1.
Attempt any five sub – questions from the following: 5
(i) Find S_{2} for
the A.P. 3, 5, 7, 9, ……… [Ans. 8]
(ii) If a = 1, b = 8 and c =
15, then find the value of b^{2} – 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 x^{2} + 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. x^{2} – 13x + 42 = 0 ]
(iv) Find the value of
determinant [Ans.
6 ]
5

2

7

4

(v) Find t_{n} 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
t_{n} = 4n – 3. [Ans. 1, 5, 9]
(ii) Solve the following
quadratic equation by factorization method: x^{2} – 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 = 105^{0} ; Play = 30^{0} ; Homework
= Others = 60^{0} ]
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 ]
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