AP ECET 2024 Biotechnology Question Paper with Answer Key PDF

AP ECET Questions

• 1.

  The integral value of \( \int \frac{\cos 2x}{\sin^2 x \cos^2 x} \, dx = \):

  • \( \csc^2 x - \sec^2 x + c \)
    
  • \( \cot x + \tan x + c \)
    
  • \( -\cot x - \tan x + c \)
    
  • \( \csc x - \sec x + c \)
    
  View Solution

  ---

• 2.

  A solution is prepared by dissolving $10 \,g$ of a non-volatile solute (molar mass, $'M^{\prime} g mol ^{-1}$ ) in $360\, g$ of water. What is the molar mass in $g\, mol ^{-1}$ of solute if the relative lowering of vapour pressure of solution is $5 \times 10^{-3}$ ?

  • 199
  • 99.5
  • 299
  • 149.5
  View Solution

  ---

• 3.

  The centre of the circle of curvature for the curve \( y = e^x \) at \( (0, 1) \) is:

  • \( (2, 3) \)
    
  • \( (-2, 3) \)
    
  • \( (2, -3) \)
    
  • \( (-2, -3) \)
    
  View Solution

  ---

• 4.

  Let $A, G, H$ and $S$ respectively denote the arithmetic mean, geometric mean, harmonic mean and the sum of the numbers $a_1 , a_2 , a_3 ....., a_n$ . Then the value of at which the function $f(x) =\displaystyle \sum^n_{k =1} (x -a_k)^2$ has minimum is

  • S
  • H
  • G
  • A
  View Solution

  ---

• 5.

  The rate constants for a reaction at $400\, K$ and $500\, K$ are $2.60 \times 10^{-5} s ^{-1}$ and $2.60 \times 10^{-3} s ^{-1}$ respectively. The activation energy of the reaction in $kJ\, mol ^{-1}$ is

  • 38.3
  • 57.4
  • 114.9
  • 76.6
  View Solution

  ---

• 6.

  The curvature of the straight line \( y = 2x + 3 \) at \( (1, 5) \) is:

  • 2
    
  • 0
    
  • \( \frac{1}{2} \)
    
  • 3
    
  View Solution