NIMCET 2027 2015 Previous Year Questions (PYQs) – Page 8 of 9
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Let $\bar{P}$ and $\bar{Q}$ denote the complements of two sets P and Q. Then the set $(P-Q)\cup (Q-P) \cup (P \cap Q)$ is
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Solution
Expression: \((P - Q) \cup (Q - P) \cup (P \cap Q)\)
Recall: \(P - Q = P \cap \bar{Q}\) and \(Q - P = Q \cap \bar{P}\).
Thus the union consists of three mutually exclusive parts:
- Elements only in \(P\): \(P \cap \bar{Q}\)
- Elements only in \(Q\): \(Q \cap \bar{P}\)
- Elements in both: \(P \cap Q\)
The union of these three pieces is precisely all elements that are in \(P\) or \(Q\):
\((P - Q) \cup (Q - P) \cup (P \cap Q) = P \cup Q\).
The radius of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}$and having it centre
at (0, 3) is
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A function $f : (0,\pi) \to R$
defined by $f(x) = 2 sin x + cos 2x$ has
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A matrix $M_r$ is defined as $M_r=\begin{bmatrix} r &r-1 \\ r-1&r \end{bmatrix} , r \in N$ then the value of $det(M_1) + det(M_2) +...+ det(M_{2015})$ is
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If $\vec{AC}=2\hat{i}+\hat{j}+\hat{k}$ and $\vec{BD}=-\hat{i}+3\hat{j}+2\hat{k}$ then the area of the quadrilateral ABCD is
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The value of $sin^{-1}\frac{1}{\sqrt{2}}+sin^{-1}\frac{\sqrt{2}-\sqrt{1}}{\sqrt{6}}+sin^{-1}\frac{\sqrt{3}-\sqrt{2}}{\sqrt{12}}+...$ to infinity , is equal to
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If two circles
$x^{2}+y^{2}+2gx+2fy=0$ and $x^{2}+y^{2}+2g'x+2f'y=0$ touch each other then whichof the following is true?
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$\int_0^\pi [cotx]dx$ where [.] denotes the greatest integer function, is equal to
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In a right angled triangle, the hypotenuse is four times the perpendicular drawn to it from the opposite vertex. The value of one of the acute angles is
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NIMCET 2027
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