Sign in
Please select an account to continue using cracku.in
↓ →
If $$5^{a} = 9^{b} = 2025$$, then the value of $$\frac{ab}{a + b}$$ = _____.
It is given,
$$5^a=9^b=2025$$
$$5^a=2025$$
Applying log on both the sides, we get
$$\log_55^a=\log_52025$$
$$a=\log_52025$$
Similarly, we get $$b=\log_92025$$
$$\dfrac{ab}{a+b}=\dfrac{1}{\dfrac{1}{a}+\dfrac{1}{b}}$$
$$\dfrac{1}{a}=\log_{2025}5$$
$$\dfrac{1}{b}=\log_{2025}9$$
$$\dfrac{1}{a}+\dfrac{1}{b}=\log_{2025}45$$
$$\dfrac{ab}{a+b}=\log_{45}2025\ =\ 2$$
The answer is option C.
Arrange the following numbers in increasing order :
A. $$\sqrt{59} - \sqrt{51}$$
B. $$\sqrt{37} - \sqrt{29}$$
C. $$\sqrt{87} - \sqrt{79}$$
D. $$\sqrt{79} - \sqrt{71}$$
Choose the correct answer from the options given below:
8 = $$\left(\sqrt{59}-\sqrt{51}\right)\left(\ \sqrt{\ 59}+\sqrt{51}\right)$$
8 = $$\left(\sqrt{37}-\sqrt{29}\right)\left(\ \sqrt{37}+\sqrt{29}\right)$$
We know that, $$\sqrt{59}+\sqrt{51}$$ is greater than $$\sqrt{37}+\sqrt{29}$$
This implies, $$\sqrt{37}-\sqrt{29}$$ is greater than $$\sqrt{59}-\sqrt{51}$$ as the product is constant.
Similarly, $$\sqrt{59}-\sqrt{51}$$ is greater than $$\sqrt{79}-\sqrt{71}$$ and $$\sqrt{79}-\sqrt{71}$$ is greater than $$\sqrt{87}-\sqrt{79}$$.
The correct order is B > A > D > C
The answer is option D.
Given below are two statements:
Statement I: $$(243)^{0.16} \times (9)^{0.1} = 0.3$$
Statement II: If $$3.105 \times 10^{P} = 0.00239 + 0.000715$$, then $$P = -3$$
In the light of the above statements choose the most appropriate answer from the options given below:
Statement I:
$$\left(243\right)^{0.16}\times\left(9\right)^{0.1}=3^{0.8}\times3^{0.2}=3$$
Therefore, statement I is incorrect.
Statement II:
$$3.105\times10^P=0.00239+0.000715$$
$$3.105\times10^P=0.003105$$
$$3105\times10^P=3.105$$
P = -3
Therefore, statement II is correct.
The answer is option D.
Yes, Logarithms, Surds and Indices is an important topic in the Quantitative Aptitude section of CMAT. It helps evaluate a candidate's mathematical reasoning, algebraic skills, and ability to simplify complex numerical expressions.
The number of Logarithms, Surds and Indices questions varies from year to year. CMAT does not prescribe a fixed number of questions from any specific Quantitative Aptitude topic.
CMAT may include questions on logarithmic laws, exponents and powers, surds and radicals, indices, simplification of expressions, and applications of these concepts in mathematical problem-solving.
Learn the fundamental concepts and important formulas, practice simplifying expressions using logarithmic identities and exponent rules, and regularly solve previous year questions and mock tests to improve speed and accuracy.
Most Logarithms, Surds and Indices questions in CMAT are of easy to moderate difficulty. With conceptual clarity and regular practice, candidates can solve them efficiently.
Cracku's CMAT Logarithms, Surds and Indices Questions provide topic-wise practice, detailed solutions, and exam-oriented problems that help candidates strengthen concepts, improve accuracy, and perform better in CMAT 2027.
Educational materials for CAT preparation
