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Algebra Question Paper for SSC students

AS PER NEW SYLLABUS PATTERN

MARKS: 40 MARKS

Q1. Attempt any five of the following sub – questions: (5)

i.            Find the first four terms of the sequence whose ‘nth’ term is 3n + 1. [Ans]
ii.          If one root of the quadratic equation  x2  - 11x + k = 0 is 9, then find the value of k. [Ans]
iii.        What is sample space [Ans]
iv.         Mohan has a hobby of solving problems everyday. He solved 2, 4, 3, 2, 4, 5, 1 problems in the last week. What is the mean number of problems solved by Mohan per day? [Ans]
v.           A die is thrown. Find the sample space 'S' and n(S) [Ans]
vi.         Find the value of discriminant for the following.  x2  - 4 √ 3 x + 4 = 0 . [Ans]

 Q2. Attempt any four of the following sub – questions: (8)

i.             Determine whether the given values of 'x'  are the roots of the given quadratic equation   6x2 – x – 2 = 0,  x = -1/2 , x = 2/3 , x = 3/ 2 (Ans)
ii.          Solve the simultaneous equations by using Graphical method. x + 3y = 7; 2x + y + 1 = 0. (Ans)
iii.        There are three boys and three girls. An environment committee of two is to be formed. Write the sample space S, the number of sample points n(S). Also Event A and n(A). Where A is the event that the committee should contain atleast one girl. [Ans]
iv.         Without actually solving the simultaneous equation given, examine whether it has unique solution, no solution or infinitely many solutions. (i) x + 3y + 4 = 0 ; 2x + 6y – 3 = 0. [Ans]
v.           A coin is tossed. Find the probability of the events. (i) Getting a head (ii) Getting a tail. [Ans]
vi.         Write the extended boundaries of 9 – 10 and 11 – 12. [Ans]

Q3. Attempt any three of the following sub – questions (9)

i.            Is the sequence is an A.P?  2/3, 4/5, 6/7 
ii.         Find the smallest positive integer n such that tn of the arithmetic sequence 20, 19 1/4, 18 1/2, .... is negative?
iii.         Form the quadratic equation whose roots are  7 + √3 and 7 - √3.
iv.        In the following experiment write the sample space S, number of sample points n(S), events P, Q, R using set and n(P), n(Q) and n(R). There are 3 men and 2 women. A 'Gramswachaatta Abhiyan' committee of two is to be formed. P is the event that the committee should contain at least one woman. Q is the event that the committee should contain one man and one woman. R is the event that there is not woman in the committee.

Q4. Attempt any TWO of the followng sub – questions: (8)

i.           In an arithmetic series, the sum of first 14 terms is -203 and the sum of the next 11 terms is –572. Find the arithmetic series.
ii.          If α and β are the roots of the equation 2x^2 - 3x - 1 = 0, find the values of (α/β) + (β/α)
iii.        Find the probability that a leap year selected at random will have only 52 Friday.

Q5. Attempt any TWO of the following subquestions.  (10)

i.            Sachin buys fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish. What is the probability that the fish taken out is a male fish?
ii.          A car left 30 minutes later than the scheduled time. in order to reach its destination 150 km away in time, it has to increase its speed by 25 km/hr from its usual speed. Find its usual speed.
iii.        If a person joins his work in 2010 with an annual salary of Rs.30,000 and receives an annual increment of `Rs. 600 every year, in which year, will his annual salary be `Rs. 39,000?

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