WBJEE 2019 Question Paper with Solution PDFs

WBJEE 2019 Questions

• 1.

  Which logic gate is represented by the following combination of logic gates?

  

  • NAND
  • AND
  • NOR
  • OR
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• 2.

  If \( {}^9P_3 + 5 \cdot {}^9P_4 = {}^{10}P_r \), then the value of \( 'r' \) is:

  • \( 4 \)
  • \( 8 \)
  • \( 5 \)
  • \( 7 \)
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• 3.

  If \( 0 \leq a, b \leq 3 \) and the equation \( x^2 + 4 + 3\cos(ax + b) = 2x \) has real solutions, then the value of \( (a + b) \) is:

  • \( \frac{\pi}{4} \)
  • \( \frac{\pi}{2} \)
  • \( \pi \)
  • \( 2\pi \)
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• 4.

  Let \( f(\theta) = \begin{vmatrix} 1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1 \end{vmatrix} \). Suppose \( A \) and \( B \) are respectively the maximum and minimum values of \( f(\theta) \). Then \( (A, B) \) is equal to:

  • \( (2, 1) \)
  • \( (2, 0) \)
  • \( (\sqrt{2}, 1) \)
  • \( \left(2, \frac{1}{\sqrt{2}}\right) \)
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• 5.

  If \( a, b, c \) are in A.P. and if the equations \( (b - c)x^2 + (c - a)x + (a - b) = 0 \) and \( 2(c + a)x^2 + (b + c)x = 0 \) have a common root, then

  • \( a^2, b^2, c^2 \) are in A.P.
  • \( a^2, c^2, b^2 \) are in A.P.
  • \( c^2, a^2, b^2 \) are in A.P.
  • \( a^2, b^2, c^2 \) are in G.P.
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