List of practice Questions

At $ T(K) $, the solubility product of $ AX $ is $ 10^{-10} $. What is the molar solubility of $ AX $ in 0.1 M HX solution?

If the eccentricity of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ is $ \sec \alpha $, then the area of the triangle formed by the asymptotes of the hyperbola with any of its tangent is:

When a mass $ m $ is connected individually to the springs $ s_1 $ and $ s_2 $, the oscillation frequencies are $ v_1 $ and $ v_2 $. If the same mass is attached to the two springs as shown in the figure, the oscillation frequency would be:

Two toroids with number of turns 400 and 200 have average radii respectively 30 cm and 60 cm. If they carry the same current, the ratio of magnetic fields in these two toroids is:

The correct order of oxidizing power of the given ions is Given: $ E^{\circ}_{\text{Mg}^{2+}/\text{Mg}} = -2.36 \, \text{V} $ and $ E^{\circ}_{\text{Cl}_2/\text{Cl}^-} = +1.36 \, \text{V}$

Evaluate the expression: \[ \frac{\sin 1^\circ + \sin 2^\circ + \dots + \sin 89^\circ}{2(\cos 1^\circ + \cos 2^\circ + \dots + \cos 44^\circ) + 1} =\]

A 4 kg mass is suspended as shown in the figure. All pulleys are frictionless and spring constant $ K $ is $ 8 \times 10^3 $ Nm$^{-1}$. The extension in spring is ( $ g = 10 $ ms$^{-2}$ )

A carrier is simultaneously modulated by two sine waves with modulation indices of 0.3 and 0.4; then the total modulation index is:

Observe the following reaction: $ 2A_2(g) + B_2(g) \xrightarrow{T(K)} 2A_2B(g) + 600 \text{ kJ} $. The standard enthalpy of formation $ (\Delta_f H^\circ) $ of $ A_2B(g) $ is:

Which of the following is an example for fibre?

Observe the following amino acids:

If $ 0<x<\frac{1}{2} $ and $ \alpha = \sin^{-1} x + \cos^{-1} \left(\frac{x}{2} +\frac{\sqrt{3} - 3x^2}{2} \right) $, then $ \tan \alpha + \cot \alpha = $:

The locus of the midpoint of the portion of the line $ x \cos \alpha + y \sin \alpha = p $ intercepted by the coordinate axes, where $ p $ is a constant, is:

If $f(x) = \begin{cases} ax^2 + bx - \frac{13}{8}, & x \le 1 \\ 3x - 3, & 1<x \le 2 \\ bx^3 + 1, & x>2 \end{cases}$is differentiable $\forall x \in \mathbb{R}$, then $ a - b = $

Which of the following is NOT a unit of permeability?

As shown in the figure, two blocks of masses $m_1$ and $m_2$ are connected to a spring of force constant $k$. The blocks are slightly displaced in opposite directions to $x_1, x_2$ distances and released. If the system executes simple harmonic motion, then the frequency of oscillation of the system ($\omega$) is:

As shown in the figure, a surface encloses an electric dipole with charges $ \pm6 \times 10^{-6} \, {C} $. The total electric flux through the closed surface is:

The electric field for an electromagnetic wave is given by $ E = 40 \sin(kz - 6 \times 10^8 t) $, where the magnitude of $ E_0 $ is in V/m.
The magnitude of the wave vector $ k $ is

The number of ions present in tris(ethane-1,2-diamine)cobalt(III) sulphate is:

The number of different ways of preparing a garland using 6 distinct white roses and 6 distinct red roses such that no two red roses come together is:

A box contains 20 percent defective bulbs. Five bulbs are randomly chosen. Find the probability that exactly 3 are defective.

Consider the following statements:
Statement I: The entropy of pure crystalline solid approaches zero as the temperature approaches absolute zero value.
Statement II: For a reaction at equilibrium, $\Delta G$ is zero.

Tropolone is an example for which of the following class of compounds?

Determine the values of $a$ and $b$ for which the function $f(x)$ defined as: \[ f(x) = \begin{cases} 1 + |\sin x|^{\left(\frac{a}{|\sin x|}\right)} & \text{if } \frac{-\pi}{6} < x < 0, \\ b & \text{if } x = 0, \\ e^{\left(\frac{\tan 2x}{\tan 3x}\right)} & \text{if } 0 < x < \frac{\pi}{6} \end{cases} \] is continuous at $x = 0$.

If $f(x) = \begin{cases} 2x + 3, & \text{if } x \leq 1 \\ 2ax + bx, & \text{if } x > 1 \end{cases}$ is differentiable $\forall x \in \mathbb{R}$, then $f(2) =$