Area of one circle is 100 times the area of other circle then the ratio of their circumferences is ………………….
A) 1:2
B) 10:1
C) 1:20
D) 30:29
1 Answers
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Two pieces of wire A and B of the same material have their lengths in the ratio 1:2, and their diameters are in the ratio 2:1.
Correct option is: (C) 1 : 8
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Consider a particle of mass \( m \) having linear momentum \( P \) at position \( r \) relative to the origin \( O \). Which of the following equations correctly relates \( r , P , L \) ? a) \( \left[\left(\frac{d L}{d t}\right)+r x\left(\frac{d P}{d t}\right)\right]=0 \) b) \( \left[\left(\frac{d L}{d t}\right)-r x\left(\frac{d P}{d t}\right)\right]=0 \) c) \( \left[\left(\frac{d L}{d t}\right) \times\left(\frac{d r}{d t}\right) \times P\right]=0 \) d) \( \left[\left(\frac{d L}{d t}\right)-\left(\frac{d r}{d t}\right) \times P\right]=0 \)
Correct answer is (b) We know that \(\tau\) = r × F ∵ \(\tau\) \(= \frac{dL}{dt},\) \(F = \frac{dP}{dt}\) \(\left(\frac{dL}{dt}\right) = r \times \left(\frac{dP}{dt}\right)\) \(\left(\frac{dL}{dt}\right) - r \times \left(\frac{dP}{dt}\right) = 0\)
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One end of copper rod is in contact with water at 100 °C and the other end in contact with ice at 0 °C. The length of the rod is 100 cm.
Correct option is: (A) 35 °C
2 Answers 8 views
Let \( \vec{a}, \vec{b}, \vec{c} \) be unit vectors such that \( \vec{a}+\vec{b}+\vec{c}=\overrightarrow{0} \). Which one of the following is correct ? [IIT-2007] (a) \( \vec{a} \times \vec{b}=\vec{b} \times \vec{c}=\vec{c} \times \vec{a}=\overrightarrow{0} \) (b) \( \overrightarrow{ a } \times \overrightarrow{ b }=\overrightarrow{ b } \times \overrightarrow{ c }=\overrightarrow{ c } \times \overrightarrow{ a } \neq \overrightarrow{0} \) (c) \( \overrightarrow{ a } \times \overrightarrow{ b }=\overrightarrow{ b } \times \overrightarrow{ c }=\overrightarrow{ a } \times \overrightarrow{ c } \neq \overrightarrow{0} \) (d) \( \vec{a} \times \vec{b}, \vec{b} \times \vec{c}, \vec{c} \times \vec{a} \) are mutually \( \perp \)
Given that \(\vec a, \vec b\) and \(\vec c\)are unit vectors. i.e., |\(\vec a\)| = |\(\vec b\)| = |\(\vec c\)| = 1 And \(\vec a\) + \(\vec b\) + \(\vec c\) = \(\vec 0\) Then \((\vec a+\vec b+\vec c).(\vec a+\vec b+\vec c)=\vec 0.\vec...
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If each dimension of a cuboid is increased by 4 times, then the total surface area becomes …………….. times the original area.
Correct option is (D) 16 Let \(l,b\;and\;h\) are length, breadth and height of the original cuboid. After increasing each dimension of cuboid by 4 times, length of formed cuboid \(=4\,l,\) breadth of formed cuboid = 4b and height of formed...
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If each dimension of a cuboid is increased by 4 times, then the total surface area becomes …………….. times the original area.
2 Answers
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The ratio of two spheres is 1 : 2, then the ratio of their surface areas is
Correct option is (C) 1 : 4 Let radii of both spheres are r and R respectively. \(\because\) \(\frac rR=\frac12\) \(\therefore\) Ratio of their surface areas \(=\frac{4\pi r^2}{4\pi R^2}\) \(=(\frac rR)^2=(\frac12)^2=\frac14\) = 1 : 4
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In a circle r = 14 cm then area of Quadrant circle is ………………… cm^2
Correct option is B) 154
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The ratio of present ages of P and Q is 3:8 and after 6 years their ages ratio is 4:9 then the age of P at present is …………….. years.
Correct option is (C) 18 Let present ages of P and Q are respectively 3x and 8x. After 6 years, age of P = 3x+6, age of Q = 8x+6. According to given condition, \(\frac{3x+6}{8x+6}=\frac49\) \(\Rightarrow\) 9 (3x+6) =...
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