Search for: Set Sn=1+q+q2+…+qn and Tn=1+q+12+q+122+…+q+12nwhere q is a real number and q≠1 If 101C1+101C2S1+…+101 C101S100=αT100 , then α is equal to Set Sn=1+q+q2+…+qn and Tn=1+q+12+q+122+…+q+12nwhere q is a real number and q≠1 If 101C1+101C2S1+…+101 C101S100=αT100 , then α is equal to A2100B299C202D200 Register to Get Free Mock Test and Study Material +91 Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Solution:Here, 101C1+101C2S1+…+101C101S100=αT100⇒101C1+101C2(1+q)+101C31+q+q2+…+101C1011+q+…+q100=2α1−1+q2101(1−q)⇒101C1(1−q)+101C21−q2+…+101C1011−q101=2α1−1+q2101⇒2101−1−(1+q)101−1=2α1−1+q2101⇒21011−1+q2101=2α1−1+q2101⇒α=2100Post navigationPrevious: If the papers of 4 students can be checked by any one of the 7 teachers. If the probability that all the 4 papers are checked by exactly 2 teachers is A then the value of 490 A must be … …… .Next: If the length of the latus rectum of an ellipse with its major axis along x-axis and center at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?Related content NEET Rank Assurance Program | NEET Crash Course 2023 JEE Main 2023 Question Papers with Solutions JEE Main 2024 Syllabus Best Books for JEE Main 2024 JEE Advanced 2024: Exam date, Syllabus, Eligibility Criteria JEE Main 2024: Exam dates, Syllabus, Eligibility Criteria JEE 2024: Exam Date, Syllabus, Eligibility Criteria NCERT Solutions For Class 6 Maths Data Handling Exercise 9.3 JEE Crash Course – JEE Crash Course 2023 NEET Crash Course – NEET Crash Course 2023