ?

8. The 11th term and the 21st term of an A.P. are 16 and 29 respectively, find :

(i) the 1st term and the common difference.

(ii) the 34th term

(iii) ‘n’ such that tn = 55.

EXERCISE - 1.4 1. Findthe sum of the first n natural numbers and hence find the sum of first 20natural numbers.

2. Find the sum of allodd natural numbers from 1 to 150.

3. Find S10 if a = 6 andd = 3.

4. Find the sum of allnumbers from 1 to 140 which are divisible by 4.

5. Find the sum of the first n odd natural numbers.

Hence find 1 + 3 + 5 +... + 101.

6. Obtain the sum of the56 terms of an A. P. whose 19th and 38th terms are 52 and 148 respectively.

7. The sum of the first55 terms of an A. P. is 3300. Find the 28th term.

8. Find the sum of thefirst n even natural numbers. Hence find the sum of first 20 even naturalnumbers.

Ex. No. 1.5

1. Find four consecutive terms in an A.P. whose sum is 12 and the sum of 3rd and 4th term is 14.

2. Find four consecutiveterms in an A.P. whose sum is –54 and the sum of 1st and 3rd term is – 30.

3. Find three consecutive terms in an A.P. whose sum is – 3 and the product of their cubes is 512.

4. In winter, the temperature at a hill station from Monday to Friday is in A.P. The sum of the temperatures

of Monday, Tuesday and Wednesday is zero and the sum of the temperatures of Thursday and Friday is 15.

Find the temperature of each of the five days.

Ex. No. 1.6

1. Mary got a job with a starting salary of Rs. 15000/- per month. She will get an incentive of Rs. 100/- per

month. What will be her salary after 20 months? [Ans.]

2. The taxi fare is Rs. 14 for the first kilometer and Rs. 2 for each additional kilometer. What will be fare for

10 kilometers ? [Ans.]

3. Mangala started doing physical exercise 10 minutes for the first day. She will increase the time of exercise

by 5 minutes per day, till she reaches 45 minutes. How many days are required to reach 45 minutes? [Ans.]

4. There is an auditorium with 35 rows of seats. There are 20 seats in the first row, 22 seats in the second row,

24 seats in the third row, and so on. Find the number of seats in the twenty fifth row. [Ans.]

5. A village has 4000 literate people in the year 2010 and this number increases by 400 per year. How many

literate people will be there till the year 2020 ? Find a formula to know the number of literate people after n

years ? [Ans.]

6. Neela saves in a ‘Mahila Bachat gat’ Rs. 2 on the first day, Rs.4 on the second day, Rs. 6 on the third day

and so on. What will be her saving in the month of February 2010 ? [Ans.]

7. Babubhai borrows Rs. 4000 and agrees to repay with a total interest of Rs. 500. in 10 instalments, each

instalment being less that the preceding instalment by Rs. 10. What should be the first and the last

instalment? [Ans.]

8. A meeting hall has 20 seats in the first row, 24 seats in the second row, 28 seats in the third row, and so on

and has in all 30 rows. How many seats are there in the meeting hall ? [Ans.]

9. Vijay invests some amount in National saving certificate. For the 1st year he invests Rs. 500, for the 2nd

year he invests Rs. 700, for the 3rd year he invests Rs. 900, and so on. How much amount he has invested in

12 years ? [Ans.]

10. In a school, a plantation program was arranged on the occasion of world environment day, on a ground of

triangular shape. The trees are to be planted as shown in the figure. One plant in the first row, two in the

second row, three in the third row and so on. If there are 25 rows then find the total number of plants to be

planted. [Ans.]

QUADRATIC EQUATIONS

EXERCISE - 2.1

1. Which of the following are quadratic equations ?

(i) 11 = – 4x2 – x

3 [Ans.]

(ii) -¾ y2 = 2y + 7 [Ans.]

(iii) (y – 2) (y + 2) = 0 [Ans.]

(iv) 3/y – 4 = y [Ans.]

(v) m3 + m + 2 = 4m [Ans.]

(vi) n – 3 = 4n [Ans.]

(vii) y2 – 4 = 11y [Ans.]

(viii) z – 7/z = 4z + 5 [Ans.]

(ix) 3y2 – 7 = √3 y [Ans.]

(x) (q2 – 4)

/q2 = - 3 [Ans.]

2. Write the following quadratic equations in standard form ax2 + bx + c = 0

(i) 7 – 4x –x2 = 0 [Ans]

(ii) 3y2 = 10y + 7 [Ans]

(iii) (m + 4) (m – 10) = 0 [Ans]

(iv) p(p – 6) = 0 [Ans]

(v) (x2/25) – 4 = 0 [Ans]

(vi) n – (7/n) = 4 [Ans]

(vii) y2 – 9 = 13y [Ans]

(viii) 2z – (5/z) = z – 6 [Ans]

(ix) x2 = –7 – √10 x [Ans]

(x) (m2 +5)/m

2 = –3 [Ans]

EXERCISE - 2.2

1. In each of the examples given below determine whether the values given against each of the quadratic

equation are the roots of the equation or not.

(i) x2 + 3x – 4 = 0, x = 1, –2, – 3 [Ans]

(ii) 4m2 – 9 = 0, m = 2, 2/3, 3/2 [Ans]

(iii) x2 + 5x – 14 = 0, x = √2 , –7, 3 [Ans]

(iv) 2p2 + 5p – 3 = 0, p = 1, ½, –3 [Ans]

(v) n2 + 4n = 0, n = 0, – 2, – 4 [Ans]

2. If one root of the quadratic equation x2 – 7x + k = 0 is 4, then find the value of k. [Ans]

3. If one root of the quadratic equation 3y2 – ky + 8 = 0 is 2/3, then find the value of k. [Ans]

4. State whether k is the root of the given equation y2 – (k – 4)y – 4k = 0. [Ans]

5. If one root of the quadratic equation kx2 – 7x + 12 = 0 is 3, then find the value of k. [Ans]

EXERCISE - 2.3

Solve the following quadratic equations by

factorization method..

(i) x2 – 5x + 6 = 0 [Ans.]

(ii) x2 + 10x + 24 = 0 [Ans.]

(iii) x2 – 13x – 30 = 0 [Ans.]

(iv) x2 – 17x + 60 = 0 [Ans.]

(v). m2 – 84 = 0 [Ans.]

(vi) x + 20

/x – 12 = 0 [Ans.]

(vii) x2 = 2(11x – 48) [Ans.]

(viii) 21x = 196 – x2

[Ans.]

(x) x2 – x – 132 = 0 [Ans.]

(xi) 5x2 – 22x – 15 = 0 [Ans.]

(xii) 3x2 – x – 10 = 0 [Ans.]

(xiii) 2x2 – 5x – 3 = 0 [Ans]

(xiv) x (2x + 3) = 35 [Ans.]

(xv) 7x2 + 4x – 20 = 0 [Ans]

(xvi) 10x2 + 3x – 4 = 0 [Ans.]

(xvii) 6x2 – 7x – 13 = 0 [Ans.]

(xviii) 3x2 + 34x + 11 = 0 [Ans.]

(xix) 3x2 – 11x + 6 = 0 [Ans.]

(xx) 3x2 – 10x + 8 = 0 [Ans.]

(xxi) 2m2 + 19m + 30 = 0 [Ans.]

(xxii) 7m2 – 84 = 0 [Ans.]

(xxiii) x2 – 3√3 x + 6 = 0 [Ans.]

EXERCISE - 2.4

Solve the following quadratic equations by completing square.

(i) x2 + 8x + 9 = 0 [Ans]

(ii) z2 + 6z – 8 = 0 [Ans]

(iii) m2 – 3m – 1 = 0 [Ans]

(iv) y2 = 3 + 4y [Ans]

(v) p2 – 12p + 32 = 0 [Ans]

(vi) x (x – 1) = 1 [Ans]

(vii) 3y2 + 7y + 1 = 0 [Ans]

(viii) 4p2 + 7 = 12p [Ans]

(ix) 6m2 + m = 2 [Ans]

EXERCISE - 2.5 1. Solve the following quadratic equations by using formula.

(i) m2 – 3m – 10 = 0 [Ans]

(ii) x2 + 3x – 2 = 0 [Ans]

(iii) x2 +

(x – 1)/3 = 0 [Ans]

(iv) 5m2 – 2m = 2 [Ans.]

(v) 7x + 1 = 6x2 [Ans.]

(vi) 2x2 – x – 4 = 0 [Ans.]

(vii) 3y2 + 7y + 4 = 0 [Ans.]

(viii) 2n2 + 5n + 2 = 0 [Ans.]

(ix) 7p2 – 5p – 2 = 0 [Ans.]

(x) 9s2 – 4 = – 6s [Ans.]

(xi) 3q2 = 2q + 8 [Ans.]

(xii) 4x2 + 7x + 2 = 0 [Ans.]

EXERCISE - 2.6 1. Find the value of discriminant of each of the following equations :

(i) x2 + 4x + 1 = 0 [Ans]

(ii) 3x2 + 2x – 1 = 0 [Ans]

(iii) x2 + x + 1 = 0 [Ans]

(iv) √3 x2 + 2√2 x – 2√3 = 0 [Ans]

(v) 4x2 + kx + 2 = 0 [Ans]

(vi) x2 + 4x + k = 0 [Ans]

2. Determine the nature of the roots of the following equations from their discriminants :

(i) y2 – 4y – 1 = 0 [Ans.]

(ii) y2 + 6y – 2 = 0 [Ans.]

(iii) y2 + 8y + 4 = 0 [Ans.]

(iv) 2y2 + 5y – 3 = 0 [Ans.]

(v) 3y2 + 9y + 4 = 0 [Ans.]

(vi) 2x2 + 5√3 x + 16 = 0 [Ans.]

3. Find the value of k for which given equation has real and equal roots :

(i) (k – 12)x2 + 2 (k – 12)x + 2 = 0 [Ans.]

(ii) k2x

2 – 2 (k – 1)x + 4 = 0 [Ans.]

EXERCISE - 2.7 1. If one root of the quadratic equation kx

2 – 5x + 2 = 0 is 4 times the other, find k. [Ans.]

2. Find k, if the roots of the quadratic equation x2 + kx + 40 = 0 are in the ratio 2 : 5. [Ans.]

3. Find k, if one of the roots of the quadratic equation kx2 – 7x + 12 = 0 is 3. [Ans.]

4. If the roots of the equation x2 + px + q = 0 differ by 1, prove that p

2 = 1 + 4q. [Ans.]

5. Find k, if the sum of the roots of the quadratic equation 4x2 + 8kx + k + 9 = 0 is equal to their

product. [Ans.]

6. If α and β are the roots of the equation x2 – 5x + 6 = 0, find[Ans.]

(i) α2+β

2

(ii) α/β +β/α

7. If one root of the quadratic equation kx2 – 20x + 34 = 0 is 5 – 2√2 , find k. [Ans.]

EXERCISE - 2.8

1. Form the quadratic equation if its roots are

(i) 5 and – 7 [Ans.]

(ii) ½ and – ¾ [Ans.]

(iii) - 3 and –11 [Ans.]

(iv) -2 and 11/2 [Ans.]

(v) ½ and – ½ [Ans.]

(vi) 0 and – 4 [Ans.]

2. Form the quadratic equation if one of the root is

(i) 3 – 2√ 5 [Ans.]

(ii) 4 – 3√ 2 [Ans.]

(iii) √ 2 + √3 [Ans.]

(iv) 2√3 – 4 [Ans.]

(v) 2+√5 [Ans.]

(vi) √ 5 - √3 [Ans.]

3. If the sum of the roots of the quadratic is 3 and sum of their cubes is 63, find the quadratic equation. [Ans.]

4. If the difference of the roots of the quadratic equation is 5 and the difference of their cubes is 215, find the

quadratic equation.[Ans.]

EXERCISE - 2.9

Solve the following equations.

(i) x4 – 3x

2 + 2 = 0 [Ans.]

(ii) (x2 + 2x) (x

2 + 2x – 11) + 24 = 0 [Ans.]

(iii) 2(x2 +

1/x

2 ) – 9(x+

1/x) + 14 = 0 [Ans.]

(iv) 35y2 +

12/y

2 = 44 [Ans.]

(v) x2 +

12/x

2 = 7 [Ans.]

(vi) (x2 + x) (x

2 + x – 7) + 10 = 0 [Ans.]

(vii) 3x4 – 13x

2 + 10 = 0 [Ans.]

(viii) 2y2 +

15/y

2 = 12 [Ans.]

EXERCISE - 2.10 1. The sum of the squares of two consecutive natural numbers is 113. Find the numbers. [Ans]

2. Tinu is younger than Pinky by three years. The product of their ages is 180. Find their ages.[Ans]

3. The length of the rectangle is greater than its breadth by 2 cm. The area of the rectangle is 24 sq.cm, find

its length and breadth.[Ans]

4. The sum of the squares of two consecutive even natural numbers is 100. Find the numbers. [Ans]

5. A natural number is greater than twice its square root by 3. Find the number. [Ans]

6. The sum of a natural number and its reciprocal is 10

/3 . Find the number. [Ans]

7. The sum of the ages of father and his son is 42 years. The product of their ages is 185, find their ages. [Ans]

8. Three times the square of a natural numbers is 363. Find the numbers. [Ans]

9. The length of one diagonal of a rhombus is less than the second diagonal by 4 cm. The area of the rhombus

is 30 sq.cm. Find the length of the diagonals. [Ans]

10. A natural number is greater than the other by 5. The sum of their squares is 73. Find those

numbers. [Ans]

11. The sum ‘S’ of the first ‘n’ natural numbers is given by S = n (n + 1)

/2 . Find ‘n’, if the sum (S) is 276. [Ans]

12. A rectangular playground is 420 sq.m. If its length is increases by 7 m and breadth is decreased by 5

metres, the area remains the same. Find the length and breadth of the playground ? [Ans]

13. The cost of bananas is increased by Re. 1 per dozen, one can get 2 dozen less for Rs. 840. Find the original

cost of one dozen of banana. [Ans]

LINEAR EQUATIONS IN TWO VARIABLES

EX. NO. 3.1

1. Solve the following simultaneous equations using graphical method :

(i) x + y = 8, x – y = 2 [Ans.]

(ii) 3x + 4y + 5 = 0; y = x + 4 [Ans.]

(iii) 4x = y – 5; y = 2x + 1 [Ans.]

(iv) x + 2y = 5; y = – 2x – 2 [Ans.]

(v) 2x + y = 6; 4 – 3x

/4 = y [Ans.]

EX. NO. 3.2

1. Find the value of the following determinants:

i. 5 2

7 4

[Ans]

ii. -3 8

6 0

[Ans]

iii. 1.2 0.03

0.57 -0.23

[Ans]

iv. 3√6 -4√2

5√3 2

[Ans]

v. -4/7 -6/35

5 -2/5

[Ans]

2. Solve the following simultaneous equations using Cramer’s rule :

(i) 3x – y = 7; x + 4y = 11 [Ans.]

(ii) 4x + 3y – 4 = 0; 6x = 8 – 5y [Ans.]

(iii). y = (5x – 10)

/2 ; 4x + 5 = - y [Ans.]

(iv) 3x + 2y + 11 = 0; 7x – 4y = 9 [Ans.]

(v) x + 18 = 2y; y = 2x – 9 [Ans.]

(vi) 3x + y = 1; 2x = 11y + 3 [Ans.]

EX. NO. 3.3

1. Without actually solving the simultaneous equations given below, decide which simultaneous equations

have unique solution, no solution or infinitely many solutions.

(i) 3x + 5y = 16; 4x – y = 6 [Ans.]

(ii) 3y = 2 – x; 3x = 6 – 9y [Ans.]

(iii) 3x – 7y = 15; 6x = 14y + 10 [Ans.]

(iv) 8y = x – 10; 2x = 3y + 7 [Ans.]

(v) (x – 2y)/3 = 1; 2x – 4y = 9/2 [Ans.]

(vi) x/2 + y/3 = 4; x/4 + y/6 = 2 [Ans.]

2. Find the value of k for which the given simultaneous equations have infinitely many solutions :

(i) 4x + y = 7; 16x + ky = 28 [Ans.]

(ii) 4y = kx – 10; 3x = 2y + 5 [Ans.]

3. Find the value of k for which are given simultaneous equations have infinitely many solutions :

(i) kx + y = k – 2; 9x + ky = k [Ans.]

(ii) kx – y + 3 – k = 0; 4x – ky + k = 0 [Ans.]

4. Find the value of p for which the given simultaneous equations have unique solution :

(i) 3x + y = 10; 9x + py = 23 [Ans.]

(ii) 8x – py + 7 = 0; 4x – 2y + 3 = 0 [Ans.]

EX. NO. 3.4 Q. Solve the following simultaneous equations.

(i) 1/x + 1/y = 8;; 4/x – 2/y = 2

(ii) 2/x + 6/y = 13; 3/x + 4/y = 12

(iii) 1/3x + 1/5y = 1/15; 1/2x + 1/3y = 1/12

Probability

EXERCISE - 4.1

1. In a each of the following experiments write the sample space S, number of sample points n (S), events P,

Q, R using set and n (P), n (Q) and n (R). Find the events among the events defined above which are :

complementary events, mutually exclusive events and exhaustive events.

(i) Three coins are tossed simultaneously :

P is the event of getting at least two heads.

Q is the event of getting no head.

R is the event of getting head on second coin. [Ans.]

(ii) A die is thrown :

P is the event of getting an odd number.

Q is the event of getting an even number.

R is the event of getting a prime number. [Ans.]

(iii) Two dice are thrown :

P is the event that the sum of the scores on the uppermost faces is a multiple of 6.

Q is the event that the sum of the scores on the uppermost faces is at least 10.

R is the event that same score on both dice. [Ans.]

(iv) There are 3 red, 3 white and 3 green balls in a bag. One ball is drawn at random from a bag :

P is the event that ball is red.

Q is the event that ball is not green.

R is the event that ball is red or white. [Ans.]

(v) Form two digit numbers using the digits 0, 1, 2, 3, 4, 5 without repeating the digits.

P is the event that the number so formed is even.

Q is the event that the number so formed is divisible by 3.

R is the event that the number so formed is greater than 50.[Ans.]

(vi) A coin is tossed and a die is thrown simultaneously :

P is the event of getting head and a odd number.

Q is the event of getting either H or T and an even number.

R is the event of getting a number on die greater than 7 and a tail. [Ans.]

(vii) There are 3 men and 2 women. A ‘Gramswachaatta Abhiyan’ committee of two is to be formed.

P is the event that the committee should contain at least one woman.

Q is the event that the committee should contain one man and one woman.

R is the event that there is not woman in the committee. [Ans.]

EXERCISE - 4.2

1. If two coins are tossed then find the probability of the events :

(i) at least one tail turns up

(ii) no head turns up

(iii) at the most one tail turns up [Ans.]

2. A coin is tossed three times then find the probability of

(i) getting head on middle coin

(ii) getting exactly one tail

(iii) getting no tail [Ans.]

3. A die is thrown then find the probability of getting

(i) an odd number

(ii) a perfect square

(iii) a number greater than 3 [Ans.]

4. Two dice are thrown find the probability of getting :

(i) The sum of the numbers on their upper faces is divisible by 9.

(ii) The sum of the numbers on their upper faces is at most 3.

(iii) The number on the upper face of the first die is less than the number on the upper face of the second

die. [Ans.]

5. A box contains 20 cards marked with the numbers 1 to 20. One card is drawn from this box. What is the

probability that number on the card is

(i) a prime number

(ii) perfect square

(iii) multiple of 5 [Ans.]

6. Two digit number are formed from the digits 0, 1, 2, 3, 4 where digits are not repeated. Find the

probability of the events that :

(i) the number formed is an even number.

(ii) the number formed is greater than 40.

(iii) the number formed is prime number. [Ans.]

7. There are three boys and two girls. A committee of two is to be formed, find the probability of events that

the committee contains :

(i) at least one girl

(ii) one boy and one girl

(iii) only boys [Ans.]

8. If a card is drawn from a pack of 52 cards. Find the probability of getting:

(i) a black card

(ii) not a black card

(iii) a card bearing number between 2 to 5 including 2 and 5 [Ans.]

9. A card is drawn at random from well shuffled pack of 52 cards. Find the probability that the card drawn is

:

(i) a spade

(ii) not of diamond [Ans.]

STATISTICS ONE

Exercise No. 5.1

1. Below is given distribution of money (in Rs.) collected by students for flood relief fund. Find mean of

money (in Rs. ) collected by a student by 'Direct Method'.

2. Following table gives age distribution of people sufering from 'Asthma due to air pollution in certain city.

Find mean age of persons suffering from 'Asthma' by 'Direct Method'.

3. The measurements (in mm) of the diameters of the head of screws are given below: Calculate mean

diameter of head of a screw of 'Assumed Mean Method'.

4. Below is given frequency distribution of marks (out of 100) obtained by the students. Calculate mean

marks scored by a student by 'Assumed Mean Method'.

5. Following table gives frequency distribution of milk (in litres) given per week by 50 cows. Find average

(mean) amount of milk given by a cow by 'Shift of Origin Method.'

6. Following table given frequency distribution of trees planted by different housing societies in a particular

locality. Find the number of trees planted by housing society by using 'step deviation method'.

7. Following table gives age distribution of people suffering from 'Asthma due to air pollution in certain city.

Find mean by 'Step Deviation method'.

8. The measurements (in mm) of the diameters of the head of screws are given below: Find mean by 'Step

deviation method'.

9. Solve by 'Assumed Mean method. Following table gives frequency distribution of trees planted by different

housing societies in a particular locality;. Find Mean.

10. Solve by 'Step Deviation Method. Below is the frequency distribution of marks (out of 100) obtained by

the students. Find mean.

Exercise No. 5.2

1. Following is the distribution of the size of certain farms from a taluka (tehasil):

2. Below is given distribution of profit in Rs. per day of a shop in certain town: Calculate median profit of a

shop.

3. Following table shows distribution of monthly expenditure (in Rs.) done by households in a certain village

on electricity: Find median expenditure done by a household on electricity per month.

4. The following table shows ages of 300 patients getting medical treatment in a hospital on a particular day.

Find median age of a patient.

Exercise No. 5.3

1. The weight of coffee (in gms) in 70 packets is given below: Determine the modal weight of coffee in a

packet.

2. Forty persons were examined for their Hemoglobin % in blood (in mg per 100 ml) and the results were

grouped as below: Determine modal value of Hemoglobin % in blood of a person.

3. The maximum bowling speed (Kms/hour) of 33 players at a cricket coaching centre is given below.

4. The following table shows frequency distribution of body weight (in gms) of fish in a pond. Find modal

body weight of a fish in a pond.

Exercise No. 5.4

1. For a certain frequency distribution the values of Mean and Mode are 54.6 and 54 respectively. Find the

value of median.

2. For a certain frequency distribution the values of Median and Mode is 95.75 and 95.5 respectively, find the

mean.

3. For a certain frequency distribution the value of Mean is 101 and Median is 100. Find the value of Mode.

STATISTICS PART TWO

Exercise No. 6.1

1. The Following data gives the number of students using different modes of transport:

Mode of transport Bicycle Bus Walk Train Car

Number of Students 140 100 70 40 10

Represent the above data using pie diagram. [Ans]

2. Following is the component wise expenditure per article. Draw a pie diagram. [Ans]

Component Raw Material Labour Transportation Packing Taxes

Expenditure (Rs.) 800 300 100 100 140

3. The area under different crops in a certain village is given below. Represent it by pie diagram: [Ans]

Crop Jowar Wheat Sugar cane Vegetables

Area in hectare 8000 6000 2000 2000

4. Electricity used by farmers during different parts of a day for irrigation is as follows:

Part of a day Morning Afternoon Evening Night

Percentage of electricity used 30 40 20 10

Draw pie diagram. [Ans]

5. The following table gives information about the monetary investment by some residents in a city:

Mode of Investment Shares Mutual funds Real estate Gold Government bonds

Percentage of residents 10 20 35 30 5

Draw a pie diagram to represent the data. [Ans]

6. The following pie diagram represents expenditure on different items in constructing a building. Answer the

following questions : [Ans]

(a) Find the expenditure of each of the items if the total construction cost is Rs. 5,40,000.

(b) Which is the item with the maximum expenditure ?

(c) Which is the item with the minimum expenditure ?

7. The following diagram represents the sectorwise loan amount in crores of Rs. distributed by a bank. From

the information answer the following questions : [Ans]

(a) If the dairy sector received Rs. 20 crores, then find the total loan disbursed.

(b) Find the loan amount for agriculture sector and also for industrial sector.

(c) How much additional amount did industrial sector received than agriculture sector.

8. The following pie diagram shows percentage of persons according to blood group. Answer the following

questions :

(a) Find the measure of central angle for each blood group.

(b) Find total number of persons if there are 600 persons of blood group B. [Ans]

Exercise No. 6.2

1. Draw the histogram to represent the following data. [Ans.]

Daily sales of a store (in Rs. ) 0 – 1000 1000 – 2000 2000 – 3000 3000 – 4000 4000 – 5000 Total

No. of days in a month 2 12 10 4 2 30

2. Represent the following data using a histogram. [Ans.]

Height of students (cm) 140 – 144 145 – 149 150 – 154 155 – 159

Number of students 2 12 10 4

3. The marks scored by students in mathematics in a certain examination are given below: [Ans.]

Marks scored 1 – 20 21 – 40 41 – 60 61 – 80 81 – 100

Number of students 3 8 19 18 6

4. Draw the histogram for the following frequency distribution:[Ans]

House rent in Rs. per month 4000 – 6000 6000 – 8000 8000 – 10000 10000 – 12000

Number of families 200 240 300 50

5. Represent the following data by histogram and hence compute mode: [Ans]

Price of Sugar per kg (in Rs.) 18 – 20 20 – 22 22 – 24 24 – 26 26 – 28 Total

Number of weeks 4 8 22 12 6 52

Exercise No. 6.3

1. Draw histogram and frequency polygon for the following frequency distribution: [Ans]

Class 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30

Frequency 20 30 50 40 10

2. Represent the following data using frequency curve: [Ans]

Electricity bill in a month

(in Rs.)

200 – 400 400 – 600 600 - 800 800 – 1000

No. of Families 362 490 185 63

3. Folowing is the frequency distribution of customers in a certain year at a departmental store: [Ans]

No. of customers 50 – 100 100 – 150 150 – 200 200 – 250 Total

No. of days. 90 98 138 39 365

Draw histogram and hence draw frequency curve.

4. Represent the following data using histogram and hence draw frequency polygon: [Ans]

No. of words typed per minute 30 – 39 40 – 49 50 – 59 60 – 69 70 – 79

No. of typists 2 8 15 12 3