The number of integer solutions of the equation 2|x|(x² + 1) = 5x² is: Options: A) 2 B) 3 C) 4 D) 5

B. 3. The equation results in integer solutions of 0, 2, and -2. Total = 3.

For some positive and distinct real numbers \(x, y\) and \(z\), if \(\frac{1}{\sqrt{y}+\sqrt{z}}\) is the arithmetic mean of \(\frac{1}{\sqrt{x}+\sqrt{z}}\) and \(\frac{1}{\sqrt{x}+\sqrt{y}}\), then the relationship which will always hold true, is Options: A) \(\sqrt{x}, \sqrt{y}\) and \(\sqrt{z}\) are in arithmetic progression B) \(\sqrt{x}, \sqrt{z}\) and \(\sqrt{y}\) are in arithmetic progression C) \(y, x\) and \(z\) are in arithmetic progression D) \(x, y\) and \(z\) are in arithmetic progression

C. \(y, x\) and \(z\) are in arithmetic progression. Step 1. Let a=√x,b=√y,c=√z. All denominators are positive. Step 2. The mean statement is 2/(b+c)=1/(a+c)+1/(a+b).

Any non-zero real numbers x, y such that y ≠ 3 and (x/y) 10, then -x > y B) x/y < y/x C) If x < 0, then -x < y D) If y < 0, then -x < y

D. If y < 0, then -x < y. Solution: We are given that (x/y) 0, or -x < y. Thus, option D is correct: if y < 0, then -x < y.

Any non-zero real numbers \(x, y\) such that \(y \neq 3\) and \(\frac{x}{y} \lt \frac{x+3}{y-3}\), will satisfy the condition Options: A) If \(y>10\), then \(-x>y\) B) If \(x \lt 0\), then \(-x \lt y\) C) If \(y \lt 0\), then \(-x \lt y\) D) \(\frac{x}{y} \lt \frac{y}{x}\)

C. If \(y \lt 0\), then \(-x \lt y\). Step 1. Subtract the fractions: x/y−(x+3)/(y−3)0.

CAT Functions and Domains Bible Top 10 Must Solve Functions and Domains Questions covering 90% of Syllabus – Page 5

All 39 Functions and Domains questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 5 of 11.

CAT 2023 Slot 1 · Quant

The number of integer solutions of the equation 2|x|(x² + 1) = 5x² is:

CAT 2023 Slot 1 · Quant

For some positive and distinct real numbers \(x, y\) and \(z\), if \(\frac{1}{\sqrt{y}+\sqrt{z}}\) is the arithmetic mean of \(\frac{1}{\sqrt{x}+\sqrt{z}}\) and \(\frac{1}{\sqrt{x}+\sqrt{y}}\), then the relationship which will always hold true, is

CAT 2023 Slot 2 · Quant

Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, Band C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe C to fill the empty tank is

CAT 2023 Slot 2 · Quant

Any non-zero real numbers x, y such that y ≠ 3 and (x/y) < ((x+3)/(y-3)) will satisfy the condition

CAT 2023 Slot 2 · Quant

Any non-zero real numbers \(x, y\) such that \(y \neq 3\) and \(\frac{x}{y} \lt \frac{x+3}{y-3}\), will satisfy the condition

Last day solving checklist

Name the unknown. Include its unit and state whether it is a count, amount, rate or parameter.
Form the relationships. Translate each given condition into an equation or restriction.
Choose the method. Use the formula, substitution, elimination, a sign chart or a bound appropriate to this concept.
Check restrictions. Check integer counts, signs, nonzero denominators, domains and all original conditions.
Verify the answer. Substitute into the original question; for an extreme, show a feasible example reaches it.

All 14 repeating CAT PYQs and how much each adds

CAT PYQ	Repeating CAT PYQ	Questions	Representative	Cumulative questions	Cumulative share
1	Reject nonphysical roots in quantity and time problems	11	CAT 2021 S1 Q16	11	21.15%
2	Logarithm base and argument restrictions	10	CAT 2021 S1 Q4	21	40.38%
3	Modulus branches and sign consistency	6	CAT 2021 S2 Q16	27	51.92%
4	Denominator zeros and composite or reciprocal inputs	5	CAT 2021 S1 Q1	32	61.54%
5	Radical arguments and square root signs	4	CAT 2023 S1 Q3	36	69.23%
6	Exponential substitutions zero bases and exponent conditions	4	CAT 2021 S2 Q15	40	76.92%
7	Feasible output range of rational expressions	3	CAT 2021 S2 Q13	43	82.69%
8	Piecewise function or region interval membership	2	CAT 2022 S3 Q6	45	86.54%
9	Positivity and nonzero roots in reciprocal identities	2	CAT 2023 S3 Q4	47	90.38%
10	Select a difference using its given sign	1	CAT 2021 S2 Q3	48	92.31%
11	Positive substitution needed for AM GM	1	CAT 2022 S3 Q2	49	94.23%
12	Given work time interval	1	CAT 2023 S3 Q8	50	96.15%
13	Select the negative shared root	1	CAT 2024 S1 Q20	51	98.08%
14	Open and closed floor band endpoints	1	CAT 2025 S1 Q22	52	100%

Based on CAT Actual Quant Papers.

CAT Functions and Domains Bible Top 10 Must Solve Functions and Domains Questions covering 90% of Syllabus – Page 5

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps