CBSE Class 11 Maths Important Questions

Below are 10 important questions from Class 11 Maths chapters that are important for preparing well and understanding concepts easily.

1. What are the different types of sets?

Ans: Sets can be classified into several types:

• Empty Set: A set with no elements, denoted by {} or Ø.

• Finite Set: A set with a limited number of elements, like {1, 2, 3}.

• Infinite Set: A set with unlimited elements, such as the set of all natural numbers.

• Universal Set: A set that contains all possible elements for a particular discussion.

• Subset: A set where all its elements are also in another set.

2. What is a function and how is it different from a relation?

Ans: A function is a specific type of relation where each input is associated with exactly one output. In contrast, a relation can have multiple outputs for a single input. For example, in the relation {(1, 2), (1, 3)}, the input 1 relates to two outputs (2 and 3), making it not a function. A function is often expressed as f(x), where f assigns exactly one value to each input x.

3. Define the six trigonometric ratios.

Ans: The six trigonometric ratios based on a right triangle are:

• Sine (sin θ): $\dfrac{Opposite side }{ Hypotenuse}$

• Cosine (cos θ): $\dfrac{Adjacent side }{ Hypotenuse}$

• Tangent (tan θ): $\dfrac{Opposite side }{ Adjacent side}$

• Cosecant (cosec θ): $\dfrac{Hypotenuse }{ Opposite side }(reciprocal of sine)$

• Secant (sec θ): $\dfrac{Hypotenuse }{ Adjacent side }(reciprocal of cosine)$

• Cotangent (cot θ): $\dfrac{Adjacent side }{ Opposite side }(reciprocal of tangent)$

4. How do you solve a quadratic equation using the quadratic formula?

Ans: The quadratic formula is used to find the roots of the equation ax² + bx + c = 0, where a, b, and c are constants. The formula is given by:

x=−b±b2−4ac2ax = $\frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}x=2a−b±b2−4ac​​$

Here, b² - 4ac is called the discriminant. If the discriminant is positive, there are two distinct real roots; if it is zero, there is one real root; and if it is negative, there are two complex roots.

5. How do you represent a linear inequality on a graph?

Ans: To represent a linear inequality like 2x + 3y < 6, first, convert it to the equation 2x + 3y = 6 and plot the line on a graph. Use a dashed line if the inequality is strict (< or >) and a solid line if it is inclusive (≤ or ≥). Then, choose a test point not on the line (like (0,0)) to see if it satisfies the inequality. Shade the region that satisfies the inequality.

6. What is the difference between permutations and combinations?

Ans: Permutations refer to the arrangements of objects where the order matters, while combinations refer to selections where the order does not matter. For example, arranging the letters A, B, and C in different ways gives permutations (ABC, ACB, etc.), while selecting 2 letters from A, B, and C gives combinations (AB, AC, BC).

7. What does the Binomial Theorem state?

Ans: The Binomial Theorem states that the expansion of (a + b)ⁿ can be expressed as:

(a + b)ⁿ =$ \sum_{r=0}^{n} \binom{n}{r} $ 

where $\binom{n}{r}(rn​) $ is the binomial coefficient representing the number of ways to choose r elements from n. This theorem is useful for calculating powers of binomials quickly.

8. What is an arithmetic progression (AP)?

Ans: An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference (d). For example, in the sequence 2, 5, 8, 11, the common difference is 3. The nth term of an AP can be calculated using the formula:

$a_n = a + (n-1)d$

where "a" is the first term.

9. What is the derivative of a function?

Ans: The derivative of a function measures how the function's value changes as its input changes. It is defined as the limit of the average rate of change of the function as the interval approaches zero. Mathematically, for a function f(x), the derivative f'(x) is given by:

f'(x) =$ \lim_{h \to 0} \frac{{f(x+h) - f(x)}}{h}$

Derivatives are fundamental in calculus and are used to find slopes of curves, optimise functions, and analyse motion.

10. How is probability defined and calculated?

Ans: Probability is a measure of the likelihood of an event occurring, ranging from 0 (impossible event) to 1 (certain event). It is calculated using the formula:

P(E) = $\dfrac{{\text{Number of favourable outcomes}}}{{\text{Total number of possible outcomes}}}$

For example, the probability of rolling a 3 on a fair six-sided die is P(3) = $\frac{1}{6}$. Understanding probability is essential for analysing risks and making informed decisions.

Here are some important questions for Class 11 Maths. To get a better understanding of each chapter, check the Chapter-wise Important Questions table. This resource will help you understand the key ideas and study well for your exams.

How do Maths Important Questions Class 11 Help you with Exams?

• Class 11 Maths Important questions highlight the main topics in each chapter. This focus allows students to concentrate their studies on what is most relevant for exams, making their preparation more effective.

• By practising these questions, students can clarify complex ideas. This deeper understanding makes it easier to recall information during the exam, leading to better performance.

• Familiarity with important questions helps students feel more prepared. As they practise, their confidence grows, reducing anxiety on exam day.

• Working through these questions helps students spot topics they struggle with. Recognizing these weak points allows for targeted studying, improving overall performance.

• Practising important questions teaches students how to manage their time effectively. By timing their practice, they learn to pace themselves, ensuring they can complete the exam

Vedantu's Class 11 Maths Important Questions are a valuable resource for students preparing for their exams. They focus on essential topics, helping students understand key concepts and improve their confidence. By practising these questions, students can identify areas for improvement and get familiar with the exam format. This targeted approach makes studying more effective and enjoyable. With Vedantu's support, students are better equipped to achieve success in their Class 11 Maths exams.

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