A class has `175` students. The following data shows the number of students obtaining one or more subjects : Mathematics `100`, Physics `70`, Chemistry `40`, Mathematics and Physics `30`, Mathematics and Chemistry `28`, Physics and Chemistry `23`, Mathematics & Physics & Chemistry `18`. How many students have offered Mathematics alone ?
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Prove that `^100 C_2^(100)C_2+^(100)C_2^(100)C_4+^(100)C_4^(100)C_6++^(100)C_(98)^(100)C_(100)=1/2[^(200)C_(98)-^(100)C_(49)]dot`
To find `S = .^(100)C_(0).^(100)C_(2)+.^(100)C_(2).^(100)C_(4)+.^(100)C_(4).^(100)C_(6)+"....."+.^(100)C_(98).^(100)C_(100)` Consider, `.^(100)C_(0).^(100)C_(2)+.^(100)C_(1).^(100)C_(3) + .^(100)C_(2).^(100)C_(4)+.^(100)C_(3)+.^(100)C_(5)+"...." + .^(100)C_(98).^(100)C_(100)` `= .^(100)C_(0).^(100)C_(98)+.^(100)C_(1).^(100)C_(97) + .^(100)C_(2).^(100)C_(96)+.^(100)C_(3).^(100)C_(95) + "....."+^(100)C_(98) .^(100)C_(0)` = Coefficients of `x^(98)` in `(1+x)^(100) (1+x)^(100)` `= .^(200)C_(98) " "(1)` Also,...
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A student can solve 2 out of 4 problems of mathematics, 3 out of 5 problem of physics, and 4 out of 5 problems of chemistry. There are equal number of
Correct Answer - B Let `P(m),P(c),P(c)` be the probabilaty of selecting a book of maths, physics, and chemistry, respectively. Clearly, `P(m)=P(P)=P(c)=1/3` Again let `P(s_(1))and P(s_(2))` be the probability that he solves...
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Mathematics, Economics, Physics, Chemistry
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2 Answers 1 views
The square of one-sixth of the number of students in a class are studying in the library and the remaining eight students are playing in the ground. W
Correct Answer - 12 or 24
2 Answers 5 views
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Correct Answer - Marks obtained by Jack = 164 Marks obtained by Jill = 157
2 Answers 2 views
A profit of Rs. 300 is made on class I ticket , and Rs. 800 is made on class II ticket. If x and y are the number of tickets of class I and class II s
Correct Answer - f=300x+800y
2 Answers 1 views
In a class of 80 students, 55 students passed in mathematics and 60 passed in chemistry. 10 stu-dents failed in both mathematics and chemistry. (i) Ho
Correct Answer - (i) 45 , (ii) 25
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`45%` of the student of a class participated in Physics Olympiad Math Olympiad. 4 students participated in both. Find how many students. (i) Are there
Correct Answer - (i) 40 , (ii) 18 , (iii) 36
2 Answers 2 views
A class has `175` students, The following description gives the number of students studying one or more of the subjects in this class, Mathematics `10
Correct Answer - (i) 60,35,13, (ii) 32
2 Answers 1 views
The mean weight of 25 students of a class is 52 kg. if the mean weight of the first 13 student of the class is 48 kg and that of the last 13 students
Correct Answer - 39 kg
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