List of practice Questions

Statement I: The function $f(x)=x^2$ is decreasing in the interval $(0,\infty)$.
Statement II: Any function $y=f(x)$ is decreasing if $\dfrac{dy}{dx}& Lt;0$.
Which of the following is correct?
The antiderivative of $\dfrac{1}{x\sqrt{x^2-1}},\; x>1$ with respect to $x$ is
The value of \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin^{7}x \, dx \] is
If $\vec{a}$ is a nonzero vector of magnitude $a$ and $\lambda$ is a nonzero scalar, then $\lambda \vec{a}$ is a unit vector if
The position vector of the midpoint of the line joining the points $P(2,3,4)$ and $Q(4,1,-2)$ is
The direction ratios of the $x$-axis are
A matrix has 13 elements. The number of possible different orders it can have is
For the matrix $A=\begin{bmatrix}5 & 0 \\ 0 & 5\end{bmatrix}$, the value of $|\text{adj}\,A|$ is
The derivative of $\sin^{-1}x$ exists in the interval
If $x-y=\pi$, then $\dfrac{dy}{dx}$ is
The minimum value of $f(x)=|x|,\; x\in \mathbb{R}$ is
Atridatta Company Limited issued 10,000, 10% debentures of ₹ 100 each on 01.04.2024 at a discount of 10% and redeemable at a premium of 10%.
Pass journal entries relating to the issue of debentures and debenture interest for the period ending 31.03.2025 assuming that interest is paid half yearly on \(30^{\text{th}}\) September and \(31^{\text{st}}\) March, tax deducted at source is 10%.
From the following Balance sheets of Sunstar Company Limited on 31.03.2024 and 31.03.2025, prepare Comparative Balance sheet :
From the following particulars, calculate :
a) Current Ratio,
b) Debt to Capital Employed Ratio,
c) Trade Receivables Turnover Ratio,
d) Trade Payables Turnover Ratio,
e) Operating Ratio and
f) Net Profit Ratio.
If a relation $R$ in the set $\{1,2,3\}$ be defined by $R=\{(1,1),(2,2)\}$, then $R$ is
The domain of $\tan^{-1}x$ is
Geetha, Latha and Sangeetha are partners sharing profits and losses in the ratio of \(5 : 3 : 2\) respectively. Latha retires from the firm. Geetha and Sangeetha decided to share future profits in the ratio of \(3 : 2\).
Calculate Gaining Ratio of Geetha and Sangeetha.
Anil, Vishal and Sunil are partners sharing profits and losses in the ratio of \(4 : 3 : 3\). Their capitals on 01.04.2025 are ₹ 1,00,000, ₹ 80,000 and ₹ 50,000 respectively.
Vishal died on 31.12.2025. The partnership deed provides the following :
a) Interest on capital at 12% per annum.
b) Salary to Vishal ₹ 2,000 per month.
c) Vishal's share of goodwill ₹ 14,000 [as per A.S. -- 26].
d) Vishal's share of accrued profit upto the date of death, based on previous year profit.
Firm's previous year profit was ₹ 36,000.
Prepare Vishal's Executors Account.
From the following particulars, prepare statement of profit and loss for the year ended 31.03.2025 as per Schedule III of Companies Act, 2013 :
LG Company Limited earned a net profit of ₹ 7,00,000 for the year ended 31.03.2025. Depreciation for the year is ₹ 1,50,000. There was a profit of ₹ 60,000 on assets sold which was transferred to statement of profit and loss.
Trade receivables decreased during the year by ₹ 55,000 and trade payables also decreased by ₹ 45,000.
Compute cash flow from operating activities by indirect method.
Govind and Sudeep are partners sharing profits and losses in the ratio of \(3 : 1\) respectively. Their Balance sheet as on 31.03.2025 is as follows :
Balance Sheet as on 31.03.2025
On 01.04.2025, they admitted Tarun into partnership on following terms :
a) Tarun should bring in ₹ 30,000 as capital for \(1/5^{\text{th}}\) share and ₹ 10,000 towards goodwill [As per A.S. -- 26].
b) Goodwill amount is withdrawn by old partners.
c) Depreciate furniture at 5%.
d) Appreciate building value by 10%.
e) Machinery revalued at ₹ 27,000.
Prepare :
i) Revaluation Account,
ii) Partners' Capital Accounts and
iii) New Balance Sheet of firm on 01.04.2025.
Anitha and Sunitha are equal partners. Their Balance Sheet on 31.03.2025 is as under :
a) Assets realised as follows :
Debtors ₹ 30,000 ; Bills Receivable ₹ 12,000 ; Computers ₹ 25,000 ; Machinery ₹ 45,000 ; Land ₹ 85,000 ; and Unrecorded investment ₹ 3,000
b) Liabilities are paid in full.
c) Cost of dissolution amounted to ₹ 6,000.
Prepare :
i) Realisation Account,
ii) Partners' Capital Accounts and
iii) Bank Account.
Supreme Company Limited issued 10,000 equity shares of ₹ 100 each at a premium of ₹ 10 per share. The amount payable is as follows :
On application ₹ 20
On allotment ₹ 50 (including premium)
On first and final call ₹ 40.
All the shares were subscribed and money duly received except the first and final call on 500 shares.
The directors forfeited these shares and re-issued them as fully paid-up at ₹ 80 per share.
Pass the necessary journal entries regarding issue, forfeiture and re-issue of shares.
Expand R.O.I.
State any two differences between fixed capital method and fluctuating capital method.