ALGEBRA SAMPLE PAPER WITH SOLUTION AS PER NEW PAPER PATTERN

Q1. Attempt any five sub – questions:           [5]

i. For the given sequence, find the next two terms. 1, 2, 4, 7, 11, ___, ____ (Ans)

ii. Write the given quadratic equation in the standard form. 3y² = 10y + 7. (Ans)

iii. Find the value of the given determinant. (Ans)

5	2
7	4

  

iv. A die is thrown. Find the sample space 'S' and n(S). (Ans)

v. Find t_n of the A.P.: 3, 6, 9, .... (Ans)

vi. Write the extended class boundaries of 19 – 20 and 21 – 22 . (Ans)

Q2. Attempt any four sub – questions: [8]

i. State whether the following sequence is an A.P. or not 1³, 2³, 3³, 4³, .... (Ans)

ii. Solve the given quadratic equation by factorization method. x² -13 x – 30 = 0. (Ans)

iii. Find D_x  and D_y  of the given simultaneous equations. 3x – 2y = 3 and 2x + y = 16. (Ans)

iv. A die is thrown. Find the probability of obtaining a perfect square on its upper surface. (Ans.)

v. For a certain frequency distribution, the values of Median and Mode are 95.75 and 95.5 respectively, Find the value of Mean. (Ans.)

vi. State whether the given equation is a quadratic or not. y + 1/y = 3   (Ans.)

Q3. Solve any three sub – questions:             [9]

i. Solve the given quadratic equation by factorization method,  3x² – x – 10 = 0.   (Ans.)

ii. If two coins are tossed simultaneously, then find the probability of the following events: (Ans.)

(a) at least one tail turns up.  

(b) no head turns up.  

(c) at the most one tail turns up.

iii. Find S₁₀ if a = 6 and d = 3.  (Ans. )

iv. Complete the following table of cumulative frequency.
(Ans.)

Class	20 – 25	25 – 30	30 – 35	35 – 40
Frequency	2	6	14	29
C.F. less than upper limit	2	?	?	?

v. The following table shows the frequency distribution of the waiting time at an ATM centre. Draw a histogram to represent the data. (Ans.)

Waiting time in seconds	0 – 30	30 – 60	60 – 90	90 – 120	120 – 150	150 – 180
No. of Customers	20	28	68	54	10	3

Q4. Attempt any two sub – questions:  [8]

i. Solve the given equation: a⁴ – 3a²  + 2 = 0. (Ans.)

ii. What is the probability of two – digit number formed from the digits 2, 3, 5, 7, 9 without repeating the digits of the events? (Ans)

(a) the number so formed is an odd number.

(b) the two – digit number so formed is a multiple of 5.

iii. Solve the simultaneous equations by using Cramer's rule.  4x = y – 5 and y = 2x + 1. (Ans)

Q5. Attempt any two sub – questions. [10]

1. If the sum of 'p' terms of and A.P. is equal to the sum of 'q' terms, then show that the sum of 'p + q' terms is zero. (click answer)

2. Solve:  16 / (x+y) + 2/(x – y) = 1 and 8/(x+y) – 12/(x – y) = 7 (Ans)

3. Draw a pie diagram to represent the world population from the following data after finding the value of 'a '. (Ans)

Country	India	China	Russia	U.S.A.	others	Total
Percentage of world Population.	15	20	a	a	25	100