KCET 2026 Mathematics Answer Key- Download PDF

KCET Questions

• 1.

  $$ \int e^x \left( \log x + \frac{1}{x^2} \right) dx = ? $$
  

  • $e^x \left\{ \log x - \frac{1}{x} \right\} + c$
    
  • $e^x \left( \log x + \frac{1}{x} \right) + c$
    
  • $e^x \{ \log x \} + c$
    
  • None
  View Solution

  ---

• 2.

  $$ \int \frac{1}{(x-3)(x-7)} \, dx = ? $$

  • $\frac{1}{4} \log \left( \frac{x+7}{x+3} \right) + c$
    
  • $\frac{1}{4} \log \left( \frac{x-7}{x+3} \right) + c$
    
  • $\frac{1}{4} \log \left( \frac{x-7}{x-3} \right) + c$
    
  • None
  View Solution

  ---

• 3.

  $$ \lim_{x \to 0} \frac{1 - \cos x}{x^2} = $$

  • $\frac{1}{3}$
    
  • $\frac{1}{2}$
    
  • 3
    
  • 2
  View Solution

  ---

• 4.

  The number of bijective functions from set $A$ to itself when $A$ contains $97$ elements, is:

  • 97
    
  • \((97)^2\)
    
  • 97!
    
  • \(2^{97}\)
  View Solution

  ---

• 5.

  $$ \int e^x (\tan x + \sec^2 x) \, dx = ? $$
  

  • $e^x \sec x + c$
    
  • $e^x \tan x + c$
    
  • $e^x \cot x + c$
    
  • $e^x \tan^2 x + c$
  View Solution

  ---

• 6.

  $$ \int \frac{dx}{x(x^{10}+1)} = $$

  • $\frac{1}{10} \log \left( \frac{x^{10}}{x^{10}+1} \right) + c$
    
  • $\frac{1}{10} \log \left( \frac{x^{10}}{x^{10}-1} \right) + c$
    
  • $\log \left( \frac{x^{10}}{x^{10}+1} \right) + c$
    
  • None
  View Solution