WBJEE · Maths · Binomial Theorem
If \({ }^{\mathrm{n}-1} \mathrm{C}_3+{ }^{\mathrm{n}-1} \mathrm{C}_4>{ }^{\mathrm{n}} \mathrm{C}_3\), then \(\mathrm{n}\) is just greater than integer
- A 5
- B 6
- C 4
- D 7
Answer & Solution
Correct Answer
(D) 7
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { Hints: }:^{n-1} C_3+{ }^{n-1} C_4>{ }^n C_3 \\ & \qquad \Rightarrow^n C_4>^n C_3 \Rightarrow \frac{n !}{4 !(n-4) !}>\frac{n !}{3 !(n-3) !} \Rightarrow \frac{1}{4}>\frac{1}{(n-3)} \Rightarrow n-3>4 \Rightarrow n>7 \end{aligned} \]
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
- The area of the region lying above \(X\) -axis, and included between the circle \(x^{2}+y^{2}=2 a x\) and the parabola \(y^{2}=a x, a>0\) isWBJEE 2018 Medium
- In a plane \(\vec{a}\) and \(\vec{b}\) are the position vectors of two points \(A\) and \(B\) respectively. A point \(P\) with position vector \(\vec{r}\) moves on that plane in such a way that \(|\vec{r}-\vec{a}| \sim|\vec{r}-\vec{b}|=c\) (real constant). The locus of \(P\) is a conic section whose eccentricity isWBJEE 2024 Easy
- Two particles \(A\) and \(B\) move from rest along a straight line with constant accelerations \(f\) and \(h,\) respectively. If \(A\) takes \(m\) seconds more than \(B\) and describes \(n\) units more than that of \(B\) acquiring the same speed, thenWBJEE 2019 Easy
- If \(\alpha\) and \(\beta\) are roots of \(x^{2}-x+1=0,\) then the value of \(\alpha^{2013}+\beta^{2013}\) isWBJEE 2013 Easy
- If \(A=\left\{5^{n}-4 n-1: n \in N\right\}\) and
\(B=\{16(n-1): n \in N],\) thenWBJEE 2016 Easy - Which of the following real valued functions is/are not even functions?WBJEE 2013 Medium
More PYQs from WBJEE
- The roots of the quadratic equation \(x^2-2 \sqrt{3} x-22=0\) are :WBJEE 2010 Easy
- If \(z=\left(\begin{array}{ccc}1 & 1+2 i & -5 i \\ 1-2 i & -3 & 5+3 i \\ 5 i & 5-3 i & 7\end{array}\right)\) then \((i=\sqrt{-1})\)WBJEE 2011 Medium
- How much solid oxalic acid (Molecular weight 126 ) has to be weighed to prepare \(100 \mathrm{~mL}\) exactly \(0.1\) (N) oxalic acid solution in water?WBJEE 2022 Easy
- The number of acidic protons in \(\mathrm{H}_{3} \mathrm{PO}_{3}\) areWBJEE 2012 Medium
- If \(\omega \neq 1\) is a cube root of unity, then the sum of the series \(S=1+2 \omega+3 \omega^2+\ldots \ldots \ldots . .+3 n \omega^{3 n-1}\) isWBJEE 2011 Hard
- The molecule/molecules that has/have delocalised lone pair(s) of electrons is/are
WBJEE 2019 Medium