FIRST YEAR MATHEMATICS – I B

TYPE OF QUESTION	VSA	SA	LA	TOTAL
No. of questions to be given	10	7	7	24
No. of questions to be answered	10	5	5	20
Marks Allotted	20/20	20/28	35/49	75/97
Estimated time (In minutes)	10 x 4 = 40	5 x 9 = 45	5 x 18 = 90	175

Scheme of Options:

Section – A: No Option

Section – B: 5 out of 7

Section – C: 5 out of 7

S. No	Weightage to content: units / Sub-units:	division	marks
1	Locus	1 x 4	04
2	Change of Axes	1 x 4	04
3	Straight Lines	2x2 + 4 + 7	15
4	Pair of Straight Lines		14
5	3D- Coordinates	1 x 2	02
6	Direction cosines & Direction ratios – 3D Geometry	1 x 7	07
7	The Plane – 3D Geometry	1 x 2	02
8	Functions, Limits, Continuity	4 + 2	06
9	Differentiations	3x2 + 4 + 7	17
10	Errors – Approximations	2	02
11	Rate measure	1x4	04
12	Tangent – Normal	2 + 7	09
13	Maxima – Minima	1x7	07
14	Partial Differentiation	1x4	04
	Total		97

II B BLUE PRINT

S.No	TOPIC	DIVISION	MARKS
1.	Circles	2x7 + 2	16
2.	System Of Circles	1X7	07
3.	Parabola	7 + 2	09
4.	Ellipse	4 + 2	06
5.	Hyperbola	4 + 2	06
6.	Polar Co-ordinates	4 + 2	06
7.	Successive Differentiations	4 + 2	06
8.	Integrations	7 + 4 + 2x2	15
9.	Definite integration	7 + 2	09
10	Numerical Integration	7 + 2	09
11.	Differential Equations	4 + 4	08
	Total	97	97

MATHS IIA BLUE PRINT

S.No	TOPIC	DIVISION	MARKS
1.	Quadratic Expressions	4+2	06
2.	Theory of Equations	7+2	09
3.	Matrices	2x7 + 4 + 2x2	22
4.	Permutations & Combinations	4 + 2 + 7	15
5.	Binomial Theorems	7 + 4 + 2	13
6.	Partial Fractions	4	04
7.	Exponential & Logarithmic series	4 + 2	06
8.	Probability	4 + 7 + 2	13
	Total		97

INTERMEDIATE PUBLIC EXAMINATION, MAY 2006

MATHEMATICS PAPER 1(A)

ALGEBRA, VECTOR ALGEBRA AND TRIGONOMETRY

TIME: 3 Hrs. Max. Marks: 75.

SECTION – A

VERY SHORT ANSWER TYPE QUESTIONS

Answer all questions. Each question carries 2 marks.

1. Find the range of the function f: A à R where A = {1, 2, 3, 4} and f(x) = x²+x-2.

2. Find a unit vector parallel to the resultant of the vectors, r₁= 2i + 4j – 5k and r₂ = I + 2j + 3k.

3. If the position vectors of the vertices A, B, C of ∆ ABC, are 7j + 10k, -i + 6j + 6k and -4i +9j +6k respectively. Prove that the triangle is right angled and isosceles.

4. If a = I + j + k and b = 2i + 3j + k , find the length of the projection of b on a and the length of the projection of a on b.

5. Prove that tan (A + 135) tan (A-135) = -1.

6. If tan A = 8/25, find the values of sin 2A and cos 2A.

7. If cosh x = 5/2, find the value of cosh 2x.

8. In ∆ ABC, express ∑ r1 cot ( A/2) in terms of ‘s’.

9. Find the values of (√3/2 – i/2)¹².

10. Expand cos 4A in powers of cos A.

SECTION – B

SHORT ANSWER TYPE QUESTIONS.

Attempt any 5 questions, Each question carries 4 marks.

11. f: R à R are defined by f(x) = 3x – 2 and g(x) = x2 + 1, then find the following

i) (g o f-1) (2) ii) (g o f ) ( x-1)

12. If x = (√3 – √2)/ (√3 +√2), y =(√3 + √2)/ (√3 +√2) then show that x² + xy + y² = 99.

13. If x = log _2a a, y = log _3a 2a and z = log _4a 3a, then show that xyz + 1 = 2yz.

14. If, a, b, c are non coplanar vectors, show that a + a2b + c, -a + 3b – 4c, a – b + 2c are non coplanar.

15. If a = 2i + 3j + 4k , b = I + j – k , compute a X (b X c) and verify that is perpendicular to a.

16. If tan ( π sin A ) = cot (π cot A), then show that sin ( A + π ) = ±1/√2 .

2 2 4

17. Show that Tan ^‑1 1/8 + Tan ^‑1 1/2 + Tan ^‑1 1/5 = π/4.

SECTION – C π

LONG ANSWER TYPE QUESTIONS

Attempt any 5 questions, each question carries 7 marks.

18. Let f : A à B and g: B à C be bisections, Prove that g o f : A à C is also bijection.

19. using the principles of Mathematical Induction, prove that 2.3+ 3.4 + 4. 5 + ………..upto π

Terms = n (n2 + 6n + 11)/3, for all n € N.

20. For any vectors,a, b , c prove that a X ( b X c) = ( a. c ) b – ( a . b ) c.

21. If A + B + C = 180⁰, prove that cos A + cos B + - cos C = - 1 + 4 cos A/2 cos B/2 cos C/2 .

22. In ∆ ABC, prove that r + r₁+ r₂ - r₃ = 4 R cos C.

23. From the top of a tree on the bank of a lake, an aeroplane in the sky makes an angle of elevation A and the of the height of the aeroplane is ‘h’. Show that h = a Sin (A + B)

Sin (A - B)

24. If the amplitude of ( z – 2 )/ ( 2 – 6i ) is π/2 , find the equation of locus of z.

II B BLUE PRINT

No	TOPIC	DIVISION	MARKS
1.	Circles	2x7 + 2	16
2.	System Of Circles	1X7	07
3.	Parabola	7 + 2	09
4.	Ellipse	4 + 2	06
5.	Hyperbola	4 + 2	06
6.	Polar Co-ordinates	4 + 2	06
7.	Successive Differentiations	4 + 2	06
8.	Integrations	7 + 4 + 2x2	15
9.	Definite integration	7 + 2	09
10	Numerical Integration	7 + 2	09
11.	Differential Equations	4 + 4	08
	Total	97	97

MATHS IIA BLUE PRINT

S.No	TOPIC	DIVISION	MARKS
1.	Quadratic Expressions	4+2	06
2.	Theory of Equations	7+2	09
3.	Matrices	2x7 + 4 + 2x2	22
4.	Permutations & Combinations	4 + 2 + 7	15
5.	Binomial Theorems	7 + 4 + 2	13
6.	Partial Fractions	4	04
7.	Exponential & Logarithmic series	4 + 2	06
8.	Probability	4 + 7 + 2	13
	Total		97

MODEL TEST PAPER II

I YEAR INTERMEDIATE

(First Year – Year-Wise Scheme)

Part III – Physical Sciences

CHEMISTRY PAPER – I

Time : 3 Hours (English Version) Max.Marks: 60

Note :Read the following instructions carefully.

1) Answer ALL questions of Section-A. Answer any SIX questions from Section-B and any Two

Questions in Section-C.

2) In Section-A questions from Serial Nos. 1 to 10 are of “Very Short Answer type”. Each question

Carries Two marks. Every answer may be limited to 2 or 3sentences. Answer all these questions

At one place in the same order.

3) In Section-B questions from Serial Nos. 11 to 18 are of “Short Answer Type”. Every question

Carries Four marks. Every answer may be limited to 75 words.

4) In Section-C questions from Serial Nos. 19 to 21 of “Long Answer Type”. Each question carries

Eight marks. Every answer may be limited to 300 words.

5) Draw labelled diagrams wherever necessary for questions in Section in Sections B and C

SECTION-A

Answer ALL questions.

1.Calculate the wave number of radiation with wavelength 4000 A⁰.

2.What is Lanthanide contraction?

3.In H₂O and HF which has higher boiling point? Why?

4.Calculate the volume occupied by 2.5 moles of CO₂ at STP.

5.What is Deuterolysis? Give example.

6.What is tha stable number of Lead? Why?

7.Why do helium and neon cannot form clathrate compounds?

8.Write the hybridization and shape of the XeO₃ molecule.

9.Define COD and BOD.

10.What are the effects of acid rains?

SECTION-B

Attempt any SIX questions:

11.A flask contains 1 gm of hydrogen, 2 gm of neon and 1.6 gms of oxygen at a pressure of 2 atm. At

27⁰C. Calculate the partial pressures of each gas and the volume of the flask.

12.Deduce a)Boyle’s law

b)Graham’s law from kinetic gas equation.

13.Balance the following Redox reaction by ion-electron method in acid medium.

H₂SO₄ + HBr --------à SO₂ + Br₂

14.Write two oxidising and two reducing properties of hydrogen peroxide.

15.Write two methods of preparation of ethane. Write the reactions of ethane.

16.What is Ozonolysis? Explain with examples.

17.Explain the purification of Bauxite by Bayer’s process with equations.

18.Explain the extractions of sodium metal by Down’s process.

SECTION-C

Attempt any TWO questions

19.State the important postulates of Bohr’s theory. Based on the postulates, explain the formation of

Different lines in various series of hydrogen atomic spectrum with diagram.

20.What is periodic property? How do the following properties change in first group and third period?

a) Nature of oxides

b)Ionisation potential

c)Metalic and non-metalic properties

21.Define Crystal Lattice Energy. Describe energy changes in the formation of sodium chloride according

to Born-Haber cycle.