AP EAMCET · Maths · Permutation Combination
The total number of positive integral solutions \((x, y, z)\) of \(x y z=24\) is
- A \(24\)
- B \(30\)
- C \(36\)
- D \(32\)
Answer & Solution
Correct Answer
(B) \(30\)
Step-by-step Solution
Detailed explanation
\(x y z=24=2^3 \times 3\) Let \(x=2^{x_1} \times 3^{y_1}\), \(y=2^{x_2} \times 3^{y_2}\) and \(z=2^{x_3} \times 3^{y_3}\) \(x_1+x_2+x_3=3\) and \(y_1+y_2+y_3=1\) Number of non-negative integral solution \(={ }^{3+3-1} C_{3-1}={ }^5 C_2=10\) Number of non-negative integral…
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
- If \(x\) is real, then the minimum value of \(y=\frac{x^2-x+1}{x^2+x+1}\) isAP EAMCET 2014 Hard
- If \(f(x)\) is differentiable on \(\mathbb{R}, f(x) f^{\prime}(-x)-f(-x) f^{\prime}(x)=0\), \(f(x) f^{\prime}(-x)=0, f(0)=3\) and \(f(3)=9\), then \((1+f(-3))^3+1=\)AP EAMCET 2023 Medium
- If \(x\) is so small that \(x^2\) and higher powers of \(x\) can be neglected, then the approximate value of \(\left(1+\frac{3}{4} x\right)^{\frac{1}{2}}\left(1-\frac{2 x}{3}\right)^{-2}\) isAP EAMCET 2019 Easy
- The sides of a \(\triangle A B C\) are given by \(a=3, b=5\) and \(c=3\). Then, \(\cos A=\)AP EAMCET 2022 Easy
- One out of 9 ships is likely to sink, when they are set on sail. When 6 ships are set on sail, the probability that exactly 3 of them will not arrive safely isAP EAMCET 2023 Medium
- The multiplicative inverse of \(\mathrm{z}\) isAP EAMCET 2023 Easy
More PYQs from AP EAMCET
- A solid ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at the speed \(60 \mathrm{~cm}^{-1}\) on the string, when the car is at rest. When the car accelerates on a horizontal road, then speed of the pulse is \(66 \mathrm{~cm}^{-1}\). The acceleration of the car is nearly \(\left(g=10 \mathrm{~ms}^{-2}\right)\)AP EAMCET 2018 Hard
- \(P\) is a variable point on the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) with foci \(F_1\) and \(F_2\). If \(A\) is the area of the triangle \(P F_1 F_2\), then the maximum value of \(A\) isAP EAMCET 2019 Medium
- In amplitude modulation, the amplitude of the carrier ware is 10 V and the amplitude of one of the side bands is 2 V . Then the modulation index isAP EAMCET 2024 Medium
- A polymer sample contains 10 molecules each with molecular mass 5,000 and 5 molecules each with molecular mass 50,000. The number average molecular mass of the polymer sample isAP EAMCET 2025 Medium
- Which one of the following gives Prussian blue colour?AP EAMCET 2013 Easy
- Positron is the antiparticle ofAP EAMCET 2023 Easy