CUET · MATHS · PYQ PAPER 2025
If \(a, b\) and \(c\) are positive real numbers, then
Match List-I with List-II
| List-I (Expression) | List-II (The Least value of the expression) |
| (A) \((a+b)(b+c)(c+a)\) | (I) \(8 a b c\) |
| (B) \((a+b+c)(a b+b c+c a)\) | (II) \(9 a^2 b^2 c^2\) |
| (C) \(\left(a^2+b^2+c^2\right)\left(a b^2+b c^2+c a^2\right)\) | (III) \(9 a b c\) |
| (D) \((a+b)^2(b+c)^2(c+a)^2\) | (IV) \(64 a^2 b^2 c^2\) |
- A (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
- B (A) - (I), (B) - (III), (C) - (II), (D) - (IV)
- C (A) - (I), (B) - (II), (C) - (IV), (D) - (III)
- D (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
Answer & Solution
Correct Answer
(B) (A) - (I), (B) - (III), (C) - (II), (D) - (IV)
Step-by-step Solution
Detailed explanation
(A) \( a+b \ge 2\sqrt{ab}, b+c \ge 2\sqrt{bc}, c+a \ge 2\sqrt{ca} \) \( (a+b)(b+c)(c+a) \ge (2\sqrt{ab})(2\sqrt{bc})(2\sqrt{ca}) = 8abc \) (A) matches (I) (B) \( a+b+c \ge 3\sqrt[3]{abc} \) \( ab+bc+ca \ge 3\sqrt[3]{(ab)(bc)(ca)} = 3\sqrt[3]{a^2b^2c^2} \)…
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
- For real numbers x and y, the relation R is defined as R = {(x, y) : x + y - \(\pi\) is an irrational number}, then the relation R is:CUET 2023 Easy
- If the function \(f(x)=\left\{\begin{array}{ll}\frac{k c e s}{\pi-2 \pi} & : x \neq \frac{\pi}{2} \\ 3 & : x=\frac{\pi}{2}\end{array}\right.\) is continuous at \(x=\frac{\pi}{2}\), then \(k\) is equal to:CUET 2025 Hard
- Consider a L.P.P, Maximize \(Z=3 x+5 y\) subject to constraints \(2 x+6 y \leq 6, x-y \geq 0, x \geq 0, y \geq 0\). Then which of the following are true?
(A) The feasible region of L.P.P is bounded region
(B) The corner points of the feasible region are \((0,0),(2,2),(0,1)\)
(C) Maximum value of Z is 9
(D) Point \((1,3)\) lies in the feasible region
Choose the correct answer from the options given below :CUET 2025 Medium - The solution of the differential equation \(\log _e\left(\frac{d y}{d x}\right)=3 x+4 y\) is given by:CUET 2025 Hard
- If \(A\) is a square matrix of order 3 and \(|A|=5\), then \([\operatorname{Adj} A] A\) is____________.CUET 2023 Hard
- Direction ratios of the line perpendicular to the lines \(\frac{x+2}{1}=\frac{y+3}{2}=\frac{z-5}{-2}\) and \(\frac{x-3}{2}=\frac{y+7}{-3}=\frac{z-2}{1}\) are:CUET 2023 Hard
More PYQs from CUET
- In which of the following, the time series may show the gradual shifts to relatively higher or lower values over a long period of time?CUET 2025 Easy
- The direction ratios of the line perpendicular to the lines \(\frac{x-7}{-6}=\frac{y+17}{4}=\frac{z-6}{2}\) and \(\frac{x+5}{6}=\frac{y+3}{3}=\frac{z-4}{-6}\) are proportional to:CUET 2023 Easy
- If \(y=e^{a \cos ^{-1} x},-1< x< 1\), then \(\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}\) is equal toCUET 2025 Medium
- The distance between a base pair (bp) in a DNA helix is approximately:CUET 2025 Hard
- The graphs of stopping potential versus frequency of incident radiation for two metals A and B are given.
Identify the correct statement(s) from the following:
(A) The slope of the graphs is equal to the Planck's constant.
(B) Intercept on the (-y) axis is equal to (work function/e).
(C) Threshold frequency for metal A is higher than metal B.
(D) Work function for metal B is greater than metal A.
Choose the correct answer from the options given below:CUET 2025 Hard - Which of the following statement(s) is/are correct
A. A plot of \(\log \frac{x}{m}\) vs \(\log p\) is linear.
B. A plot of \(\log [x]\) vs time is linear for a first order reaction \(x \rightarrow p\).
C. A plot of vapour pressure vs temperature is linear at constant volume.
D. A plot of \(\log p\) vs \(\frac{1}{T}\) is linear at constant temperature.
E. A plot of \(\frac{1}{\text { Concentration of the reactant }}\) vs time gives a straight line for a second order reaction.
Choose the correct answer from the options given below :CUET 2023 Easy