List of practice Questions

Asha and Indra were partners in a firm sharing profits and losses in the ratio of 3 : 2. Their Balance Sheet on 31st March, 2025 was as following : Balance Sheet of Asha and Indra as at 31st March, 2025

On 1st April, 2025, Suraj was admitted for 1/4th share in the profits of the firm on the following terms : (i) Suraj will bring capital proportionate to his share in the profits of the firm. (ii) Goodwill of the firm was valued at ₹ 1,00,000 and Suraj will bring his share of goodwill premium in cash. (iii) Furniture was taken over by Asha at ₹ 1,00,000. (iv) A liability of ₹ 5,000 included in creditors was not likely to arise. (v) Plant and Machinery was revalued at ₹ 4,35,000. Prepare Revaluation Account and Partners' capital accounts on Suraj's admission. Show the calculation of proportionate capital clearly.

The value of the integral \[ \int_{3}^{6} \frac{\sqrt{x}}{\sqrt{9 - x} + \sqrt{x}} \, dx \] is:

A function \( f : \mathbb{R} \to \mathbb{R} \) satisfies \[ f\!\left(\frac{x+y}{3}\right) = \frac{f(x) + f(y) + f(0)}{3} \quad \text{for all } x,y \in \mathbb{R}. \] If \( f'' \) is differentiable at \( x = 0 \), then \( f \) is:

Question:
If \[ f(x) = \begin{cases} x^2 + 3x + a, & x \le 1 \\ bx + 2, & x > 1 \end{cases} \] for \( x \in \mathbb{R} \), and the function is everywhere differentiable, then:

The set of points of discontinuity of the function \[ f(x) = x - [x], \quad x \in \mathbb{R} \] is:

Let \[ A = \begin{bmatrix} 5 & 5\alpha & \alpha \\ 0 & \alpha & 5\alpha \\ 0 & 0 & 5 \end{bmatrix} \] If \[ |A|^2 = 25 \] then \( |\alpha| \) equals:

If \( a, b, c \) are positive real numbers each distinct from unity, then the value of the determinant \[ \begin{vmatrix} 1 & \log_a b & \log_a c \\ \log_b a & 1 & \log_b c \\ \log_c a & \log_c b & 1 \end{vmatrix} \] is:

If \( f(x)=\frac{3x-4{2x-3} \), then \( f(f(f(x))) \) will be:}

Let \( u+v+w=3 \), \( u,v,w \in \mathbb{R} \) and \( f(x)=ux^2+vx+w \) be such that \[ f(x+y)=f(x)+f(y)+xy,\quad \forall x,y \in \mathbb{R}. \] Then \( f(1) \) equals:

Let \( f(x)=\max\{x+[x],\, x-[x]\ \), where \( [x] \) is the greatest integer \( \le x \). Then} \[ \int_{-3}^{3} f(x)\,dx \] has the value:

The concentration of the reactant is reduced from $0.6 \text{ mol L}^{-1}$ to $0.2 \text{ mol L}^{-1}$ in 5 minutes in a first order reaction. Calculate rate constant of the reaction. ($\log 3 = 0.48$)

The solution set of the equation \[ x \in \left(0,\frac{\pi}{2}\right), \quad \tan(\pi \tan x) = \cot(\pi \cot x) \] is:

Why transition elements form interstitial compounds?

If \( 0\le a,b \le 3 \) and the equation \[ x^2 + 4 + 3\cos(ax+b) = 2x \] has real solutions, then the value(s) of \( (a+b) \) is/are:

Why second ionization enthalpies of chromium and copper are exceptionally higher than those of their neighbouring elements?

If the equation \[ \sin^2x - (p+2)\sin x - (p+3) = 0 \] has a solution, then \( p \) must lie in:

Write the unit of (i) second order reaction and (ii) zero order reaction.

The population \( p(t) \) of a certain mouse species follows \[ \frac{dp}{dt} = 0.5p - 450. \] If \( p(0)=850 \), then the time at which population becomes zero is:}

Define Effective collision.

Indicate the type of isomerism exhibited by the following complex: $[Co(en)_3]Cl_3$

Define coordination number.