Basic Applications of Calculus

32 Practice MCQs available for CA Foundation

Paper

Paper 3: Quantitative Aptitude

Exam Weightage

3-5 Marks

Key Topics

Limits, Continuity, Derivatives, Integrals

This chapter covers Limits, Continuity, Derivatives, Integrals and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

Exam Strategy Tip

This topic carries 3-5 Marks weightage. Focus on understanding core concepts rather than memorizing.

All 32 Questions

2008
The lim⁡x→2x2−4x+4x−2=\displaystyle \lim_{x \to 2} \frac{x^2-4x+4}{x-2} =
MCQ
4035
Find the value of lim⁡x→4x2−2x−8x−4\displaystyle \lim_{x \to 4} \frac{x^2 - 2x - 8}{x - 4}
MCQ
4036
Evaluate: ∫24(3x−2)2dx\displaystyle \int_2^4 (3x - 2)^2 dx
MCQ
4037
Determine f(x)\displaystyle f(x), given that f′(x)=12x2−4x\displaystyle f'(x) = 12x^2 - 4x and f(−3)=17\displaystyle f(-3) = 17
MCQ
4038
Find dydx\displaystyle \frac{dy}{dx} where x=et+e−t2\displaystyle x = \frac{e^t + e^{-t}}{2} and y=et−e−t2\displaystyle y = \frac{e^t - e^{-t}}{2}
MCQ
4039
What is the differential function of x2+2\displaystyle \sqrt{x^2 + 2} ?
MCQ
4136
Find dydx\displaystyle \frac{dy}{dx} for x2y2+y=0\displaystyle x^2y^2+y = 0.
MCQ
4137
The cost function of an organisation as C(x)=500−5x2+x33\displaystyle C(x) = 500-5x^2+\frac{x^3}{3}, where x\displaystyle x denotes the output. Find the level of output at which marginal cost is the minimum.
MCQ
4138
The value of ∫04x+3x+2dx\displaystyle \int_{0}^{4} \frac{x+3}{x+2} dx is
MCQ
4139
The value of ∫342x1+x2dx\displaystyle \int_{3}^{4} \frac{2x}{1+x^2} dx is
MCQ
4214
If f(x)=3e2x\displaystyle f(x) = 3e^{2x}, then f′(x)−2xf(x)+16f(0)−f′(0)\displaystyle f'(x) - 2xf(x) + \frac{1}{6}f(0) - f'(0) is equal to
MCQ
4215
The cost of production of an item is given as C=50x−5x2+x36\displaystyle C=50x - 5x^2 + \frac{x^3}{6} where 'x' is number of items to be produced. If the average cost and marginal cost are equal then, what quantity of items should be produced?
MCQ
4217
The cost function of a company is given by C(x)=600x−10x2+x32\displaystyle C(x) = 600x - 10x^2 + \frac{x^3}{2} where x denotes the output. Find the level of output (in nearest integer) at which average cost is minimum.
MCQ
4271
Evaluate the integral ∫01(2x2−x3)dx\displaystyle \int_0^1(2x^2-x^3)dx
MCQ
4335
Find the value of lim⁡x→4x2−2x−8x−4\displaystyle \lim_{x \to 4} \frac{x^2 - 2x - 8}{x - 4}
MCQ
4336
Evaluate: ∫24(3x−2)2dx\displaystyle \int_2^4 (3x - 2)^2 dx
MCQ
4337
Determine f(x)\displaystyle f(x), given that f′(x)=12x2−4x\displaystyle f'(x) = 12x^2 - 4x and f(−3)=17\displaystyle f(-3) = 17
MCQ
4338
Find dydx\displaystyle \frac{dy}{dx} where x=et+e−t2\displaystyle x = \frac{e^t + e^{-t}}{2} and y=et−e−t2\displaystyle y = \frac{e^t - e^{-t}}{2}
MCQ
4339
What is the differential function of x2+2\displaystyle \sqrt{x^2 + 2} ?
MCQ
4436
Find dydx\displaystyle \frac{dy}{dx} for x2y2+y=0\displaystyle x^2y^2+y = 0.
MCQ
4437
The cost function of an organisation as C(x)=500−5x2+x33\displaystyle C(x) = 500-5x^2+\frac{x^3}{3}, where x\displaystyle x denotes the output. Find the level of output at which marginal cost is the minimum.
MCQ
4438
The value of ∫04x+3x+2dx\displaystyle \int_{0}^{4} \frac{x+3}{x+2} dx is
MCQ
4439
The value of ∫342x1+x2dx\displaystyle \int_{3}^{4} \frac{2x}{1+x^2} dx is
MCQ
4514
If f(x)=3e2x\displaystyle f(x) = 3e^{2x}, then f′(x)−2xf(x)+16f(0)−f′(0)\displaystyle f'(x) - 2xf(x) + \frac{1}{6}f(0) - f'(0) is equal to
MCQ
4515
The cost of production of an item is given as C=50x−5x2+x36\displaystyle C=50x - 5x^2 + \frac{x^3}{6} where 'x' is number of items to be produced. If the average cost and marginal cost are equal then, what quantity of items should be produced?
MCQ
4517
The cost function of a company is given by C(x)=600x−10x2+x32\displaystyle C(x) = 600x - 10x^2 + \frac{x^3}{2} where x denotes the output. Find the level of output (in nearest integer) at which average cost is minimum.
MCQ
4571
Evaluate the integral ∫01(2x2−x3)dx\displaystyle \int_0^1(2x^2-x^3)dx
MCQ
5544
Question 5 (a) SemiCon Pvt. Ltd. (SPL) is engaged in manufacturing of semiconductors from 2024. It wants to build best quality semiconductor and display design with innovative ecosystem to enable India's emergence as a global hub for electronics manufacturing. Placing core values as priority, it wants to articulate its aspirations to stakeholders with a guiding beacon to keep inspiring its workforce. Identify and explain one component of strategic intent indicating above intentions. Why is such component important? State its essentials. (1+1+1+2 = 5 Marks) (b) 'Twaran', a small and mid-sized business, wants to use latest digital technologies for improved procedures and products. Primary aim: competitive edge by digital transformation. It wants to deal with regular changes firmly and transform its management techniques. Identify the strategy required for digital transformation. State the most preferred practices. (1+4 = 5 Marks) (c) MaAi group acquired a business dealing in product 'Nota' in 2020. It was not contributing as expected. In 2023, emphasis was placed on change in management and improvement in internal efficiency. In 2024, positive outcome was still absent, and the company decided to get rid of the business. Identify retrenchment strategies in (i) 2023 and (ii) 2024. State reasons for adopting the 2024 strategy. (1+1+3 = 5 Marks)
Subjective
5545
Question 6 (a) Explain the importance of values, as one of the components of strategic intent for a company. What are common examples of values? How are values different from intent? (3+1+1 = 5 Marks) (b) In order to get better performance and sustainable competitive advantages, a company has to focus on the characteristics of its resources and capabilities. Explain the major characteristics of resources and capabilities. (5 Marks)
Subjective
5546
Question 7 (a) What do you mean by value chain analysis? Delineate the support activities in value chain analysis, as stated by Michael Porter. (1+4 = 5 Marks) (b) Explain differentiation strategy as one of the generic strategies by Michael Porter. What are the major bases of differentiation? Also outline the strategies which can help achieve the differentiation strategy. (1+2+2 = 5 Marks)
Subjective
5547
Question 8 (a) What do you mean by Key Success Factors (KSF)? Structure the questions to which can help identify KSFs of a company. Also state how the understanding can help ascertain sustainable competitive advantages. (1+2+2 = 5 Marks) (b) Explain in brief the expansion strategy as one of the corporate strategy. Also state the characteristics of expansion strategy. (1+4 = 5 Marks) OR "A manager as a strategic leader has to play many leadership roles", while explaining the statement in brief, delineate the leadership roles which a manager has to play in pushing for a good strategy execution. (1+4 = 5 Marks)
Subjective
2009
What is the value of lim⁡y→2y2−4y−2\displaystyle \lim_{y \to 2} \frac{y^2-4}{y-2}
MCQ

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