TS EAMCET · Maths · Permutation Combination
If \({ }^{(n-1)} C_3+{ }^{(n-1)} C_4>{ }^n C_3\), then the minimum value of \(n\) is
- A 5
- B 6
- C 7
- D 8
Answer & Solution
Correct Answer
(D) 8
Step-by-step Solution
Detailed explanation
Given, \({ }^{n-1} C_3+{ }^{n-1} C_4>{ }^n C_3\) \(\begin{array}{lc} \therefore & { }^n C_4>{ }^n C_3 \\ & {\left[\because{ }^n C_r+{ }^n C_{r-1}={ }^{n+1} C_r\right]} \\ \Rightarrow & n-4>3 \\ \Rightarrow & n>7 \\ \therefore & n=8 \end{array}\)
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 \(f(x)\) is a real function defined on \([-1,1]\), then the function \(g(x)=f(5 x+4)\) is defined on the intervalTS EAMCET 2015 Easy
- If \(\omega\) is a complex cube root of unity, then \(\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}\) is equal toTS EAMCET 2008 Medium
- If \(z=x+i y\) and if the point P represents \(z\) in the Argand plane, then the locus of \(z\) satisfying the equation \(|z-1|+|z+i|=2\) isTS EAMCET 2024 Medium
- The values of \(p\) and \(q\) so that the function \[ f(x)=\left\{\begin{array}{cl} (1+\mid \sin x)^{\frac{p}{\sin x}}, \frac{-\pi}{6} < x < 0 \ q & , x=0 \ e^{\frac{\sin 2 x}{\sin 3 x}} & , 0 < x < \frac{\pi}{6} \end{array}\right. \] is continuous at \(x=0\), areTS EAMCET 2016 Hard
- If \(f(x)\)
\(\left|\begin{array}{ccc}1 & x & x+1 \\ 2 x & x(x-1) & x(x+1) \\ 3 x(x-1) & x(x-1)(x-2) & (x-1) x(x+1)\end{array}\right|\)
then \(f(2012)\) is equal toTS EAMCET 2012 Medium - If \(\overrightarrow{A B}\) is the focal chord of the parabola \(y^2=16 x\) and \(A=(1,-4)\), then the equation of the normal to the parabola at the point \(\mathrm{B}\) isTS EAMCET 2023 Easy
More PYQs from TS EAMCET
- Which of the following reaction is feasible?TS EAMCET 2023 Hard
- A resistance network is connected to a battery as shown in the figure below. If the internal resistance of the battery is \(5 \Omega\), then the value of \(R\) (in \(\Omega\) ) for maximum power delivered to the network is
TS EAMCET 2018 Medium - If \(x_1, x_2, x_3\) are the real roots of the equation \(x^3-x^2 \tan \theta+x \tan ^2 \theta+\tan \theta=0\) and \(0 < \theta < \frac{\pi}{4}\), then the value of \(\tan ^{-1} x_1+\tan ^{-1} x_2+\tan ^{-1} x_3\) at \(\theta=\frac{\pi}{12}\) isTS EAMCET 2019 Hard
- The range of the real valued function \(f(x)=\operatorname{Sin}^{-1}\left(\sqrt{x^2+x+1}\right)\) isTS EAMCET 2025 Medium
- In the given circuit, a charge of \(+80 \mu \mathrm{C}\) is given to upper plate of a \(4 \mu \mathrm{F}\) capacitor. At steady state, the charge on the upper plate of the \(3 \mu \mathrm{F}\) capacitor is
TS EAMCET 2017 Medium - At T(K), 0.1 moles of a non-volatile solute was dissolved in 0.9 moles of a volatile solvent. The vapour pressure of pure solvent is 0.9 bar. What is the vapour pressure (in bar) of solution?TS EAMCET 2024 Easy