### Algebra October 2014 Board Paper with Solution

1. Attempt any five sub – questions from the following: 5
(i) Find S2 for the A.P. 3, 5, 7, 9, ……… [Ans. 8]
(ii) If a = 1, b = 8 and c = 15, then find the value of b2 – 4ac.  [Ans. 4]
(iii) Find the width of the class 35 – 45. [Ans. 10]
(iv) By using two variables, write the following statement in mathematical form: The cost of two tables and five chairs is Rs. 2,200. [Ans. 2x + 5y = 2200 ]
(v) If n(A) = 1 and n(S) = 13, then find P(A). [Ans. 1/13]
(vi) For solving the quadratic equation x2 + 8x = - 15 by completing square method, find the third term. [Ans. 16]

2. Attempt any four sub – question from the following: 8
(i) Find the first four terms in an A.P. when a = 10 and d = 3. [Ans. 10, 13, 16, 19]
(ii) Prepare the cumulative frequency (less than type) table from the following distribution table: [Ans. C.F. : 2, 5, 12, 20, 25]
 Class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 Frequency 2 3 7 8 5

(iii) Form the quadratic equation if the roots are 6 and 7. [Ans. x2 – 13x + 42 = 0 ]
(iv) Find the value of determinant [Ans. 6 ]

 5 2 7 4

(v) Find tn for the A.P. 3, 8, 13, 18, ……[Ans.  5n – 2 ]

(vi) Three coins are tossed simultaneously, find S and n(S) [Ans. S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} n(S) = 8]

3. Attempt any three sub – questions from the following. 9

(i) Find the first three terms of the sequence, whose nth terms is  tn = 4n – 3. [Ans. 1, 5, 9]

(ii) Solve the following quadratic equation by factorization method: x2 – 5x – 36 = 0. [Ans. x = 9 or – 4 ]

(iii) Two – digit numbers are formed from the digits 0, 1, 2, 3, 4 where digits are not repeated. Find the probability of the events that:

(a) the number formed is an even number. [Ans. 5/8]

(b) the number formed is a prime number. [Ans. 5/16]

(iv) Below is given the distribution of money (in Rs. ) Collected by students for flood relief fund. [Ans. Rs. 23.80]

 Money (In Rs.) 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 Number of Students 5 7 5 2 6
Find mean of money (in Rs. ) collected by a student using ‘Direct Method’.

(v) The number of hours, spent by a school boy in different activities in a day is given below. [Ans. The measure of the θ for Sleep = School = 1050 ; Play = 300 ; Homework = Others = 600  ]

 Activity Sleep School Play Homework Others Total Number of Hours 7 7 2 4 4 24
Represent the above information using pie diagram.

4. Attempt any two sub – questions from the following. (8)
(i) Babubhai borrows Rs. 4000 and agrees to repay with a total interest of Rs. 500 in 10 instalments, each instalment being less than the preceding instalment by Rs. 10, what should be the first and last instalments? [Ans. First Instalment = Rs. Rs. 495; Last Instament = Rs. 405 ]

(ii) Solve the following simultaneous equations: [Ans. x = 5/2 ;  y = - 2 ]

[ 27 / ( x – 2 ) ] + [ 31 / ( y + 3 ) ] ;
[ 31 / (x – 2) ] + [ 27 / ( y + 3 ) ]

(iii) Two dice are thrown, find the probability of getting:

(a) the sum of the numbers on their upper faces is at least 10. [Ans. 1/6]

(b) the sum of the numbers on their upper faces is divisible by 5. [Ans. 7/36 ]

(c) the number on the upper face of the first die is greater than the number on the upper face of the second die. [Ans. 5/12]

5. Attempt any two of the sub – questions from the following: 10
(i) When the son will be as old as his father today, the sum of their ages then will be 126 years. When the father was as old as his son today, the sum of their ages then was 38 years. Find their present ages. [Ans. Father’s Present Age = 52 years; Son’s Present Age = 30 years]

(ii) The following is the frequency distribution with unknown frequencies:
 Class 60 – 70 70 – 80 80 – 90 90 – 100 Total Frequency a/2 3a/2 2a a 60
Find the value of a, hence find the frequencies. Draw a histogram and frequency polygon on the same coordinate system. [Ans. a = 10; Frequencies 60 – 70 = 5 ; 70 – 80 = 15 ; 80 – 90 = 20 ; 90 – 100 = 10 ]

(iii) From the same place at 7 a.m. A started walking in the north at the speed of 4 km/hr. After 1 hour B started cycling in the east at a speed of 8 km/hr. At what time will they be as a distance of 20 km apart from each other? [Ans. At 10 a.m. ]

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