JEE Mains · Maths · STD 11 - 1. set theory
The number of elements in the set \(S=\{(x, y, z): x, y, z \in Z, x+2 y+3 z=42\) \(\mathrm{x}, \mathrm{y}, \mathrm{z} \geq 0\}\) ...........
- A \(167\)
- B \(169\)
- C \(168\)
- D \(165\)
Answer & Solution
Correct Answer
(B) \(169\)
Step-by-step Solution
Detailed explanation
\(x+2 y+3 z=42\), \(x, y, z \geq 0\) \(z=0\) \(x+2 y=42 \Rightarrow 22\) \(z=1\) \(x+2 y=39 \Rightarrow 20\) \(z=2\) \(x+2 y=36 \Rightarrow 19\) \(z=3\) \(x+2 y=33 \Rightarrow 17\) \(z=4\) \(x+2 y=30 \Rightarrow 16\) \(z=5\) \(x+2 y=27 \Rightarrow 14\) \(z=6\)…
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 stair-case of length \(l\) rests against a vertical wall and a floor of a room. Let \(P\) be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio \(1 : 2\). If the staircase begins to slide on the floor, then the locus of \(P\) isJEE Mains 2014 Hard
- If \(0\, \le \,x\, < \frac{\pi }{2},\) then the number of values of \(x\) for which \(sin\,x -sin\,2x + sin\,3x=0,\) isJEE Mains 2019 Hard
- Number of functions \(f:\{1,2, \ldots, 100\} \rightarrow\{0,1\}\), that assign 1 to exactly one of the positive integers less than or equal to 98 , is equal to ________.JEE Mains 2025 Medium
- Let \(P_n=\alpha^n+\beta^n, n \in \mathbf{N}\). If \(P_{10}=123, P_9=76\), \(P_8=47\) and \(P_1=1\), then the quadratic equation having roots \(\frac{1}{\alpha}\) and \(\frac{1}{\beta}\) is :JEE Mains 2025 Medium
- If \(\frac{1}{2 \times 3 \times 4}+\frac{1}{3 \times 4 \times 5}+\frac{1}{4 \times 5 \times 6}+\ldots+\) \(\frac{1}{100 \times 101 \times 102}=\frac{ k }{101}\), then \(34\,k\) is equal to \(.....\)JEE Mains 2022 Hard
- Let \(f(x)=x^2+9, g(x)=\frac{x}{x-9}\) and \(\mathrm{a}=\mathrm{fog}(10), \mathrm{b}=\operatorname{gof}(3)\). If \(\mathrm{e}\) and \(1\) denote the eccentricity and the length of the latus rectum of the ellipse \(\frac{x^2}{a}+\frac{y^2}{b}=1\), then \(8 e^2+1^2\) is equal to.JEE Mains 2024 Hard
More PYQs from JEE Mains
- If the three lines \(x - 3y = p, ax + 2y = q\) and \(ax + y = r\) form a right-angled triangle thenJEE Mains 2013 Hard
- Let the eccentricity of the hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) be \(\frac{5}{4}\). If the equation of the normal at the point \(\left(\frac{8}{\sqrt{5}}, \frac{12}{5}\right)\) on the hyperbola is \(8 \sqrt{5} x +\beta y =\lambda\), then \(\lambda-\beta\) is equal toJEE Mains 2022 Medium
- Let \(z \in C\) the set of complex numbers. Then the equation, \(2\left| {z + 3i} \right| - \left| {z - i} \right| = 0\) representsJEE Mains 2017 Hard
- Which of the following is true for \(y ( x )\) that satisfies the differential equation \(\frac{d y}{d x}=x y-1+x-y ; y(0)=0\)JEE Mains 2021 Medium
- Let \(\mathrm{n}\) be an odd natural number such that the variance of \(1,2,3,4, \ldots, \mathrm{n}\) is \(14 .\) Then \(\mathrm{n}\) is equal to ..... .JEE Mains 2021 Medium
- Let the line \(2 \mathrm{x}+3 \mathrm{y}-\mathrm{k}=0, \mathrm{k}>0\), intersect the \(\mathrm{x}\)-axis and \(\mathrm{y}\)-axis at the points \(\mathrm{A}\) and \(\mathrm{B}\), respectively. If the equation of the circle having the line segment \(\mathrm{AB}\) as a diameter is \(\mathrm{x}^2+\mathrm{y}^2-3 \mathrm{x}-2 \mathrm{y}=0\) and the length of the latus rectum of the ellipse \(\mathrm{x}^2+9 \mathrm{y}^2=\mathrm{k}^2\) is \(\frac{\mathrm{m}}{\mathrm{n}}\), where \(\mathrm{m}\) and \(\mathrm{n}\) are coprime, then \(2 \mathrm{~m}+\mathrm{n}\) is equal toJEE Mains 2024 Hard