JEE Mains · Maths · STD 11 - 14. probability
The probability that two randomly selected subsets of the set \(\{1,2,3,4,5\}\) have exactly two elements in their intersection, is :
- A \(\frac{65}{2^{7}}\)
- B \(\frac{65}{2^{8}}\)
- C \(\frac{135}{2^{9}}\)
- D \(\frac{35}{2^{7}}\)
Answer & Solution
Correct Answer
(C) \(\frac{135}{2^{9}}\)
Step-by-step Solution
Detailed explanation
Total subsets \(=2^{5}=32\) Probability \(=\frac{{ }^{5} C _{2} \times 3^{3}}{32 \times 32}=\frac{10 \times 27}{12^{10}}=\frac{135}{2^{9}}\)
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
- Let the point \((p, p+1)\) lie inside the region \(E=\left\{(x, y): 3-x \leq y \leq \sqrt{9-x^2}, 0 \leq x \leq 3\right\}\) If the set of all values of \(p\) is the interval \((a, b)\). then \(b^2+b-a^2\) is equal to \(.................\).JEE Mains 2023 Hard
- A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is \(q\). If \(p : q = m\) \(: n\), where \(m\) and \(n\) are coprime, then \(m + n\) is equal to \(..........\).JEE Mains 2023 Hard
- \(\lim _{x \rightarrow 0}\left(\frac{(x+2 \cos x)^{3}+2(x+2 \cos x)^{2}+3 \sin (x+2 \cos x)}{(x+2)^{3}+2(x+2)^{2}+3 \sin (x+2)}\right)^{\frac{100}{x}}\)is equal to\(.....\)JEE Mains 2022 Hard
- The mean of the numbers \(a, b, 8,5,10\) is \(6\) and their variance is \(6.8\). If \(M\) is the mean deviation of the numbers about the mean, then \(25\; M\) is equal toJEE Mains 2022 Hard
- The triangle of maximum area that can be inscribed in a given circle of radius \('r'\) is ...... .JEE Mains 2021 Hard
- For \(a \in C\), let \(A =\{z \in C: \operatorname{Re}( a +\overline{ z }) > \operatorname{Im}(\bar{a}+z)\}\) and \(B=\{z \in C: \operatorname{Re}(a+\bar{z}) < \operatorname{Im}(\bar{a}+z)\}\). Then among the two statements : \((S 1)\) : If \(\operatorname{Re}(A), \operatorname{Im}(A) > 0\), then the set \(A\) contains all the real numbers \((S2)\): If \(\operatorname{Re}(A), \operatorname{Im}(A) < 0\), then the set \(B\) contains all the real numbers,JEE Mains 2023 Hard
More PYQs from JEE Mains
- Let \(f: R \rightarrow R\) be a function defined as \(f(x)=\left\{\begin{array}{cl}\frac{\sin (a+1) x+\sin 2 x}{2 x} & , \text { if } x<0 \\ b & , \text { if } x=0 \\ \frac{\sqrt{x+b x^{3}}-\sqrt{x}}{b x^{5 / 2}} & , \text { if } x>0\end{array}\right.\) . If \(f\) is continuous at \(x=0,\) then the value of \(a + b\) is equal to ....... .JEE Mains 2021 Hard
- The area (in sq. units) of the region \(\left\{(x, y): 0 \leq y \leq x^{2}+1,0 \leq y \leq x+1\right.\) \(\left.\frac{1}{2} \leq x \leq 2\right\}\) isJEE Mains 2020 Hard
- The integral \(\int {\frac{{dx}}{{(1 + \sqrt x ) \cdot \sqrt x \sqrt {1 - x} }}} \) is equal to (where \(c\) is a constant of integration)JEE Mains 2016 Hard
- The locus of the mid-point of the line segment joining the focus of the parabola \(y^{2}=4 a x\) to a moving point of the parabola, is another parabola whose directrix isJEE Mains 2021 Hard
- Consider the region \(R=\left\{(x, y): x \leq y \leq 9-\frac{11}{3} x^2, x \geq 0\right\}\).
The area, of the largest rectangle of sides parallel to the coordinate axes and inscribed in R , is:JEE Mains 2025 Hard - Let the functions \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be defined as \(f(x)=\left\{\begin{array}{ll}x+2, & x<0 \\ x^{2}, & x \geq 0\end{array}\right.\) and \(g(x)=\left\{\begin{array}{lr}x^{3}, & x<1 \\ 3 x-2, & x \geq 1\end{array}\right.\) Then, the number of points in \(R\) where \((fog)( x )\) is \(NOT\) differentiable is equal toJEE Mains 2021 Hard