MCQ
Let U be the universal set containing 700 elements. If A, B are subsets of U such that $\text{n(A)}=200,\text{ n(B)}=300$ and $\text{n(A}\cap\text{B)}=100.$ Then, $\text{n(A}'\cap\text{B}')=$
- A400
- B600
- ✓300
- DNone of these.
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$2.$ Equation of a common tangent with positive slope to the circle as well as to the hyperbola is
$(A)$ $2 x-\sqrt{5} y-20=0$ $(B)$ $2 x-\sqrt{5} y+4=0$
$(C)$ $3 x-4 y+8=0$ $(D)$ $4 x-3 y+4=0$
$2.$ Equation of the circle with $\mathrm{AB}$ as its diameter is
$(A)$ $x^2+y^2-12 x+24=0$ $(B)$ $x^2+y^2+12 x+24=0$
$(C)$ $\mathrm{x}^2+\mathrm{y}^2+24 \mathrm{x}-12=0$ $(D)$ $x^2+y^2-24 x-12=0$
Give hte answer question $1, 2$
| $List-I$ | $List-II$ |
| ($I$) $\left\{x \in\left[-\frac{2 \pi}{3}, \frac{2 \pi}{3}\right]: \cos x+\sin x=1\right\}$ | ($P$) has two elements |
| ($II$) $\left\{x \in\left[-\frac{5 \pi}{18}, \frac{5 \pi}{18}\right]: \sqrt{3} \tan 3 x=1\right\}$ | ($Q$) has three elements |
| ($III$) $\left\{x \in\left[-\frac{6 \pi}{5}, \frac{6 \pi}{5}\right]: 2 \cos (2 x)=\sqrt{3}\right\}$ | ($R$) has four elements |
| ($I$) $\left\{x \in\left[-\frac{6 \pi}{5}, \frac{6 \pi}{5}\right]: 2 \cos (2 x)=\sqrt{3}\right\}$ | ($S$) has five elements |
| ($VI$) $\left\{x \in\left[-\frac{7 \pi}{4}, \frac{7 \pi}{4}\right]: \sin x-\cos x=1\right\}$ | ($T$) has six elements |
The correct option is: