MTH101 Midterm Solved Paper 2

MIDTERM EXAMINATION MTH101- Calculus And Analytical Geometry

Q1. If f is a twice differentiable function at a stationary point (1 marks)

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 line (1 marks)

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 line (1 marks)

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

n d x dx nx

n n x 

n n x 

1) n n x 

Q5. If (1 marks)

y x then dy dx 

1. 1
2. -1

x

x

Q6. If (1 marks)

xy  then dy dx 

1. 0

x

x

x

Q7. If (1 marks)

x y then dy dx 

1. 2

Consider a function ( ) 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