Undergraduate Exam Prep Resources for Competitive Exams

My Learning Cart

Undergraduate

Download Q&A

Undergraduate MCQ & Objective Questions

The undergraduate level is a crucial phase in a student's academic journey, especially for those preparing for school and competitive exams. Mastering this stage can significantly enhance your understanding and retention of key concepts. Practicing MCQs and objective questions is essential, as it not only helps in reinforcing knowledge but also boosts your confidence in tackling important questions during exams.

What You Will Practise Here

Fundamental concepts in Mathematics and Science
Key definitions and theories across various subjects
Important formulas and their applications
Diagrams and graphical representations
Critical thinking and problem-solving techniques
Subject-specific MCQs designed for competitive exams
Revision of essential topics for better retention

Exam Relevance

Undergraduate topics are integral to various examinations such as CBSE, State Boards, NEET, and JEE. These subjects often feature a mix of conceptual and application-based questions. Common patterns include multiple-choice questions that assess both theoretical knowledge and practical application, making it vital for students to be well-versed in undergraduate concepts.

Common Mistakes Students Make

Overlooking the importance of understanding concepts rather than rote memorization
Misinterpreting questions due to lack of careful reading
Neglecting to practice numerical problems that require application of formulas
Failing to review mistakes made in previous practice tests

FAQs

Question: What are some effective strategies for solving undergraduate MCQ questions?
Answer: Focus on understanding the concepts, practice regularly, and review your answers to learn from mistakes.

Question: How can I improve my speed in answering objective questions?
Answer: Time yourself while practicing and gradually increase the number of questions you attempt in a set time.

Start your journey towards mastering undergraduate subjects today! Solve practice MCQs and test your understanding to ensure you are well-prepared for your exams. Your success is just a question away!

Engineering Entrance Medical Entrance

Q. Find the roots of the equation 3x² - 12x + 12 = 0. (2021)

A. 2
B. 4
C. 0
D. 3

Solution

Dividing by 3 gives x² - 4x + 4 = 0, which factors to (x - 2)² = 0, hence the root is 2.

Correct Answer: A — 2

Q. Find the roots of the equation 4x² - 12x + 9 = 0. (2023)

A. 1
B. 2
C. 3
D. 0

Solution

This is a perfect square: (2x - 3)² = 0, hence the root is x = 1.5.

Correct Answer: B — 2

Q. Find the roots of the equation x² + 2x - 8 = 0. (2022)

A. -4 and 2
B. 4 and -2
C. 2 and -4
D. 0 and 8

Solution

Factoring gives (x + 4)(x - 2) = 0, hence the roots are 4 and -2.

Correct Answer: B — 4 and -2

Q. Find the slope of the tangent line to f(x) = 2x^3 - 3x^2 + 4 at x = 1. (2021)

A. 1
B. 2
C. 3
D. 4

Solution

f'(x) = 6x^2 - 6. f'(1) = 6(1)^2 - 6 = 0.

Correct Answer: B — 2

Q. Find the slope of the tangent line to f(x) = x^2 + 2x at x = 1. (2022)

A. 2
B. 3
C. 4
D. 5

Solution

f'(x) = 2x + 2. At x = 1, f'(1) = 4.

Correct Answer: A — 2

Q. Find the solution of the differential equation dy/dx = y^2.

A. y = 1/(C - x)
B. y = C/(x - 1)
C. y = Cx
D. y = e^(x)

Solution

This is a separable equation. Integrating gives y = 1/(C - x).

Correct Answer: A — y = 1/(C - x)

Q. Find the solution of the differential equation y' = 3y + 6.

A. y = Ce^(3x) - 2
B. y = Ce^(3x) + 2
C. y = 2e^(3x)
D. y = 3Ce^(x)

Solution

This is a linear first-order equation. The integrating factor is e^(3x). The solution is y = Ce^(3x) + 2.

Correct Answer: B — y = Ce^(3x) + 2

Q. Find the solution of the equation dy/dx = y^2 - 1.

A. y = tan(x + C)
B. y = C/(1 - Cx)
C. y = 1/(C - x)
D. y = C/(x + 1)

Solution

This is a separable equation. The solution is y = tan(x + C).

Correct Answer: A — y = tan(x + C)

Q. Find the solution of the equation y' + 2y = 0.

A. y = Ce^(-2x)
B. y = Ce^(2x)
C. y = 2Ce^x
D. y = Ce^x

Solution

This is a first-order linear differential equation. The solution is y = Ce^(-2x).

Correct Answer: A — y = Ce^(-2x)

Q. Find the sum of the first 15 terms of the geometric series where the first term is 2 and the common ratio is 3.

A. 143
B. 145
C. 146
D. 147

Solution

The sum of the first n terms of a geometric series is S_n = a(1 - r^n) / (1 - r). Here, a = 2, r = 3, n = 15. So, S_15 = 2(1 - 3^15) / (1 - 3) = 2(1 - 14348907) / -2 = 14348906.

Correct Answer: C — 146

Q. Find the sum of the first 5 terms of the series 1, 4, 9, 16, ...

A. 30
B. 31
C. 32
D. 33

Solution

The series is the sum of squares: 1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 1 + 4 + 9 + 16 + 25 = 55.

Correct Answer: B — 31

Q. Find the term containing x^3 in the expansion of (x + 5)^6.

A. 150
B. 200
C. 250
D. 300

Solution

The term containing x^3 is C(6,3) * (5)^3 = 20 * 125 = 250.

Correct Answer: A — 150

Q. Find the term containing x^3 in the expansion of (x - 1)^5.

A. -5
B. 10
C. -10
D. 5

Solution

The term containing x^3 is C(5,3) * x^3 * (-1)^2 = 10 * x^3 * 1 = 10.

Correct Answer: C — -10

Q. Find the term independent of x in the expansion of (x^2 - 2x + 3)^4. (2022)

A. 81
B. 108
C. 54
D. 27

Solution

The term independent of x occurs when the powers of x cancel out. The term is 81.

Correct Answer: A — 81

Q. Find the term independent of x in the expansion of (x^2 - 3x + 1)^5. (2023)

A. -15
B. 10
C. 5
D. 0

Solution

The term independent of x occurs when the powers of x cancel out. The term is C(5,2)(-3)^2(1)^3 = 45.

Correct Answer: A — -15

Q. Find the term independent of x in the expansion of (x^2 - 4x + 4)^4. (2020)

A. 16
B. 64
C. 256
D. 0

Solution

The expression can be rewritten as (x - 2)^4. The term independent of x occurs when k = 4, which gives us (-2)^4 = 16.

Correct Answer: C — 256

Q. Find the term independent of x in the expansion of (x^2 - 4x + 4)^6. (2020)

A. 6
B. 12
C. 24
D. 36

Solution

The expression can be rewritten as (x - 2)^6. The term independent of x occurs when k = 3, which gives us 6C3 * (-2)^3 = 20 * (-8) = -160. The term independent of x is 24.

Correct Answer: C — 24

Q. Find the value of (3 + 2)^3 using the binomial theorem.

A. 25
B. 27
C. 30
D. 32

Solution

Using the binomial theorem, (3 + 2)^3 = C(3,0) * 3^3 * 2^0 + C(3,1) * 3^2 * 2^1 + C(3,2) * 3^1 * 2^2 + C(3,3) * 3^0 * 2^3 = 27 + 54 + 36 + 8 = 125.

Correct Answer: B — 27

Q. Find the value of 3^3 - 2^3. (2020)

A. 19
B. 25
C. 21
D. 27

Solution

3^3 = 27 and 2^3 = 8, so 27 - 8 = 19.

Correct Answer: A — 19

Q. Find the value of 5! (5 factorial). (2019)

A. 120
B. 100
C. 150
D. 90

Solution

5! = 5 × 4 × 3 × 2 × 1 = 120.

Correct Answer: A — 120

Q. Find the value of 5^3. (2019)

A. 125
B. 150
C. 100
D. 75

Solution

5^3 = 5 × 5 × 5 = 125.

Correct Answer: A — 125

Q. Find the value of 9 × 9 - 3 × 3. (2019)

A. 72
B. 78
C. 81
D. 66

Solution

9 × 9 = 81 and 3 × 3 = 9, so 81 - 9 = 72.

Correct Answer: A — 72

Q. Find the value of 9 × 9 - 5 × 5. (2019)

A. 56
B. 56
C. 81
D. 64

Solution

9 × 9 = 81 and 5 × 5 = 25, so 81 - 25 = 56.

Correct Answer: A — 56

Q. Find the value of 9 × 9 - 5 × 5. (2023) 2023

A. 56
B. 70
C. 50
D. 80

Solution

9 × 9 = 81 and 5 × 5 = 25, so 81 - 25 = 56.

Correct Answer: A — 56

Q. Find the value of 9 × 9 - 7. (2019)

A. 74
B. 81
C. 72
D. 70

Solution

9 × 9 = 81, then 81 - 7 = 74.

Correct Answer: C — 72

Q. Find the value of k for which the equation x² + 4x + k = 0 has no real roots. (2020)

A. -5
B. -6
C. -4
D. -3

Solution

The discriminant must be negative: 4² - 4*1*k < 0, which gives k > 4, so the minimum value is -6.

Correct Answer: B — -6

Q. Find the value of k for which the equation x² + kx + 16 = 0 has equal roots. (2022)

A. -8
B. -4
C. 4
D. 8

Solution

For equal roots, the discriminant must be zero: k² - 4*1*16 = 0, thus k² = 64, k = ±8. The value of k can be -8.

Correct Answer: A — -8

Q. Find the value of k for which the equation x² + kx + 9 = 0 has no real roots. (2023)

A. -6
B. -4
C. -2
D. 0

Solution

For no real roots, the discriminant must be negative: k² - 4*1*9 < 0, thus k² < 36, hence k < -6 or k > 6.

Correct Answer: A — -6

Q. Find the value of k if the equation x² + kx + 16 = 0 has no real roots. (2022)

A. k < 8
B. k > 8
C. k < 0
D. k > 0

Solution

For no real roots, the discriminant must be less than zero: k² - 4*1*16 < 0, which gives k > 8.

Correct Answer: B — k > 8

Q. Find the value of \( x \) if \( \begin{vmatrix} 1 & 2 \\ 3 & x \end{vmatrix} = 0 \). (2023)

A. 1
B. 2
C. 3
D. 4

Solution

Setting the determinant to zero: \( 1*x - 2*3 = 0 \) gives \( x - 6 = 0 \) or \( x = 6 \).

Correct Answer: C — 3

Showing 781 to 810 of 5514 (184 Pages)

School

College

Degree

Competitve

Skills

Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely