CUET · MATHS · PYQ PAPER 2025
The inequality \(\frac{5 x-2}{3}-\frac{7 x-3}{5}>\frac{x}{4}\) holds when
- A \(x \in(-4, \infty)\)
- B \(x \in(4, \infty)\)
- C \(x \in(-\infty, 2]\)
- D \(x \in(-\infty, 4]\)
Answer & Solution
Correct Answer
(B) \(x \in(4, \infty)\)
Step-by-step Solution
Detailed explanation
\(60\left(\frac{5 x-2}{3}\right) - 60\left(\frac{7 x-3}{5}\right) > 60\left(\frac{x}{4}\right)\) \(20(5x - 2) - 12(7x - 3) > 15x\) \(100x - 40 - 84x + 36 > 15x\) \(16x - 4 > 15x\) \(x > 4\) \(x \in (4, \infty)\)
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
- Let \(A=\left[a_{i j}\right]_{3 \times 3}\) be a matrix, defined by \(a_{i j}=\left\{\begin{array}{ll}2 i+3 j & , i < j \\ 6 & , i=j \\ 3 i-2 j & , i > j\end{array}\right.\). The number of elements in A. which are greater than 6, isCUET 2025 Hard
- The integrating factor of the differential equation \(\frac{d y}{d x}=x+x y\) is:CUET 2025 Medium
- If \(95 \%\) confidence interval for the population mean was reported to be 140 to 150 and \(\sigma=25\), then the size of the sample used in this study is:
[Given: \(Z_{0.025}=1.96\) ]CUET 2025 Hard - A random variable X has the following probability distribution
Then the value of k/4 isX 2 3 4 5 P(X) 5/k 7/k 9/k 11/k CUET 2025 Hard - Consider the LPP, Min Z = x + 3y subject to the conditions:
\(2 x+y \geq 2\)
\(x+2 y \geq 4\),
\(x \geq 0, y \geq 0\).
Which of the following statement is correct about the feasible region of the above LPP.CUET 2023 Hard - Two biased dice are thrown together. For the first die \(P(6)=1 / 2\), other scores are equally likely. While for the second die, \(P (1)=2 / 5\) and other scores are equally likely then the mean for the probability distribution of 'the number of ones seen', will beCUET 2023 Easy
More PYQs from CUET
- A die is thrown twice and the sum of the numbers appearing is observed to be 6 .
The probability that the number 4 has appeared at least once is:CUET 2023 Medium - Which of the following statements is/are true?
(A) The vector sum of the three sides of a triangle in order is \(\vec{c}\)
b (B) The magnitude (r), direction ratios (a, b, c) and direction cosines (l, m, n) of any vector \(\vec{r}=a \hat{i}+b \hat{j}+c \hat{k}\) are related as \(l=\frac{a}{r}, m=\frac{b}{r}, n=\frac{c}{r}\)
(C) If θ is the angle between two vectors \(\vec{a}\) and \(\vec{b}\), then their cross product is given as \(\vec{a} \times \vec{b}=|\vec{a}||\vec{b}| \sin \theta\)
(D) The cross product of two vectors is commutative
Choose the correct answert from the option given below :CUET 2025 Easy - Choose the examples of first order reactions.
(A) Artificial radioactive decay of unstable nuclei
(B) Hydrogenation of ethylene
(C) Thermal decomposition of HI on gold surface
(D) Decomposition of N2O
Choose the correct answer from the options given below:CUET 2025 Easy - A uniformly charged infinite plane sheet of charge density \( 2 \times 10^{-8} \text{ C m}^{-2} \) is held in air.
What will be the separation between two equipotential surfaces in the region of electric field produced by the sheet, if the potential difference between them is 10 V? (\( \varepsilon_0 = 8.85 \times 10^{-12} \text{ C}^2\text{N}^{-1}\text{m}^{-2} \))CUET 2025 Easy - A 200-turn coil of self-inductance 20 mH carries a current of 4 mA. The magnetic flux linked with each turn of the coil is:CUET 2025 Hard
- \(\int \frac{\left(x^4-x\right)^{1 / 4}}{x^5} d x\) is equal toCUET 2025 Medium