MTH101 Midterm Past Paper

MIDTERM EXAMINATION

Fall 2009

MTH101- Calculus And Analytical Geometry (Session - 5) Ref No: 1087754 Time: 60 min

Q1. If (1 marks)

f is a twice differentiable function at a stationary point 0x and f x then f has

relative …………. At 0x

1. Minima
2. Maxima
3. None of these

Correct answer: Maxima

Note:Maxima(If Maxima refers to local maximum)

Q2. A (1 marks)

line x x is called ------------ for the graph of a function f if f x or f x as x approaches 0x from the right or from the left

1. Horizontal asymptotes
2. None of these
3. Vertical asymptotes

Correct answer: Vertical asymptotes

Q3. A (1 marks)

line y y is called a ………………. for the graph f if lim lim x x f x y or f x y

1. Vertical asymptotes
2. Horizontal asymptotes
3. None of these

Correct answer: None of these

Q4. According to Power-Rule of differentiation, if (1 marks)

n f x x where n is a real number, then

Q10. Consider a function ( ) (1 marks)

h x and a constant c then

d c h x dx

1. 0

d h x dx d h cx dx d c h x dx

Q11. [cosec ] (1 marks)

d x dx

1 cos x

cos 1 cos x x

cos 1 cos x x

1 cos x

Q12. Chain rule is a rule for differentiating ___________ of functions. (1 marks)

1. Product
2. Sum
3. Difference
4. Composition

Correct answer: Product

Q13. The (1 marks)

power rule, n n d x nx dx holds if n is __________

1. An integer
2. A rational number
3. An irrational number
4. All of the above

Correct answer: An integer

Q14. Let a function f be defined on an interval, and let (1 marks)

1x and 2x denote points in that interval. If

f x f x whenever x x then which of the following statement is correct?

1. f is an increasing function.
2. f is a decreasing function.
3. f is a constant function.

Correct answer: f is an increasing function.

Q15. If f (1 marks)

x on an open interval (a,b), then which of the following statement is correct?

1. f is concave up on (a, b).
2. f is concave down on (a, b).
3. f is linear on (a, b).

Correct answer: f is concave up on (a, b).

Q16. If f (1 marks)

x on an open interval (a,b) then which of the following statement is correct?

1. f is concave up on (a, b).
2. f is concave down on (a, b)
3. f is linear on (a, b).

Correct answer: f is concave down on (a, b)

Q17. [ln ] (1 marks)

d If x then x dx

1. 1
2. x