(Q). In a certain test there are n questions. In this test 2ᵏ students gave wrong answers to at least n-k questions. k = 0, 1, 2, ……n. If the number of wrong answers is 8191 then what is the value of n? Solution:- Number of students who gave wrong answers...
(Q). Let A and B be two sets containing 2 & 4 elements respectively. The number of subsets of A×B having 3 or more elements is?Solution:-A×B having will have 2×4 = 8 elements∴ Required number of ways= 2⁸ – ⁸C₀ – ⁸C₁ – ⁸C₂= 256 – 1 – 8...
(Q). A committee of 12 is to be formed from 9 women and 8 men.(i). In how many ways this can be done if at least 5 women have to be included in a committee?(ii). In how many of these committees women are in majority?(iii). In how many of these committees the men are...
(Q). In an election the number of contestant is one more than the number of seats. A voter can give minimum 1 and maximum equal to the number of seats. Then find the number of contestant if a particular voter can vote in 510 different ways.Solution:-Let the number of...
(Q). Consider a set s = {1, 2, 3, ………., 200}, two elements p and q are selected from this set s such that 7ᵖ + 7ᑫ is divisible by 5. In how many ways this selection can be done?Solution:-For a number to be divisible by 5, its last digit i.e. unit...
(Q). In the previous question to vote for 1 candidate a voter needs 1 ballot paper then which one of the following could be the total number of ballot paper:(i). 4401(ii). 4402(iii). 4403(iv). 4405Solution:-From the answer of previous question a particular voter can...
(Q). In an election number of contestants is one more than the number of seats. If a voter can give minimum 1 and maximum equal to the number of seats vote then in how many different ways a particular voter can vote?(i) 2044(ii)2045(iii) 2046(iv) none of...
(Q). A class has 30 students out of which 23 are boys & 7 are girls. In how many ways 15 students can be selected if 5 seats are reserved for girls student? Solution:- 5G×10B + 6G×9B + 7G×8B = ⁷C₅ײ³C₁₀ + ⁷C₆ײ³C₉ + ⁷C₇ײ³C₈ ...
(Q). In the previous question if a prticular student Amit came with Rohit but not with shyamu then find the number of ways to select 4 students out of 10 students.Solution:-Number of ways = ¹⁰⁻²⁻¹C₄₋₂ = ⁷C₂ ...
(Q). A class has 10 students. In how many ways 4 students can be selected if a particular student amit is selected ‘x’ times and out of those ‘x’ times another student Rohit came ‘y’ times with Amit. By what percentage...
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