AP ECET 2026 B.Sc Mathematics Question Paper: Download Answer Key with Solution PDF

AP ECET Questions

• 1.

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

  • 2
    
  • 0
    
  • \( \frac{1}{2} \)
    
  • 3
    
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• 2.

  If \( A = \begin{pmatrix} 2 & x + 9 \\ 1 & 2x \end{pmatrix} \) is invertible, then \( x \neq \):

  • 4
    
  • 1
    
  • 3
    
  • 5
    
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• 3.

  If $f: R \rightarrow[-1,1]$ and $g: R \rightarrow A$ are two surjective mappings and $\sin \left(g(x)-\frac{\pi}{3}\right)=\frac{f(x)}{2} \sqrt{4-f^{2}(x)}$, then $A=$

  • $\left[ 0 , \frac{2\pi}{3}\right]$
  • [-1 , 1]
  • $\left( \frac{-\pi}{2} , \frac{\pi}{2}\right)$
  • $(0 , \pi )$
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• 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
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• 5.

  Let $f(x) = x^2 + 2x + 2, g(x) = - x^2 + 2x - 1 $ and $a, b$ be the extreme values of $f(x), g(x)$ respectively. If $c$ is the extreme value of $\frac{f}{g} (x)$ (for x $\neq$ 1), then $a + 2b + 5c + 4$ =

  • 2
  • 1
  • 4
  • 3
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• 6.

  The sum of the four digit even numbers that can be formed with the digits 0,3,5,4 with out repetition is

  • 14684
  • 43536
  • 46526
  • 52336
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