CUET UG Applied Mathematics Booster Test 3 - Shares, Debentures and Depreciation -

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CUET UG Applied Mathematics Booster Test 3 - 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 3 - Shares, Debentures and Depreciation

1 / 20

QUESTION 1 OF 20

The total stock capital raised over time (t) is defined by the rate function
\(C^{'}(t)=100t^{2}\)
Evaluate
\(\int_{0}^{3}\,100t^{2} dt\)
to determine the exact capital raised.

Answer Review

1 The total stock capital raised over time (t) is defined by the rate function
\(C^{'}(t)=100t^{2}\)
Evaluate
\(\int_{0}^{3}\,100t^{2} dt\)
to determine the exact capital raised.

A 300

B 100

C 900

D 2700

💡 Short Explanation

Integrate the given rate function. Substitute the limits (0) and (3).

✅ Correct Answer Explanation

Given, ∫₀³ 100t² dt The integral of 100t² is 100t³ / 3 Applying the limits, [100t³ / 3]₀³ = (100 × 3³) / 3 − 0 = (100 × 27) / 3 = 900 Therefore, Capital Raised = 900. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: Incorrect evaluation.
Option B: Too small.
Option D: Equals (100\times27), forgetting to divide by 3.

🎯 Strategy

used

Definite Integration

Application:

Integrate first, then apply the limits.

Final Logic:

Since
(100 × 27) / 3 = 900
Option C is correct.

🧠 Memory Trick

"∫ t² dt = t³ / 3"

📚 Class XII – Applied Mathematics – Chapter: Calculus Applications

2 A portfolio consists of shares from two companies represented by the vector
\(\vec{P}=10\hat{i}+24\hat{j}\)
Find the magnitude
\(∣\vec{P}∣\), representing the total number of shares.

A 34

B 14

C 240

D 26

💡 Short Explanation

Use the magnitude formula for a vector.

✅ Correct Answer Explanation

For P = 10i + 24j The magnitude is |P| = √(10² + 24²) = √(100 + 576) = √676 = 26 Therefore, |P| = 26. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: Adds components instead of using Pythagoras.
Option B: Incorrect square root.
Option C: Multiplies the components.

🎯 Strategy

used

Vector Magnitude

Application:

Use
Plain text:
|P| = √(x² + y²)

Final Logic:

Since
√676 = 26,
Option D is correct.

🧠 Memory Trick

"Square → Add → Square Root."

📚 Class XII – Applied Mathematics – Chapter: Vectors

3 Find the cost (C) of ₹7200, 8% stock at 90.
(Assume the standard face value of stock = ₹100.)

A ₹6480

B ₹6580

C ₹7200

D ₹8000

💡 Short Explanation

"At 90" means the market price is ₹90 for every ₹100 face value. Multiply the face value investment by (\frac{90}{100}).

✅ Correct Answer Explanation

Cost of purchase is 7200 × (90 / 100) = 6480 Therefore, C = ₹6480 Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: Incorrect multiplication.
Option C: Equals face value.
Option D: Greater than the face value investment.

🎯 Strategy

used

Stock Purchase Formula

Application:

Multiply the face value by the quoted market price percentage.

Final Logic:

Since
7200 × 0.9 = 6480
Option A is correct.

🧠 Memory Trick

"Stock at 90 ⇒ Pay only 90% of Face Value."

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

4 The market value of a stock varies linearly as:
\(M(t)=100+4t\)
Find the bounded area under the curve from \(t=0\) to \(t=5\):
\(\int_{0}^{5}\,(100+4t) dt\)

A 500

B 550

C 600

D 120

💡 Short Explanation

Integrate the linear function. Substitute the upper and lower limits.

✅ Correct Answer Explanation

Given, ∫₀⁵ (100 + 4t) dt Integrating, = 100t + 2t² Applying the limits, [100t + 2t²]₀⁵ = (100 × 5) + (2 × 25) = 500 + 50 = 550 Therefore, Area = 550. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: Ignores the (2t^2) term.
Option C: Incorrect integration.
Option D: Too small.

🎯 Strategy

used

Definite Integration

Application:

Integrate the function and substitute the given limits.

Final Logic:

Since
500+50=550,
Option B is correct.

🧠 Memory Trick

"Integrate First, Then Apply Limits."

📚 Class XII – Applied Mathematics – Chapter: Calculus Applications

5 Which of the following conditions correctly represent shares or bonds sold at par?
(i) Current Yield = Coupon Yield
(ii) Market Price \((M)=\)Face Value \(\left(F\right)\)
(iii) Yield to Maturity (YTM) \(<\)Current Yield

A (i) only

B (ii) only

C (i) and (ii) only

D (i), (ii), and (iii)

💡 Short Explanation

At par means market price equals face value. In this case, the current yield equals the coupon yield. YTM is equal to the current yield at par, not less than it.

✅ Correct Answer Explanation

When a bond or share is sold at par, M=F. Also, Current Yield > Coupon Yield Further, YTM > Current Yield > Coupon Yield Therefore, Statement (iii) is false because YTM is equal, not less than the current yield. Hence, Statements (i) and (ii) are correct. Therefore, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: Omits statement (ii).
Option B: Omits statement (i).
Option D: Includes the incorrect statement (iii).

🎯 Strategy

used

Concept Recall

Application:

Recall the relationships among market price, coupon yield, current yield, and YTM when a bond sells at par.

Final Logic:

At par,
M = F
Coupon Yield = Current Yield = YTM

🧠 Memory Trick

"At Par = Everything Equal."

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

📄 Passage

A bond's current yield is mathematically 9% and its coupon yield is 8%.

The bond satisfies the condition of being sold at:

A Par

B Premium

C Face Value

D Discount

💡 Short Explanation

When current yield is greater than coupon yield, the market price is below the face value. Therefore, the bond is selling at a discount.

✅ Correct Answer Explanation

For a bond sold at a discount, Coupon Yield < Current Yield < YTM Here, 8% < 9%. Since the current yield exceeds the coupon yield, the bond is trading below its face value. Therefore, The bond is sold at a discount. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: At par implies coupon yield equals current yield.
Option B: Premium implies current yield is less than coupon yield.
Option C: Face value alone does not describe the market status.

🎯 Strategy

used

Yield Comparison

Application:

Compare coupon yield with current yield.

Final Logic:

Since
Current Yield > Coupon Yield
the bond sells at a discount.

🧠 Memory Trick

"Higher Current Yield ⇒ Lower Price ⇒ Discount."

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

📄 Passage

A bond's current yield is mathematically 9% and its coupon yield is 8%.

According to the principles of shares, dividend (D) is strictly calculated as a percentage on which variable?

A Face Value ((F))

B Market Value ((M))

C Discounted Value

D Premium Value

💡 Short Explanation

Dividend is always declared on the face value of a share. It is not calculated using the market price.

✅ Correct Answer Explanation

The dividend per share is calculated as Dividend = r% × Face Value where (r%) = Dividend rate (F) = Face value of the share The market value affects the yield, not the dividend itself. Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: Market value is used for calculating yield, not dividend.
Option C: Dividend is never based on discounted value.
Option D: Premium affects the purchase price, not the dividend calculation.

🎯 Strategy

used

Formula Recall

Application:

Remember the standard dividend formula.

Final Logic:

Dividend is always calculated on the face value.

🧠 Memory Trick

"Dividend → Face Value; Yield → Market Value."

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

8 Out of 100 valid dividend formulas, 100 declare dividends on Face Value ((F)), and 0 declare dividends on Market Value ((M)).
What is the exact probability (P(E)) that a randomly chosen correct mathematical model calculates dividend based on (F)?

A 0.6

B 1.0

C 0.0

D 0.5

💡 Short Explanation

Every valid dividend formula uses the face value. Therefore, the probability is 1.

✅ Correct Answer Explanation

Number of favourable outcomes: 100 Total number of valid formulas: 100 Hence, P(E) = 100 / 100 = 1 Therefore, P(E) = 1.0. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: Incorrect probability.
Option C: Would mean no formula uses face value.
Option D: Would mean only half the formulas use face value.

🎯 Strategy

used

Probability Formula

Application:

Use
P(E) = Favourable Outcomes / Total Outcomes

Final Logic:

Since every valid formula uses face value,
P(E) = 1.

🧠 Memory Trick

"All Correct Models → Probability = 1."

📚 Class XII – Applied Mathematics – Chapter: Probability & Financial Mathematics

9 Let (B) denote brokerage.
Which of the following statements about the application of (B) is mathematically incorrect?

A (B) is added to the cost price when stock is purchased.

B (B) is subtracted from the selling price when stock is sold.

C (B) is calculated as a percentage of the company's total profit.

D The broker's charge is called brokerage.

💡 Short Explanation

Brokerage is charged on the value of the transaction. It is not based on the company's profit.

✅ Correct Answer Explanation

Brokerage is a fee charged by the broker for executing a purchase or sale of securities. It is generally calculated as a percentage of the purchase value or selling value, not the company's profits. Therefore, Option C is mathematically incorrect.

❓ Why Other Options Are Incorrect

Why Other Options Are Correct

Option A: Brokerage is added while purchasing shares.
Option B: Brokerage is deducted while selling shares.
Option D: Brokerage is the fee paid to the broker.

🎯 Strategy

used

Concept Recall

Application:

Differentiate between brokerage charges and company profits.

Final Logic:

Brokerage depends on the transaction amount, not the company's earnings.

🧠 Memory Trick

"Brokerage Follows the Trade, Not the Company's Profit."

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

10 A person sells ₹5000, 12% stock at ₹156.
Calculate the Selling Price (S.P.) of the stock before deducting brokerage.

A ₹6000

B ₹7200

C ₹7500

D ₹7800

💡 Short Explanation

"₹5000 stock" refers to the face value. Selling price is calculated using the market quotation.

✅ Correct Answer Explanation

The selling price is S.P. = 5000 × (156 / 100) Therefore, = 5000 × 1.56 = 7800 Hence, Selling Price = ₹7800. Thus, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: Underestimates the market value.
Option B: Incorrect multiplication.
Option C: Does not use the quoted market price correctly.

🎯 Strategy

used

Stock Quotation Formula

Application:

Multiply the face value of the stock by the quoted market price percentage.

Final Logic:

Since
5000 × (156 / 100) = 7800
Option D is correct.

🧠 Memory Trick

"Selling Price = Face Value × (Market Quote ÷ 100)."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Sale of Shares and Brokerage

11 Assertion (A): Equity shareholders' liability is mathematically unlimited.
Reason (R): They do not have the right to participate in organizational affairs.

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 have limited liability, not unlimited liability. They do have voting rights and can participate in company affairs.

✅ Correct Answer Explanation

Assertion (A): The statement is false because equity shareholders are liable only up to the unpaid amount (if any) on their shares. Their liability is limited. Reason (R): The statement is also false because equity shareholders have the right to: Vote in company meetings, Elect directors, Participate in important decisions. Therefore, Both Assertion and Reason are false. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: Liability is not unlimited.
Option C: Both statements are false.
Option D: The reason is also false.

🎯 Strategy

used

Assertion–Reason Analysis

Application:

Evaluate each statement independently before checking whether one explains the other.

Final Logic:

Equity shareholders have limited liability and voting rights.

🧠 Memory Trick

"Equity = Limited Liability + Voting Rights."

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

12 The risk index (R_i) of a stock over 5 days is
\(\left\{10,\ 15,\ 20,\ 25,\ 30\right\}\)
What is the 3-day moving average (MA_3) for the final three days
\(\left\{20,\ 25,\ 30\right\}\)?

A 20

B 25

C 30

D 15

💡 Short Explanation

Compute the average of the last three observations.

✅ Correct Answer Explanation

The final three values are 20, 25, 30 Their average is (20 + 25 + 30) / 3 = 75 / 3 = 25 Therefore, MA₃ = 25. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: First moving average, not the final one.
Option C: Maximum value, not the average.
Option D: Too small.

🎯 Strategy

used

Moving Average

Application:

Average the required consecutive observations.

Final Logic:

Since
75 / 3 = 25
Option B is correct.

🧠 Memory Trick

"Moving Average = Sum ÷ Number of Terms."

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

13 A ₹2,000, 8% bond is redeemable at the end of 10 years at ₹2,100, and the required yield is 10% effective.
Match the bond variables in List I with their correctly calculated numerical values in List II.

List I	List II
1. Face Value	a. ₹160
2. Redemption Value (C)	b. ₹1,792
3. Periodic Interest Payment (R)	c. ₹2,100
4. Purchase Price of the Bond (V)	d. ₹2,000

A 1–a, 2–d, 3–c, 4–b

B 1–d, 2–c, 3–a, 4–b

C 1–b, 2–c, 3–a, 4–d

D 1–d, 2–a, 3–c, 4–b

💡 Short Explanation

Identify each quantity and match it with its corresponding value.

✅ Correct Answer Explanation

Face Value = ₹2,000 → d • Redemption Value = 105% × 2000 = ₹2,100 → c • Annual Interest = 8% × 2000 = ₹160 → a Purchase Price • Purchase Price Given as ₹1,792 → b Hence, 1-d, 2-c, 3-a, 4-b.Therefore, Option B is correct.

❓ Why Other Options Are Incorrect

They mismatch one or more bond variables.

🎯 Strategy

used

Variable Identification

Application:

Determine each value separately before matching.

Final Logic:

Correct correspondence is
1-d, 2-c, 3-a, 4-b.

🧠 Memory Trick

"Face → Redemption → Interest → Price."

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

14 If fixed interest \(I=160\) per year is plotted linearly against time \(t\) for \(n=10\) years, the area \(A\) under the curve represents total interest.
Evaluate:
\(A=\int_{0}^{10}\,160 dt\)

A 16

B 160

C 800

D 1600

💡 Short Explanation

The integral of a constant equals the constant multiplied by the interval length.

✅ Correct Answer Explanation

Given, A = ∫₀¹⁰ 160 dt Since 160 is constant, A = 160(t)│₀¹⁰ = 160(10) = 1600 Therefore, A = 1600. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: Incorrect computation.
Option B: Represents only one year's interest.
Option C: Uses only five years.

🎯 Strategy

used

Constant Function Integration

Application:

Multiply the constant by the length of the interval.

Final Logic:

Since
160 × 10 = 1600
Option D is correct.

🧠 Memory Trick

"Area Under a Constant = Height × Width."

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

15 Arrange the logical steps to compare expected mathematical incomes \(I_{1}\)and \(I_{2}\)from two different stock investments:
1. Calculate income \(I_{1}\)from the first stock.
2. Assume a common total investment amount \(X\).
3. Calculate income \(I_{2}\)from the second stock and evaluate \(I_{1}>I_{2}\).

A 2, 1, 3

B 1, 2, 3

C 3, 2, 1

D 2, 3, 1

💡 Short Explanation

Begin with the same investment amount for both options. Calculate the income from the first investment. Then calculate and compare the income from the second investment.

✅ Correct Answer Explanation

The correct sequence is: Step 1: Assume a common investment amount X. ↓ Step 2: Calculate the income from the first stock, I_1. ↓ Step 3: Calculate the income from the second stock, I_2, and compare the two. Hence, 2, 1, 3. Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

They attempt to compare incomes before fixing a common investment amount or before calculating both incomes.

🎯 Strategy

used

Sequential Reasoning

Application:

Use a common investment amount before comparing different investments.

Final Logic:

Investment → Income 1 → Income 2 & Comparison.

🧠 Memory Trick

"Equal Investment First, Comparison Last."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Comparison of Investments

16 A \(₹2000\), \(8\%\)bond is redeemable at the end of \(n=10\) years at \(105\%\).
Evaluate the mathematical redemption value \(C\).

A ₹2000

B ₹2100

C ₹2050

D ₹2200

💡 Short Explanation

Redemption value equals the face value multiplied by the redemption percentage.

✅ Correct Answer Explanation

Given, Face Value F=₹2000. Redeemable at 105%. Therefore, C = 1.05 × 2000 = ₹2100 Hence, C = ₹2100. Therefore, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: Represents redemption at par.
Option C: Incorrect multiplication.
Option D: Represents 110% redemption.

🎯 Strategy

used

Redemption Formula

Application:

Multiply the face value by the redemption percentage.

Final Logic:

Since
2000 ×1.05=2100,
Option B is correct.

🧠 Memory Trick

"105% = Face Value × 1.05."

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

17 Mathematically, \(D(t)>0\). Which of the following is NOT a cause of this positive depreciation function?

A Passage of time

B Wear and tear

C Increase in market demand

D Outdated technology

💡 Short Explanation

Depreciation occurs because assets lose value through usage, age, or obsolescence—not because demand increases.

✅ Correct Answer Explanation

Common causes of depreciation include: Passage of time, Physical wear and tear, Technological obsolescence. An increase in market demand generally raises an asset's market value rather than causing depreciation. Therefore, Option C is not a cause of depreciation.

❓ Why Other Options Are Incorrect

Why Other Options Are Correct

Option A: Assets deteriorate over time.
Option B: Continuous use reduces value.
Option D: New technology makes older assets less valuable.

🎯 Strategy

used

Concept Recall

Application:

Identify factors that reduce an asset's value.

Final Logic:

Higher market demand does not create depreciation.

🧠 Memory Trick

"Time, Wear, Obsolescence ↓ Value; Demand ↑ Value."

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

18 Which algebraic equations can be properly used when calculating straight-line depreciation \(D\)?
(i) \(D=\frac{C-S}{n}\)
(ii) \(C-S=\sum D_{i}\)
(iii) \(D=C(1-r)^{n}\)

A (i) only

B (iii) only

C (ii) and (iii) only

D (i) and (ii) only

💡 Short Explanation

The Straight-Line Method uses a constant annual depreciation. The Reducing Balance Method uses the exponential formula.

✅ Correct Answer Explanation

For the Straight-Line Method, Annual depreciation is D = (C − S) / n Also, Total depreciation equals C − S = ΣDᵢ However, D = C(1 − r)^n is associated with the Reducing Balance Method, not the Straight-Line Method. Therefore, Statements (i) and (ii) are correct. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: Ignores statement (ii).
Option B: Uses the wrong depreciation method.
Option C: Includes the incorrect statement (iii).

🎯 Strategy

used

Formula Identification

Application:

Differentiate between Straight-Line and Reducing Balance formulas.

Final Logic:

Only statements (i) and (ii) belong to the Straight-Line Method.

🧠 Memory Trick

"Straight Line → Divide; Reducing Balance → Exponential."

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

19 An asset costing \(C=₹15,000\) is expected to have a useful life of \(n=5\) years and a scrap value \(S=₹3,000\).
Evaluate the annual depreciation \(D\) using the straight-line equation.

A ₹2,400

B ₹3,000

C ₹2,000

D ₹2,500

💡 Short Explanation

Under the Straight-Line Method (SLM), annual depreciation is constant. Subtract the scrap value from the original cost and divide by the useful life.

✅ Correct Answer Explanation

The Straight-Line Method formula is D = (C − S) / n where: • C = ₹15,000 • S = ₹3,000 • n = 5 years Substituting the values, D = (15,000 − 3,000) / 5 = 12,000 / 5 = 2,400 Therefore, D = ₹2,400 per year. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: ₹3,000 ignores the useful life calculation.
Option C: Incorrect division.
Option D: Would be correct only if the scrap value were ₹2,500.

🎯 Strategy

used

Straight-Line Depreciation Formula

Application:

Subtract the scrap value from the cost and divide by the useful life.

Final Logic:

Since
(15,000 − 3,000) / 5 = 2,400
Option A is correct.

🧠 Memory Trick

"SLM = (Cost − Scrap Value) ÷ Useful Life."

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

20 A machine costing
A machine costing \(C=₹50,000\) depreciates at a constant rate of \(r=8\%\).
The book value at the end of the 7th year is:
\(S_{7}=50,000(0.92)^{7}=27,892.33\)
The book value at the end of the 8th year is:
\(S_{8}=25,660.94\)
Calculate the numerical depreciation charge \(\Delta D\) for the 8th year:

A ₹2,000.00

B ₹2,231.39

C ₹2,500.50

D ₹4,000.00

💡 Short Explanation

Depreciation for a year equals the reduction in book value during that year. Subtract the ending book value from the beginning book value.

✅ Correct Answer Explanation

Depreciation during the 8th year is ΔD = S₇ − S₈ Substituting the values, = 27,892.33 − 25,660.94 = 2,231.39 Therefore, ΔD = ₹2,231.39. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: Underestimates the depreciation.
Option C: Incorrect subtraction.
Option D: Does not correspond to the reducing balance calculation.

🎯 Strategy

used

Book Value Difference

Application:

Subtract the current year's ending book value from the previous year's ending book value.

Final Logic:

Since
27,892.33-25,660.94=2,231.39,
Option B is correct.

🧠 Memory Trick

"Yearly Depreciation = Previous Book Value − Current Book Value."

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

CUET UG Applied Mathematics Booster Test 3 - Shares, Debentures and Depreciation

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