Maths Questions

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

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Solution : Probability of guessing a correct answer, p = \(1\over 3\) and probability of guessing a wrong answer, qย  = \(2\over 3\) So, the probability of guessing 4 or more correct answers is = \(^5C_4\) \(({1\over 3})^4\). \(2\over 3\) + \(^5C_5\) \(({1\over 3})^5\) = \(5.2\over {3^5}\) + \(1\over {3^5}\) = \(11\over {3^5}\) Similar Questions โ€ฆ

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is Read More ยป

All the students of a class performed poorly in mathematics. The teacher decided to give grace marks of 10 to each of the students. Which statistical measure will not change even after the grace marks were given ?

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Question : All the students of a class performed poorly in mathematics. The teacher decided to give grace marks of 10 to each of the students. Which statistical measure will not change even after the grace marks were given ? (a) Mean (b) Median (c) Mode (d) Variance Solution : If initially all marks were โ€ฆ

All the students of a class performed poorly in mathematics. The teacher decided to give grace marks of 10 to each of the students. Which statistical measure will not change even after the grace marks were given ? Read More ยป

If C and D are two events such that C \(\subset\) D and P(D) \(\ne\) 0, then the correct statement among the following is

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Question : If C and D are two events such that C \(\subset\) D and P(D) \(\ne\) 0, then the correct statement among the following is (a) P(C/D) \(\ge\) P(C) (b) P(C/D) < P(C) (c) P(C/D) = \(P(D)\over P(C)\) (d) P(C/D) = P(C) Solution : As P(C/D) = \(P(C \cap D)\over P(D)\) = \(P(C)\over P(D)\)ย  โ€ฆ

If C and D are two events such that C \(\subset\) D and P(D) \(\ne\) 0, then the correct statement among the following is Read More ยป

Consider 5 independent Bernoulliโ€™s trials each with probability of success p. If the probability of atleast one failure is greater than or equal to \(31\over 32\), then p lies in the interval

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Solution : Here, n = 5 and r \(\ge\) 1 \(\therefore\)ย  ย p(X = r) = \(^nC_r\) \(p^{n-r}\) \(q^r\) P(X \(\ge\) 1) = 1 โ€“ P(X = 0) = 1 โ€“ \(^5C_0 . p^5 . q^0\) \(\ge\) \(31\over 32\)ย  ย [Given] \(\implies\)ย  ย \(p^5\) \(\le\) 1 โ€“ \(31\over 32\) = \(1\over 32\) \(\therefore\)ย  p \(\le\) \(1\over 2\) and โ€ฆ

Consider 5 independent Bernoulliโ€™s trials each with probability of success p. If the probability of atleast one failure is greater than or equal to \(31\over 32\), then p lies in the interval Read More ยป

The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is

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Solution : Let us assume that the coordinates of the center of the circle are C(h,k) and its radius is r. Now, since the circle touches X-axis at (1,0), hence its radius should be equal to ordinate of center. \(\implies\) r = k Hence, the equation of circle is \((x โ€“ h)^2 + (y โ€“ โ€ฆ

The length of the diameter of the circle which touches the X-axis at the point (1,0) and passes through the point (2,3) is Read More ยป

The variance of first 50 even natural numbers is

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Solution : \({\sigma^2}\) = \(\sum(x_i โ€“ \bar{x})^2\over n\) \(\bar{X}\) = \(\sum x_i\over n\) = \(2 + 4 + 6 + 8 + โ€ฆ.. + 100\over 50\) = 51 \({\sigma^2}\) = \(2^2 + 4^2 + โ€ฆ. + 100^2\over 50\) โ€“ \(51^2\) = 833 Similar Questions The mean and variance of a random variable X having a โ€ฆ

The variance of first 50 even natural numbers is Read More ยป

Let A and B be two events such that P(A \(\cup\) B)โ€™ = 1/6, P(A \(\cap\) B) = 1/4 and P(A)โ€™ = 1/4 where Aโ€™ stands for complement of A. Then prove that events A and B independent

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Solution : Given P(A \(\cup\) B)โ€™ = 1/6, P(A \(\cap\) B) = 1/4 and P(A)โ€™ = 1/4 \(\therefore\)ย  ย P(A \(\cup\) B) = 1 โ€“ P(A \(\cup\) B)โ€™ = 1 โ€“ \(1\over 6\) = \(5\over 6\) and P(A) = 1 โ€“ P(A)โ€™ = 1 โ€“ \(1\over 4\) = \(3\over 4\) P(A \(\cup\) B) = P(A) + โ€ฆ

Let A and B be two events such that P(A \(\cup\) B)โ€™ = 1/6, P(A \(\cap\) B) = 1/4 and P(A)โ€™ = 1/4 where Aโ€™ stands for complement of A. Then prove that events A and B independent Read More ยป

The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by

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Solution : The number of ways to n people on circular table is (n-1)! So, first we fix position of men, the number of ways to sit men = 5! Now, women can sit in the gaps between men, there are 6 gaps between 5 mens, So, women can sit in \(^6P_5\) ways Hence, total โ€ฆ

The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by Read More ยป

A student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. The number of choices available to him is

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Solution : The number of choices available to him = \(^5C_4\) x \(^8C_6\) + \(^5C_5\) x\(^8C_5\) = 5.4.7 + 8.7 = 140 + 56 = 196 Similar Questions The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given โ€ฆ

A student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. The number of choices available to him is Read More ยป

The number of ways of distributing 8 identical balls in 3 distinct boxes, so that none of the boxes is empty, is

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Solution : The number of ways of distributing n identical things in m different boxes is \(^{n-1}C_{m-1}\) So, Required number of ways = \(^{8-1}C_{3-1}\) = \(^7C_2\) = 21 Similar Questions A student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. โ€ฆ

The number of ways of distributing 8 identical balls in 3 distinct boxes, so that none of the boxes is empty, is Read More ยป
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