1.
Attempt any five of the following subquestions: [5]
(i) State whether the following sequence is an A.P. or not?
1, 4, 7, 10, …..
(ii) A card is drawn from the pack of 25 cards labelled with numbers 1
to 25. Write the sample space for this random experiment.
(iii) Find the value of x + y , if
12x + 13y = 29 and
13x + 12y = 21.
(iv) For a sequence if
Sn = n ÷ (n+1)
then find the value of S10.
(v) Verify whether 1 is the root of the quadratic equation :
x2 + 3x - 4 = 0.
(vi) If x + y = 5 and x = 3, then find the value of y.
2. Attempt any four of the following subquestions: [8]
1. Solve the following quadratic equation by factorization method.
x2 - 7x + 12 = 0 .
2. Find the term t10 of an A.P. :
4, 9, 14, …….
3. If the point A(2, 3) lies on the graph of the equation 5x + ay = 19, then find a.
4. A die is thrown. If A is an event of getting an odd number, then write the sample space and event A in set notation.
5. For a certain frequency distribution, the value of Mean is 101 and Median is 100. Find the value of Mode.
6. If one root of the quadratic equation
kx2 - 7x + 5 = 0
is 1, then find the value of k.
3. Attempt any three of the following sub questions:
1. Area under different crops in a certain village is given below.
Represent it by a pie diagram.
|
Crop
|
Area in Hectares
|
|
Jowar
|
40
|
|
Wheat
|
60
|
|
Sugarcane
|
50
|
|
Vegetables
|
30
|
2. If two coins are tossed, then find the probability of the event that at the most one tail turns up.
3. Solve the following simultaneous equations using graphical method.
x + y = 7;
x - y = 5.
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 second row.
5. Solve the following quadratic equation by completing square method.
x2 + 11x + 24 = 0.
4. Attempt any two of the following subquestions: [8]
1. Two digit number are formed using the digits 0, 1, 2, 3, 4, 5, where
digits are not repeated.
P is the event that the number so formed is even.
Q is the event that the number so formed is greater than 50.
R is the event that the number so formed is divisible by 3.
Then write the sample space S and events P, Q, R using set notation.
2. The following table shows ages of 300 patients getting medical
treatment in a hospital on a particular day.
|
Age ( in years)
|
No. of Patients.
|
|
10 - 20
|
60
|
|
20 - 30
|
42
|
|
30 - 40
|
55
|
|
40 - 50
|
70
|
|
50 - 60
|
53
|
|
60 - 70
|
20
|
Find the median age of the patients.
3. If α + β = 5 and α3 + β3 = 35, find the
quadratic equation whose roots are α and β.
5.
Attempt any two of the following subquestions: [10]
1. 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 the last instalments?
2. On the first day of the sale of tickets of a drama, in all 35 tickets
were sold. If the rates of the tickets were Rs. 20 and Rs. 40. per ticket
and the total collection was Rs. 900, find the number of tickets sold of each
rate.
3. Given below is the frequency distribution of driving speeds (in
km/hour) of the vehicles of 400 college students:
|
Speed ( in km/hr)
|
No. of Students
|
|
20 - 30
|
6
|
|
30 - 40
|
80
|
|
40 - 50
|
156
|
|
50 - 60
|
98
|
|
60 - 70
|
60
|
Draw Histogram and hence the frequency polygon for the above data.
