State whether the following statements are true or false. Correct if false.
i. Nonmetallic character increases from left to right across a period.
ii. Nonmetallic character increases down a group.
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Generally metallic character in period from left to right
B) decreases
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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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The sum value of the series \( \sin p+x \sin (p+q)+ \) \( \left[\left(x^{2}\right) / 2 !\right] \sin (p+2 q)+\ldots \ldots . . \) is
Given series is sin(p + x) sin(p + q) + x2/2! sin(p + 2q) + .... We know that eiα = cos α + i sin α. We develop new series cos p + x cos(p +...
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Explain the variations in effective nuclear charge. i. Across a period ii. Down a group
i. Across a period: As we move across a period, atomic number increases by one and thus, actual nuclear charge (Z) increases by +1 at a time. However, the valence shell remains...
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Explain the trend in electronegativity i. across a period ii. down a group
i. Across a period: a. As we move across a period from left to right in the periodic table, the effective nuclear charge increases steadily. b. Hence, due to the increase in...
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Explain the variation of the following property of elements down a group and across a period. i. Metallic character ii. Nonmetallic character
The variation observed in the metallic and nonmetallic character of elements can be explained in the terms of ionization enthalpy and electron gain enthalpy. i. Metallic character: The ionization enthalpy decreases down the...
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(1.) If \( T={ }_{B}^{A}\left(\begin{array}{cc}0.25 & 0.75 \\ 0.3 & \alpha\end{array}\right) \) is a transition probability matrix, then the value of \( \alpha \) is a) \( 0.5 \) b) \( 0.7 \) c) 0 /d) \( 0.6 \) 2. Rank of matrix \( \left(\begin{array}{cccc}1 & -1 & 2 & 0 \\ 0 & 2 & 0 & 3\end{array}\right) \) is a) 1 b) 0 c) 2 d) \( -1 \)
Is there any answer
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State the trends in the following properties of group 1 and group 2 elements down a group.
Sr. no. Property Down a group i Atomic radii Increases ii Ionic radii Increases iii Ionization enthalpy Decreases iv Electronegativity Decreases v Standard reduction potential Decreases
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H.C.F of \( \left(x^{2}-3 x+2\right) \) and \( \left(x^{2}-4 x+3\right) \)
x2 −3x+2=x 2 −2x−x+2 x(x−2)−1(x−2)=(x−2)(x−1) Now x2 −4x+3=x 2 −3x−x+3 x(x−3)−1(x−3)=(x−3)(x−1) Thus, the only common factor is (x-1)
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