Question for CAT Previous Year Questions: Surds & Indices
Try yourself:Let a, b, m and n be natural numbers such that a > 1 and b > 1. If ambn = 144145, then the largest possible value of n mis
[2023]
Explanation
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Question for CAT Previous Year Questions: Surds & Indices
Try yourself:Let n be any natural number such that 5n-1 < 3n+1. Then, the least integer value of m that satisfies 3n+1 <2n+m for each such n, is
[2023]
Correct Answer : 5
Explanation
It is given that 5n-1 < 3n+1, where n is a natural number. By inspection, we can say that the inequality holds when n = 1, 2, 3 4, and 5.
Now, we need to find the least integer value of m that satisfies 3n+1 <2n+m
For, n =1, the least integer value of m is 2.
For, n = 2, the least integer value of m is 3
For, n = 3, the least integer value of m is 4.
For, n = 4, the least integer value of m is 4.
For, n= 5, the least integer value of m is 5.
Hence, the least integer value of m such that for all the values of n, the equation holds is 5.
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Question for CAT Previous Year Questions: Surds & Indices
Try yourself:Let A be the largest positive integer that divides all the numbers of the form 3k + 4k + 5k, and B be the largest positive integer that divides all the numbers of the form 4k + 3(4k) + 4k+2, where k is any positive integer. Then (A + B) equals
[2022]
Correct Answer : 82
Explanation
A is the HCF of 3k + 4k + 5k for different values of k.
FAQs on Surds & Indices CAT Previous Year Questions with Answer PDF
1. What is the difference between a surd and an index?
Ans. A surd is an irrational number that cannot be expressed as a simple fraction, while an index is the small number written at the top of a root symbol indicating the root's degree.
2. How can surds be simplified?
Ans. Surds can be simplified by rationalizing the denominator, which involves multiplying the numerator and denominator by the conjugate of the denominator.
3. What are some common properties of indices?
Ans. Some common properties of indices include the product rule (a^m * a^n = a^(m+n)), the quotient rule (a^m / a^n = a^(m-n)), and the power rule ((a^m)^n = a^(m*n)).
4. How are surds and indices used in real-life applications?
Ans. Surds and indices are used in various fields such as engineering, physics, and finance to solve complex mathematical problems and make calculations more efficient.
5. Can surds and indices be used in calculus?
Ans. Yes, surds and indices are frequently used in calculus to solve problems involving limits, derivatives, and integrals, making them essential concepts for advanced mathematical analysis.