Class 11 Maths MCQs and Answers by Practicing these MCQs of Maths Class 11 will guide students to have a quick revision for all the concepts present in each chapter and prepare for final exams. Students can solve NCERT Class 11 Maths Permutation and Combination MCQs with Answers to know their preparation level. Class 11 Maths MCQs are available for free download on livemcqs.com. The best website for CBSE students now provides Permutation and Combination class 11 Notes Mathematics latest chapter wise notes for quick preparation for CBSE exams and school-based annual examinations.

## Class 11 Maths MCQs and Answers

### Chapter-1. Sets and their Representations

The study of sets and their representations is a fascinating subject that has been the focus of research for many years. Sets can be represented in multiple ways, but the most useful for mathematics is by using a Venn diagram. A Venn diagram allows us to illustrate how sets overlap each other, as well as showing which elements are common between two sets.

A set is a collection of distinct objects. These objects are called the elements of the set and can be denoted by symbols, such as x or y, or sometimes by their names. A simple example is the set of all ten digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. To denote that an object x is an element of the set S we use a special symbol ? (called epsilon) and write x ? S. For example 2 ? {0, 1, 2, 3, 4, 5} and 10 ? {1/2 ?}.

We can also make statements about elements that are not in a set by using the symbol ? (that’s the Greek letter phi) placed between a set symbol and an element symbol. For example: “10 ? {0, 1/2 ?}” means that 10 is not an element of the set {0, 1/2 ?}. We can also use this symbol to say that an element is not in one of several sets.

### Chapter-2. Relation And Function

Relation and Function are directly related to each other. Let us first talk about relations. The relation is a correspondence between two or more objects. In other words, we can say that relation is a connection or association between two or more things. The relation can be represented by the ordered pairs (x, y). A set of ordered pairs forms the relation. For example:-

If x=1, y=2

Then, the ordered pair (x, y) = (1, 2)

In a friendly tone: One thing that you should keep in mind is that each pair of objects cannot form more than one relation.

For example:-If B={(a, b), (c, d)} is a relation from A to B then it can’t be represented as follows:-{(a, c), (b, d)}Now let us discuss function in detail. As I already said that relation and function are directly related to each other. We know that function is a special type of relation in which each element of the domain corresponds to exactly one value in range.

### Chapter-3. Trigonometric Functions

Trigonometric functions are functions of angles. Not just any angles, though: the angles must be measured in a circular sense. So, if you’re going to measure an angle, you’re going to have to start with a circle as your reference. This is important because it means that the different trigonometric functions are related to one another. The values for sine, cosine, and tangent are all related to the ratio between sides of a right triangle. In fact, these ratios are so closely related that they depend on each other!

Trigonometric Functions and Right Triangles: It’s important to remember that trigonometric ratios only work for right triangles, which means that all of the triangles in this unit will have one angle equal to 90° or ?/2 radians. The basic shapes you need to know before getting started with trigonometry include the equilateral triangle (all sides equal, all angles equal), the isosceles triangle (two sides equal, two angles equal), and the right triangle (one angle equal to 90°). These three types of triangles will be used throughout trigonometry and will often come up in proofs and problems.

### Chapter-4. Principle Of Mathematical Induction

The principle of mathematical induction, also known as complete induction, is a tool that can be used to prove certain propositions. Before proving any proposition by induction, the statement must be true for a specific case. This is known as the basic step or base case. The next step is to assume that the proposition holds for a specific value n and then prove it for n+1. This is called the inductive step. If a proposition is true for all integers greater than 0, it is also true for n=0.

### Chapter-5. Complex Numbers And Quadratic Equations

The quadratic equation was first formulated by the Babylonians and has been around for centuries. Although it’s one of the most simple equations, it can be difficult to understand, especially when you first come across it. It’s a second-degree polynomial equation, meaning that the highest exponent on the variable is two. It is generally written as ax^2 + bx + c = 0, where a, b and c are coefficients and x represents an unknown variable.

A quadratic equation will always have two solutions or roots–that is, two values of x that satisfy the equation. These are known as complex numbers because they use both negative and positive values to represent a real number. For example, if you have an equation of 2x^2 + 3x – 2 = 0, you can use either algebra or a graphing calculator to find that the solutions are -1/4 and 1/2. These are complex numbers because they contain both positive and negative values.

### Chapter-6. Linear Inequalities

Mathematically speaking, inequality is an equation that is not necessarily equal to the other side. The number line is a great way to represent inequalities because it shows how two values can be equal, less than, or greater than each other. A linear inequality is a statement of the form Ax + By ? C or Ax + By ? C, where A, B, and C are real numbers, and x and y are variables. For example, the linear inequalities 3x + 4y < 1 and 4x – 2y > 0 are both examples of linear inequalities. These can also be written as equations. To graph these on a number line, we would first solve for x. In the first example, we’d set 3x + 4y = 1 and then subtract y from both sides to get 3x = 1 – 4y. We’d then divide both sides by 3 to get x = (1/3) – (4/3)y. So when graphed on the number line we would see that when x = (1/3) – (4/3)y that value would always be less than 1.

### Chapter-7. Permutation And Combination

Permutation and combination are two mathematical concepts that are both important, but might not be as apparent to some people as they are to others. Permutations are a method of enumerating a set of items from an ordered sequence, so if you have a set of numbers and you want to know their order, the first thing you’ll need is the rule for how many permutations there will be. If there’s only one way to order the items in your set, then there’s only one permutation. If there’s more than one way to order them, then each of those ways counts as a permutation. For example, if you have five numbers and you want to know their order, the first thing you’ll need is the rule for how many different orders there will be. If there’s only one way to order them, then there’s only one permutation: all five numbers are in the same place, in numerical order. If there is more than one way to order them, then each of those ways counts as a permutation. So you can see that this set of five numbers has three permutations: A is followed by B and then C; B is followed by A and then C or C is followed by B and then A.

### Chapter-8. Binomial Theorem

The Binomial Theorem is a simple way to expand the product of two terms that are both powers of a single variable. As a high school student, you may have had to memorize the coefficients of this expansion. If you did, you might remember how tedious that was. There’s a much easier way to compute these coefficients: Pascal’s Triangle.

Pascal’s Triangle is an arithmetic arrangement of numbers that follows a particular pattern. The triangle begins with the number 1 at the top, and every entry after is constructed by adding together the two entries above it. This means each number in the triangle is a sum of two numbers from the row above it (from either diagonal). This process continues indefinitely, creating an infinite triangle.

However, if we look at the first several rows of Pascal’s Triangle, we can see a pattern emerge between the coefficients of terms in an expansion using the Binomial Theorem. As we move down any given column in Pascal’s Triangle, it appears as though these numbers are simply the coefficients of each term in an expansion using the Binomial Theorem.

### Chapter-9. Sequences And Series

The word sequence is often used in reference to the number of elements in a finite list or set and series are often used in reference to an infinite sum.

A sequence is the arrangement of terms of a given set in a specific order. Sequences are usually denoted using uppercase letters, and the individual elements of the sequence are denoted by lowercase letters. The nth term denotes the number at the nth position. In a sequence, each element has a unique predecessor and successor, except for the first and last elements which have no predecessor or successor respectively.

A series is the sum of all the terms of a sequence up until some point. A series is denoted by sigma notation. The nth partial sum (up until term n) is denoted Sn, and it’s defined as:

?ni=1an=a1+a2+?+an

Series are often used to find patterns and generate closed-form expressions for sequences that follow a certain pattern. Infinite series are especially useful because they can be used to approximate values that cannot be computed directly from other expressions or values.

### Chapter-10. Straight Lines

Straight lines are the most fundamental of all geometric shapes, and one of the simplest to define. A straight line is a one-dimensional figure that has no thickness. It is infinitely long but does not cover any area. All points on the line are equidistant from each other and therefore it contains exactly 180 degrees of curvature (or zero degrees, if you prefer).

Straight lines are also referred to as “degenerate polygons” or “singularities” and they exist in two forms: boundless (e.g., an infinite line) and finite (e.g., a line segment). The infinite variety is the only type that can be extended indefinitely in both directions and is, therefore, the only type of straight line that can be used to define a plane or space.

The simplest way to construct a straight line is by drawing it between two points, but this method doesn’t always work. For example, you can draw a line between any two points on Earth, but if you drew a straight line between any point on Earth and the North Pole, your straight line wouldn’t be straight because it would be curved by the Earth’s surface.

### Chapter-11. Conic Sections

Conic sections are the curves formed when a plane intersects a cone. For example, a circle is a conic section that’s formed by a plane intersecting the surface of a cone at a parallel distance to its base. A parabola is another conic section that occurs when the plane intersects the surface of the cone at an angle that’s neither parallel nor perpendicular to its base. There are three other types of conic sections: ellipses, hyperbolas, and circles.

A circle is a conic section that’s formed when a plane intersects the surface of a cone at right angles. It looks like an oval with two equal-length sides, but it has one significant difference from other ovals: it has an infinite number of points along its circumference (the line segment around its perimeter). This means that if you draw a line through any point on the circumference, you will be able to draw an infinite number of lines through it.

### Chapter-12. Introduction To Three Dimensional Geometry

Three-dimensional geometry is the study of geometric objects that extend three dimensions. These objects can be considered as solid figures or regions of space in three-dimensional Euclidean space. These objects can be easily visualized by drawing them on paper or a whiteboard or they can be drawn using computer software like GeoGebra or Mathematica. Most commonly known 3-dimensional figures are cubes, cuboids, rectangular prisms, and cylinders.

### Chapter-13. Limits And Derivatives

In this chapter, we will study the relationship between limits and derivatives. You can think of a derivative as a generalization of the slope of a line. In this chapter, we will study the relationship between limits and derivatives. You can think of a derivative as a generalization of the slope of a line. We say that f is differentiable at x = c if there is a number f ?(c) such that f is differentiable at x = c if there is a number f ?(c) such that, if as x approaches c, f'(x) approaches f'(c). , if as x approaches c, f'(x) approaches f'(c).

A limit is essentially a value that a function approaches. For example, the limit of f(x) as x approaches 0 can be written as limit?0f(x). A derivative is the slope of a function at any given point. Calculus can be used to find the maximum or minimum value of a function, as well as determine where that value occurs.

### Chapter-14. Mathematical Reasoning

Mathematical reasoning focuses on logic and quantification as opposed to calculation or computation. The goal is for you to learn how to reason mathematically and solve problems rather than focus on memorizing formulas or following procedures. In other words, the emphasis is on thinking and understanding rather than tedious calculations that could be easily done with a calculator (or even your phone).

While there are plenty of rules in math that seem to come ‘out of nowhere,’ they generally don’t serve many purposes beyond being easily-defined points in space that can be used as reference points for more complex concepts. Learning what these rules are is important, but understanding why they exist will help you learn more about mathematics and its applications in the world around us.

### Chapter-15. Statistics

Statistics is a branch of mathematics dealing with the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional, to begin with, a statistical population or a statistical model process to be studied. Populations can be diverse groups of people or objects such as “all people living in a country” or “every atom composing a crystal”. Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.[1]

When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation. Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation).

### Chapter-16. Probability

Probability is the study of chance events. It can tell you how likely something is to happen. So it’s all about working out how many chances there are of something happening, if there are lots of chances then it is likely to happen. For example, if you roll a dice there is a chance that it will land on any number from 1 to 6. There are six chances in total so the probability of rolling a 1 or a 6 is one in six. If you roll the dice again there are still six chances that it will land on any number so the probability is still one in six. Probability doesn’t change, even after an event has happened.