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S.S.C. Public Examinations
Mathematics Paper - I
Model Paper (English Version)
Time: 2 1__
2
Hours PARTS A & B Max. Marks: 50
Instructions: 1) Answer the questions under Part - A on a separate answer book.
2) Write the answer to the questions under Part - B on the question
paper itself and attach it to the answer book of Part - A.
Time: 2 Hours PART- A Marks: 35
SECTION - I
Note: 1) Answer any FIVE questions, choosing atleast TWO from each of the
following Groups A & B.
2) Each question carries TWO marks. 5 × 2 = 10
GROUP-A
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(Statements and Sets, Functions, Polynomials Over Integers)
1. Write the truth table of Disjunction.
2. P, Q are the subsets of a universal set µ prove that P∩Q' = P − Q.
f(x + h) − f(x)
3. If f(x) = x 2 + 2x + 3 ∀ x ∈ R find ⎯⎯⎯⎯⎯⎯ where h ≠ 0.
h
4. Find the value of m so that x 4 − 2x 3 + 3x 2 − mx + 5 may be exactly divisible by
x − 3.
GROUP- B
(Linear Programming, Real Numbers, Progressions)
5. Indicate the polygonal region represented by the systems of inequations x ≥ 0,
x ≤ 4, x ≥ y.
6. Solve ⎢5 − x − 3
⎢ ≤ 1.
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√ ⎯ 1 + x − 1
7. Evaluate x→0
Lt ⎯⎯⎯
x
8. If 7 times the 7 th term of an A.P. is equal to 11 times the 11 th term. Show that the
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18 th term of it is zero.
SECTION - II
Note: 1) Answer any FOUR of the following SIX questions.
2) Each question carries ONE mark. 4 × 1 = 4
9. Write the converse and contrapositive of the statement "If x is even then x 2 is
even''.
1 − x
10. If f(x) = ⎯⎯ (x ≠−1) find f(0) and f(1).
1 + x
11. Expand ∑ a 2 (b 2 − c 2 ).
12. Define Iso - profit lines.
13. If (x 2/3 ) p = x 2 , find 'p'.
t n−1
14. If t 1 = 1, t n
= ⎯⎯ (n ≥ 2) of a series. Find t 3 .
n
SECTION - III
Note: 1) Answer any FOUR questions choosing atleast TWO from each of the
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following Groups A & B.
2) Each question carries FOUR marks. 4 × 4 = 16
GROUP - A
(Statements and Sets, Functions, Polynomials Over Integers)
15. If A, B are two subsets of a Universal set µ then show that (A∪B)' = A' ∩ B'.
16. Let f(x) = x − 1, g(x) = x 2 − 2, h(x) = x 3 − 3 for x ∈ R, find (i) (fog)oh,
(ii) fo(goh).
17. Let f be given by f(x) = x + 2 and f has the domain
{x/2 ≤ x ≤ 5}. Find f −1 and its domain and range.
18. Find the independent term of 'x' in the expansion of
( 6x2 5
) 8 − ⎯ .
x 2
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GROUP- B
(Linear Programming, Real Numbers, Progressions)
19. A manufacturer makes two models A and B of a product. Each model should be
processed by two machines. To complete one unit of model A machines I and II
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must work 1 hour and 2 hours respectively. To complete one unit of model B
machines I and II must work 4 hrs and 2 hrs respectively. Machine I may not
operate more than 8 hours per day, and machine II not more than 10 hours per day.
If the profits on models A and B per unit are Rs.200 and Rs.280 respectively, how
many units of each model should the manufacturer produce per day to maximise
his profit
1 1 1
20. If lmn = 1 then show that ⎯⎯ + ⎯⎯ + ⎯⎯ = 1
1+l + m −1 1+m+n −1 1+n+l −1
21. The sum of 6 terms which form an A.P. is 345 the difference between the first and
the last term is 55. Find the 6 terms.
22. The A.M., G.M. and H.M. of two positive numbers are A, G, H respectively. Show
that A ≥ G ≥ H.
SECTION - IV
(Polynomials Over Integers, Linear Programming)
Note: 1) Answer ANY ONE question from the following.
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2) The question carries FIVE marks. 1 × 5 = 5
23. Using the graph of y = x 2 , solve x 2 − x − 2 = 0.
24. Minimise f = 4x + 3y subject to x + y ≤ 8000, 2x + y ≤ 1000, 0 ≤ x ≤ 400,
0 ≤ y ≤ 700.
TIME: 30 MINUTES PART - B MARKS: 15
Instructions: 1) Answer all the questions.
2) Each question carries ⎯ 1 2
mark.
3) Marks will not be awarded for any over - written, re-written or erased answers.
I. Write 'CAPITAL LETTER' of the correct answer in the brackets provided
against each question.
1. p Λ t ≡ p ( )
A) Identity Law B) Idempotent Law
C) Associative Law D) Complement Law
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2. If A B then A − B = ( )
⊃
A) A B) B C) ∅ D) µ
3. If f(x) = 1 − x, fog(x) = 2x ∀ x ∈ R then g(x) = ( )
A) 2x B) 1 − 2x C) 1 − x D) 2x + 1
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4. f = {(x, 2013)/ x ∈ N} is a ( )
A) One - One function B) Bijective function
C) Constant function D) Identity function
5. y = mx 2 (m < 0) lies in the Quadrant ( )
A) I, II B) II, III C) III, IV D) I, IV
6. n C 0 + n C n = ( )
A) 0 B) n C) 1 D) 2
7. If x > 0, y < 0 then the point (x, y) lies in the Quadrant ( )
A) I B) II C) III D) IV
8. If 2 x+1 = 4 x−1 then x = ( )
A) 2 B) 3 C) 4 D) 5
9. If ∑n = 15 then ∑n 2 = ( )
A) 225 B) 55 C) 215 D) 30
10. The A.M. and G.M. of two numbers are 16 and 8 respectively. Then their harmonic
mean is ( )
A) 4 B) 8 C) 16 D) 32
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II. Fill in the blanks
11. If A B and B A then ........
12. If (a + b, 1) = (5, a − b) then 2a + 3b is ........
x + 1
13. If f(x) = ⎯ ∀ x ∈ R − {1} then 3f(2) − 2f(3) = ........
x − 1
14. If the number of terms in the expansion of (x + y) n+1 is 5 then n = .......
15. If a < 0, then the point (−a, −a) lies in ..... Quadrant.
16. Equation of Y - axis is .....
1 1 1
17. Sum of the series 1 + ⎯ + ⎯ + ⎯ + ....... is .......
3 3 2 3 3
⊃ ⊃
18. If k a , k b , k c are in G.P. then a, b, c are in ......
19. The limiting position of secant of a circle is ......
20. If x 1/2 = 0.1 = 0.1 then x 3/2 = ........
III. Find the correct answers for the questions under Group - A, selecting them
from Group - B.
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i) Group - A Group - B
21. If n(A) = 15, n(B) = 20 ( ) A) F
n(A∪B) = 30 then n(A∩B) =
22. The truth value of ( ) B) −5/3
If 2 × 5 = 10 then 2 − 5 = 3
23. The zero of the function ( ) C) 5
f(x) = 3x + 5 ∀ x ∈ R is
24. The sum of the roots of the ( ) D) −3 √ ⎯ 3
Quadratic equation
√ ⎯ 3 x 2 + 9x + 6 √ ⎯ 3 = 0 is
25. The discriminant of the quadratic ( ) E) −3/5
equation px 2 + qx = r
F) q 2 − 4pr
G) T
H) q 2 + 4pr
ii) Group - A Group - B
26. If P = 1 − 4
x + 2 − 3
y then the value ( ) I) x = k
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of P at (0, 15)
27. Solution set of the inequations x ≥ k, x ≤ k is ( ) J) −5/2
3x − 5
28. Lt ⎯⎯
x→∞ 5x + 2
( ) K) 1
29. x a(b−c) . x b(c−a) . x c(a−b) = x r then r = ( ) L) 10
30. If − − 2 , x, − − 7 are in G.P. then x = 7 2
Solutions To Part - B
( ) M) ±1
N) 3/5
O) 0
P) −1
I. 1-A; 2-C; 3-B; 4-C; 5-C; 6-D; 7-D; 8-B; 9-B; 10-A.
II. 11) A = B 12) 12 13) 5 14) 3 15) First Quadrant 16) x = 0
17) 3/2 18) A.P. 19) Tangent 20) 0.001
III. i) 21-C; 22-A; 23-B; 24-D; 25-H.
ii) 26-L; 27-I; 28-N; 29-O; 30-M
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REG - MP - 13