MCQ
Which of the following equations has $2$ as a root ?
- ✓$ 2 x^2-7 x+6=0 $
- B$ x^2-4 x+5=0 $
- C$ 3 x^2-6 x-2=0 $
- D$ x^2+3 x-12=0 $
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Column $I$
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Column $II$
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| $(a)$ | A man goes $10m$ due east and then $20m$ due north. His distance from the starting point is $.... m.$ | $(p)$ | $25\sqrt{3}$ |
| $(b)$ | In an equilateral triangle with each side $10\ cm,$ the altitude is $ ..... \ cm.$ | $(q)$ | $5\sqrt{3}$ |
| $(c)$ | The area of an equilateral triangle having each side $10\ cm$ is $.... \ cm^2.$ | $(r)$ | $10\sqrt{5}$ |
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The length of diagonal of a rectangle having length $8m$ and breadth $6m$ is $.... m.$
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$(s)$ | $10$ |
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Assertion (A)
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Reason (R)
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A hemisphere of radius 7cm is to be painted outside on the surface. The total cost of painting at ₹ 5 per $cm^2$ is ₹ 2300.
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The total surface volume of a hemisphere is $3\pi\text{r}^2.$
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| $a.$ | The radii of the circular ends of a bucket, in the form of the frustum of a cone of height $30\ cm,$ are $20\ cm$ and $10\ cm$ respectively. The capacity of the bucket is $ ......cm^3$. | $p. $ |
$2418\pi$ |
| $b.$ | The radii of the circular ends of a conical bucket of height $15\ cm$ are $20$ and $12\ cm$ respectively. The slant height of the bucket is $ ...... \ cm.$ | $q.$ | $22000$ |
| $c.$ | The radii of the circular ends of a solid frustum of a cone are $33\ cm$ and $27\ cm$ and its slant height is $10\ cm$. The total surface area of the bucket is $....cm^2$. | $r.$ | $12$ |
| $d.$ | Three solid metallic spheres of radii $3\ cm, 4\ cm$ and $5\ cm$ are melted to form a single solid sphere. The diameter of the resulting sphere is $...... \ cm.$ | $s.$ | $17$ |
