List of practice Questions

Using the rules for significant figures, the correct answer for the expression
\(\frac{0.02858 × 0.112}{ 0.5702}\)
will be

Let S be the set of all the natural numbers, for which the line 
\(\frac{x}{a}+\frac{y}{b}=2 \)
is a tangent to the curve
\((\frac{x}{a})^n+(\frac{y}{b})^n=2 \)
at the point (a, b), ab ≠ 0. Then :

If the initial pressure of a gas 0.03 atm, the mass of the gas absorbed per gram of the adsorbent is ____× 10^–2g

A student needs to prepare a buffer solution of propanoic acid and its sodium salt with pH 4. The ratio of 
\(\frac{[CH_3CH_2COO^−]}{[CH_3CH_2COOH] }\)
required to make buffer is _____.
Given : K_a(CH₃CH₂COOH) = 1.3 × 10^–5

Let f : R → R be a differentiable function such that
\(f(\frac{π}{4})=\sqrt2,f(\frac{π}{2})=0 \) and \(f′(\frac{π}{2})=1\)
and let
\(g(x) = \int_{x}^{\frac{\pi}{4}} \left(f'(t)\sec(t) + \tan(t)\sec(t)f(t)\right) \, dt\)
for\( x∈(\frac{π}{4},\frac{π}{2})\) Then \(\lim_{{x \to \frac{\pi}{2}^-}} g(x)\)is equal to