WBJEE · Maths · Permutation Combination
Let N be the number of quadratic equations with coefficients from {0, 1, 2, ....., 9) such that 0 is a solution of each equation. Then the value of N is
- A \(2^9\)
- B \(3^9\)
- C 90
- D 81
Answer & Solution
Correct Answer
(C) 90
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Hint: } a x^2+b x+c=0 \\ & \text {one root is zero } \Rightarrow c=0 \\ & a \neq 0, a=1,2,3, \ldots 9 \\ & b=0, \ldots \ldots .9 \end{aligned}\) Number of value of \(N=9 \times 10=90\)
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 \(b_{1} b_{2}=2\left(c_{1}+c_{2}\right)\) and \(b_{1}, b_{2}, c_{1}, c_{2}\) are all real numbers, then at least one of the equations \(\bar{x}^{2}+h_{1} x+c_{1}=0\) and \(x^{2}+b_{2} x+c_{2}=0\) hasWBJEE 2018 Easy
- If \(f(x)=\frac{e^x}{1+e^x}, l_1=\int_{f(-a)}^{f(a)} x g(x(1-x)) d x\) and \(l_2=\int_{f(-a)}^{f(a)} g(x(1-x)) d x\), then the value of \(\frac{l_2}{l_1}\) isWBJEE 2024 Medium
- Let \(P\) and \(T\) be the subsets of \(x\), \(y\) -plane defined by \(P=\left\{(x, y): x>0, y>0\right.\) and \(\left.x^{2}+y^{2}=1\right\}\), \(T=\left\{(x, y): x>0, y>0\right.\) and \(\left.x^{8}+y^{8} < 1\right\}\). Then, \(P \cap T\) isWBJEE 2019 Medium
- \(f(x)=\left\{\begin{array}{cc}{[x]+[-x],} & \text { when } x \neq 2 \\ \lambda & \text { when } x=2\end{array}\right.\)
If \(f(x)\) is continuous at \(x=2\), the value of \(\lambda\) will beWBJEE 2011 Medium - Consider a tangent to the ellipse \(\frac{x^{2}}{2}+\frac{y^{2}}{1}=1\) at any point. The locus of the midpoint of the portion intercepted between the axes isWBJEE 2020 Medium
- \(\lim _{x \rightarrow 0} \frac{\tan \left(\left[-\pi^2\right] x^2\right)-x^2 \tan \left(\left[-\pi^2\right]\right)}{\sin ^2 x}\) equalsWBJEE 2025 Medium
More PYQs from WBJEE
- A square conducting loop is placed near an infinitely long current carrying wire with one edge parallel to the wire as shown in the figure. If the current in the straight wire is suddenly halved. which of the following statements will be true? "The loop will .......".
WBJEE 2019 Medium - \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{F}^{18}\) is a \(\mathrm{F}^{18}\) radio-isotope labelled organic compound. \(\mathrm{F}^{18}\) decays by positron emission. The product resulting on decay isWBJEE 2017 Medium
- If the \(n\) terms \(a_1, a_2, \ldots \ldots \ldots . ., a_n\) are in A.P. with increment \(r\), then the difference between the mean of their squares & the square of their mean isWBJEE 2023 Medium
- For \(-\frac{\pi}{2} < x < \frac{3 \pi}{2}, \quad\) the \(\quad\) value \(\quad\) of \(\frac{d}{d x}\left\{\tan ^{-1} \frac{\cos x}{1+\sin x}\right\}\) is equal toWBJEE 2012 Medium
- Let \(p, q\) and \(r\) be the side4s opposite to the angles \(P, Q\) and \(R,\) respectively in a \(\Delta P Q R\). Then, \(2 p r \sin \left(\frac{p-Q+R}{2}\right)\) equalsWBJEE 2012 Easy
- The common chord of the circles \(x^{2}+y^{2}-4 x-4 y=0 \quad\) and \(\quad 2 x^{2}+2 y^{2}=32\) subtends at the origin an angle equal toWBJEE 2017 Medium