The correct statements among the following are:
i. Saline hydrides produce \( \text{H}_2 \) gas when reacted with water.
ii. Presently ~77% of the industrial dihydrogen is produced from coal.
iii. Commercially marketed \( \text{H}_2 \text{O}_2 \) contains 3% \( \text{H}_2 \text{O}_2 \).
Step 1: Statement (i) is true because saline hydrides like NaH react with water to produce hydrogen gas (\( \text{H}_2 \)).
Step 2: Statement (ii) is false because most industrial hydrogen is produced from natural gas, not coal.
Step 3: Statement (iii) is true because commercially available \( \text{H}_2 \text{O}_2 \) typically contains 3% hydrogen peroxide. Thus, the correct answer is (B) i, iii only.
At \( 27^\circ C \), the degree of dissociation of weak acid (HA) in its 0.5M aqueous solution is 1%. Its \( K_a \) value is approximately:
In a one litre flask, 2 moles of \( A_2 \) was heated to \( T(K) \) and the above equilibrium is reached. The concentrations at equilibrium of \( A_2 \) and \( B_2 \) are \( C_1(A_2) \) and \( C_2(B_2) \) respectively. Now, one mole of \( A_2 \) was added to flask and heated to \( T(K) \) to establish the equilibrium again. The concentrations of \( A_2 \) and \( B_2 \) are \( C_3(A_2) \) and \( C_4(B_2) \) respectively. What is the value of \( C_3(A_2) \) in mol L\(^{-1}\)?
Given the function:
\[ f(x) = \begin{cases} \frac{(2x^2 - ax +1) - (ax^2 + 3bx + 2)}{x+1}, & \text{if } x \neq -1 \\ k, & \text{if } x = -1 \end{cases} \]
If \( a, b, k \in \mathbb{R} \) and \( f(x) \) is continuous for all \( x \), then the value of \( k \) is:
Given the function:
\[ f(x) = \begin{cases} \frac{2x e^{1/2x} - 3x e^{-1/2x}}{e^{1/2x} + 4e^{-1/2x}}, & \text{if } x \neq 0 \\ 0, & \text{if } x = 0 \end{cases} \]
Determine the differentiability of \( f(x) \) at \( x = 0 \).
A magnet suspended in a uniform magnetic field is heated so as to reduce its magnetic moment by 19%. By doing this, the time period of the magnet approximately
A Carnot heat engine has an efficiency of 10%. If the same engine is worked backward to obtain a refrigerator, then the coefficient of performance of the refrigerator is
Match the following physical quantities with their respective dimensional formulas.