Class 11 Math: Sequences and Series Important Exam Questions

NexPro Tools Mathematics TeamJune 5, 20266 min read

Preparing for school exams or final CBSE boards requires practicing questions patterned after official grading schemes. We have compiled a list of crucial questions for Class 11 Sequences and Series to help you test your mastery.

Exam-Pattern Questions and Answers

Question 1 (HARD)

Case-Study 2: One triangular shaped pond is there in a park. Three friends Rani, Mansi, Sneha are sitting at the corners of the triangular park. They are studying in Class XI in an International. Rani marked her position as (2, -2), Mansi marked as (1, 1) and Sneha marked her position as (-1, 0) as shown in figure given below. Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 12 Based on the above information

This is a descriptive problem. Work out all steps on paper before checking the solution.

Solution Explanation & Steps: wer the following questions. (i) Find the equation of lines formed by Rani and Mansi. (1) (ii) Find the Slope of equation of line formed by Rani and Sneha. (1) (iii) Find the equation of median of lines through Rani. (1) (iv) Find the equation of altitude through Mansi. (1) Ans: (i) The equation of line AB is 2 11 ( 1)2 1y x - -- = - - 2 1 1 1 2 1 ( )y yy y x x x x [ ] -- = -[ ] -[ ]  ⇒ y -1 = - 3x + 3 ⇒ 3x + y = 4 (ii) Slope of equation of line AC is (iii) Let D be the mid-point of BC. Coordinates of D are 1 1 0 1 1, 0,2 2 2 - +( ) ( ) =( ) ( )( ) ( ) ∴ Equation of AD is 1 222 ( 2)0 2y x + + = - - ⇒ 52 ( 2)4y x -+ = - ⇒ 4y + 8 = - 5x + 10 ⇒ 5x + 4y = 2 (iv) Slope of AC = - 2/3 ∴ Slope of BE = 3/2 [∵ BE ⊥ AC] Equation of altitude through B is 31 ( 1)2y x- = - ⇒ 3x - 2y =1

Question 2 (HARD)

Three numbers are in AP their sum is 15. If 1, 3, 9 be added to them respectively they form a GP. Find the numbers.

This is a descriptive problem. Work out all steps on paper before checking the solution.

Solution Explanation & Steps: Let these numbers be a - d, a, a + d (keeping in mind the rule of selection of three numbers in AP). Given that (a - d) + a + (a + d) = 15 ⇒ 3a = 15 ⇒ a = 5 ∴ The numbers are now 5 - d, 5, 5 + d. Adding 1, 3, 9 in the numbers respectively. We get the new numbers i.e., 5 - d + 1, 5 + 3, 9 + 5 + d are in GP ⇒ 6 - d, 8, 14 + d form a GP ⇒ 8 14 6 8 d d +=- ⇒ 64 = (6 - d) (14 + d) ⇒ 64 = 84 - 14d + 6d - d2 ⇒ d2 + 8d - 20 = 0 ⇒ d2 + 10d - 2d - 20 = 0 ⇒ (d + 10) (d - 2) = 0 ⇒ d = -10 or d = 2 Therefore, the numbers are 15, 5, -5 or 3, 5, 7. OR Find the value of n, so that 1 1n n n n a b a b + ++ + may be geometric mean between a and b. Ans. 1 1n n n n a b a b + ++ + is the G.M. between a and b. 1 1n n n n a b aba b + ++⇒ = +

Question 3 (HARD)

Case-Study 1: Two students, Anil and Vijay, appeared in a highly competitive examination. Anil has been preparing part-time while managing a job, which has left him with limited preparation time. On the other hand, Vijay, though dedicated, has struggled with certain key concepts. Based on their preparation and past performance, the probability that Anil will qualify the examination is estimated to be 0.05, and the probability that Vijay will qualify is estimated at 0.10. Additionally, the probability that both students will qualify together, due to their independent preparation and individual strengths, is calculated as 0.02. Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 11 (a) Find the probability that at least one of them will qualify the exam. (b) Find the probability that at least one of them will not qualify the exam. (c) Find the probability that both Anil and Vijay will not qualify the exam. (d) Find the probability that only one of them will qualify the exam.

This is a descriptive problem. Work out all steps on paper before checking the solution.

Solution Explanation & Steps: (a) P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.05 + 0.10 - 0.02 = 0.13 (b) Probability of at least one of them does not qualify = P(A' ∪ B') = P((A ∩ B)′) = 1 - P(A ∩ B) = 1 - 0.02 = 0.98 (c) Probability that both Anil and Vijay will not qualify the exam = P(A' ∩ B') = P((A ∪ B)′) = 1 - P(A ∪ B) = 1 - 0.13 = 0.87 (d) Probability that only one of them will qualify the exam = P((A - B) ∪ (B - A)) = P(A - B) + P(B - A) = P(A ∪ B) - P(A ∩ B) = 0.13 - 0.02 = 0.11

Grading Step-Marking Guidelines

Remember that teachers award partial marks for writing down formulas, stating the given variables, and drawing diagrams. Never leave a question blank on an exam. Write down the relevant formulas and initial substitution steps to secure partial credits.

📚 Class 11 Math Resource Hub for Sequences and Series: • 🧮 Interactive Solver: Solve Sequences and Series Problems - Verify steps in real-time. • 📝 Timed Practice Quiz: Take Sequences and Series Online Quiz - Test your speed and concepts. • 📄 Printable Worksheet: Download Sequences and Series PDF Worksheet - Interactive problems with answers. • 📐 Formula Sheet: View Sequences and Series Key Equations - Complete revision references. • 🔄 Next Topic Guide: Straight Lines Study Notes • 🎓 Syllabus Overview: Class 11 Mathematics Portal - Access all chapter guides.
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