COMEDK · Maths · 1. Basic of Mathematics
The value of \(a^{\log _b c}-c^{\log _b a}\), where \(a, b, c>0\) but \(a, b, c \neq 1\), is
- A a
- B b
- C c
- D 0
Answer & Solution
Correct Answer
(D) 0
Step-by-step Solution
Detailed explanation
\(\begin{array}{ll}\text { Let } y=C^{\log _b a} \\ \Rightarrow \quad \log _C y=\log _b a \\ \Rightarrow \quad \frac{\log y}{\log c}=\frac{\log a}{\log b} & {\left[\because \log _a b=\frac{\log b}{\log a}\right]}\end{array}\)…
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 \(A=\left[\begin{array}{lll}a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a\end{array}\right]\) then \(|\operatorname{adj} A|=\)COMEDK 2025 Easy
- A bag contans white balls and red balls. balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then is equal toCOMEDK 2022 Medium
- The function \(f: X \rightarrow Y\) defined by \(f(x)=\sin x\) is one-one but not onto if \(X\) and \(Y\) are respectively, is equal toCOMEDK 2016 Easy
- The differential equation of all non-vertical lines in a plane isCOMEDK 2023 Easy
- The most economical proportion of the height of a covered box of fixed volume whose base is a rectangle with one side three times as long as the other, isCOMEDK 2024 Medium
- Express the set \(A=\{1,7,17,31,49\}\) in set builder formCOMEDK 2024 Easy
More PYQs from COMEDK
- \(\mathrm{Mg}\) is an important component ofCOMEDK 2015 Easy
- Let \(\mathrm{ABC}\) be a triangle with equations of its sides \(\mathrm{AB}, \mathrm{BC}\). \(\mathrm{CA}\) respectively are \(x-2=0, y-5=0\) and \(5 x+2 y-10=0\). Then the orthocentre of triangle lies on the lineCOMEDK 2024 Medium
- A current of 2 A is passed through the primary coil. The total flux linked with the secondary coil, which is closely wound over the primary is \(2000 \times 10^{-6}\) weber. What is the induced emf in the secondary if the current through the primary increases at a rate of \(0.2 \mathrm{As}^{-1}\) ?COMEDK 2025 Easy
- A lens of power \(+1 \mathrm{D}\) is made in contact with another lens of power \(-2 \mathrm{D}\) the combination will then act as a:COMEDK 2023 Easy
- Two moles of an ideal gas at 1 bar pressure and 298 K is expanded into vacuum to double the volume. The work done is:COMEDK 2025 Easy
- \(\lim _{x \rightarrow 0} \dfrac{\sqrt{1-\cos 2 x}}{x \sqrt{2}}\)COMEDK 2025 Medium