CUET · MATHS · PYQ PAPER 2025
Consider the line \(\vec{r}=-2 \hat{i}+3 \hat{j}+\hat{k}+\lambda(5 \hat{i}-3 \hat{j}-\hat{k})\). Match List-I with List-II
| List-I | List-II |
| (A) A point on the given line | (I) \(\left(\frac{5}{\sqrt{35}}, \frac{-3}{\sqrt{35}}, \frac{-1}{\sqrt{35}}\right)\) |
| (B) Direction ratios of the given line | (II) (2, 3, 1) |
| (C) Direction cosines of the given line | (III) (5, -3, -1) |
| (D) Direction ratios of a line perpendicular to given line | (IV) (-2, 3, 1) |
Choose the correct answer from the options given below:
- A (А) - (III), (В) - (I), (C) - (IV), (D) - (I)
- B (A) - (IV), (B) - (III), (С) - (I), (D) - (II)
- C (А) - (III), (B) - (IV), (C) - (II), (D) - (I)
- D (A) - (IV), (B) - (I), (C) - (II), (D) - (III)
Answer & Solution
Correct Answer
(B) (A) - (IV), (B) - (III), (С) - (I), (D) - (II)
Step-by-step Solution
Detailed explanation
(A) Point on line \(\vec{r}=\vec{a}+\lambda \vec{b}\) is \(\vec{a}\). Point: \((-2, 3, 1)\). Match: (A) - (IV) (B) Direction ratios are coefficients of \(\lambda\) in \(\vec{b}\). Direction ratios: \((5, -3, -1)\). Match: (B) - (III) (C) Direction cosines are direction ratios…
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
- If \(|\vec{a}|=7\) then \(|3 \vec{a}|\) is:CUET 2023 Medium
- Match list-I with List -II
Choose the correct answer from the options given below:List-I List-II (A) An observed set of population selected for analysis (I) Parameter (B) A specific characteristic of the population (II) Hypothesis (C) A specific characteristic of the sample (III) Statistic (D) A statement made about a population parameter for testing (IV) Sample CUET 2025 Easy - If the following data is obtained from a simple random sample : 6, 7, 9, 10, 11, 17
Then the point estimate of population standard deviation is :CUET 2025 Easy - The solution of the differential equation \(\frac{d y}{d x}=1+x+y^2+x y^2\) is:CUET 2023 Medium
- If \(y=\sin ^{-1} x+\sin ^{-1} \sqrt{1-x^2}, x \in(-1,0)\), then \(\frac{d y}{d x}\) is equal toCUET 2025 Hard
- The value of \(\tan ^2\left(\sec ^{-1} 2\right)\) is:CUET 2023 Medium
More PYQs from CUET
- If \(A=\left[\begin{array}{ccc}0 & 2 & c \\ a & b & -1 \\ -5 & 1 & 0\end{array}\right]\) is a skew-symmetric matrix, then \((a+b+c)^3=\)CUET 2023 Medium
- The value of integral \(\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x\), where \(\alpha\) is a constant is :CUET 2023 Hard
- In the context of the Photoelectric effect, identify the statements which support quantum nature of light.
(A) The electric charge of photoelectrons is quantized
(B) The maximum kinetic energy of photoelectrons depends on the frequency of the incident light, but is independent of its intensity
(C) The photoelectric emission is an instantaneous process without any apparent time lag, even when the incident radiation is made exceedingly dim
(D) There is a minimum frequency of light below which no photoelectrons are emitted
Choose the correct answer from the options given below:CUET 2025 Easy - Choose the correct statements from the following:
A. The minimum energy required to free the electron from the ground state of the hydrogen atom is 13.6 J
B. The principle quantum number n labels the stationary states in the ascending order of energy
C. Bohr gave the basic idea of discrete energy levels
D. de Broglie hypothesis provided an explanation for Bohr's second postulate for the quantization of angular momentum of the orbiting electron
E. line spectrum provides useful information about the atomic structure.
Choose the correct answer from the options given below:CUET 2023 Hard - Azeotropes are binary mixtures havingCUET 2025 Medium
- Three magnetic materials : (A) Paramagnetic, (B) Diamagnetic, (C) Ferromagnetic. The correct order of increasing magnetic susceptibility is :CUET 2024 Hard