CUET UG Applied Mathematics Booster Test 2 - Shares, Debentures and Depreciation -

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CUET UG Applied Mathematics Booster Test 2 - Shares, Debentures and Depreciation

⏱️ 30 Minutes

❓ 20 Questions

📌 Answers are locked once submitted — results and explanations appear at the end.

CUET UG Applied Mathematics Booster Test 2 - Shares, Debentures and Depreciation

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QUESTION 1 OF 20

Let the continuous flow of stock capital investment be \(C(t)=e^{0.02t}\). Evaluate
\(\int_{0}^{1}\,50e^{0.02t} dt\)
approximately to find the accumulated capital.
(Use \(e^{0.02}\approx 1.0202\))

Answer Review

1 Let the continuous flow of stock capital investment be \(C(t)=e^{0.02t}\). Evaluate
\(\int_{0}^{1}\,50e^{0.02t} dt\)
approximately to find the accumulated capital.
(Use \(e^{0.02}\approx 1.0202\))

A ₹25

B ₹50.5

C ₹101

D ₹20

💡 Short Explanation

Integrate the exponential function. Apply the limits. The accumulated capital is approximately ₹50.5.

✅ Correct Answer Explanation

Given, ∫₀¹ 50e^(0.02t) dt Integrating, = 50[(e^(0.02t))/0.02]₀¹ = 2500(e^0.02 − 1) Using, e^0.02 ≈ 1.0202 we obtain, 2500(1.0202 − 1) = 2500(0.0202) = 50.5 Therefore, Accumulated Capital = ₹50.5 Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: ₹25
Underestimates the integral.
Option C: ₹101
Approximately double the correct value.
Option D: ₹20
Incorrect evaluation.

🎯 Strategy

used

Definite Integration

Application:

Integrate the exponential function and substitute the limits.

Final Logic:

Since
2500(1.0202 − 1) = 50.5
Option B is correct.

🧠 Memory Trick

"For (e^{kt}), integrate as (\frac{e^{kt}}{k})."

📚 Class XII – Applied Mathematics – Chapter: Calculus Applications in Financial Mathematics

2 A company divides its capital into
N=500
identical shares.
If a buyer randomly selects one share, what is the probability
P(X)
of selecting a specific share (X)?

A 0.500

B 0.005

C 0.002

D 0.020

💡 Short Explanation

Every share has an equal chance of being selected. Probability equals one divided by the total number of shares.

✅ Correct Answer Explanation

Probability of selecting one particular share is P(X) = 1/500 = 0.002 Therefore, P(X) = 0.002 Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: Represents half the shares.
Option B: Equals 1/200.
Option D: Equals 1/50.

🎯 Strategy

used

Basic Probability

Application:

Probability = Favourable Outcomes ÷ Total Outcomes.

Final Logic:

Since
1/500 = 0.002
Option C is correct.

🧠 Memory Trick

"One specific object ⇒ Probability = 1 ÷ Total Objects."

📚 Class XII – Applied Mathematics – Chapter: Probability – Topic: Basic Probability

3 Which of the following statements is INCORRECT regarding Face Value (F)?

A It is the original value printed on the share certificate.

B It is also known as nominal value.

C Dividend \(=r\%\times F\)

D (F) frequently changes based on market demand.

💡 Short Explanation

Face value is fixed by the company. Market value changes, not face value.

✅ Correct Answer Explanation

Face value is the nominal value printed on the share certificate. It remains fixed unless altered through corporate actions such as a stock split. Market demand affects only the market value, not the face value. Therefore, Option D is incorrect

❓ Why Other Options Are Incorrect

Why Other Options Are Correct

Option A: Correct definition.
Option B: Face value is also called nominal value.
Option C: Dividend is calculated on face value.

🎯 Strategy

used

Concept Recall

Application:

Distinguish between face value and market value.

Final Logic:

Market demand changes market value, not face value.

🧠 Memory Trick

"Face Value is Fixed; Market Value Moves."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Face Value of Shares

4 The market value (M) fluctuates. If the market value vector of two shares is
\(\vec{V}=104\hat{i}+90\hat{j},\)
what is the squared magnitude \(∣\vec{V}∣^{2}\)?

A 18916

B 10400

C 194

D 9360

💡 Short Explanation

Use the formula for the squared magnitude of a vector. Square each component and add them together.

✅ Correct Answer Explanation

For a vector V = ai + bj The squared magnitude is |V|² = a² + b² Here, a = 104, b = 90 Therefore, |V|² = 104² + 90² = 10816 + 8100 = 18916 Hence, |V|² = 18916 Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: Uses only (104^2).
Option C: Adds the components instead of squaring them.
Option D: Incorrect arithmetic.

🎯 Strategy

used

Vector Magnitude Formula

Application:

Apply
|V|² = a² + b²
Since,
104² + 90² = 18916
Option A is correct.

🧠 Memory Trick

"Square → Add → Magnitude²."

📚 Class XII – Applied Mathematics – Chapter: Vectors

5 Find the purchase price \(V\) of a ₹600, 8% bond payable semi-annually, redeemable at par (\(C=F\)) in \(n=5\) years, if the yield rate is 8% per annum compounded semi-annually.

A ₹405.3

B ₹600

C ₹194.7

D ₹648

💡 Short Explanation

The coupon rate equals the yield rate. When coupon rate equals yield rate, the bond sells at par.

✅ Correct Answer Explanation

Given, Face value F = ₹600 Coupon rate = 8% Yield rate = 8% Since, Coupon Rate = Yield Rate the purchase price equals the face value. Therefore, V = ₹600 Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: Lower than the par value.
Option C: Much below the correct purchase price.
Option D: Represents a premium price, which is incorrect here.

🎯 Strategy

used

Bond Pricing Rule

Application:

Recall that when coupon rate equals yield rate, the bond sells at par.

Final Logic:

Since
Coupon Rate = Yield Rate
V = F = ₹600

🧠 Memory Trick

"Coupon Rate = Yield Rate ⇒ Bond at Par."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Bond Valuation

6 Which mathematical relations are valid for shares traded in the open market?
(i) Discount \(=F-M\)(when \(M<F\))
(ii) Premium \(=M-F\)(when \(M>F\))
(iii) Par value condition is \(M+F=0\)

A (i) only

B (iii) only

C (i) and (ii) only

D (ii) and (iii) only

💡 Short Explanation

Discount equals face value minus market value. Premium equals market value minus face value. At par means (M=F), not (M+F=0).

✅ Correct Answer Explanation

When a share sells below face value, Discount = F − M When a share sells above face value, Premium = M − F At par, M = F not M + F = 0 Therefore, Statements (i) and (ii) are correct, while statement (iii) is false. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: Ignores the premium relation.
Option B: Statement (iii) is false.
Option D: Includes the incorrect statement (iii).

🎯 Strategy

used

Formula Recall

Application:

Recall the standard formulas for premium, discount, and par.

Final Logic:

Only statements (i) and (ii) are mathematically correct.

🧠 Memory Trick

"Discount = Face − Market; Premium = Market − Face."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Shares at Premium and Discount

7 Match the following numerical scenarios regarding shares and dividends in List I with their correct calculated values in List II.

List I (Scenarios)	List II (Calculated Values)
1. The total dividend income from 200 shares of face value ₹100 each, paying an 8% annual dividend.	a. ₹6,480
2. The total cost to purchase ₹7,200 worth of stock at a market value of ₹90.	b. 60
3. The total cost to purchase ₹4,500 worth of stock at a ₹4 premium (assuming face value is ₹100).	c. ₹4,680
4. The number of shares held if the total investment is ₹5,400 and the market value of one share is ₹90.	d. ₹1,600

A 1–d, 2–a, 3–c, 4–b

B 1–a, 2–d, 3–b, 4–c

C 1–d, 2–c, 3–a, 4–b

D 1–b, 2–a, 3–d, 4–c

💡 Short Explanation

Calculate each scenario individually and match it with the corresponding value.

✅ Correct Answer Explanation

(1) Dividend Income Dividend per share = 8% × 100 = ₹8 For 200 shares, 200 × 8 = ₹1,600 So, 1 → d (2) Purchase Cost Market value per share = ₹90. To obtain stock worth ₹7,200 (face value), Cost = 7200 × (90/100) = ₹6,480 So, 2 → a (3) Purchase Cost at ₹4 Premium Market value = 100 + 4 = ₹104 Cost of ₹4,500 face value stock: 4500 × (104/100) = ₹4,680 So, 3 → c (4) Number of Shares 5400 / 90 = 60 So, 4 → b Hence, 1 – d, 2 – a, 3 – c, 4 – b Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

The remaining options mismatch one or more calculated values.

🎯 Strategy

used

Individual Calculation

Application:

Solve each numerical case separately before matching.

Final Logic:

Correct matching is
1 – d, 2 – a, 3 – c, 4 – b

🧠 Memory Trick

"Solve Each → Then Match."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Shares and Dividend

8 Arrange the steps to calculate total dividend \(D_{total}\), knowing dividend is paid on face value:
1. Calculate dividend per share: \(D_{single}=r\%\times F\).
2. Multiply by number of shares: \(D_{total}=N\times D_{single}\).
3. Identify \(F\) and dividend rate \(r\%\).

A 3, 1, 2

B 1, 2, 3

C 2, 3, 1

D 3, 2, 1

💡 Short Explanation

First identify the face value and dividend rate. Then calculate the dividend per share. Finally multiply by the number of shares.

✅ Correct Answer Explanation

The logical order is: Step 1 Identify F, r% ↓ Step 2 Compute D_single = r% × F ↓ Step 3 Compute D_total = N × D_single Thus, 3, 1, 2 Hence, Option A is correct.

❓ Why Other Options Are Incorrect

They attempt calculations before identifying the required information.

🎯 Strategy

used

Sequential Reasoning

Application:

Follow the natural order of dividend computation.

Final Logic:

Identify → Calculate per share → Multiply.

🧠 Memory Trick

"Know Face Value → Find Dividend → Multiply."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Dividend Calculation

9 The total cost function of buying (x) shares at market value (M) with brokerage (B) per share is
\(C\left(x\right)=\left(M+B\right)x.\)
What is the slope (m) of this linear function?
Answer: B

A \(M-B\)

B \(M+B\)

C \(x\)

D \(B\)

💡 Short Explanation

The slope of a linear function is the coefficient of the variable.

✅ Correct Answer Explanation

The equation is C(x) = (M + B)x Comparing with y = mx the slope is m = M + B Therefore, m = M + B Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: Incorrect expression.
Option C: Variable, not slope.
Option D: Ignores market value.

🎯 Strategy

used

Linear Function

Application:

Identify the coefficient of the independent variable.

Final Logic:

For
C(x) = (M + B)x
The slope equals
M + B

🧠 Memory Trick

"Slope = Coefficient of x."

📚 Class XII – Applied Mathematics – Chapter: Coordinate Geometry / Financial Mathematics

10 A broker subtracts charges over four selling transactions:
₹10, ₹12, ₹14, ₹16.
What are the 3-period moving averages \(MA_{3}\)?

A 10, 12

B 14, 16

C 12, 14

D 12, 15

💡 Short Explanation

Compute the average of every consecutive group of three observations.

✅ Correct Answer Explanation

First moving average: First moving average: (10 + 12 + 14) / 3 = 12 Second moving average: (12 + 14 + 16) / 3 = 14 Therefore, MA₃ = (12, 14) Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: Uses original observations.
Option B: Does not calculate averages.
Option D: Second average is incorrect.

🎯 Strategy

used

Moving Average

Application:

Average each consecutive block of three observations.

Final Logic:

The moving averages are
12,;14.

🧠 Memory Trick

"Slide the Window, Then Average."

📚 Class XII – Applied Mathematics – Chapter: Statistics – Topic: Moving Average

11 Assertion (A): Equity shareholders always receive a fixed rate of dividend (r%).
Reason (R): Equity shareholders are the owners of the company and bear the highest risk.

A Both A and R are false

B A is true, R is false

C Both A and R are true, and R is the correct explanation of A

D A is false, R is true

💡 Short Explanation

Equity shareholders do not receive a fixed dividend. Their dividend depends on the company's profits and dividend policy. They are the owners and therefore bear the highest risk.

✅ Correct Answer Explanation

Assertion (A): The statement is false because equity shareholders receive dividends only when declared by the company. Their dividend is not fixed. Reason (R): The statement is true because equity shareholders are the owners of the company and are paid only after all other obligations have been met. Hence, they bear the highest level of investment risk. Therefore, Assertion is false, but Reason is true. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: Incorrect because the reason is true.
Option B: Incorrect because the assertion is false.
Option C: Incorrect because equity dividends are not fixed.

🎯 Strategy

used

Assertion–Reason Analysis

Application:

Check each statement separately before deciding whether the reason explains the assertion.

Final Logic:

Equity shareholders have ownership rights but no guaranteed dividend.

🧠 Memory Trick

"Equity = Ownership + Variable Dividend."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Equity Shares

12 Because equity shareholders are the owners of the company, what comparative level of risk do they bear?

A Highest risk

B No risk

C Lowest risk

D Fixed risk

💡 Short Explanation

Equity shareholders receive returns only after all creditors and preference shareholders have been paid. Therefore, they bear the highest risk.

✅ Correct Answer Explanation

Equity shareholders are the residual claimants of the company. This means: They receive dividends only if profits are available. They receive payment after all liabilities are settled during liquidation. Consequently, Equity shareholders bear the highest risk. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: Equity investment always carries risk.
Option C: Debenture holders generally face lower risk.
Option D: Risk is not fixed; it depends on company performance.

🎯 Strategy

used

Concept Recall

Application:

Recall the rights and position of equity shareholders in a company.

Final Logic:

Ownership brings the highest level of financial risk.

🧠 Memory Trick

"Higher Ownership → Higher Risk."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Equity Shares

📄 Passage

"Debentures are written instruments of debt that companies issue. L&T Finance Limited came up with a public issue of secured, redeemable, non-convertible debentures of face value ₹1,000 each for an amount of ₹500 crore."

Etymologically, the word 'debenture' is derived from:

A "Dividend" meaning profit

B "Debere" meaning to borrow or loan

C "Datum" meaning given

D "Deduce" meaning subtract

💡 Short Explanation

The word debenture originates from the Latin word Debere. It means to owe, borrow, or loan.

✅ Correct Answer Explanation

A debenture is a written acknowledgement of debt. The term comes from the Latin word Debere, meaning "to owe" or "to borrow." Therefore, B is correct

❓ Why Other Options Are Incorrect

Option A: Dividend relates to profit distribution.
Option C: "Datum" means something given.
Option D: "Deduce" means infer or conclude.

🎯 Strategy

used

Terminology Recall

Application:

Remember the origin of the financial term.

Final Logic:

Debenture comes from Debere, meaning to borrow.

🧠 Memory Trick

"Debenture → Debt → Debere."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Debentures

📄 Passage

According to the passage context, do debenture holders carry voting rights?

A Yes, equal to equity shareholders

B Yes, but only in emergencies

C No, because they are creditors and not owners

D No, because they are preference shareholders

💡 Short Explanation

Debenture holders lend money to the company. They are creditors, not owners. Therefore, they do not have voting rights.

✅ Correct Answer Explanation

A debenture represents a loan given to the company. Debenture holders: Receive fixed interest. Are creditors. Do not participate in company management. Hence, Debenture holders have no voting rights. Therefore, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: Voting rights belong to equity shareholders.
Option B: No such emergency voting provision exists.
Option D: Debenture holders are creditors, not preference shareholders.

🎯 Strategy

used

Concept Recall

Application:

Differentiate between owners and creditors.

Final Logic:

Only shareholders possess voting rights; debenture holders do not.

🧠 Memory Trick

"Debt Gives Interest, Not Voting Rights."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Debentures

15 Let the income from Investment A be represented by a rectangle of height 70.5 and base 10, and Investment B by a rectangle of height 68.25 and base 10.
Find the absolute difference in bounded area \(\Delta A\)(representing total income difference over 10 years).

A 10.5

B 25.5

C 200.5

D 22.5

💡 Short Explanation

Area of a rectangle = Base × Height. Find the areas of both rectangles and subtract them.

✅ Correct Answer Explanation

Area representing Investment A: Aₐ = 10 × 70.5 = 705 Area representing Investment B: Aᵦ = 10 × 68.25 = 682.5 Difference in area: ΔA = 705 − 682.5 = 22.5 Therefore, ΔA = 22.5 Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: Incorrect subtraction.
Option B: Does not equal the difference between the two areas.
Option C: Much larger than the actual difference.

🎯 Strategy

used

Area Comparison

Application:

Compute each rectangle's area and subtract.

Final Logic:

Since
705-682.5=22.5,
Option D is correct.

🧠 Memory Trick

"Area = Base × Height; Compare by Subtracting."

📚 Class XII – Applied Mathematics – Chapter: Mensuration Applications in Financial Mathematics

16 A man buys ₹25 face value shares in a company which pays a dividend of 9%. The investment yields 10% on his purchase price.
Let (M) be the market price at which he bought the shares. Find (M).

A ₹22.50

B ₹25.00

C ₹27.50

D ₹30.00

💡 Short Explanation

Dividend is calculated on face value. Yield is calculated on market price. Equate the two to find the purchase price.

✅ Correct Answer Explanation

Dividend per share: = 9% × 25 = ₹2.25 Yield formula: Yield = (Dividend / Market Price) × 100 Given, 10 = (2.25 / M) × 100 Therefore, M = (2.25 × 100) / 10 = 22.5 Hence, M = ₹22.50 Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: Gives only a 9% yield.
Option C: Produces a yield below 9%.
Option D: Produces an even smaller yield.

🎯 Strategy

used

Yield Formula

Application:

Use
Yield = (Dividend / Market Price) × 100

Final Logic:

Solving the equation gives
M = ₹22.50

🧠 Memory Trick

"Yield Uses Market Price; Dividend Uses Face Value."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Yield on Shares

17 Let \(C\) be the original cost and \(S\) be the scrap value. Identify the incorrect statement regarding depreciation:

A Depreciation \(=f(t)\), where value decreases over time

B Total depreciation \(=C+S\)

C Book value \(=C-accumulated depreciation\)

D Reduced efficiency accelerates the depreciation function

💡 Short Explanation

Total depreciation equals the difference between cost and scrap value. It is not the sum of cost and scrap value.

✅ Correct Answer Explanation

The correct formula is Total Depreciation = C − S Therefore, C + S is mathematically incorrect. Hence, Option B is the incorrect statement.

❓ Why Other Options Are Incorrect

Why Other Options Are Correct

Option A: Asset value decreases with time.
Option C: Standard book value formula.
Option D: Greater wear generally increases depreciation.

🎯 Strategy

used

Formula Recall

Application:

Recall the basic depreciation formula.

Final Logic:

Depreciation is
C-S,
not
C+S.

🧠 Memory Trick

"Depreciation = Cost − Scrap."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Depreciation

18 The total depreciation (wearing value) (W) is mathematically equal to:
(i) \(W=C-S\)
(ii) \(W=C+S\)
(iii) \(W=\sum D_{i}\)(sum of annual depreciations over useful life)

A (i) only

B (ii) only

C (i) and (iii) only

D (ii) and (iii) only

💡 Short Explanation

Total depreciation equals the original cost minus scrap value. It is also equal to the sum of annual depreciation charges.

✅ Correct Answer Explanation

The total depreciation is W = C − S Also, W = \sum D_i where D_i represents the depreciation for each year. However, C+S has no meaning in depreciation calculations. Therefore, Statements (i) and (iii) are correct. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: Ignores statement (iii).
Option B: Uses an incorrect formula.
Option D: Includes the incorrect statement (ii).

🎯 Strategy

used

Formula Verification

Application:

Check each mathematical relationship individually.

Final Logic:

Only
C − S
and
∑Dᵢ
represent total depreciation.

🧠 Memory Trick

"Total Depreciation = Cost − Scrap = Sum of Annual Depreciation."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Depreciation

19 A machine has:
Cost \(C=₹10,000\)
Useful life \(n=4\) years
Scrap value \(S=0\)
Find the accumulated depreciation \(\sum D\) after 2 years using the Straight Line Method.

A ₹2,500

B ₹10,000

C ₹7,500

D ₹5,000

💡 Short Explanation

First calculate the annual depreciation using the Straight-Line Method. Multiply it by the number of years.

✅ Correct Answer Explanation

The annual depreciation under the Straight-Line Method is D = (C − S) / n Substituting the values, D = (10,000 − 0) / 4 = 10,000 / 4 = ₹2,500 Accumulated depreciation after 2 years is 2 × 2,500 = ₹5,000 Therefore, ∑D = ₹5,000 Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: ₹2,500 is depreciation for one year only.
Option B: ₹10,000 is the original cost.
Option C: ₹7,500 represents depreciation after three years.

🎯 Strategy

used

Straight-Line Depreciation

Application:

Calculate annual depreciation first, then multiply by the number of completed years.

Final Logic:

Since
₹2,500 × 2 = ₹5,000
Option D is correct.

🧠 Memory Trick

"SLM: Annual Depreciation × Number of Years = Accumulated Depreciation."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Straight-Line Method of Depreciation

20 In the Reducing Balance Method, the book value at the end of the (n)-th year is given by
\(S_{n}=C(1-r)^{n}\)
What does (r) represent?

A Rate of depreciation

B Rate of interest

C Residual value

D Repayment instalment

💡 Short Explanation

In the Reducing Balance Method, a fixed percentage of depreciation is applied each year. This percentage is represented by (r).

✅ Correct Answer Explanation

The formula Sₙ = C(1 − r)ⁿ gives the book value after (n) years, where: (C) = Original cost, (S_n) = Book value after (n) years, (r) = Annual rate of depreciation. Each year, the asset loses the fraction (r) of its current book value. Therefore, Sₙ = C(1 − r)ⁿ Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: The formula concerns depreciation, not interest.
Option C: Residual (scrap) value is the final value of the asset, not the rate.
Option D: Repayment instalments relate to loans, not depreciation.

🎯 Strategy

used

Formula Interpretation

Application:

Identify the meaning of each symbol in the depreciation formula.

Final Logic:

In
Sₙ = C(1 − r)ⁿ
(r) always denotes the annual depreciation rate.

🧠 Memory Trick

"Reducing Balance → Reduce by Rate (r) every year."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Reducing Balance Method of Depreciation

CUET UG Applied Mathematics Booster Test 2 - Shares, Debentures and Depreciation

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