Differential Calculus NAT Level - 1 - IIT JAM MCQ

The correct answer is: 3.14

It is necessary that at the point of maxima or minima of a function, say f, f ' will become zero.

The correct answer is: 0

The correct answer is: 0.008

Solving, we get

Thus, max value is 

The correct answer is: 1

Let the two numbers be x & y

⇒ x + 3y = 60 ....(1)

Now, let z = xy = product of two numbers.

Putting x = 30 in (1), we get y = 10 and 

Hence, z is maximum when x = 30 and y = 10.
The correct answer is: 300

Since f(x) is a function so, 

Value of α = 5

The correct answer is: 5

f(x) = x³ – 18x² + 96x

= 3(x – 4)(x – 8)
Put f'(x) = 0, we get x = 4, 8
f''(x) = 6x – 36 = 6(x – 6)
which is positive at x = 8 and negative at x = 4

Now, f(0) = 0,  f(8) = 128
f(4) = 160,      f(9) = 135
∴  least value is 0 and greatest value is 160.

The correct answer is: 160

⇒ 

Solving, we get  

r = 12x² - 4
s = 4
t = 12y² – 4
at (-√2, √2)
r = 20, s = 4, t = 20
rt - s² > 0 and r > 0  ∴ minimum

The correct answer is: 2

∵  [.] greatest integer function
The correct answer is: 1

For max. or min value of u,

Solving these equations, we get
x = y = a

at x = a, y = a
r = 2, s = 1, t = 2
rt – s² = 4 – 1 = 3 > 0 and r > 0

Therefore, u is min at x = a, y = a and min. value is 3a².
The correct answer is: 3