MTH101 Midterm Solved Papers 1-5

Calculus & Analytical Geometry-I

MIDTERM SOLVED PAPERS (PAPER #1)

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

Q2. 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

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

Q4. If (1 marks)

f x x x then f x

x + x +

x x x x

Q5. (tan (1 marks)

d x dx

1. sec x

sec x sec co x

sec co 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
2. -2
3. 0
4. -3

Q8. [sec ] (1 marks)

d x dx

1 sin x

sin 1 sin x x

1 sin x

sin 1 sin x x g f f g f

g f f g f

Q12. [cosec ] (1 marks)

d x dx

1 cos x

cos 1 cos x x

cos 1 cos x x

1 cos x

Q13. If (1 marks)

y f g h x

u g h x

v h x then dy dx =

dy du dv du dv dx

dy du dv du dv dx

dv du dy du dv dx

Q14. Chain rule is a rule for differentiating ___________ of functions. (1 marks)

1. Product
2. Sum