The CAT QA section requires speed and accuracy, along with a thorough understanding of the Square and Square Roots. This article provides a set of MCQs on Square and Square Roots to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.
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CAT MCQs on Square and Square Roots
1. If \(x = (4096)^{7+4√3}\), then which of the following equals \(64\) ?
A
\(\frac{x^7}{x^{2\sqrt3}}\)
B
\(\frac{x^7}{x^{4\sqrt3}}\)
C
\(\frac{x\frac{7}{2}}{x^{\frac{4}{\sqrt3}}}\)
D
\(\frac{x\frac{7}{2}}{x^{2\sqrt3}}\)
2. If f \((5+x) = f (5-x)\) for every real x, and \(f(x)=0\) has four distinct real roots, then the sum of these roots is
A
0
B
40
C
10
D
20
3. The number of distinct real roots of the equation \(\bigg(\frac{x+1}{x}\bigg)^2-3\bigg(\frac{x+1}{x}\bigg)+2=0\) equals
[This Question was asked as TITA]
[This Question was asked as TITA]
A
2
B
3
C
4
D
1
4. If \(\sqrt{5x+9}\)+\(\sqrt{5x-9}\)=\(3(2-\sqrt2)\) then \(\sqrt{10x+9}\) is equal to
A
\(3\sqrt7\)
B
\(4\sqrt5\)
C
\(3\sqrt31\)
D
\(2\sqrt7\)
5. The number of the real roots of the equation 2cos(x(x+1)) = 2x + 2-x is
A
2
B
1
C
infinite
D
0
6. The product of the distinct roots of |x² - x - 6 | = x + 2 is
A
-8
B
-24
C
-4
D
-16
7. The real root of the equation \(2^{6x}+2^{3x+2}-21=0\) is
A
\(\frac{log_27}{3}\)
B
\(log_2\ 9\)
C
\(\frac{log_2\ 3}{3}\)
D
\(log_2\ 27\)
8. Let \(a_1,a_2,….\) be integers such that \(a_1-a_2+a_3-a_4+…..+(-1)^{n-1}a_n=n\), for all \(n≥1\),then \(a_{51}+a_{52}+….+a_{1023} \) equals
A
-1
B
10
C
0
D
1
9. How many factors of \(2^4\times3^5\times10^4\) are perfect squares which are greater than 1 ?
A
44
B
38
C
45
D
22
10. Let A be a real number. Then the roots of the equation \(x^2-4x-log_{2}A=0 \) are real and distinct if and only if
A
\(A>\frac{1}{16}\)
B
\(A>\frac{1}{8}\)
C
\(A<\frac{1}{16}\)
D
\(A<\frac{1}{8}\)
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