Janardan Rai Nagar Rajasthan Vidyapeeth 2006 B.Tech MATHEMATICS – I - Question Paper

Model Question Paper

BF1- MATHEMATICS I

Time : 3 hrs Maximum marks : 75

 

Instruction:

1. Question paper is divided into Group A, Group B and Group C

2. Each Group is 25 Marks

3. Figure to the right in bracket indicates marks.

4. Good Handwriting is expected

5. Assume suitable data if necessary.

 

Group A (25 Marks)

 

Answer any three questions (Question 1 is compulsory)

 

Q.1 Evaluate

( 5)

Q.2 If sin y = x sin (a+y) , prove that (10)

Q.3 If y ^1/m + y ^-1/m = 2x , show that

(x² 1) y_n+2 + ( 2n +1) x y_n+1 + (n² m²) y_n = 0 (10)

Q.4 If ( 1 x² ) + ( 1 y² ) = a ( x y), prove that dy/dx = ( 1- y² )^1/2 /

( 1- x² )^1/2 (10)

Q.5 Find the differential co-efficient of tan^-1 2x/(1-x² ) with respect to sin^-1 2x / (1+x²) (10)

 

Group B (25 Marks)

 

Answer any three questions (Questions 6 is compulsory)

 

(5)

Q.6 Integrate

Q.7 Find the area bounded by the curves y² = 9x & x² = 9y (10)

Q.8 Find the value of the n th derivative of y = e ^{m sin-1 x} for x = 0. (10)

Q.9 Show that = (10)

Q.10. Show that a) x / ( 1 + x) < log ( 1 + x ) < x " x > 0

b) x x²/2 < log ( 1+x) < x x² / 2 ( 1 + x) " x > 0 (10)

 

 

 

 

 

 

 

 

 

Group C (25 Marks)

All Questions are Compulsory.

 

Q.11 Fill in the blanks ( each question carry 2 marks)

 

1. A generalization of Rolles theorem is = ___________________

 

2. If f(x) = log[(1-x)/ (1+x)], then f(a) +f(b) = _______________

3. ( sin ( ax + b ) ) = _______________

4. = _______________

5. The volume of a sphere of radius a is _______________

 

Q.11 Multiple choice question. (Each question carry 2 marks)

 

1)      For what value of x the equation x/x=1 is not valid?

i) x=1 ii) x=2 iii) x=0 iv) All

 

2)      The function y = x³ with domain R is

i) Invertible ii) Rational iii) Not invertible iv) None

 

3)      A function is called strictly decreasing if

i) x₂ > x₁ f ( x₂ ) < f ( x₁) ii) x₂ < x₁ f ( x₂ ) < f ( x₁)

 

iii) x₂ > x₁ f ( x₂ ) > f ( x₁) iv) x₂ < x₁ f ( x₂ ) > f ( x₁)

 

4. ( tan ^-1 x ) =

a) b)1 + x² c) d)1 - x²

5. The values of x for which f(x) has extreme values are called

a) Turning values b) critical value c) stationary d) maximum value

 

Q.11 True or false (each question carry 1 marks).

 

1.If the sign of f(x) is first + and then - , the function has a maximum value.

 

2.If x and y are functions of t then

3.The symbol which denotes a member of a domain of a function is called an Independent

variable.

4. The symbol denoting the member of the range of a function is called a Dependent variable.

5. dx = log sec x .

 

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