maths p1 mp2

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Half-Yearly Examinations - Maths Paper-I

Model Paper-II

Part-A

Time : 2 Hours Maximum Marks : 35

Section-I

Group-A

(Statements & Sets, Functions, Polynomials)

1. Write the converse, Inverse and contrapositive of the conditional : "In a triangle ABC if

AB= AC then B = C".

2. A and B are two subsets of a universal set . Then show that AB= AB' = BA'.

3. Let f(x) - x2+2x+3, then find the value of ??

4. Define Remainder Theorem and prove it?

Group-B

(Linear programming, Real numbers, Progressions)

5. Shade the region represented by the inequation 4x+3y12 .

6. If ;; then show that..

7. Solve .

8. Determine the 12th term of a G.P. whose 8th term is 192 and common ratio is 2.

Section-II

8x -1 3

11x = (a - a )2

2a = x + x 1+

f(x + h) - f(x) (h 0)h



10. Let f: AB and let f have an inverse function f1 BA. State property of f for which its

inverse exists.

11. Find the sum and product of the roots of the equation.

12. Maximise the objective function at (0,120) and (80, 40).

13. Solve the equation when x>0?

14. Find the values of x so that are three consecutive terms of a G.P.

Section-III

Group-A

15. If A, B are two sub-sets of a universal set then prove that (AB)' = A'B'.

16. Let f: R {2}R be defined by show that ..

17. Let f: RR be defined by f(x) = 2x+3. Find a formula f1(4), {f1(x)/2.

18. Find the independent term of 'x' in the expansion of ..

Group-B

(Linear programming, Real numbers, progressions)

19. A sweet shop makes gift packet of sweets which weight 7kg each with a combination of A

and B sweets. Atleast 3 kg of A and no more than 5 kg of B should be used. The shop make

a profit of Rs.10 and A and Rs. 20 on B per obtain maximum profit (graph need not be

drawn).

20. If ax= by= cz and show that .

y 2z=x x + z

b c=a b

12

256x -x

2x +1f xx - 2

=

2x +1f(x) =x - 2

2 7,x, 7 2

xx. x x=


21. Find the sum to n terms of the series 0.5+0.55+0.555+ ----- n terms?

22. If (b+c), (c+a), (c+a), (a+b) are in H.P. Show that are in A.P.

Section-IV

(Polynomials, Linear programming)

23. Draw the graph of y= x25x+6. and Find the solution of x25x+6=0.

24. Maximise f= 2x+y subject to the constraints 2x+5y 8, x0 and y0 .

PART-B

Marks : 30=15

1. Which of the biconditional statements is true . ( )

A) 47 = 28 4+7 = 12 B) 47=20 47 = 3

C) 4+7 = 10 47 = 3 D) 4>7 4+7 = 11

2. A and B are disjoint sets. If n(A)= 4, n(AB)=10, then n(B)= . ( )

A) 5 B) 4 C) 6 D) 14

3. If f: R R ; f(x) = 3x+2, then f1(x) is equal to . ( )

A) 3x2 B) 2x+3 C) x2/3 D) 2x3

4. The discriminant of the quadratic equation 2x27x+3=0 is . ( )

2 2 21 1 1, ,a b c



5. If x33x2+4x2 is divided by x1, then the quotient is = . ( )

A) x22x+1 B) x2+2x2 C) 0 D) 2

6. The point that belongs to the region of x+3y< 5 is = . ( )

A) (1,0) B) (2,3) C) (3, 2) D) (6,0)

7. If x1/2 =0.1 then x3/2 = . ( )

A) 0.01 B) 0.001 C) 0.001 D) 1

8. = . ( )

A) m.an1 B) n.an1 C) D)

9. The relation between A.M. and G.M. and H.M. is = . ( )

A) A2 = GH B) G2= AH

C) H2= AG D) AG=H

10. If x, y, z are in A.P. then 2y = . ( )

A) x+z B) xz C) xy D) xz

Answers : 1. B 2. C 3. C 4. C 5. A

n mn am

m nm an

m m

n nx a

a - aLtx - a



II. Fill in the blanks with suitable words. Marks : 10=5

11. The symbol for existential quantifier is .

12. If AB then AB = .

13. If A = {1,2}, B= {3,4} then AB = .

14. The range of the function f(x)=3 is = .

15. The quadratic equation, whose roots are 3 and 5 is .

16. The system of parallel line defined by an objective function are called .

17. If f(x)= 5x2 then .

18. .

19. The 7th term of in the progression .

20. The Harmonic mean of 6 and 3 is .

Answers

11. 12. A

13. {(1.3), (1,4), (2,3), (2,4)} 14. 3

15. x2+2x15=0 16. Iso profit lines

17. 45 18. a + b

19. 1/13 20. 4

1 1 11, , , ,....3 5 7

a + b + 2 aba b+

x 3Lt f(x)



III. Match the following. Marks : 10=5

Group-A Group-B

21. (AB)' = A'B' ( ) A) 2

22. If f(x) = x then f is ( ) B) 5

23. f={ (1,2), (2,2), (3,2)} ( ) C) De Morgan's Law

The range of f =

24. 5C4 + 5C1 = ( ) D) 0

25. The descriminant of ( ) E) complement law

x26x+9=0 F) Identity function

G) 3

H) 5

Answers : 21. C 22. F 23. A 24. B 25. D

Group-A Group-B

26. If the Isoprofit line coincides ( ) A) 8

with the edge of the feasible

region, the LPP has

27. = ( ) B) 10

28. If = 0 then x= ( ) C) 1

29. ( ) D) infinite solutions

30. If 2/7, x, 16/7 are in A.P. ( ) E) 4/3

10

n 165 n

6 9x

( )3416



G) 2/3

H) 12

Answers : 26.D 27. A 28. G 29. B 30. C


maths p1 mp2

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