MHT CET · Maths · Properties of Triangles
In a triangle ABC with usual notations if \(\angle A=30^{\circ}\), then the value of \(\left(1+\frac{a}{c}+\frac{b}{c}\right)\left(1+\frac{c}{b}-\frac{a}{b}\right)=\)
- A \(\sqrt{3}-2\)
- B \(2+\sqrt{5}\)
- C \(\sqrt{3}+2\)
- D \(2-\sqrt{5}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{3}+2\)
Step-by-step Solution
Detailed explanation
\(\left(1+\frac{a}{c}+\frac{b}{c}\right)\left(1+\frac{c}{b}-\frac{a}{b}\right) = \frac{(c+a+b)}{c} \frac{(b+c-a)}{b}\) \(= \frac{(b+c)^2 - a^2}{bc} \)
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
- For the following probability distribution, the standard deviation of the random variable X is
X 2 3 4 P(X=x) 0.2 0.5 0.3 MHT CET 2025 Medium - If variance of \(x_1, x_2 \ldots \ldots, x_{\mathrm{n}}\) is \(\sigma_x^2\), then the variance of \(\lambda x_1, \lambda x_2, \ldots \ldots, \lambda x_n(\lambda \neq 0)\) isMHT CET 2023 Easy
- \(\int_{2}^{3} \frac{x}{x^{2}-1} d x=\)MHT CET 2020 Easy
- \(\int \mathrm{e}^{2 x} \frac{(\sin 2 x \cos 2 x-1)}{\sin ^2 2 x} \mathrm{~d} x=\)MHT CET 2025 Medium
- If \(\mathrm{f}(\mathrm{x})=\frac{\mathrm{x}}{2}-1\), then on the interval \([0, \pi]\) where [.] represents greatest integer functionMHT CET 2022 Medium
- If \(\mathrm{A}=\left[\begin{array}{rr}1 & 2 \\ -1 & 4\end{array}\right]\) and \(\mathrm{A}^{-1}=\alpha \mathrm{I}+\beta \mathrm{A}\)
\(\alpha, \beta \in \mathrm{R}\) where I is the identity matrix of order 2 , then \(4(\alpha+\beta)=\)MHT CET 2025 Medium
More PYQs from MHT CET
- A photon has wavelength \(3 \mathrm{~nm}\), then its momentum and energy respectively will be
\(
[\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}, \mathrm{c}=\text { velocity of light }\) \(=3 \times 10^8 \mathrm{~m} / \mathrm{s}]
\)MHT CET 2021 Hard - Which one of the following blood vessel does NOT possess any valve at its point of connection with heart?MHT CET 2021 Easy
- If X is a binomial variable with range \(\{0,1,2,3,4\}\) and \(P(X=3)=3 P(X=4)\) then the parameter ' \(p\) ' of the binomial distribution isMHT CET 2025 Medium
- Two sound waves travelling in the same direction have displacement
\(\begin{aligned}
& y_1=a \sin (0 \cdot 2 \pi x-50 \pi t) \text { and } \\
& y_2=a \sin (0 \cdot 15 \pi x-46 \pi t)
\end{aligned}\)
How many times, a listener can hear sound of maximum intensity in one second?MHT CET 2025 Medium - In \(\triangle \mathrm{ABC}, \mathrm{m} \angle \mathrm{B}=\frac{\pi}{3}\) and \(\mathrm{m} \angle \mathrm{C}=\frac{\pi}{4}\). Let point \(\mathrm{D}\) divide \(\mathrm{BC}\) internally in the ratio \(1: 3\), then \(\frac{\sin (\angle B A D)}{\sin (\angle C A D)}\) has the valueMHT CET 2023 Medium
- What is the difference in molar mass of a member of homologous series from its neighboring members in gram per mole?MHT CET 2021 Easy