Agniveer Airforce Mathematics Questions and Answers

Sets, relations, and functions MCQs

Question: Which of the following is an example of a finite set? 

• a) Set of all real numbers 
• b) Set of natural numbers 
• c) Set of prime numbers 
• d) Set of integers 

Answer: b) Set of natural numbers Justification: The set of natural numbers has a definite starting point (1) and ends at a specific number, making it a finite set.

3-dimensional geometry 

Question: How many vertices does a pyramid have? 

• a) 4 
• b) 5 
• c) 6 
• d) 8

Answer: (b) 5 Justification: A pyramid has one base and several triangular faces that meet at a common vertex. Therefore, it has five vertices.

Application of derivatives MCQs

Question: Which concept of calculus is used to find the maximum or minimum values of a function? 

• a) Differentiation 
• b) Integration 
• c) Limit 
• d) Series

Answer: (a) Differentiation Justification: Differentiation is used to find the derivative of a function, which helps in identifying the critical points where the function attains maximum or minimum values.

Application of integrals MCQs

Question: Which concept of calculus is used to find the area under a curve? 

• a) Differentiation 
• b) Integration 
• c) Limit 
• d) Series

Answer: (b) Integration Justification: Integration is used to find the area under a curve. It involves calculating the definite integral of the function over a given interval.

Binomial Theorem MCQs

Question: What does the binomial coefficient represent?

• a) The sum of the exponents in a binomial expression 
• b) The coefficient of the first term in a binomial expansion 
• c) The coefficient of each term in a binomial expansion 
• d) The product of the exponents in a binomial expression

Answer: (c) The coefficient of each term in a binomial expansion Justification: The binomial coefficient, denoted as nCr or C(n, r), represents the coefficient of each term in the expansion of (a + b)^n. It determines the number of ways to choose r items from a set of n items.

Cartesian system of rectangular coordinates MCQs

Question: Which quadrant does the point (-4, 5) lie in? 

• a) First quadrant 
• b) Second quadrant 
• c) Third quadrant 
• d) Fourth quadrant

Answer: (b) Second quadrant Justification: In the Cartesian system, the x-coordinate represents the horizontal position, and the y-coordinate represents the vertical position. Since the x-coordinate is negative (-4) and the y-coordinate is positive (5), the point (-4, 5) lies in the second quadrant.

Circles and family of circles MCQs

Question: What is the equation of a circle with center (0, 0) and radius 7? 

• a) x^2 + y^2 = 7 
• b) x^2 + y^2 = 49 
• c) (x – 7)^2 + (y + 7)^2 = 0 
• d) (x + 7)^2 + (y – 7)^2 = 49

Answer: (b) x^2 + y^2 = 49 Justification: The equation of a circle with center (h, k) and radius r is given by (x – h)^2 + (y – k)^2 = r^2. In this case, the center is (0, 0) and the radius is 7. Substituting these values, we get x^2 + y^2 = 49.

Complex Numbers MCQs

Question: What is the modulus of the complex number -4 + 3i? 

• a) 7 
• b) -7 
• c) 5 
• d) -5

Answer: (c) 5 Justification: The modulus (or absolute value) of a complex number a + bi is calculated as √(a^2 + b^2). In this case, the modulus of -4 + 3i is √((-4)^2 + 3^2) = √(16 + 9) = √25 = 5.

Conic sections MCQs

Question: The equation x^2/9 + y^2/16 = 1 represents which conic section? 

• a) Circle 
• b) Ellipse 
• c) Parabola
• d) Hyperbola

Answer: (b) Ellipse Justification: The equation x^2/a^2 + y^2/b^2 = 1 represents an ellipse, where a and b are the semi-major and semi-minor axes, respectively.

Differential equations MCQs

Question: The solution to the differential equation dy/dx = 2x is: 

• a) y = x^2 
• b) y = 2x 
• c) y = x^2 + C 
• d) y = 2x + C

Answer: (a) y = x^2 + C Justification: The given differential equation is separable. Integrating both sides with respect to x, we get y = x^2 + C, where C is the constant of integration.