JEE Mains · Maths · STD 11 - 6. permutation and combination
Let \(S=\{1,2,3,5,7,10,11\}\). The number of nonempty subsets of \(S\) that have the sum of all elements a multiple of \(3\) , is \(........\)
- A \(42\)
- B \(43\)
- C \(41\)
- D \(40\)
Answer & Solution
Correct Answer
(B) \(43\)
Step-by-step Solution
Detailed explanation
Elements of the type \(3 k =3\) Elements of the type \(3 k +1=1,7,9\) Elements of the type \(3 k +2=2,5,11\) Subsets containing one element \(S_1=1\) Subsets containing two elements \(S_2={ }^3 C_1 \times{ }^3 C_1=9\) Subsets containing three elements…
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
- An experiment succeeds twice as often as it fails. The probability of at least \(5\) successes in the six trials of this experiment isJEE Mains 2016 Hard
- Let the points \(\left(\frac{11}{2}, \alpha\right)\) lie on or inside the triangle with sides \(x+y=11, x+2 y=16\) and \(2 x+3 y=29\). Then the product of the smallest and the largest values of \(\alpha\) is equal to :JEE Mains 2025 Medium
- If the mean and variance of six observations \(7,10,11,15, a, b\) are \(10\) and \(\frac{20}{3}\), respectively, then the value of \(|a-b|\) is equal to:JEE Mains 2021 Medium
- If the sum of the first ten terms of the series \({\left( {1\frac{3}{5}} \right)^2} + {\left( {2\frac{2}{5}} \right)^2} + {\left( {3\frac{1}{5}} \right)^2} + {4^2} + \;\;.\;.\;.\;.\;,\) is \(\frac{{16}}{5}m\) then \(m\) is equal to :JEE Mains 2016 Hard
- Let \(n \in N\) and \([x]\) denote the greatest integer less than or equal to \(x\). If the sum of \((n+1)\) terms \({ }^{n} C_{0}, 3 .{ }^{n} C_{1}, 5 .{ }^{n} C_{2}, 7 .{ }^{n} C_{3}, \ldots\) is equal to \(2^{100} \cdot 101\), then \(2\left[\frac{n-1}{2}\right]\) is equal to \(....\)JEE Mains 2021 Hard
- Let \(g\) be a differentiable function such that \(\int_0^x g(t) d t=x-\int_0^x \operatorname{tg}(t) d t, x \geq 0\) and let \(y=y(x)\) satisfy the differential equation \(\frac{d y}{d x}-y \tan x=\) \(2(x+1) \sec x g(x), x \in\left[0, \frac{\pi}{2}\right)\). If \(y(0)=0\), then \(y\left(\frac{\pi}{3}\right)\) is equal toJEE Mains 2025 Medium
More PYQs from JEE Mains
- A point \(P\) moves on the line \(2x -3y + 4 = 0\). If \(Q(1, 4)\) and \(R(3, -2)\) are fixed points, then the locus of the centroid of \(\Delta PQR\) is a lineJEE Mains 2019 Hard
- Let \(f:\left[ { - 2,3} \right] \to \left[ {0,\infty } \right)\) be a continuous function such that \(f(1-x) = f(x)\) for all \(x \in \left[ { - 2,3} \right]\) . If \(R_1\) is the numerical value of the area of the region bounded by \(y =f (x), x = -2, x = 3\) and the axis of \(x\) and \({R_2} = \int\limits_{ - 2}^3 {x\,f\left( x \right)} dx\) , thenJEE Mains 2013 Hard
- If \(A\, = \,\left[ {\begin{array}{*{20}{c}}
{{e^t}}&{{e^{ - t}}\,\cos \,t}&{{e^{ - t}}\,\sin \,t}\\
{{e^t}}&{ - {e^{ - t}}\,\cos \, - {e^{ - t}}\,\sin \,t}&{ - {e^{ - t}}\,\sin \,t\, + \,{e^{ - t}}\,\cos \,t}\\
{{e^t}}&{2{e^{ - t}}\,\sin \,t}&{2{e^{ - t}}\,\cos \,t}
\end{array}} \right]\) Then \(A\) isJEE Mains 2019 Hard - If the image of the point \(P(1, 2, a)\) in the line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{7-z}{2}\) is \(Q(5,b,c)\), then \(a^{2}+b^{2}+c^{2}\) is equal toJEE Mains 2026 Hard
- If \(\left({ }^{30} C_1\right)^2+2\left({ }^{30} C_2\right)^2+3\left({ }^{30} C_3\right)^2 \ldots \ldots \ldots . .30\left({ }^{30} C_{30}\right)^2=\frac{\alpha 60!}{(30!)^2}\), then \(\alpha\) is equal toJEE Mains 2023 Medium
- If \(f(x)=\sin \left(\cos ^{-1}\left(\frac{1-2^{2 x}}{1+2^{2 x}}\right)\right)\) and its first derivative with respect to \(x\) is \(-\frac{ b }{ a } \log _{ e } 2\) when \(x =1,\) where \(a\) and \(b\) are integers, then the minimum value of \(\left| a ^{2}- b ^{2}\right|\) is.........JEE Mains 2021 Hard