JEE Mains · Maths · STD 12 - 13. probability
From a lot of \(10\) items, which include \(3\) defective items, a sample of \(5\) items is drawn at random. Let the random variable \(\mathrm{X}\) denote the number of defective items in the sample. If the variance of \(X\) is \(\sigma^2\), then \(96 \sigma^2\) is equal to ....................
- A \(56\)
- B \(87\)
- C \(61\)
- D \(12\)
Answer & Solution
Correct Answer
(A) \(56\)
Step-by-step Solution
Detailed explanation
\(\mathrm{X}=\) denotes number of defective \(X\) \(0\) \(1\) \(2\) \(3\) \(\mathrm{P}(\mathrm{x}) \) \(\frac{7}{15}\) \(\frac{5}{12}\) \(\frac{5}{12}\) \(\frac{1}{12}\) \( \mathrm{x}_1^2 \) \(0\) \(1\) \(4\) \(9\) \( \mathrm{P}_{\mathrm{i}} \mathrm{x}_1^2 \) \(0\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- A ray of light is incident along a line which meets another line, \(7x- y+ 1 =0\), at the point \((0, 1)\) . The ray is then reflected from this point along the line, \(y + 2x = 1\) . Then the equation of the line of incidence of the ray of light isJEE Mains 2016 Hard
- Let \(f\) be any function continuous on \([\mathrm{a}, \mathrm{b}]\) and twice differentiable on \((a, b) .\) If for all \(x \in(a, b)\) \(f^{\prime}(\mathrm{x})>0\) and \(f^{\prime \prime}(\mathrm{x})<0,\) then for any \(\mathrm{c} \in(\mathrm{a}, \mathrm{b})\) \(\frac{f(\mathrm{c})-f(\mathrm{a})}{f(\mathrm{b})-f(\mathrm{c})}\) is greater thanJEE Mains 2020 Hard
- A person throws two fair dice. He wins \(Rs.\, 15\) for throwing a doublet (same numbers on the two dice), wins \(Rs.\,12\) when the throw results in the sum of \(9\), and loses \(Rs.\, 6\) for any other outcome on the throw. Then the expected gain/loss (in \(Rs.\)) of the person isJEE Mains 2019 Hard
- Let \(R= \{(3, 3) (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)\}\) be a relation on the set \(A= \{3, 5, 9, 12\}.\) Then, \(R\) isJEE Mains 2013 Hard
- Let \(A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right], x \in R\) and \(A^{4}=\left[a_{i j}\right] .\) If \(a_{11}=109,\) then \(a_{22}\) is equal toJEE Mains 2020 Hard
- \(\sum_{r=1}^{20}\left(r^{2}+1\right)(r !)\) is equal to:JEE Mains 2022 Hard
More PYQs from JEE Mains
- If \(2\int_0^1 {{{\tan }^{ - 1}}}\,xdx = \int_0^1 {{{\cot }^{ - 1}}}\,(1 - x + {x^2})dx,\) then \(\int_0^1 {{{\tan }^{ - 1}}}\, (1 - x + {x^2})dx\) is equal toJEE Mains 2016 Hard
- If \(x,y,z\) are in \(A.P.\) and \({\tan ^{ - 1}}x,{\tan ^{ - 1}}y\) and \({\tan ^{ - 1}}z\) are also in other \(A.P.\) then . . .JEE Mains 2013 Medium
- A straight line through origin \(O\) meets the lines \(3y= 10 - 4x\) and \(8x + 6y+ 5 = 0\) at points\( A\) and \(B\) respectively. Then \(O\) divides the segment \(AB\) in the ratioJEE Mains 2016 Hard
- Let \(\mathrm{X}\) be a random variable with distribution.
If the mean of \(X\) is \(2.3\) and variance of \(X\) is \(\sigma^{2}\), then \(100 \sigma^{2}\) is equal to :\(\mathrm{x}\) \(-2\) \(-1\) \(3\) \(4\) \(6\) \(\mathrm{P}(\mathrm{X}=\mathrm{x})\) \(\frac{1}{5}\) \(\mathrm{a}\) \(\frac{1}{3}\) \(\frac{1}{5}\) \(\mathrm{~b}\) JEE Mains 2021 Hard - If two parallel chords of a circle, having diameter \(4\, units\), lie on the opposite sides of the centre and subtend angles \({\cos ^{ - 1}}\left( {\frac{1}{7}} \right)\) and \({\sec ^{ - 1}}\left( 7 \right)\) at the centre respectively, then the distance between these chords, isJEE Mains 2017 Hard
- Let \(y = y ( x )\) be the solution of the differential equation \(\left( x ^2-3 y ^2\right) dx +3 xy dy =0, y (1)=1\). Then \(6 y^2(e)\) is equal toJEE Mains 2023 Medium