- Question 1
**Attempt any five of the following sub questions :****[5]**(i) State whether the following sequence is an Arithmetic Progression or not :

3, 6, 12, 24,.......(ii) If one root of the quadratic equation is $3-2\sqrt{5}$, then write another root of the equation. (iii) There are 15 tickets bearing the numbers from 1 to 15 in a bag and one ticket is drawn from this bag at random. Write the sample space (S) and n(S). (iv) Find the class mark of the class 35-39. (v) Write the next two terms of the A.P. whose first term is 3 and the common difference is 4. (vi) Find the values of a, b, c for the quadratic equation 2x ^{2}= x + 3 by comparing with standard form ax^{2}+ bx + c = 0

- Question 2
**Attempt any four of the following sub questions :****[8]**(i) Find the first two terms of the sequence for which S _{n}is given below :S_{n }= n^{2 }(n + 2)(ii) Find the value of discriminant (Δ) for the quadratic equation : X^{2}+ 5x + 1 = 0(iii) Write the equation of X-axis. Hence find the point of intersection of the

graph of the equation x + y = 3 with the X-axis.(iv) For a certain frequency distribution the values of Assumed mean (A) = 1200, ${\mathrm{\Sigma f}}_{\mathrm{i}}{\mathrm{d}}_{\mathrm{i}}=700\mathrm{and}{\mathrm{\Sigma f}}_{\mathrm{i}}$ = 100. Find the value of mean $\left(\overline{)\mathrm{X}}\right)$. (v) Two coins are tossed simultaneously. Write the sample space (S). n(S), the following event A using set notation and n(A), Where ‘A’ is the event of getting at the most one tail.’ (vi) Find the value of k for which the given simultaneous equation have infinity many solution : kx + 2y = 6

9x + 6y = 18

- Question 3
**Attempt any three of the following sub questions :****[9]**(i) How many three digit natural numbers are divisible by 2? (ii) Solve the following quadratic equation by factorization method : 3*x*^{2}– 22*x*+ 40 = 0(iii) Solve the following simultaneous equation by using Cramer’s rule : *x*+ 2*y*= 4; 3*x*+ 4*y*= 6(iv) Two dice are thrown. Find the probability of the event that the product of the numbers on their upper faces is 12. (v) The following is the frequency distribution of waiting time at ATM centre; draw histogram to represent the data : **Waiting time (In seconds)****Number of Customers**0–30

30–60

60–90

90–120

120–15010

54

68

28

20

- Question 4
**Attempt any two of the following sub equations :****[8]**(i) Three horses A, B and C are in a race, A is twice as likely to win as B and B is twice as likely to win as C. What are their probabilities of winning? (ii) The following is the distribution of the size of certain farms from a taluka (tehasil) : **Size of Farms (in acres)****Number of Farms**5 – 15

15 – 25

25 – 35

35 – 45

45 – 55

55 – 65

65 – 757

12

17

25

31

5

3(iii) The following pie diagram represents the sectorwise loan amount in crores of rupees

distributed by a bank. From the information answer the following questions :

(a) If the dairy sector receives `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 receive than agriculture sector?

- Question 5
**Attempt any two of the following sub questions :****[10]**(i) If the cost of bananas in increased by 10 per dozen, one can get 3 dozen

less for 600. Find the original cost of one dozen of bananas.(ii) If the sum of first p terms of an A.P. is equal to the sum of first q terms,

then show that the sum of its first (p + q) terms is zero where p ≠ q.(iii) Solve the following simultaneous equations : $\frac{1}{3\mathrm{x}}-\frac{1}{4\mathrm{y}}+1=0\phantom{\rule{0ex}{0ex}}\frac{1}{5\mathrm{x}}+\frac{1}{2\mathrm{y}}=\frac{4}{15}$