JEE Mains · Maths · STD 11 - 13. statistics
If the mean and variance of eight numbers \(3,7,9,12,13,20, x\) and \(y\) be \(10\) and \(25\) respectively, then \(\mathrm{x} \cdot \mathrm{y}\) is equal to
- A \(48\)
- B \(56\)
- C \(54\)
- D \(58\)
Answer & Solution
Correct Answer
(C) \(54\)
Step-by-step Solution
Detailed explanation
\(\frac{3+7+9+12+13+20+x+y}{8}=10\) \(x+y=16\) \(\frac{\Sigma x^{2}}{n}-\left(\frac{\Sigma x}{n}\right)^{2}=25\) \(3^{2}+7^{2}+9^{2}+12^{2}+13^{2}+20^{2}+\mathrm{x}^{2}+\mathrm{y}^{2}=1000\) \(x^{2}+y^{2}=148\) \(x y=54\)
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 \(S=\{1,2,3,4,5,6\} .\) Then the probability that a randomly chosen onto function \(\mathrm{g}\) from \(\mathrm{S}\) to \(\mathrm{S}\) satisfies \(g(3)=2 g(1)\) is :JEE Mains 2021 Medium
- Let \(a \in R\) and let \(\alpha, \beta\) be the roots of the equation \(x^2+60^{\frac{1}{4}} x+a=0\). If \(\alpha^4+\beta^4=-30\), then the product of all possible values of \(a\) is \(......\)JEE Mains 2023 Hard
- If \((20)^{19}+2(21)(20)^{18}+3(21)^2(20)^{17}+\ldots \ldots\). \(+20(21)^{19}= k (20)^{19}\), then \(k\) is equal toJEE Mains 2023 Hard
- The equation of a normal to the curve \(\sin \,y = x\,\sin \,\left( {\frac{\pi }{3} + y} \right)\) at \(x\, = 0\), isJEE Mains 2015 Hard
- If the equations \({x^2} + 2x + 3 = 0\) and \(a{x^2} + bx + c = 0,a,b,c \in R\) have a common root ,then \(a:b:c = \) .. . .JEE Mains 2013 Easy
- If a circle \(C,\) whose radius is \(3,\) touches externally the circle, \(x^2 + y^2 + 2x - 4y - 4 = 0\) at the point \((2, 2),\) then the length of the intercept cut by circle \(c,\) on the \(x-\) axis is equal toJEE Mains 2018 Hard
More PYQs from JEE Mains
- Lets \(S=\{z \in C:|z-1|=1\) and \((\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2 \sqrt{2}\}\). Let \(\mathrm{z}_1, \mathrm{z}_2\) \(\in S\) be such that \(\left|z_1\right|=\max _{z \in S}|z|\) and \(\left|z_2\right|=\min _{z \in S}|z|\). Then \(\left|\sqrt{2} z_1-z_2\right|^2\) equals :JEE Mains 2024 Hard
- Let \(H _{ n }=\frac{ x ^2}{1+ n }-\frac{ y ^2}{3+ n }=1, n \in N\). Let \(k\) be the smallest even value of \(n\) such that the eccentricity of \(H _{ k }\) is a rational number. If \(l\) is length of the latus return of \(H _{ k }\), then \(21 l\) is equal to \(.......\).JEE Mains 2023 Hard
- The sum of the series
\(2 \times 1 \times{ }^{20} \mathrm{C}_4-3 \times 2 \times{ }^{20} \mathrm{C}_5+4 \times 3 \times{ }^{20} \mathrm{C}_6-5 \times 4\) \(\times { }^{20} \mathrm{C}_7+\ldots+18 \times 17 \times{ }^{20} \mathrm{C}_{20}\), is equal toJEE Mains 2025 Medium - Given that the slope of the tangent to a curve \(y = y(x)\) at any point \((x, y)\) is \(\frac{{2y}}{{{x^2}}}\). If the curve passes through the centre of the circle \(x^2 + y^2 - 2x - 2y = 0\), then its equation isJEE Mains 2019 Hard
- For all twice differentiable functions \(f: R \rightarrow R,\) with \(f(0)=f(1)=f^{\prime}(0)=0\)JEE Mains 2020 Hard
- The foot of the perpendicular drawn from the origin, on the line, \(3x + y = \lambda \,\left( {\lambda \ne 0} \right)\) is \(P\). If the line meets \(x-\) axis at \(A\) and \(y-\) axis at \(B\), then the ratio \(BP : PA\) isJEE Mains 2018 Hard